Finite Group Databasebeta

← C4×C3⋊Dic3×AGL(1,𝔽7) #72246431

Subgroups — C4×C3⋊Dic3×AGL(1,𝔽7) #72246431

Order 6048.

1728 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊Dic3×ΓL(1,𝔽8)⋊C4C212yesmaximal, complemented
2C4×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C211yesmaximal, characteristic, complemented
3C4×ΓL(1,𝔽8)×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C4×D7×C3⋊Dic3C311yesmaximal, characteristic, complemented
5C2×C3⋊Dic3×AGL(1,𝔽7)C212yesmaximal
6C2×C32×C4×AGL(1,𝔽7)C211yesmaximal, characteristic
7C4×Dic3×AGL(1,𝔽7)—31nomaximal
8C4×Dic3×AGL(1,𝔽7)—33nomaximal
9C22×C32×AGL(1,𝔽7)C2211yescharacteristic
10C2×C32×C4×ΓL(1,𝔽8)C2211yescharacteristic
11C2×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2212yes—
12C2×ΓL(1,𝔽8)×C3⋊Dic3C2212yes—
13C2×C32×ΓL(1,𝔽8)⋊C4C2211yescharacteristic
14C32×C4×AGL(1,𝔽7)C414yescomplemented
15C3⋊Dic3×AGL(1,𝔽7)C418yesdirect product factor
16C2×C32×C4×D7C2×C311yescharacteristic
17C2×D7×C3⋊Dic3C2×C312yes—
18C2×C3×C4×AGL(1,𝔽7)—23no—
19C2×C3×C4×AGL(1,𝔽7)—21no—
20C2×C3×C4×AGL(1,𝔽7)D311yescharacteristic
21C2×C3×C4×AGL(1,𝔽7)D313yes—
22C2×Dic3×AGL(1,𝔽7)—32no—
23C2×Dic3×AGL(1,𝔽7)—36no—
24C4×C3⋊Dic21C2×C311yescharacteristic, complemented
25C4×C7×C3⋊Dic3C2×C311yescharacteristic, complemented
26Dic7×C3⋊Dic3C2×C312yescomplemented
27C4×C3⋊(ΓL(1,𝔽8)⋊C4)—31no—
28C4×C3⋊(ΓL(1,𝔽8)⋊C4)—33no—
29C4×Dic3×ΓL(1,𝔽8)—31no—
30C4×Dic3×ΓL(1,𝔽8)—33no—
31Dic3×ΓL(1,𝔽8)⋊C4—32no—
32Dic3×ΓL(1,𝔽8)⋊C4—36no—
33C2×C3×C4×C3⋊Dic3—71nomaximal, Hall
34C22×C32×ΓL(1,𝔽8)C2311yescharacteristic
35C2×C32×AGL(1,𝔽7)C2×C414yes—
36C2×C32×AGL(1,𝔽7)C2×C412yes—
37C32×C4×ΓL(1,𝔽8)C2×C412yescomplemented
38C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2×C414yescomplemented
39ΓL(1,𝔽8)×C3⋊Dic3C2×C414yescomplemented
40C32×ΓL(1,𝔽8)⋊C4C2×C412yescomplemented
41C4×Dic3×D7—31no—
42C4×Dic3×D7—33no—
43C42×AGL(1,𝔽7)—91no—
44C22×C32×D7C22×C311yescharacteristic
45C22×C3×AGL(1,𝔽7)—23no—
46C22×C3×AGL(1,𝔽7)—21no—
47C22×C3×AGL(1,𝔽7)C2×D311yescharacteristic
48C22×C3×AGL(1,𝔽7)C2×D313yes—
49C2×C32×C4×C7C22×C311yescharacteristic
50C2×C3⋊Dic21C22×C312yes—
51C2×C7×C3⋊Dic3C22×C312yes—
52C2×C32×Dic7C22×C311yescharacteristic
53C32×C4×D7C3×C414yescomplemented
54C2×C3×C4×ΓL(1,𝔽8)—23no—
55C2×C3×C4×ΓL(1,𝔽8)—21no—
