Finite Group Databasebeta

← C2×#72245545 #72245700

Subgroups — C2×#72245545 #72245700

Order 6048.

3264 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094716C211yesmaximal, characteristic, complemented
2C23×C3⋊(C3⋊AGL(1,𝔽7))C211yesmaximal, characteristic, complemented
3C2×C32×(C22⋊D7)⋊C3C211yesmaximal, characteristic, complemented
4C2×#13094715C211yesmaximal, characteristic, complemented
5C2×ΓL(1,𝔽8)×#638C211yesmaximal, characteristic, complemented
6#72245545C218yesmaximal, direct product factor
7C2×#13094713C211yesmaximal, characteristic, complemented
8C2×#11759581C311yesmaximal, characteristic, complemented
9C2×#66694⋊C3—31nomaximal
10C2×#66694⋊C3—32nomaximal
11C2×#66694⋊C3—31nomaximal
12C22×C3⋊D3×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
13C23×C32×ΓL(1,𝔽8)C2211yescharacteristic, complemented
14C22×C3⋊(C3⋊AGL(1,𝔽7))—24no—
15C22×C3⋊(C3⋊AGL(1,𝔽7))C2211yescharacteristic
16C22×C3⋊(C3⋊AGL(1,𝔽7))C2211yescharacteristic, complemented
17C22×C3⋊(C3⋊AGL(1,𝔽7))C2214yescomplemented
18C22×C3⋊D3×ΓL(1,𝔽8)C2211yescharacteristic, complemented
19C22×C32×AGL(1,𝔽7)C2211yescharacteristic, complemented
20C2×C3⋊D3×AGL(1,𝔽7)—24no—
21C2×C3⋊D3×AGL(1,𝔽7)C2214yescomplemented
22ΓL(1,𝔽8)×#638C2214yescomplemented
23C2×ΓL(1,𝔽8)×C3⋊Dic3C2211yescharacteristic, complemented
24C32×(C22⋊D7)⋊C3C2214yescomplemented
25C2×C32×ΓL(1,𝔽8)⋊C4C2211yescharacteristic, complemented
26#13094716C2214yescomplemented
27#13094715C2214yescomplemented
28#13094713C2214yescomplemented
29C23×C3⋊D21C2×C311yescharacteristic, complemented
30C22×D7×C3⋊D3C2×C311yescharacteristic, complemented
31C23×C3⋊AGL(1,𝔽7)—31no—
32C23×C3⋊AGL(1,𝔽7)—32no—
33C23×C3⋊AGL(1,𝔽7)—31no—
34C22×D3×AGL(1,𝔽7)—31no—
35C22×D3×AGL(1,𝔽7)—31no—
36C22×D3×AGL(1,𝔽7)—32no—
37C2×C7×#638C2×C311yescharacteristic, complemented
38C2×C32×C22⋊D7C2×C311yescharacteristic, complemented
39#11759581C2×C318yescomplemented
40C2×#92678C2×C311yescharacteristic, complemented
41C2×#92677C2×C311yescharacteristic, complemented
42C2×#92675C2×C311yescharacteristic, complemented
43C2×ΓL(1,𝔽8)×#67—31no—
44C2×ΓL(1,𝔽8)×#67—32no—
45C2×ΓL(1,𝔽8)×#67—31no—
46C2×C3×(C22⋊D7)⋊C3—21no—
47C2×C3×(C22⋊D7)⋊C3—22no—
48C2×C3×(C22⋊D7)⋊C3—21no—
49C2×C3×(C22⋊D7)⋊C3D311yescharacteristic, complemented
50C2×C3×(C22⋊D7)⋊C3D312yescomplemented
51C2×C3×(C22⋊D7)⋊C3D311yescharacteristic, complemented
52#66694⋊C3—38no—
53#66694⋊C3—316no—
54#66694⋊C3—38no—
55C2×#4247⋊C3—31no—
56C2×#4247⋊C3—32no—
57C2×#4247⋊C3—31no—
58C2×#4246⋊C3—31no—
59C2×#4246⋊C3—32no—
60C2×#4246⋊C3—31no—
61C2×(C3⋊AGL(1,𝔽7))⋊C4—31no—
62C2×(C3⋊AGL(1,𝔽7))⋊C4—32no—
63C2×(C3⋊AGL(1,𝔽7))⋊C4—31no—
64C2×C3×D4×C3⋊D3—71nomaximal, Hall
65C22×C32×ΓL(1,𝔽8)—22no—
66C22×C32×ΓL(1,𝔽8)C2311yescharacteristic
67C22×C32×ΓL(1,𝔽8)C2312yescomplemented
68C2×C3⋊(C3⋊AGL(1,𝔽7))—22no—
69C2×C3⋊(C3⋊AGL(1,𝔽7))—28no—
70C2×C3⋊(C3⋊AGL(1,𝔽7))D414yescomplemented
71C2×C3⋊(C3⋊AGL(1,𝔽7))C2312yes—
72C2×C3⋊(C3⋊AGL(1,𝔽7))C2312yescomplemented
73C2×C3⋊D3×ΓL(1,𝔽8)—22no—
74C2×C3⋊D3×ΓL(1,𝔽8)C2312yescomplemented
75C2×C32×AGL(1,𝔽7)—22no—
76C2×C32×AGL(1,𝔽7)C2312yescomplemented
77C3⋊D3×AGL(1,𝔽7)—28no—
78ΓL(1,𝔽8)×C3⋊Dic3C2312yescomplemented
79C32×ΓL(1,𝔽8)⋊C4C2312yescomplemented
80C2×#66694—31no—
81C2×#66694—31no—
82C2×#66694—32no—
83C2×D4×AGL(1,𝔽7)—91no—
84C23×C32×C7C22×C311yescharacteristic, complemented
85C22×C3⋊D21—24no—
86C22×C3⋊D21C22×C311yescharacteristic
87C22×C3⋊D21C22×C314yescomplemented
88C22×C3⋊D21C22×C311yescharacteristic, complemented
89C22×C7×C3⋊D3C22×C311yescharacteristic, complemented
90C22×C32×D7C22×C311yescharacteristic, complemented
91C23×C3×ΓL(1,𝔽8)—21no—
92C23×C3×ΓL(1,𝔽8)—22no—
93C23×C3×ΓL(1,𝔽8)—21no—
94C23×C3×ΓL(1,𝔽8)C2×D311yescharacteristic, complemented
95C23×C3×ΓL(1,𝔽8)C2×D312yescomplemented
96C23×C3×ΓL(1,𝔽8)C2×D311yescharacteristic, complemented
97C2×D7×C3⋊D3—24no—
98C2×D7×C3⋊D3C22×C314yescomplemented
99C22×C3⋊AGL(1,𝔽7)—31no—
100C22×C3⋊AGL(1,𝔽7)—32no—
101C22×C3⋊AGL(1,𝔽7)—31no—
102C22×C3⋊AGL(1,𝔽7)—31no—
103C22×C3⋊AGL(1,𝔽7)—32no—
104C22×C3⋊AGL(1,𝔽7)—31no—
105C22×C3⋊AGL(1,𝔽7)—34no—
106C22×C3⋊AGL(1,𝔽7)—38no—
107C22×C3⋊AGL(1,𝔽7)—34no—
108C22×C3⋊AGL(1,𝔽7)—64no—
109C22×C3⋊AGL(1,𝔽7)—64no—
110C22×C3⋊AGL(1,𝔽7)—68no—
111C22×D3×ΓL(1,𝔽8)—31no—
112C22×D3×ΓL(1,𝔽8)—32no—
113C22×D3×ΓL(1,𝔽8)—31no—
