Finite Group Databasebeta

← #13253865

Subgroups — #13253865

Order 1792.

654 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739521C211yesmaximal, characteristic
2C4×C7×C22⋊C8C211yesmaximal, characteristic
3#11729289C211yesmaximal, characteristic
4#11725481C214yesmaximal
5C22×C42×C7C2211yescharacteristic
6C22×C4⋊Dic7—21no—
7C2×#6487—21no—
8C2×#6432C411yescharacteristic, complemented
9C2×C7×C22⋊C8C2212yes—
10C2×C4×C7×C8—21no—
11#89984—21no—
12#89984C2212yes—
13C2×C7⋊#95—21no—
14C2×C7⋊#95C2212yes—
15#89707C411yescharacteristic, complemented
16#89701—21no—
17#89700—21no—
18#89700C412yescomplemented
19C7×#336—21no—
20#9885—71nomaximal, Sylow
21C23×C4×C7D411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7C2311yescharacteristic
24C23×Dic7—22no—
25C22×Dic14—21no—
26C22×C7×C8—22no—
27C2×C42×C7—42no—
28C2×C42×C7C2×C411yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C4⋊Dic7—24no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—42no—
38C2×C4⋊Dic7—42no—
39C2×C4⋊Dic7C2×C412yes—
40C2×C4⋊Dic7C2×C412yes—
41#6487—42no—
42#6487—42no—
43C2×Dic7⋊C4—22no—
44#6432—42no—
45C7×C22⋊C8—22no—
46C7×C22⋊C8Q814yescomplemented
47C4×C7×C8—42no—
48C7⋊#95—22no—
49C7⋊#95—22no—
50C7⋊#95—24no—
51C7⋊#95—42no—
52#2857—71no—
53C4×C22⋊C8D711yescharacteristic
54C4⋊#95—71no—
55#1294—74no—
56C24×C7C2×D411yescharacteristic
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—41no—
60C22×C4×C7—41no—
61C22×C4×C7—41no—
62C22×C4×C7—41no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7D812yes—
68C22×C4×C7SD1612yes—
69C22×C4×C7SD1612yes—
70C22×C4×C7Q1612yes—
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×Q812yes—
74C22×C4×C7#4112yes—
75C22×Dic7—24no—
76C22×Dic7—22no—
77C22×Dic7—22no—
78C22×Dic7—42no—
79C22×Dic7—42no—
80C22×Dic7—42no—
81C22×Dic7—42no—
82C22×Dic7—42no—
83C22×Dic7—42no—
84C2×Dic14—42no—
85C2×Dic14—42no—
86C2×Dic14—42no—
87C2×C7×C8—24no—
88C2×C7×C8—42no—
89C2×C7×C8—42no—
90C42×C7—22no—
91C42×C7—22no—
92C42×C7—41no—
93C42×C7—41no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C4⋊Dic7—42no—
97C4⋊Dic7—42no—
98C4⋊Dic7—48no—
99C4⋊Dic7—42no—
100C4⋊Dic7—42no—
101C4⋊Dic7—42no—
102Dic7⋊C4—44no—
103C2×C4⋊Q8—71no—
104C2×C22⋊Q8—141no—
105C22×C4⋊C4—141no—
106C22×C42C2×D711yescharacteristic
107C2×C22⋊C8C2×D712yes—
108C2×C4×C8—21no—
109#391—141no—
110#389—72no—
111#389—141no—
112#384—71no—
113#380—72no—
114#380—141no—
115C2×#95—72no—
116C2×#95—141no—
117#336—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7C2×C22⋊C411yescharacteristic
123C23×C7#12411yescharacteristic
124C23×C7C4⋊Q811yescharacteristic
125C23×C7C2×D811yescharacteristic
126C23×C7C2×SD1611yescharacteristic
127C23×C7C2×SD1611yescharacteristic
128C23×C7C2×Q1611yescharacteristic
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—24no—
140C2×C4×C7—24no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7#9912yes—
146C2×C4×C7#10212yes—
147C2×C4×C7#10212yes—
148C2×C4×C7#10312yes—
149C2×C4×C7#10312yes—
150C2×C4×C7#10412yes—
151C2×C4×C7C4×Q812yes—
152C2×C4×C7C22⋊Q812yes—
153C2×Dic7—44no—
154C2×Dic7—44no—
155C2×Dic7—44no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7—42no—
160C2×Dic7—42no—
161C2×Dic7—42no—
162C2×Dic7—82no—
163C2×Dic7—82no—
164C2×Dic7—82no—
165C2×Dic7—82no—
166Dic14—84no—
167C7×C8—44no—
168C22×Q8—141no—
169C23×C4—142no—
170C23×C4D2811yescharacteristic
171C23×C4D2811yescharacteristic
172C23×C4C22×D711yescharacteristic
173C22×C8—22no—
174C4⋊Q8—282no—
175C22⋊Q8—282no—
176C22⋊Q8—282no—
177C2×C4⋊C4—72no—
178C2×C4⋊C4—72no—
179C2×C4⋊C4—144no—
180C2×C4⋊C4—142no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4—282no—
185C2×C4⋊C4—282no—
186C2×C22⋊C4—142no—
187C2×C42—42no—
188C2×C42C4×D711yescharacteristic
189C2×C42C4×D711yescharacteristic
190C2×C42C22⋊D711yescharacteristic
191C2×C42C22⋊D711yescharacteristic
192C22⋊C8—22no—
193C22⋊C8Dic1414yescomplemented