56C2×C3×C4×ΓL(1,𝔽8)C2×D311yescharacteristic
57C2×C3×C4×ΓL(1,𝔽8)C2×D313yes—
58D7×C3⋊Dic3C3×C418yescomplemented
59C2×C3⋊(ΓL(1,𝔽8)⋊C4)—32no—
60C2×C3⋊(ΓL(1,𝔽8)⋊C4)—36no—
61C2×Dic3×ΓL(1,𝔽8)—32no—
62C2×Dic3×ΓL(1,𝔽8)—36no—
63C2×C3×ΓL(1,𝔽8)⋊C4—23no—
64C2×C3×ΓL(1,𝔽8)⋊C4—21no—
65C2×C3×ΓL(1,𝔽8)⋊C4C2×D311yescharacteristic
66C2×C3×ΓL(1,𝔽8)⋊C4C2×D313yes—
67C3×C4×AGL(1,𝔽7)—212no—
68C3×C4×AGL(1,𝔽7)—24no—
69C3×C4×AGL(1,𝔽7)Dic314yescomplemented
70C3×C4×AGL(1,𝔽7)Dic3112yescomplemented
71Dic3×AGL(1,𝔽7)—38no—
72Dic3×AGL(1,𝔽7)—324no—
73C22×C33×C4—71no—
74C22×C3×C3⋊Dic3—72no—
75C3×C4×C3⋊Dic3—71no—
76C3×C4×C3⋊Dic3—72no—
77C3×C4×C3⋊Dic3—141no—
78C2×C32×ΓL(1,𝔽8)C22×C412yes—
79C2×C32×ΓL(1,𝔽8)C22×C411yescharacteristic
80C32×AGL(1,𝔽7)C4214yescomplemented
81C2×C3×C4×D7C3×D311yescharacteristic
82C2×C3×C4×D7C3×D313yes—
83C2×Dic3×D7—32no—
84C2×Dic3×D7—36no—
85C2×C4×AGL(1,𝔽7)—21no—
86C2×C4×AGL(1,𝔽7)—23no—
87C2×C4×AGL(1,𝔽7)—92no—
88C2×C4×AGL(1,𝔽7)C3⋊D311yescharacteristic
89C4×Dic21—31no—
90C4×Dic21—33no—
91C4×C7×Dic3—31no—
92C4×C7×Dic3—33no—
93C42×ΓL(1,𝔽8)—91no—
94Dic3×Dic7—32no—
95Dic3×Dic7—36no—
96C4×ΓL(1,𝔽8)⋊C4—91no—
97C4×ΓL(1,𝔽8)⋊C4—92no—
98C2×C4×C3⋊Dic3—71no—
99C2×C3×C4×Dic3—211no—
100C2×C3×C4×Dic3—213no—
101C22×C32×C7C23×C311yescharacteristic
102C2×C32×D7C2×C3×C414yes—
103C2×C32×D7C2×C3×C412yes—
104C22×C3×ΓL(1,𝔽8)—23no—
105C22×C3×ΓL(1,𝔽8)—21no—
106C22×C3×ΓL(1,𝔽8)C22×D311yescharacteristic
107C22×C3×ΓL(1,𝔽8)C22×D313yes—
108C2×C3×AGL(1,𝔽7)—212no—
109C2×C3×AGL(1,𝔽7)—24no—
110C2×C3×AGL(1,𝔽7)—26no—
111C2×C3×AGL(1,𝔽7)—22no—
112C2×C3×AGL(1,𝔽7)C4×D314yes—
113C2×C3×AGL(1,𝔽7)C4×D3112yes—
114C2×C3×AGL(1,𝔽7)C2×Dic312yes—
115C2×C3×AGL(1,𝔽7)C2×Dic316yes—
116C32×C4×C7C2×C3×C412yescomplemented
117C3⋊Dic21C2×C3×C414yescomplemented
118C7×C3⋊Dic3C2×C3×C414yescomplemented
119C32×Dic7C2×C3×C412yescomplemented
120C3×C4×ΓL(1,𝔽8)—26no—
121C3×C4×ΓL(1,𝔽8)—22no—
122C3×C4×ΓL(1,𝔽8)C2×Dic312yescomplemented
123C3×C4×ΓL(1,𝔽8)C2×Dic316yescomplemented
124C3⋊(ΓL(1,𝔽8)⋊C4)—34no—
125C3⋊(ΓL(1,𝔽8)⋊C4)—312no—
126Dic3×ΓL(1,𝔽8)—34no—
127Dic3×ΓL(1,𝔽8)—312no—
128C3×ΓL(1,𝔽8)⋊C4—26no—
129C3×ΓL(1,𝔽8)⋊C4—22no—
130C3×ΓL(1,𝔽8)⋊C4C2×Dic312yescomplemented
131C3×ΓL(1,𝔽8)⋊C4C2×Dic316yescomplemented
132C42×D7—91noHall
133C23×C33—71no—
134C2×C33×C4—71no—
135C2×C33×C4—74no—
136C2×C33×C4—141no—