114C22×C3×AGL(1,𝔽7)—21no—
115C22×C3×AGL(1,𝔽7)—22no—
116C22×C3×AGL(1,𝔽7)—21no—
117C22×C3×AGL(1,𝔽7)C2×D311yescharacteristic, complemented
118C22×C3×AGL(1,𝔽7)C2×D312yescomplemented
119C22×C3×AGL(1,𝔽7)C2×D311yescharacteristic, complemented
120C2×D3×AGL(1,𝔽7)—34no—
121C2×D3×AGL(1,𝔽7)—34no—
122C2×D3×AGL(1,𝔽7)—38no—
123C2×D3×AGL(1,𝔽7)—64no—
124C2×D3×AGL(1,𝔽7)—64no—
125C2×D3×AGL(1,𝔽7)—68no—
126C7×#638C22×C314yescomplemented
127C2×C7×C3⋊Dic3C22×C311yescharacteristic, complemented
128C32×C22⋊D7C22×C314yescomplemented
129C2×C32×Dic7C22×C311yescharacteristic, complemented
130#92678C22×C314yescomplemented
131#92677C22×C314yescomplemented
132#92675C22×C314yescomplemented
133ΓL(1,𝔽8)×#67—34no—
134ΓL(1,𝔽8)×#67—38no—
135ΓL(1,𝔽8)×#67—34no—
136C2×Dic3×ΓL(1,𝔽8)—31no—
137C2×Dic3×ΓL(1,𝔽8)—32no—
138C2×Dic3×ΓL(1,𝔽8)—31no—
139C3×(C22⋊D7)⋊C3—24no—
140C3×(C22⋊D7)⋊C3—28no—
141C3×(C22⋊D7)⋊C3—24no—
142C3×(C22⋊D7)⋊C3C2×D314yescomplemented
143C3×(C22⋊D7)⋊C3C2×D318yescomplemented
144C3×(C22⋊D7)⋊C3C2×D314yescomplemented
145C2×C3×ΓL(1,𝔽8)⋊C4—21no—
146C2×C3×ΓL(1,𝔽8)⋊C4—22no—
147C2×C3×ΓL(1,𝔽8)⋊C4—21no—
148C2×C3×ΓL(1,𝔽8)⋊C4C2×D311yescharacteristic, complemented
149C2×C3×ΓL(1,𝔽8)⋊C4C2×D312yescomplemented
150C2×C3×ΓL(1,𝔽8)⋊C4C2×D311yescharacteristic, complemented
151#4247⋊C3—34no—
152#4247⋊C3—34no—
153#4247⋊C3—38no—
154#4246⋊C3—34no—
155#4246⋊C3—34no—
156#4246⋊C3—38no—
157(C3⋊AGL(1,𝔽7))⋊C4—34no—
158(C3⋊AGL(1,𝔽7))⋊C4—34no—
159(C3⋊AGL(1,𝔽7))⋊C4—38no—
160C23×C3×C3⋊D3—71no—
161C23×C3×C3⋊D3—71no—
162C2×C33×D4—71no—
163C2×C3×#638—71no—
164C2×C3×#638—141no—
165C3×D4×C3⋊D3—78no—
166C2×C3×C4⋊(C3⋊D3)—71no—
167C2×C3×C4×C3⋊D3—71no—
168C2×C32×ΓL(1,𝔽8)—22no—
169C2×C32×ΓL(1,𝔽8)C2×D412yescomplemented
170C2×C32×ΓL(1,𝔽8)C2411yescharacteristic
171C3⋊(C3⋊AGL(1,𝔽7))—22no—
172C3⋊(C3⋊AGL(1,𝔽7))C2×D414yescomplemented
173C3⋊D3×ΓL(1,𝔽8)—22no—
174C32×AGL(1,𝔽7)—22no—
175C23×D21—31no—
176C23×D21—31no—
177C23×D21—32no—
178C22×D3×D7—31no—
179C22×D3×D7—31no—
180C22×D3×D7—32no—
181C23×AGL(1,𝔽7)—91no—
182C23×AGL(1,𝔽7)—91no—
183C2×C7×#67—31no—
184C2×C7×#67—31no—
185C2×C7×#67—32no—
186C2×C3×C22⋊D7C3×D311yescharacteristic, complemented
187C2×C3×C22⋊D7C3×D311yescharacteristic, complemented
188C2×C3×C22⋊D7C3×D312yescomplemented
189C2×D4×ΓL(1,𝔽8)—91no—
190#66694—38no—
191#66694—38no—
192#66694—316no—
193C2×#4247—31no—
194C2×#4247—31no—
195C2×#4247—32no—
196C2×#4246—31no—
197C2×#4246—31no—
198C2×#4246—32no—
199C2×D21⋊C4—31no—
200C2×D21⋊C4—31no—
201C2×D21⋊C4—32no—
202C2×(C22⋊D7)⋊C3—21no—
203C2×(C22⋊D7)⋊C3—22no—
204C2×(C22⋊D7)⋊C3—21no—
205C2×(C22⋊D7)⋊C3—91no—
206C2×(C22⋊D7)⋊C3C3⋊D311yescharacteristic, complemented
207D4×AGL(1,𝔽7)—98no—
208C2×C4⋊AGL(1,𝔽7)—91no—
209C2×C4×AGL(1,𝔽7)—91no—
210C2×D4×C3⋊D3—71no—
211C2×C3×D3×D4—211no—
212C2×C3×D3×D4—212no—
213C2×C3×D3×D4—211no—
214C22×C32×C7—22no—
215C22×C32×C7C23×C311yescharacteristic
216C22×C32×C7C23×C312yescomplemented
217C2×C3⋊D21—22no—
218C2×C3⋊D21—28no—
219C2×C3⋊D21C3×D414yescomplemented
220C2×C3⋊D21C23×C312yes—
221C2×C3⋊D21C23×C312yescomplemented
222C2×C7×C3⋊D3—22no—
223C2×C7×C3⋊D3C23×C312yescomplemented
224C2×C32×D7—22no—
225C2×C32×D7C23×C312yescomplemented
226C22×C3×ΓL(1,𝔽8)—21no—
227C22×C3×ΓL(1,𝔽8)—22no—
228C22×C3×ΓL(1,𝔽8)—22no—
229C22×C3×ΓL(1,𝔽8)—22no—
230C22×C3×ΓL(1,𝔽8)—21no—
231C22×C3×ΓL(1,𝔽8)—22no—
232C22×C3×ΓL(1,𝔽8)—24no—
233C22×C3×ΓL(1,𝔽8)—24no—
234C22×C3×ΓL(1,𝔽8)—22no—
235C22×C3×ΓL(1,𝔽8)—42no—
236C22×C3×ΓL(1,𝔽8)—42no—
237C22×C3×ΓL(1,𝔽8)—44no—
238C22×C3×ΓL(1,𝔽8)C22×D311yescharacteristic
239C22×C3×ΓL(1,𝔽8)C22×D312yes—
240C22×C3×ΓL(1,𝔽8)C22×D311yescharacteristic
241C22×C3×ΓL(1,𝔽8)C22×D312yescomplemented
242C22×C3×ΓL(1,𝔽8)C22×D314yescomplemented
243C22×C3×ΓL(1,𝔽8)C22×D312yescomplemented
244D7×C3⋊D3—28no—
245C2×C3⋊AGL(1,𝔽7)—34no—
246C2×C3⋊AGL(1,𝔽7)—34no—
247C2×C3⋊AGL(1,𝔽7)—38no—
248C2×C3⋊AGL(1,𝔽7)—32no—
249C2×C3⋊AGL(1,𝔽7)—32no—
250C2×C3⋊AGL(1,𝔽7)—34no—
251C2×C3⋊AGL(1,𝔽7)—32no—
252C2×C3⋊AGL(1,𝔽7)—32no—
253C2×C3⋊AGL(1,𝔽7)—34no—
254C2×C3⋊AGL(1,𝔽7)—68no—
255C2×C3⋊AGL(1,𝔽7)—68no—
256C2×C3⋊AGL(1,𝔽7)—616no—
257C2×C3⋊AGL(1,𝔽7)—62no—
258C2×C3⋊AGL(1,𝔽7)—62no—
259C2×C3⋊AGL(1,𝔽7)—64no—
260C2×D3×ΓL(1,𝔽8)—32no—
261C2×D3×ΓL(1,𝔽8)—32no—
262C2×D3×ΓL(1,𝔽8)—34no—
263C2×D3×ΓL(1,𝔽8)—62no—
264C2×D3×ΓL(1,𝔽8)—62no—