194C4×C8—42no—
195#95—142no—
196#95—142no—
197#95—144no—
198#95—282no—
199C22×C7—21no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7#39111yescharacteristic
212C22×C7C2×#9911yescharacteristic
213C22×C7#41011yescharacteristic
214C22×C7C2×#10211yescharacteristic
215C22×C7C2×#10311yescharacteristic
216C22×C7C2×#10411yescharacteristic
217C22×C7#42111yescharacteristic
218C22×C7#48611yescharacteristic
219C22×C7#48711yescharacteristic
220C22×C7#49811yescharacteristic
221C22×C7#50011yescharacteristic
222C4×C7—22no—
223C4×C7—22no—
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—22no—
227C4×C7#32714yes—
228Dic7—84no—
229Dic7—82no—
230Dic7—82no—
231C24C2×D2811yescharacteristic
232C2×Q8—282no—
233C2×Q8—282no—
234C2×Q8—282no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—144no—
242C22×C4—142no—
243C22×C4—142no—
244C22×C4—282no—
245C22×C4—282no—
246C22×C4—282no—
247C22×C4—282no—
248C22×C4—282no—
249C22×C4—282no—
250C22×C4#113212yes—
251C22×C4#113212yes—
252C22×C4D5612yes—
253C22×C4Dic2812yes—
254C22×C4(C2×D7)⋊C411yescharacteristic
255C22×C4(C2×D7)⋊C411yescharacteristic
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4(C2×D7)⋊C411yescharacteristic
258C22×C4C2×Dic1412yes—
259C22×C4C2×C4×D711yescharacteristic
260C22×C4#115712yes—
261C22×C4C2×C22⋊D711yescharacteristic
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—282no—
266C4⋊C4—282no—
267C4⋊C4—282no—
268C4⋊C4—288no—
269C4⋊C4—282no—
270C4⋊C4—284no—
271C4⋊C4—282no—
272C22⋊C4—282no—
273C22⋊C4—282no—
274C42—22no—
275C42—22no—
276C42—41no—
277C42—41no—
278C2×C7—21no—
279C2×C7—21no—
280C2×C7—21no—
281C2×C7—21no—
282C2×C7C2×#32711yescharacteristic
283C2×C7#150311yescharacteristic
284C2×C7#151711yescharacteristic
285C2×C7#152011yescharacteristic
286C2×C7#198611yescharacteristic
287C2×C7#199011yescharacteristic
288C2×C7#199611yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23#643211yescharacteristic
294C23#643811yescharacteristic
295C23C2×#113211yescharacteristic
296C23C2×#113211yescharacteristic
297C23C2×D5611yescharacteristic
298C23C2×Dic2811yescharacteristic
299C23C2×(C2×D7)⋊C411yescharacteristic
300Q8—564no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—284no—
318C2×C4—284no—
319C2×C4—284no—
320C2×C4—282no—
321C2×C4—282no—
322C2×C4—282no—
323C2×C4—282no—
324C2×C4—282no—
325C2×C4—282no—
326C2×C4—562no—
327C2×C4—562no—
328C2×C4—562no—
329C2×C4—562no—
330C2×C4#638012yes—
331C2×C4#639012yes—
332C2×C4#639012yes—
333C2×C4#639512yes—
334C2×C4#639512yes—
335C2×C4#639912yes—
336C2×C4C4×Dic1412yes—
337C2×C4#648712yes—
338C8—44no—
339C7#988511yescharacteristic, complemented, Sylow
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22#8945211yescharacteristic
353C22#8945311yescharacteristic
354C22#8945411yescharacteristic
355C22#8946611yescharacteristic
356C22#8970111yescharacteristic
357C22C2×#638011yescharacteristic
358C22#8977811yescharacteristic
359C22C2×#639011yescharacteristic
360C22C2×#639511yescharacteristic
361C22C2×#639911yescharacteristic
362C22#8991111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—564no—
369C4—562no—
370C4—562no—
371C4#8926514yes—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1172721111yescharacteristic
377C2#1172753111yescharacteristic
378C2#1172762211yescharacteristic
379C2C2×#8926511yescharacteristic
380C2#1172770011yescharacteristic
381C2#1172854411yescharacteristic
382C2#1172854611yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC4×C22⋊C8D7
hypocenterC7#9885
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
8. C2×#6432C4semidirect
15. #89707C4semidirect
18. #89700C4semidirect
46. C7×C22⋊C8Q8semidirect
193. C22⋊C8Dic14semidirect
339. C7#9885semidirect

Maximal subgroups

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

subgroupindex
#117395212
C4×C7×C22⋊C82
#117292892
#117254812
#98857