137C2×C3×C3⋊Dic3—72no—
138C2×C3×C3⋊Dic3—78no—
139C2×C3×C3⋊Dic3—142no—
140C32×ΓL(1,𝔽8)C2×C4211yescharacteristic, complemented, Hall
141C22×C3×D7C2×C3×D311yescharacteristic
142C22×C3×D7C2×C3×D313yes—
143C22×AGL(1,𝔽7)—21no—
144C22×AGL(1,𝔽7)—23no—
145C22×AGL(1,𝔽7)C2×C3⋊D311yescharacteristic
146C2×C3×C4×C7C2×C3×D311yescharacteristic
147C2×C3×C4×C7C2×C3×D313yes—
148C2×Dic21—32no—
149C2×Dic21—36no—
150C2×C7×Dic3—32no—
151C2×C7×Dic3—36no—
152C2×C3×Dic7C2×C3×D311yescharacteristic
153C2×C3×Dic7C2×C3×D313yes—
154C3×C4×D7C3×Dic314yescomplemented
155C3×C4×D7C3×Dic3112yescomplemented
156C2×C4×ΓL(1,𝔽8)—21no—
157C2×C4×ΓL(1,𝔽8)—23no—
158C2×C4×ΓL(1,𝔽8)—92no—
159C2×C4×ΓL(1,𝔽8)C2×C3⋊D311yescharacteristic
160Dic3×D7—38no—
161Dic3×D7—324no—
162C2×ΓL(1,𝔽8)⋊C4—21no—
163C2×ΓL(1,𝔽8)⋊C4—23no—
164C2×ΓL(1,𝔽8)⋊C4—92no—
165C2×ΓL(1,𝔽8)⋊C4C2×C3⋊D311yescharacteristic
166C4×AGL(1,𝔽7)—24no—
167C4×AGL(1,𝔽7)—212no—
168C4×AGL(1,𝔽7)—98no—
169C4×AGL(1,𝔽7)C3⋊Dic314yesdirect product factor
170C22×C32×C4—71no—
171C22×C32×C4—73no—
172C22×C32×C4—71no—
173C22×C32×C4—143no—
174C22×C32×C4—141no—
175C22×C3⋊Dic3—72no—
176C22×C3×Dic3—212no—
177C22×C3×Dic3—216no—
178C4×C3⋊Dic3—71no—
179C4×C3⋊Dic3—72no—
180C4×C3⋊Dic3AGL(1,𝔽7)11yescharacteristic, direct product factor
181C3×C4×Dic3—211no—
182C3×C4×Dic3—213no—
183C3×C4×Dic3—212no—
184C3×C4×Dic3—216no—
185C3×C4×Dic3—421no—
186C3×C4×Dic3—423no—
187C2×C32×C7C22×C3×C412yes—
188C2×C32×C7C22×C3×C411yescharacteristic
189C32×D7C3×C4214yescomplemented
190C2×C3×ΓL(1,𝔽8)—26no—
191C2×C3×ΓL(1,𝔽8)—22no—
192C2×C3×ΓL(1,𝔽8)—23no—
193C2×C3×ΓL(1,𝔽8)—21no—
194C2×C3×ΓL(1,𝔽8)C2×C4×D312yes—
195C2×C3×ΓL(1,𝔽8)C2×C4×D316yes—
196C2×C3×ΓL(1,𝔽8)C22×Dic311yescharacteristic
197C2×C3×ΓL(1,𝔽8)C22×Dic313yes—
198C3×AGL(1,𝔽7)—212no—
199C3×AGL(1,𝔽7)—24no—
200C3×AGL(1,𝔽7)C4×Dic314yescomplemented
201C3×AGL(1,𝔽7)C4×Dic3112yescomplemented
202C2×C4×D7—92no—
203C2×C4×D7C3×C3⋊D311yescharacteristic
204C42×C7—91no—
205C4×Dic7—91no—
206C4×Dic7—92no—
207C22×C33—74no—
208C22×C33—72no—
209C22×C33—141no—
210C33×C4—72no—
211C33×C4—142no—
212C3×C3⋊Dic3—74no—
213C3×C3⋊Dic3—144no—
214C2×C3×C42—631no—
215C2×C4×Dic3—211no—
216C2×C4×Dic3—213no—
217C22×C3×C7C22×C3×D311yescharacteristic
218C22×C3×C7C22×C3×D313yes—
219C2×C3×D7C3×C4×D314yes—
220C2×C3×D7C3×C4×D3112yes—