265C2×D3×ΓL(1,𝔽8)—64no—
266C2×C3×AGL(1,𝔽7)—22no—
267C2×C3×AGL(1,𝔽7)—22no—
268C2×C3×AGL(1,𝔽7)—24no—
269C2×C3×AGL(1,𝔽7)—22no—
270C2×C3×AGL(1,𝔽7)—22no—
271C2×C3×AGL(1,𝔽7)—24no—
272C2×C3×AGL(1,𝔽7)—42no—
273C2×C3×AGL(1,𝔽7)—42no—
274C2×C3×AGL(1,𝔽7)—44no—
275C2×C3×AGL(1,𝔽7)C22×D312yescomplemented
276C2×C3×AGL(1,𝔽7)C22×D312yescomplemented
277C2×C3×AGL(1,𝔽7)C22×D314yescomplemented
278D3×AGL(1,𝔽7)—68no—
279D3×AGL(1,𝔽7)—68no—
280D3×AGL(1,𝔽7)—616no—
281C7×C3⋊Dic3C23×C312yescomplemented
282C32×Dic7C23×C312yescomplemented
283Dic3×ΓL(1,𝔽8)—32no—
284Dic3×ΓL(1,𝔽8)—32no—
285Dic3×ΓL(1,𝔽8)—34no—
286C3×ΓL(1,𝔽8)⋊C4—22no—
287C3×ΓL(1,𝔽8)⋊C4—22no—
288C3×ΓL(1,𝔽8)⋊C4—24no—
289C3×ΓL(1,𝔽8)⋊C4C22×D312yescomplemented
290C3×ΓL(1,𝔽8)⋊C4C22×D312yescomplemented
291C3×ΓL(1,𝔽8)⋊C4C22×D314yescomplemented
292C2×D4×D7—91noHall
293C23×C33—71no—
294C23×C33—141no—
295C22×C3×C3⋊D3—71no—
296C22×C3×C3⋊D3—71no—
297C22×C3×C3⋊D3—74no—
298C22×C3×C3⋊D3—74no—
299C22×C3×C3⋊D3—144no—
300C22×C3×C3⋊D3—144no—
301C22×C3×C3⋊D3—141no—
302C33×D4—74no—
303C2×C33×C4—71no—
304C3×#638—74no—
305C3×#638—144no—
306C2×C3×C3⋊Dic3—141no—
307C3×C4⋊(C3⋊D3)—74no—
308C3×C4×C3⋊D3—74no—
309C32×ΓL(1,𝔽8)C22×D411yescharacteristic, complemented, Hall
310C23×C3×C7C2×C3×D311yescharacteristic, complemented
311C23×C3×C7C2×C3×D311yescharacteristic, complemented
312C23×C3×C7C2×C3×D312yescomplemented
313C22×D21—31no—
314C22×D21—31no—
315C22×D21—32no—
316C22×D21—31no—
317C22×D21—31no—
318C22×D21—32no—
319C22×D21—34no—
320C22×D21—34no—
321C22×D21—38no—
322C22×D21—64no—
323C22×D21—64no—
324C22×D21—68no—
325C22×D3×C7—31no—
326C22×D3×C7—31no—
327C22×D3×C7—32no—
328C22×C3×D7C2×C3×D311yescharacteristic, complemented
329C22×C3×D7C2×C3×D311yescharacteristic, complemented
330C22×C3×D7C2×C3×D312yescomplemented
331C23×ΓL(1,𝔽8)—21no—
332C23×ΓL(1,𝔽8)—22no—
333C23×ΓL(1,𝔽8)—21no—
334C23×ΓL(1,𝔽8)—91no—
335C23×ΓL(1,𝔽8)C2×C3⋊D311yescharacteristic, complemented
336C2×D3×D7—34no—
337C2×D3×D7—34no—
338C2×D3×D7—38no—
339C2×D3×D7—64no—
340C2×D3×D7—64no—
341C2×D3×D7—68no—
342C22×AGL(1,𝔽7)—21no—
343C22×AGL(1,𝔽7)—22no—
344C22×AGL(1,𝔽7)—21no—
345C22×AGL(1,𝔽7)—91no—
346C22×AGL(1,𝔽7)—91no—
347C22×AGL(1,𝔽7)—94no—
348C22×AGL(1,𝔽7)—94no—
349C22×AGL(1,𝔽7)—184no—
350C22×AGL(1,𝔽7)—184no—
351C22×AGL(1,𝔽7)C2×C3⋊D311yescharacteristic, complemented
352C7×#67—34no—
353C7×#67—34no—
354C7×#67—38no—
355C2×C7×Dic3—31no—
356C2×C7×Dic3—31no—
357C2×C7×Dic3—32no—
358C3×C22⋊D7C2×C3×D314yescomplemented
359C3×C22⋊D7C2×C3×D314yescomplemented
360C3×C22⋊D7C2×C3×D318yescomplemented
361C2×C3×Dic7C2×C3×D311yescharacteristic, complemented
362C2×C3×Dic7C2×C3×D311yescharacteristic, complemented
363C2×C3×Dic7C2×C3×D312yescomplemented
364D4×ΓL(1,𝔽8)—94no—
365C2×C4×ΓL(1,𝔽8)—91no—
366#4247—34no—
367#4247—34no—
368#4247—38no—
369#4246—34no—
370#4246—34no—
371#4246—38no—
372D21⋊C4—34no—
373D21⋊C4—34no—
374D21⋊C4—38no—
375(C22⋊D7)⋊C3—24no—
376(C22⋊D7)⋊C3—28no—
377(C22⋊D7)⋊C3—24no—
378(C22⋊D7)⋊C3—94no—
379(C22⋊D7)⋊C3C2×C3⋊D314yescomplemented
380C2×ΓL(1,𝔽8)⋊C4—21no—
381C2×ΓL(1,𝔽8)⋊C4—22no—
382C2×ΓL(1,𝔽8)⋊C4—21no—
383C2×ΓL(1,𝔽8)⋊C4C2×C3⋊D311yescharacteristic, complemented
384C4⋊AGL(1,𝔽7)—94no—
385C4×AGL(1,𝔽7)—94no—
386C23×C3⋊D3—71no—
387C23×C3⋊D3—71no—
388C23×C3×D3—211no—
389C23×C3×D3—211no—
390C23×C3×D3—212no—
391C23×C3×D3—211no—
392C23×C3×D3—211no—
393C23×C3×D3—212no—
394C2×C32×D4—71no—
395C2×C32×D4—72no—
396C2×C32×D4—71no—
397C2×C32×D4—71no—
398C2×C32×D4—141no—
399C2×C32×D4—142no—
400C2×C32×D4—141no—
401C2×#638—71no—
402C2×#638AGL(1,𝔽7)11yescharacteristic, complemented
403D4×C3⋊D3—78no—
404C2×C4⋊(C3⋊D3)—71no—
405C2×C4×C3⋊D3—71no—
406C2×C3×#67—211no—
407C2×C3×#67—211no—
408C2×C3×#67—211no—
409C2×C3×#67—212no—
410C2×C3×#67—422no—
411C2×C3×#67—421no—
412C3×D3×D4—218no—
413C3×D3×D4—218no—
414C3×D3×D4—2116no—
415C2×C3×D12—211no—
416C2×C3×D12—211no—
417C2×C3×D12—212no—
418C2×C3×C4×D3—211no—
419C2×C3×C4×D3—211no—
420C2×C3×C4×D3—212no—
421C2×C32×C7—22no—
422C2×C32×C7C2×C3×D412yescomplemented
423C2×C32×C7C24×C311yescharacteristic
424C3⋊D21—22no—
425C3⋊D21C2×C3×D414yescomplemented
426C7×C3⋊D3—22no—
427C32×D7—22no—
428C2×C3×ΓL(1,𝔽8)—21no—
429C2×C3×ΓL(1,𝔽8)—22no—
430C2×C3×ΓL(1,𝔽8)—22no—
431C2×C3×ΓL(1,𝔽8)—22no—
432C2×C3×ΓL(1,𝔽8)—21no—
433C2×C3×ΓL(1,𝔽8)—24no—
434C2×C3×ΓL(1,𝔽8)—22no—
435C2×C3×ΓL(1,𝔽8)—22no—
436C2×C3×ΓL(1,𝔽8)—24no—
437C2×C3×ΓL(1,𝔽8)—42no—
438C2×C3×ΓL(1,𝔽8)—42no—
439C2×C3×ΓL(1,𝔽8)—44no—
440C2×C3×ΓL(1,𝔽8)D3×D412yescomplemented
441C2×C3×ΓL(1,𝔽8)D3×D414yescomplemented
442C2×C3×ΓL(1,𝔽8)D3×D412yescomplemented
443C2×C3×ΓL(1,𝔽8)C23×D311yescharacteristic
444C2×C3×ΓL(1,𝔽8)C23×D312yes—
445C2×C3×ΓL(1,𝔽8)C23×D311yescharacteristic
446C3⋊AGL(1,𝔽7)—34no—
447C3⋊AGL(1,𝔽7)—34no—
448C3⋊AGL(1,𝔽7)—38no—
449C3⋊AGL(1,𝔽7)—62no—
450C3⋊AGL(1,𝔽7)—62no—
451C3⋊AGL(1,𝔽7)—64no—
452D3×ΓL(1,𝔽8)—62no—
453D3×ΓL(1,𝔽8)—62no—
454D3×ΓL(1,𝔽8)—64no—
455C3×AGL(1,𝔽7)—22no—
456C3×AGL(1,𝔽7)—22no—
457C3×AGL(1,𝔽7)—24no—
458C3×AGL(1,𝔽7)—42no—
459C3×AGL(1,𝔽7)—42no—
460C3×AGL(1,𝔽7)—44no—
461C23×D7—91no—
462C23×D7—91no—
463C2×C7×D4—91no—
464C2×C22⋊D7—91no—
465C2×C22⋊D7C3×C3⋊D311yescharacteristic, complemented
466D4×D7—98no—
467C2×D28—91no—
468C2×C4×D7—91no—
469C22×C33—72no—
470C22×C33—141no—
471C22×C33—142no—
472C22×C33—142no—
473C22×C33—282no—
474C2×C3×C3⋊D3—72no—
475C2×C3×C3⋊D3—74no—
476C2×C3×C3⋊D3—72no—
477C2×C3×C3⋊D3—148no—
478C2×C3×C3⋊D3—148no—
479C2×C3×C3⋊D3—142no—
480C2×C3×C3⋊D3—142no—
481C2×C3×C3⋊D3—282no—
482C33×C4—72no—
483C3×C3⋊Dic3—142no—
484C22×C3×D4—631no—
485C2×D3×D4—211no—
486C2×D3×D4—211no—
487C2×D3×D4—212no—
488C22×C3×C7—22no—
489C22×C3×C7—22no—
490C22×C3×C7—24no—
491C22×C3×C7C22×C3×D311yescharacteristic
492C22×C3×C7C22×C3×D311yescharacteristic
493C22×C3×C7C22×C3×D312yes—
494C22×C3×C7C22×C3×D312yescomplemented
495C22×C3×C7C22×C3×D312yescomplemented
496C22×C3×C7C22×C3×D314yescomplemented
497C2×D21—32no—
498C2×D21—32no—
499C2×D21—34no—
500C2×D21—34no—
501C2×D21—34no—
502C2×D21—38no—
503C2×D21—32no—
504C2×D21—32no—
505C2×D21—34no—
506C2×D21—68no—
507C2×D21—68no—
508C2×D21—616no—
509C2×D21—62no—
510C2×D21—62no—
511C2×D21—64no—
512C2×D3×C7—32no—
513C2×D3×C7—32no—
514C2×D3×C7—34no—
515C2×D3×C7—62no—
516C2×D3×C7—62no—
517C2×D3×C7—64no—
518C2×C3×D7—22no—
519C2×C3×D7—22no—
520C2×C3×D7—24no—
521C2×C3×D7C22×C3×D312yescomplemented
522C2×C3×D7C22×C3×D312yescomplemented
523C2×C3×D7C22×C3×D314yescomplemented
524C22×ΓL(1,𝔽8)—22no—
525C22×ΓL(1,𝔽8)—21no—
526C22×ΓL(1,𝔽8)—22no—
527C22×ΓL(1,𝔽8)—21no—
528C22×ΓL(1,𝔽8)—22no—
529C22×ΓL(1,𝔽8)—24no—
530C22×ΓL(1,𝔽8)—22no—
531C22×ΓL(1,𝔽8)—42no—
532C22×ΓL(1,𝔽8)—44no—
533C22×ΓL(1,𝔽8)—42no—
534C22×ΓL(1,𝔽8)—92no—
535C22×ΓL(1,𝔽8)—182no—
536C22×ΓL(1,𝔽8)C22×C3⋊D311yescharacteristic
537C22×ΓL(1,𝔽8)C22×C3⋊D312yescomplemented
538D3×D7—68no—
539D3×D7—68no—
540D3×D7—616no—
541C2×AGL(1,𝔽7)—22no—
542C2×AGL(1,𝔽7)—22no—
543C2×AGL(1,𝔽7)—24no—
544C2×AGL(1,𝔽7)—22no—
545C2×AGL(1,𝔽7)—42no—
546C2×AGL(1,𝔽7)—44no—
547C2×AGL(1,𝔽7)—42no—
548C2×AGL(1,𝔽7)—92no—
549C2×AGL(1,𝔽7)—94no—
550C2×AGL(1,𝔽7)—92no—
551C2×AGL(1,𝔽7)—188no—
552C2×AGL(1,𝔽7)—188no—
553C2×AGL(1,𝔽7)—182no—
554C2×AGL(1,𝔽7)C22×C3⋊D312yescomplemented
555C3×Dic7C22×C3×D312yescomplemented
556C3×Dic7C22×C3×D312yescomplemented
557C3×Dic7C22×C3×D314yescomplemented
558C7×Dic3—32no—
559C7×Dic3—32no—
560C7×Dic3—34no—
561C4×ΓL(1,𝔽8)—92no—
562ΓL(1,𝔽8)⋊C4—22no—
563ΓL(1,𝔽8)⋊C4—24no—
564ΓL(1,𝔽8)⋊C4—22no—
565ΓL(1,𝔽8)⋊C4C22×C3⋊D312yescomplemented
566C23×C32—71no—
567C23×C32—71no—
568C23×C32—71no—
569C23×C32—72no—
570C23×C32—71no—
571C23×C32—141no—
572C23×C32—141no—
573C23×C32—142no—
574C23×C32—142no—
575C23×C32—141no—
576C23×C32—141no—
577C23×C32—282no—
578C23×C32—281no—
579C23×C32C2×AGL(1,𝔽7)11yescharacteristic, complemented
580C22×C3⋊D3—71no—
581C22×C3⋊D3—71no—
582C22×C3⋊D3—74no—
583C22×C3⋊D3—74no—
584C22×C3⋊D3—144no—
585C22×C3⋊D3—144no—
586C22×C3⋊D3C2×AGL(1,𝔽7)11yescharacteristic, complemented
587C22×C3×D3—211no—
588C22×C3×D3—211no—
589C22×C3×D3—211no—
590C22×C3×D3—212no—
591C22×C3×D3—214no—
592C22×C3×D3—211no—
593C22×C3×D3—214no—
594C22×C3×D3—211no—
595C22×C3×D3—212no—
596C22×C3×D3—214no—
597C22×C3×D3—218no—
598C22×C3×D3—214no—
599C22×C3×D3—218no—
600C22×C3×D3—421no—
601C22×C3×D3—422no—
602C22×C3×D3—424no—
603C22×C3×D3—424no—
604C22×C3×D3—424no—
605C22×C3×D3—428no—
606C22×C3×D3—424no—
607C22×C3×D3—428no—
608C32×D4—74no—
609C32×D4—74no—
610C32×D4—74no—
611C32×D4—78no—
612C32×D4—144no—
613C32×D4—144no—
614C32×D4—148no—
615C2×C32×C4—71no—
616C2×C32×C4—71no—
617C2×C32×C4—71no—
618C2×C32×C4—72no—
619C2×C32×C4—141no—