221C2×C3×D7C2×C3×Dic312yes—
222C2×C3×D7C2×C3×Dic316yes—
223C22×ΓL(1,𝔽8)—21no—
224C22×ΓL(1,𝔽8)—23no—
225C22×ΓL(1,𝔽8)C22×C3⋊D311yescharacteristic
226C2×AGL(1,𝔽7)—24no—
227C2×AGL(1,𝔽7)—212no—
228C2×AGL(1,𝔽7)—22no—
229C2×AGL(1,𝔽7)—26no—
230C2×AGL(1,𝔽7)C4×C3⋊D314yes—
231C2×AGL(1,𝔽7)C2×C3⋊Dic312yes—
232C3×C4×C7C2×C3×Dic312yescomplemented
233C3×C4×C7C2×C3×Dic316yescomplemented
234Dic21—34no—
235Dic21—312no—
236C3×Dic7C2×C3×Dic312yescomplemented
237C3×Dic7C2×C3×Dic316yescomplemented
238C7×Dic3—34no—
239C7×Dic3—312no—
240C4×ΓL(1,𝔽8)—22no—
241C4×ΓL(1,𝔽8)—26no—
242C4×ΓL(1,𝔽8)—94no—
243C4×ΓL(1,𝔽8)C2×C3⋊Dic312yescomplemented
244ΓL(1,𝔽8)⋊C4—22no—
245ΓL(1,𝔽8)⋊C4—26no—
246ΓL(1,𝔽8)⋊C4—94no—
247ΓL(1,𝔽8)⋊C4C2×C3⋊Dic312yescomplemented
248C23×C32—71no—
249C23×C32—71no—
250C23×C32—73no—
251C23×C32—143no—
252C23×C32—141no—
253C2×C32×C4—71no—
254C2×C32×C4—74no—
255C2×C32×C4—71no—
256C2×C32×C4—73no—
257C2×C32×C4—74no—
258C2×C32×C4—712no—
259C2×C32×C4—143no—
260C2×C32×C4—141no—
261C2×C32×C4—1412no—
262C2×C32×C4—144no—
263C2×C32×C4—141no—
264C2×C32×C4—143no—
265C2×C32×C4—283no—
266C2×C32×C4—281no—
267C2×C32×C4C2×AGL(1,𝔽7)11yescharacteristic
268C2×C3⋊Dic3—72no—
269C2×C3⋊Dic3—78no—
270C2×C3⋊Dic3C2×AGL(1,𝔽7)12yes—
271C2×C3×Dic3—212no—
272C2×C3×Dic3—216no—
273C2×C3×Dic3—218no—
274C2×C3×Dic3—2124no—
275C2×C3×Dic3—422no—
276C2×C3×Dic3—426no—
277C32×C7C2×C3×C4211yescharacteristic, complemented
278C3×ΓL(1,𝔽8)—23no—
279C3×ΓL(1,𝔽8)—21no—
280C3×ΓL(1,𝔽8)C2×C4×Dic311yescharacteristic, complemented
281C3×ΓL(1,𝔽8)C2×C4×Dic313yescomplemented
282C22×D7C2×C3×C3⋊D311yescharacteristic
283C2×C4×C7—92no—
284C2×C4×C7C2×C3×C3⋊D311yescharacteristic
285C2×Dic7—92no—
286C2×Dic7C2×C3×C3⋊D311yescharacteristic
287C4×D7—98no—
288C4×D7C3×C3⋊Dic314yescomplemented
289C2×C33—74no—
290C2×C33—142no—
291C2×C33—141no—
292C22×C3×C4—71no—
293C22×C3×C4—71no—
294C22×C3×C4—73no—
295C22×C3×C4—141no—
296C22×C3×C4—143no—
297C22×C3×C4—632no—
298C22×Dic3—212no—
299C22×Dic3—216no—
300C3×C42—632no—
301C3×C42—631no—
302C3×C42—1261no—
303C4×Dic3—31no—
304C4×Dic3—33no—
305C4×Dic3—212no—
306C4×Dic3—216no—
307C4×Dic3—211no—
308C4×Dic3—213no—
309C2×C3×C7C2×C3×C4×D312yes—
310C2×C3×C7C2×C3×C4×D316yes—
311C2×C3×C7C22×C3×Dic311yescharacteristic
312C2×C3×C7C22×C3×Dic313yes—
313C3×D7C3×C4×Dic314yescomplemented