620C2×C32×C4—141no—
621C2×C32×C4—142no—
622#638—74no—
623#638C2×AGL(1,𝔽7)14yescomplemented
624C2×C3⋊Dic3C2×AGL(1,𝔽7)11yescharacteristic, complemented
625C4⋊(C3⋊D3)—74no—
626C4×C3⋊D3—74no—
627C3×#67—214no—
628C3×#67—214no—
629C3×#67—214no—
630C3×#67—218no—
631C3×#67—424no—
632C3×#67—428no—
633C2×C3×Dic3—211no—
634C2×C3×Dic3—421no—
635C2×C3×Dic3—422no—
636C3×D12—214no—
637C3×D12—214no—
638C3×D12—218no—
639C3×C4×D3—214no—
640C3×C4×D3—214no—
641C3×C4×D3—218no—
642C32×C7C22×C3×D411yescharacteristic, complemented
643C3×ΓL(1,𝔽8)—21no—
644C3×ΓL(1,𝔽8)—22no—
645C3×ΓL(1,𝔽8)—21no—
646C3×ΓL(1,𝔽8)C2×D3×D411yescharacteristic, complemented
647C3×ΓL(1,𝔽8)C2×D3×D412yescomplemented
648C3×ΓL(1,𝔽8)C2×D3×D411yescharacteristic, complemented
649C23×C7—91no—
650C23×C7C2×C3×C3⋊D311yescharacteristic, complemented
651C22×D7—91no—
652C22×D7—91no—
653C22×D7—94no—
654C22×D7—94no—
655C22×D7—184no—
656C22×D7—184no—
657C22×D7C2×C3×C3⋊D311yescharacteristic, complemented
658C7×D4—94no—
659C2×C4×C7—91no—
660C22⋊D7—94no—
661C22⋊D7C2×C3×C3⋊D314yescomplemented
662C2×Dic7C2×C3×C3⋊D311yescharacteristic, complemented
663D28—94no—
664C4×D7—94no—
665C2×C33—142no—
666C2×C33—141no—
667C2×C33—142no—
668C2×C33—282no—
669C3×C3⋊D3—74no—
670C3×C3⋊D3—142no—
671C3×C3⋊D3—282no—
672C24×C3—631no—
673C24×C3—631no—
674C23×D3—211no—
675C23×D3—211no—
676C23×D3—212no—
677C23×D3—211no—
678C23×D3—211no—
679C23×D3—212no—
680C2×C3×D4—71no—
681C2×C3×D4—71no—
682C2×C3×D4—71no—
683C2×C3×D4—72no—
684C2×C3×D4—141no—
685C2×C3×D4—142no—
686C2×C3×D4—141no—
687C2×C3×D4—631no—
688C2×C3×D4—638no—
689C2×C3×D4—631no—
690C2×C3×D4—1261no—
691C22×C3×C4—631no—
692C2×#67—31no—
693C2×#67—31no—
694C2×#67—32no—
695C2×#67—211no—
696C2×#67—211no—
697C2×#67—212no—
698D3×D4—218no—
699D3×D4—218no—
700D3×D4—2116no—
701C2×D12—211no—
702C2×D12—211no—
703C2×D12—212no—
704C2×C4×D3—211no—
705C2×C4×D3—211no—
706C2×C4×D3—212no—
707C2×C3×C7—22no—
708C2×C3×C7—22no—
709C2×C3×C7—24no—
710C2×C3×C7C3×D3×D412yescomplemented
711C2×C3×C7C3×D3×D412yescomplemented
712C2×C3×C7C3×D3×D414yescomplemented
713C2×C3×C7C23×C3×D311yescharacteristic
714C2×C3×C7C23×C3×D311yescharacteristic
715C2×C3×C7C23×C3×D312yes—
716D21—34no—
717D21—34no—
718D21—38no—
719D21—62no—
720D21—62no—
721D21—64no—
722C3×D7—22no—
723C3×D7—22no—
724C3×D7—24no—
725D3×C7—62no—
726D3×C7—62no—
727D3×C7—64no—
728C2×ΓL(1,𝔽8)—22no—
729C2×ΓL(1,𝔽8)—21no—
730C2×ΓL(1,𝔽8)—22no—
731C2×ΓL(1,𝔽8)—21no—
732C2×ΓL(1,𝔽8)—22no—
733C2×ΓL(1,𝔽8)—24no—
734C2×ΓL(1,𝔽8)—22no—
735C2×ΓL(1,𝔽8)—42no—
736C2×ΓL(1,𝔽8)—44no—
737C2×ΓL(1,𝔽8)—42no—
738C2×ΓL(1,𝔽8)—182no—
739C2×ΓL(1,𝔽8)D4×C3⋊D312yescomplemented
740C2×ΓL(1,𝔽8)C23×C3⋊D311yescharacteristic
741AGL(1,𝔽7)—22no—
742AGL(1,𝔽7)—42no—
743AGL(1,𝔽7)—44no—
744AGL(1,𝔽7)—42no—
745AGL(1,𝔽7)—94no—
746AGL(1,𝔽7)—182no—
747C22×C32—22no—
748C22×C32—72no—
749C22×C32—72no—
750C22×C32—72no—
751C22×C32—74no—
752C22×C32—71no—
753C22×C32—72no—
754C22×C32—142no—
755C22×C32—142no—
756C22×C32—142no—
757C22×C32—144no—
758C22×C32—142no—
759C22×C32—142no—
760C22×C32—142no—
761C22×C32—144no—
762C22×C32—142no—
763C22×C32—141no—
764C22×C32—144no—
765C22×C32—142no—
766C22×C32—141no—
767C22×C32—142no—
768C22×C32—282no—
769C22×C32—282no—
770C22×C32—284no—
771C22×C32—282no—
772C22×C32—284no—
773C22×C32—282no—
774C22×C32—282no—
775C22×C32—284no—
776C22×C32—282no—
777C22×C32—281no—
778C22×C32—284no—
779C22×C32—282no—
780C22×C32C22×AGL(1,𝔽7)11yescharacteristic
781C22×C32C22×AGL(1,𝔽7)12yescomplemented
782C2×C3⋊D3—22no—
783C2×C3⋊D3—74no—
784C2×C3⋊D3—72no—
785C2×C3⋊D3—72no—
786C2×C3⋊D3—148no—
787C2×C3⋊D3—148no—
788C2×C3⋊D3—142no—
789C2×C3⋊D3C22×AGL(1,𝔽7)12yescomplemented
790C2×C3×D3—212no—
791C2×C3×D3—212no—
792C2×C3×D3—214no—
793C2×C3×D3—212no—
794C2×C3×D3—214no—
795C2×C3×D3—214no—
796C2×C3×D3—218no—
797C2×C3×D3—212no—
798C2×C3×D3—212no—
799C2×C3×D3—214no—
800C2×C3×D3—422no—
801C2×C3×D3—424no—
802C2×C3×D3—422no—
803C2×C3×D3—428no—
804C2×C3×D3—428no—
805C2×C3×D3—428no—
806C2×C3×D3—4216no—
807C2×C3×D3—428no—
808C2×C3×D3—4216no—
809C2×C3×D3—422no—
810C2×C3×D3—422no—
811C2×C3×D3—424no—
812C2×C3×D3—842no—
813C2×C3×D3—844no—
814C32×C4—72no—
815C32×C4—72no—
816C32×C4—72no—
817C32×C4—74no—
818C32×C4—142no—
819C32×C4—142no—
820C32×C4—144no—