314C3×D7C3×C4×Dic3112yescomplemented
315C2×ΓL(1,𝔽8)—22no—
316C2×ΓL(1,𝔽8)—21no—
317C2×ΓL(1,𝔽8)—26no—
318C2×ΓL(1,𝔽8)—23no—
319C2×ΓL(1,𝔽8)C2×C4×C3⋊D312yes—
320C2×ΓL(1,𝔽8)C22×C3⋊Dic311yescharacteristic
321AGL(1,𝔽7)—24no—
322AGL(1,𝔽7)—212no—
323AGL(1,𝔽7)C4×C3⋊Dic314yesdirect product factor
324C22×C32—74no—
325C22×C32—72no—
326C22×C32—74no—
327C22×C32—712no—
328C22×C32—72no—
329C22×C32—76no—
330C22×C32—146no—
331C22×C32—142no—
332C22×C32—1412no—
333C22×C32—144no—
334C22×C32—141no—
335C22×C32—143no—
336C22×C32—283no—
337C22×C32—281no—
338C22×C32C22×AGL(1,𝔽7)11yescharacteristic
339C32×C4—72no—
340C32×C4—72no—
341C32×C4—76no—
342C32×C4—146no—
343C32×C4—142no—
344C32×C4—142no—
345C32×C4—146no—
346C32×C4—286no—
347C32×C4—282no—
348C32×C4C4×AGL(1,𝔽7)12yescomplemented
349C3⋊Dic3—74no—
350C3⋊Dic3C4×AGL(1,𝔽7)14yesdirect product factor
351C3×Dic3—214no—
352C3×Dic3—2112no—
353C3×Dic3—424no—
354C3×Dic3—4212no—
355C2×C42—631noSylow
356C22×C7C22×C3×C3⋊D311yescharacteristic
357C2×D7C3×C4×C3⋊D314yes—
358C2×D7C2×C3×C3⋊Dic312yes—
359C4×C7—94no—
360C4×C7C2×C3×C3⋊Dic312yescomplemented
361Dic7—94no—
362Dic7C2×C3×C3⋊Dic312yescomplemented
363C33—141noSylow
364C23×C3—71no—
365C23×C3—71no—
366C23×C3—73no—
367C23×C3—141no—
368C23×C3—143no—
369C2×C3×C4—71no—
370C2×C3×C4—71no—
371C2×C3×C4—73no—
372C2×C3×C4—74no—
373C2×C3×C4—74no—
374C2×C3×C4—712no—
375C2×C3×C4—144no—
376C2×C3×C4—141no—
377C2×C3×C4—143no—
378C2×C3×C4—1412no—
379C2×C3×C4—141no—
380C2×C3×C4—141no—
381C2×C3×C4—283no—
382C2×C3×C4—632no—
383C2×C3×C4—638no—
384C2×C3×C4—1262no—
385C2×C3×C4D3×AGL(1,𝔽7)11yescharacteristic
386C2×C3×C4D3×AGL(1,𝔽7)13yes—
387C2×Dic3—32no—
388C2×Dic3—36no—
389C2×Dic3—218no—
390C2×Dic3—2124no—
391C2×Dic3—212no—
392C2×Dic3—216no—
393C3×C7C2×C3×C4×Dic311yescharacteristic, complemented
394C3×C7C2×C3×C4×Dic313yescomplemented
395ΓL(1,𝔽8)—21no—
396ΓL(1,𝔽8)—23no—
397ΓL(1,𝔽8)C2×C4×C3⋊Dic311yescharacteristic, complemented
398C2×C32—74no—
399C2×C32—74no—
400C2×C32—712no—
401C2×C32—1412no—
402C2×C32—144no—
403C2×C32—142no—
404C2×C32—141no—
405C2×C32—146no—
406C2×C32—143no—
407C2×C32—286no—
408C2×C32—283no—
409C2×C32—282no—
410C2×C32—281no—
411C2×C32C2×C4×AGL(1,𝔽7)12yes—
412C2×C32C2×C4×AGL(1,𝔽7)11yescharacteristic
413C22×C4—71no—
414C22×C4—632no—