821C3⋊Dic3C22×AGL(1,𝔽7)12yescomplemented
822C3×Dic3—212no—
823C3×Dic3—422no—
824C3×Dic3—424no—
825C22×D4—631noSylow
826C22×C7—22no—
827C22×C7—92no—
828C22×C7—182no—
829C22×C7C22×C3×C3⋊D311yescharacteristic
830C22×C7C22×C3×C3⋊D312yescomplemented
831C2×D7—22no—
832C2×D7—92no—
833C2×D7—94no—
834C2×D7—92no—
835C2×D7—188no—
836C2×D7—188no—
837C2×D7—182no—
838C2×D7C22×C3×C3⋊D312yescomplemented
839C4×C7—92no—
840Dic7C22×C3×C3⋊D312yescomplemented
841C33—141noSylow
842C23×C3—71no—
843C23×C3—71no—
844C23×C3—71no—
845C23×C3—72no—
846C23×C3—141no—
847C23×C3—142no—
848C23×C3—141no—
849C23×C3—141no—
850C23×C3—281no—
851C23×C3—282no—
852C23×C3—281no—
853C23×C3—634no—
854C23×C3—631no—
855C23×C3—631no—
856C23×C3—634no—
857C23×C3—1261no—
858C23×C3—1264no—
859C23×C3—1264no—
860C23×C3D3×AGL(1,𝔽7)11yescharacteristic, complemented
861C23×C3D3×AGL(1,𝔽7)11yescharacteristic, complemented
862C23×C3D3×AGL(1,𝔽7)12yescomplemented
863C22×D3—31no—
864C22×D3—31no—
865C22×D3—32no—
866C22×D3—214no—
867C22×D3—214no—
868C22×D3—218no—
869C22×D3—211no—
870C22×D3—211no—
871C22×D3—212no—
872C22×D3—211no—
873C22×D3—211no—
874C22×D3—212no—
875C22×D3—214no—
876C22×D3—214no—
877C22×D3—218no—
878C22×D3—424no—
879C22×D3—424no—
880C22×D3—428no—
881C22×D3—424no—
882C22×D3—424no—
883C22×D3—428no—
884C3×D4—74no—
885C3×D4—74no—
886C3×D4—74no—
887C3×D4—78no—
888C3×D4—144no—
889C3×D4—148no—
890C3×D4—144no—
891C3×D4—634no—
892C3×D4—634no—
893C3×D4—1264no—
894C2×C3×C4—71no—
895C2×C3×C4—71no—
896C2×C3×C4—71no—
897C2×C3×C4—72no—
898C2×C3×C4—141no—
899C2×C3×C4—142no—
900C2×C3×C4—141no—
901C2×C3×C4—634no—
902C2×C3×C4—1261no—
903#67—34no—
904#67—34no—
905#67—38no—
906#67—214no—
907#67—214no—
908#67—218no—
909C2×Dic3—31no—
910C2×Dic3—31no—
911C2×Dic3—32no—
912D12—214no—
913D12—214no—
914D12—218no—
915C4×D3—214no—
916C4×D3—214no—
917C4×D3—218no—
918C3×C7C2×C3×D3×D411yescharacteristic, complemented
919C3×C7C2×C3×D3×D411yescharacteristic, complemented
920C3×C7C2×C3×D3×D412yescomplemented
921ΓL(1,𝔽8)—21no—
922ΓL(1,𝔽8)—22no—
923ΓL(1,𝔽8)—21no—
924ΓL(1,𝔽8)C2×D4×C3⋊D311yescharacteristic, complemented
925C2×C32—22no—
926C2×C32—72no—
927C2×C32—71no—
928C2×C32—142no—
929C2×C32—142no—
930C2×C32—142no—
931C2×C32—142no—
932C2×C32—144no—
933C2×C32—144no—
934C2×C32—142no—
935C2×C32—142no—
936C2×C32—141no—
937C2×C32—142no—
938C2×C32—141no—
939C2×C32—282no—
940C2×C32—282no—
941C2×C32—284no—
942C2×C32—282no—
943C2×C32—284no—
944C2×C32—282no—
945C2×C32—282no—
946C2×C32—284no—
947C2×C32—284no—
948C2×C32—282no—
949C2×C32—282no—
950C2×C32—281no—
951C2×C32D4×AGL(1,𝔽7)12yescomplemented
952C2×C32C23×AGL(1,𝔽7)11yescharacteristic
953C3⋊D3—22no—
954C3⋊D3—74no—
955C3⋊D3—142no—
956C3×D3—214no—
957C3×D3—214no—
958C3×D3—218no—
959C3×D3—422no—
960C3×D3—422no—
961C3×D3—422no—
962C3×D3—424no—
963C3×D3—842no—
964C3×D3—844no—
965C24—631no—
966C24—631no—
967C2×D4—71no—
968C2×D4—91no—
969C2×D4—631no—
970C2×D4—631no—
971C2×D4—638no—
972C22×C4—631no—
973C2×C7—22no—
974C2×C7—182no—
975C2×C7C3×D4×C3⋊D312yescomplemented
976C2×C7C23×C3×C3⋊D311yescharacteristic
977D7—22no—
978D7—94no—
979D7—182no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—24no—
983C22×C3—72no—
984C22×C3—72no—
985C22×C3—72no—
986C22×C3—74no—
987C22×C3—142no—
988C22×C3—144no—
989C22×C3—142no—
990C22×C3—142no—
991C22×C3—142no—
992C22×C3—142no—
993C22×C3—144no—
994C22×C3—141no—
995C22×C3—142no—
996C22×C3—282no—
997C22×C3—282no—
998C22×C3—284no—
999C22×C3—282no—
1000C22×C3—282no—
1001C22×C3—284no—
1002C22×C3—282no—
1003C22×C3—281no—
1004C22×C3—282no—
1005C22×C3—281no—
1006C22×C3—282no—
1007C22×C3—284no—
1008C22×C3—282no—
1009C22×C3—632no—
1010C22×C3—634no—
1011C22×C3—632no—
1012C22×C3—1262no—
1013C22×C3—1268no—
1014C22×C3—1262no—
1015C22×C3—1268no—
1016C22×C3—2522no—
1017C22×C3C2×D3×AGL(1,𝔽7)11yescharacteristic
1018C22×C3C2×D3×AGL(1,𝔽7)11yescharacteristic
1019C22×C3C2×D3×AGL(1,𝔽7)12yes—
1020C22×C3C2×D3×AGL(1,𝔽7)12yescomplemented
1021C22×C3C2×D3×AGL(1,𝔽7)12yescomplemented
1022C22×C3C2×D3×AGL(1,𝔽7)14yescomplemented
1023C2×D3—32no—
1024C2×D3—32no—
1025C2×D3—34no—
1026C2×D3—62no—
1027C2×D3—62no—
1028C2×D3—64no—
1029C2×D3—214no—
1030C2×D3—214no—
1031C2×D3—218no—
1032C2×D3—212no—
1033C2×D3—212no—
1034C2×D3—214no—
1035C2×D3—212no—
1036C2×D3—212no—