415C42—91no—
416C42—632no—
417C42—631no—
418C2×C7C2×C3×C4×C3⋊D312yes—
419C2×C7C22×C3×C3⋊Dic311yescharacteristic
420D7C3×C4×C3⋊Dic314yescomplemented
421C22×C3—72no—
422C22×C3—74no—
423C22×C3—74no—
424C22×C3—712no—
425C22×C3—72no—
426C22×C3—76no—
427C22×C3—142no—
428C22×C3—144no—
429C22×C3—146no—
430C22×C3—1412no—
431C22×C3—141no—
432C22×C3—141no—
433C22×C3—283no—
434C22×C3C2×D3×AGL(1,𝔽7)11yescharacteristic
435C22×C3C2×D3×AGL(1,𝔽7)13yes—
436C3×C4—72no—
437C3×C4—72no—
438C3×C4—76no—
439C3×C4—142no—
440C3×C4—146no—
441C3×C4—142no—
442C3×C4—142no—
443C3×C4—286no—
444C3×C4—634no—
445C3×C4—1264no—
446C3×C4Dic3×AGL(1,𝔽7)12yescomplemented
447C3×C4Dic3×AGL(1,𝔽7)16yescomplemented
448Dic3—34no—
449Dic3—312no—
450Dic3—214no—
451Dic3—2112no—
452C32—141no—
453C32—143no—
454C32—283no—
455C32—281no—
456C32C42×AGL(1,𝔽7)11yescharacteristic, complemented
457C23—71no—
458C2×C4—71no—
459C2×C4—74no—
460C2×C4—92no—
461C2×C4—638no—
462C2×C4—632no—
463C2×C4C3⋊D3×AGL(1,𝔽7)11yescharacteristic
464C7C2×C3×C4×C3⋊Dic311yescharacteristic, complemented, Sylow
465C2×C3—74no—
466C2×C3—74no—
467C2×C3—712no—
468C2×C3—144no—
469C2×C3—1412no—
470C2×C3—142no—
471C2×C3—142no—
472C2×C3—141no—
473C2×C3—141no—
474C2×C3—286no—
475C2×C3—283no—
476C2×C3C4×D3×AGL(1,𝔽7)12yes—
477C2×C3C4×D3×AGL(1,𝔽7)16yes—
478C2×C3C2×Dic3×AGL(1,𝔽7)11yescharacteristic
479C2×C3C2×Dic3×AGL(1,𝔽7)13yes—
480C22—74no—
481C22—72no—
482C22C2×C3⋊D3×AGL(1,𝔽7)11yescharacteristic
483C4—72no—
484C4—94no—
485C4—634no—
486C4C3⋊Dic3×AGL(1,𝔽7)12yesdirect product factor
487C3—141no—
488C3—141no—
489C3—283no—
490C3C4×Dic3×AGL(1,𝔽7)11yescharacteristic, complemented
491C3C4×Dic3×AGL(1,𝔽7)13yescomplemented
492C2—74no—
493C2C4×C3⋊D3×AGL(1,𝔽7)12yes—
494C2C2×C3⋊Dic3×AGL(1,𝔽7)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4C3⋊D3×AGL(1,𝔽7)
commutator, hypocenterC32×C7C2×C3×C42
FrattiniC22C2×C3⋊D3×AGL(1,𝔽7)
FittingC2×C32×C4×C7C22×C3
socle, cosocleC22×C32×C7C23×C3
prime radicalC22×C32×AGL(1,𝔽7)C22
LCSG ▷ C32×C7
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C3⋊Dic3×ΓL(1,𝔽8)⋊C4C2semidirect
2. C4×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2semidirect
3. C4×ΓL(1,𝔽8)×C3⋊Dic3C2semidirect
4. C4×D7×C3⋊Dic3C3semidirect
14. C32×C4×AGL(1,𝔽7)C4semidirect
15. C3⋊Dic3×AGL(1,𝔽7)C4direct (N × H)