1037C2×D3—214no—
1038C2×D3—428no—
1039C2×D3—428no—
1040C2×D3—4216no—
1041C2×D3—428no—
1042C2×D3—428no—
1043C2×D3—4216no—
1044C2×D3—422no—
1045C2×D3—422no—
1046C2×D3—424no—
1047C3×C4—72no—
1048C3×C4—72no—
1049C3×C4—72no—
1050C3×C4—74no—
1051C3×C4—142no—
1052C3×C4—144no—
1053C3×C4—142no—
1054C3×C4—1262no—
1055Dic3—32no—
1056Dic3—32no—
1057Dic3—34no—
1058C32—71no—
1059C32—142no—
1060C32—141no—
1061C32—141no—
1062C32—282no—
1063C32—281no—
1064C32C2×D4×AGL(1,𝔽7)11yescharacteristic, complemented
1065C23—71no—
1066C23—91no—
1067C23—634no—
1068C23—631no—
1069C23—631no—
1070C23—634no—
1071C23—1264no—
1072C23—1264no—
1073C23C3⋊D3×AGL(1,𝔽7)11yescharacteristic, complemented
1074D4—74no—
1075D4—94no—
1076D4—634no—
1077D4—634no—
1078C2×C4—71no—
1079C2×C4—91no—
1080C2×C4—634no—
1081C7C2×C3×D4×C3⋊D311yescharacteristic, complemented, Sylow
1082C2×C3—22no—
1083C2×C3—22no—
1084C2×C3—24no—
1085C2×C3—142no—
1086C2×C3—142no—
1087C2×C3—142no—
1088C2×C3—144no—
1089C2×C3—142no—
1090C2×C3—141no—
1091C2×C3—282no—
1092C2×C3—282no—
1093C2×C3—284no—
1094C2×C3—282no—
1095C2×C3—282no—
1096C2×C3—284no—
1097C2×C3—282no—
1098C2×C3—282no—
1099C2×C3—284no—
1100C2×C3—282no—
1101C2×C3—281no—
1102C2×C3—282no—
1103C2×C3—281no—
1104C2×C3—634no—
1105C2×C3—1262no—
1106C2×C3—2522no—
1107C2×C3#66694⋊C312yescomplemented
1108C2×C3#66694⋊C312yescomplemented
1109C2×C3#66694⋊C314yescomplemented
1110C2×C3C22×D3×AGL(1,𝔽7)11yescharacteristic
1111C2×C3C22×D3×AGL(1,𝔽7)11yescharacteristic
1112C2×C3C22×D3×AGL(1,𝔽7)12yes—
1113D3—62no—
1114D3—62no—
1115D3—64no—
1116D3—214no—
1117D3—214no—
1118D3—218no—
1119D3—422no—
1120D3—422no—
1121D3—424no—
1122C22—22no—
1123C22—72no—
1124C22—92no—
1125C22—142no—
1126C22—182no—
1127C22—634no—
1128C22—632no—
1129C22—632no—
1130C22—1268no—
1131C22—1268no—
1132C22—1262no—
1133C22C2×C3⋊D3×AGL(1,𝔽7)11yescharacteristic
1134C22C2×C3⋊D3×AGL(1,𝔽7)12yescomplemented
1135C4—72no—
1136C4—92no—
1137C3—141no—
1138C3—281no—
1139C3—282no—
1140C3—281no—
1141C3C2×#66694⋊C311yescharacteristic, complemented
1142C3C2×#66694⋊C311yescharacteristic, complemented
1143C3C2×#66694⋊C312yescomplemented
1144C2—22no—
1145C2—142no—
1146C2—182no—
1147C2—634no—
1148C2—1262no—
1149C2C22×C3⋊D3×AGL(1,𝔽7)11yescharacteristic
1150C2#7224554512yesdirect product factor
subgroupG/H
centerC22C2×C3⋊D3×AGL(1,𝔽7)
commutator, cosocleC2×C32×C7C24×C3
FrattiniC2C22×C3⋊D3×AGL(1,𝔽7)
FittingC23×C32×C7C22×C3
socleC22×C32×C7C23×C3
hypercenterC23C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#13094716C2semidirect
2. C23×C3⋊(C3⋊AGL(1,𝔽7))C2semidirect
3. C2×C32×(C22⋊D7)⋊C3C2semidirect
4. C2×#13094715C2semidirect
5. C2×ΓL(1,𝔽8)×#638C2semidirect
6. #72245545C2direct (N × H)
7. C2×#13094713C2semidirect
8. C2×#11759581C3semidirect
12. C22×C3⋊D3×AGL(1,𝔽7)C2semidirect
13. C23×C32×ΓL(1,𝔽8)C22semidirect
16. C22×C3⋊(C3⋊AGL(1,𝔽7))C22semidirect
17. C22×C3⋊(C3⋊AGL(1,𝔽7))C22semidirect
18. C22×C3⋊D3×ΓL(1,𝔽8)C22semidirect
19. C22×C32×AGL(1,𝔽7)C22semidirect
21. C2×C3⋊D3×AGL(1,𝔽7)C22semidirect
22. ΓL(1,𝔽8)×#638C22semidirect
23. C2×ΓL(1,𝔽8)×C3⋊Dic3C22semidirect
24. C32×(C22⋊D7)⋊C3C22semidirect
25. C2×C32×ΓL(1,𝔽8)⋊C4C22semidirect
26. #13094716C22semidirect
27. #13094715C22semidirect
28. #13094713C22semidirect
29. C23×C3⋊D21C2×C3semidirect
30. C22×D7×C3⋊D3C2×C3semidirect
37. C2×C7×#638C2×C3semidirect
38. C2×C32×C22⋊D7C2×C3semidirect
39. #11759581C2×C3semidirect
40. C2×#92678C2×C3semidirect
41. C2×#92677C2×C3semidirect
42. C2×#92675C2×C3semidirect
49. C2×C3×(C22⋊D7)⋊C3D3semidirect
50. C2×C3×(C22⋊D7)⋊C3D3semidirect
51. C2×C3×(C22⋊D7)⋊C3D3semidirect
67. C22×C32×ΓL(1,𝔽8)C23semidirect
70. C2×C3⋊(C3⋊AGL(1,𝔽7))D4semidirect
72. C2×C3⋊(C3⋊AGL(1,𝔽7))C23semidirect
74. C2×C3⋊D3×ΓL(1,𝔽8)C23semidirect
76. C2×C32×AGL(1,𝔽7)C23semidirect
78. ΓL(1,𝔽8)×C3⋊Dic3C23semidirect
79. C32×ΓL(1,𝔽8)⋊C4C23semidirect
84. C23×C32×C7C22×C3semidirect
87. C22×C3⋊D21C22×C3semidirect
88. C22×C3⋊D21C22×C3semidirect
89. C22×C7×C3⋊D3C22×C3semidirect
90. C22×C32×D7C22×C3semidirect
94. C23×C3×ΓL(1,𝔽8)C2×D3semidirect
95. C23×C3×ΓL(1,𝔽8)C2×D3semidirect
96. C23×C3×ΓL(1,𝔽8)C2×D3semidirect
98. C2×D7×C3⋊D3C22×C3semidirect
117. C22×C3×AGL(1,𝔽7)C2×D3semidirect
118. C22×C3×AGL(1,𝔽7)C2×D3semidirect
119. C22×C3×AGL(1,𝔽7)C2×D3semidirect