24. C4×C3⋊Dic21C2×C3semidirect
25. C4×C7×C3⋊Dic3C2×C3semidirect
26. Dic7×C3⋊Dic3C2×C3semidirect
37. C32×C4×ΓL(1,𝔽8)C2×C4semidirect
38. C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2×C4semidirect
39. ΓL(1,𝔽8)×C3⋊Dic3C2×C4semidirect
40. C32×ΓL(1,𝔽8)⋊C4C2×C4semidirect
53. C32×C4×D7C3×C4semidirect
58. D7×C3⋊Dic3C3×C4semidirect
69. C3×C4×AGL(1,𝔽7)Dic3semidirect
70. C3×C4×AGL(1,𝔽7)Dic3semidirect
80. C32×AGL(1,𝔽7)C42semidirect
116. C32×C4×C7C2×C3×C4semidirect
117. C3⋊Dic21C2×C3×C4semidirect
118. C7×C3⋊Dic3C2×C3×C4semidirect
119. C32×Dic7C2×C3×C4semidirect
122. C3×C4×ΓL(1,𝔽8)C2×Dic3semidirect
123. C3×C4×ΓL(1,𝔽8)C2×Dic3semidirect
130. C3×ΓL(1,𝔽8)⋊C4C2×Dic3semidirect
131. C3×ΓL(1,𝔽8)⋊C4C2×Dic3semidirect
140. C32×ΓL(1,𝔽8)C2×C42semidirect
154. C3×C4×D7C3×Dic3semidirect
155. C3×C4×D7C3×Dic3semidirect
169. C4×AGL(1,𝔽7)C3⋊Dic3direct (N × H)
180. C4×C3⋊Dic3AGL(1,𝔽7)direct (N × H)
189. C32×D7C3×C42semidirect
200. C3×AGL(1,𝔽7)C4×Dic3semidirect
201. C3×AGL(1,𝔽7)C4×Dic3semidirect
232. C3×C4×C7C2×C3×Dic3semidirect
233. C3×C4×C7C2×C3×Dic3semidirect
236. C3×Dic7C2×C3×Dic3semidirect
237. C3×Dic7C2×C3×Dic3semidirect
243. C4×ΓL(1,𝔽8)C2×C3⋊Dic3semidirect
247. ΓL(1,𝔽8)⋊C4C2×C3⋊Dic3semidirect
277. C32×C7C2×C3×C42semidirect
280. C3×ΓL(1,𝔽8)C2×C4×Dic3semidirect
281. C3×ΓL(1,𝔽8)C2×C4×Dic3semidirect
288. C4×D7C3×C3⋊Dic3semidirect
313. C3×D7C3×C4×Dic3semidirect
314. C3×D7C3×C4×Dic3semidirect
323. AGL(1,𝔽7)C4×C3⋊Dic3direct (N × H)
348. C32×C4C4×AGL(1,𝔽7)semidirect
350. C3⋊Dic3C4×AGL(1,𝔽7)direct (N × H)
360. C4×C7C2×C3×C3⋊Dic3semidirect
362. Dic7C2×C3×C3⋊Dic3semidirect
393. C3×C7C2×C3×C4×Dic3semidirect
394. C3×C7C2×C3×C4×Dic3semidirect
397. ΓL(1,𝔽8)C2×C4×C3⋊Dic3semidirect
420. D7C3×C4×C3⋊Dic3semidirect
446. C3×C4Dic3×AGL(1,𝔽7)semidirect
447. C3×C4Dic3×AGL(1,𝔽7)semidirect
456. C32C42×AGL(1,𝔽7)semidirect
464. C7C2×C3×C4×C3⋊Dic3semidirect
486. C4C3⋊Dic3×AGL(1,𝔽7)direct (N × H)
490. C3C4×Dic3×AGL(1,𝔽7)semidirect
491. C3C4×Dic3×AGL(1,𝔽7)semidirect

Maximal subgroups

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

subgroupindex
C3⋊Dic3×ΓL(1,𝔽8)⋊C42
C4×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))2
C4×ΓL(1,𝔽8)×C3⋊Dic32
C4×D7×C3⋊Dic33
C2×C3⋊Dic3×AGL(1,𝔽7)2
C2×C32×C4×AGL(1,𝔽7)2
C4×Dic3×AGL(1,𝔽7)3
C2×C3×C4×C3⋊Dic37