126. C7×#638C22×C3semidirect
127. C2×C7×C3⋊Dic3C22×C3semidirect
128. C32×C22⋊D7C22×C3semidirect
129. C2×C32×Dic7C22×C3semidirect
130. #92678C22×C3semidirect
131. #92677C22×C3semidirect
132. #92675C22×C3semidirect
142. C3×(C22⋊D7)⋊C3C2×D3semidirect
143. C3×(C22⋊D7)⋊C3C2×D3semidirect
144. C3×(C22⋊D7)⋊C3C2×D3semidirect
148. C2×C3×ΓL(1,𝔽8)⋊C4C2×D3semidirect
149. C2×C3×ΓL(1,𝔽8)⋊C4C2×D3semidirect
150. C2×C3×ΓL(1,𝔽8)⋊C4C2×D3semidirect
169. C2×C32×ΓL(1,𝔽8)C2×D4semidirect
172. C3⋊(C3⋊AGL(1,𝔽7))C2×D4semidirect
186. C2×C3×C22⋊D7C3×D3semidirect
187. C2×C3×C22⋊D7C3×D3semidirect
188. C2×C3×C22⋊D7C3×D3semidirect
206. C2×(C22⋊D7)⋊C3C3⋊D3semidirect
216. C22×C32×C7C23×C3semidirect
219. C2×C3⋊D21C3×D4semidirect
221. C2×C3⋊D21C23×C3semidirect
223. C2×C7×C3⋊D3C23×C3semidirect
225. C2×C32×D7C23×C3semidirect
241. C22×C3×ΓL(1,𝔽8)C22×D3semidirect
242. C22×C3×ΓL(1,𝔽8)C22×D3semidirect
243. C22×C3×ΓL(1,𝔽8)C22×D3semidirect
275. C2×C3×AGL(1,𝔽7)C22×D3semidirect
276. C2×C3×AGL(1,𝔽7)C22×D3semidirect
277. C2×C3×AGL(1,𝔽7)C22×D3semidirect
281. C7×C3⋊Dic3C23×C3semidirect
282. C32×Dic7C23×C3semidirect
289. C3×ΓL(1,𝔽8)⋊C4C22×D3semidirect
290. C3×ΓL(1,𝔽8)⋊C4C22×D3semidirect
291. C3×ΓL(1,𝔽8)⋊C4C22×D3semidirect
309. C32×ΓL(1,𝔽8)C22×D4semidirect
310. C23×C3×C7C2×C3×D3semidirect
311. C23×C3×C7C2×C3×D3semidirect
312. C23×C3×C7C2×C3×D3semidirect
328. C22×C3×D7C2×C3×D3semidirect
329. C22×C3×D7C2×C3×D3semidirect
330. C22×C3×D7C2×C3×D3semidirect
335. C23×ΓL(1,𝔽8)C2×C3⋊D3semidirect
351. C22×AGL(1,𝔽7)C2×C3⋊D3semidirect
358. C3×C22⋊D7C2×C3×D3semidirect
359. C3×C22⋊D7C2×C3×D3semidirect
360. C3×C22⋊D7C2×C3×D3semidirect
361. C2×C3×Dic7C2×C3×D3semidirect
362. C2×C3×Dic7C2×C3×D3semidirect
363. C2×C3×Dic7C2×C3×D3semidirect
379. (C22⋊D7)⋊C3C2×C3⋊D3semidirect
383. C2×ΓL(1,𝔽8)⋊C4C2×C3⋊D3semidirect
402. C2×#638AGL(1,𝔽7)semidirect
422. C2×C32×C7C2×C3×D4semidirect
425. C3⋊D21C2×C3×D4semidirect
440. C2×C3×ΓL(1,𝔽8)D3×D4semidirect
441. C2×C3×ΓL(1,𝔽8)D3×D4semidirect
442. C2×C3×ΓL(1,𝔽8)D3×D4semidirect
465. C2×C22⋊D7C3×C3⋊D3semidirect
494. C22×C3×C7C22×C3×D3semidirect
495. C22×C3×C7C22×C3×D3semidirect
496. C22×C3×C7C22×C3×D3semidirect
521. C2×C3×D7C22×C3×D3semidirect
522. C2×C3×D7C22×C3×D3semidirect
523. C2×C3×D7C22×C3×D3semidirect
537. C22×ΓL(1,𝔽8)C22×C3⋊D3semidirect
554. C2×AGL(1,𝔽7)C22×C3⋊D3semidirect
555. C3×Dic7C22×C3×D3semidirect
556. C3×Dic7C22×C3×D3semidirect
557. C3×Dic7C22×C3×D3semidirect
565. ΓL(1,𝔽8)⋊C4C22×C3⋊D3semidirect
579. C23×C32C2×AGL(1,𝔽7)semidirect
586. C22×C3⋊D3C2×AGL(1,𝔽7)semidirect
623. #638C2×AGL(1,𝔽7)semidirect
624. C2×C3⋊Dic3C2×AGL(1,𝔽7)semidirect
642. C32×C7C22×C3×D4semidirect
646. C3×ΓL(1,𝔽8)C2×D3×D4semidirect
647. C3×ΓL(1,𝔽8)C2×D3×D4semidirect
648. C3×ΓL(1,𝔽8)C2×D3×D4semidirect
650. C23×C7C2×C3×C3⋊D3semidirect
657. C22×D7C2×C3×C3⋊D3semidirect
661. C22⋊D7C2×C3×C3⋊D3semidirect
662. C2×Dic7C2×C3×C3⋊D3semidirect
710. C2×C3×C7C3×D3×D4semidirect
711. C2×C3×C7C3×D3×D4semidirect
712. C2×C3×C7C3×D3×D4semidirect
739. C2×ΓL(1,𝔽8)D4×C3⋊D3semidirect
781. C22×C32C22×AGL(1,𝔽7)semidirect
789. C2×C3⋊D3C22×AGL(1,𝔽7)semidirect
821. C3⋊Dic3C22×AGL(1,𝔽7)semidirect
830. C22×C7C22×C3×C3⋊D3semidirect
838. C2×D7C22×C3×C3⋊D3semidirect
840. Dic7C22×C3×C3⋊D3semidirect
860. C23×C3D3×AGL(1,𝔽7)semidirect
861. C23×C3D3×AGL(1,𝔽7)semidirect
862. C23×C3D3×AGL(1,𝔽7)semidirect
918. C3×C7C2×C3×D3×D4semidirect
919. C3×C7C2×C3×D3×D4semidirect
920. C3×C7C2×C3×D3×D4semidirect
924. ΓL(1,𝔽8)C2×D4×C3⋊D3semidirect
951. C2×C32D4×AGL(1,𝔽7)semidirect
975. C2×C7C3×D4×C3⋊D3semidirect
1020. C22×C3C2×D3×AGL(1,𝔽7)semidirect
1021. C22×C3C2×D3×AGL(1,𝔽7)semidirect
1022. C22×C3C2×D3×AGL(1,𝔽7)semidirect
1064. C32C2×D4×AGL(1,𝔽7)semidirect
1073. C23C3⋊D3×AGL(1,𝔽7)semidirect
1081. C7C2×C3×D4×C3⋊D3semidirect
1107. C2×C3#66694⋊C3semidirect
1108. C2×C3#66694⋊C3semidirect
1109. C2×C3#66694⋊C3semidirect
1134. C22C2×C3⋊D3×AGL(1,𝔽7)semidirect
1141. C3C2×#66694⋊C3semidirect
1142. C3C2×#66694⋊C3semidirect
1143. C3C2×#66694⋊C3semidirect
1150. C2#72245545direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#130947162
C23×C3⋊(C3⋊AGL(1,𝔽7))2
C2×C32×(C22⋊D7)⋊C32
C2×#130947152
C2×ΓL(1,𝔽8)×#6382
#722455452
C2×#130947132
C2×#117595813
C2×#66694⋊C33
C22×C3⋊D3×AGL(1,𝔽7)2
C2×C3×D4×C3⋊D37