Finite Group Databasebeta

← #16819434

Subgroups — #16819434

Order 3712.

618 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D29C211yesmaximal, characteristic
2C2×#11745153C211yesmaximal, characteristic, complemented
3C2×#11745185C211yesmaximal, characteristic, complemented
4C2×#11745173C211yesmaximal, characteristic, complemented
5#14271126C211yesmaximal, characteristic, complemented
6C4×#90781C211yesmaximal, characteristic, complemented
7C2×C29×#104C211yesmaximal, characteristic, complemented
8C2×#41×C29C2211yescharacteristic
9#41×D29—22no—
10#41×D29—22no—
11#41×D29—22no—
12#41×D29—22no—
13C2×#90809C411yescharacteristic, complemented
14C2×Q8×D29C411yescharacteristic, complemented
15C2×#90807—21no—
16C2×#90807C411yescharacteristic, complemented
17C2×D4×D29—21no—
18C2×D4×D29C411yescharacteristic, complemented
19C2×#90805—21no—
20C2×#90805C2211yescharacteristic
21C22×C4×D29—21no—
22C22×C4×D29C2211yescharacteristic
23C2×M16×C29C2211yescharacteristic, complemented
24C2×C42×C29C2211yescharacteristic, complemented
25C2×#90781—21no—
26C2×C4×Dic29C2211yescharacteristic, complemented
27C2×#90777C2211yescharacteristic, complemented
28C29×#104—22no—
29#11745185—22no—
30#11745179—21no—
31#11745173—22no—
32#11745168—21no—
33#11745168—21no—
34#11745153—22no—
35C23×D29—21no—
36C23×D29D411yescharacteristic
37#41×C29—21no—
38#41×C29—21no—
39#41×C29D412yes—
40#41×C29D412yes—
41C2×Q8×C29C2×C411yescharacteristic
42C2×D4×C29—21no—
43C2×D4×C29C2×C411yescharacteristic
44C22×C4×C29—21no—
45C22×C4×C29—21no—
46C22×C4×C29C2311yescharacteristic
47C2×C22⋊D29—21no—
48C2×C22⋊D29—21no—
49C2×C22⋊D29—21no—
50C22×Dic29—21no—
51C22×Dic29—21no—
52C22×Dic29D411yescharacteristic
53#90809—22no—
54#90809—22no—
55Q8×D29—22no—
56Q8×D29—22no—
57#90807—24no—
58#90807—24no—
59#90807—22no—
60#90807—22no—
61D4×D29—24no—
62D4×D29—24no—
63D4×D29—22no—
64D4×D29—22no—
65#90805—24no—
66#90805—24no—
67#90805—21no—
68#90805—21no—
69#90805D412yes—
70#90805D412yes—
71C2×D116—21no—
72C2×D116C2×C411yescharacteristic
73C2×C4×D29—24no—
74C2×C4×D29—24no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×C4×D29—21no—
82C2×C4×D29C2×C411yescharacteristic
83C2×C4×D29C2×C411yescharacteristic
84C2×C4×D29D411yescharacteristic
85C2×C4×D29D411yescharacteristic
86C2×Dic58—21no—
87C2×Dic58C2×C411yescharacteristic
88M16×C29—21no—
89M16×C29—21no—
90C2×C8×C29—21no—
91C42×C29—21no—
92C42×C29—21no—
93#90781—24no—
94C4×Dic29—21no—
95C4×Dic29—21no—
96#90777—21no—
97#90777—21no—
98C2×#6597—21no—
99C23×C29—21no—
100C23×C29C2×D411yescharacteristic
101C22×D29—24no—
102C22×D29—21no—
103C22×D29—21no—
104C22×D29—21no—
105C22×D29—22no—
106C22×D29—41no—
107C22×D29—42no—
108C22×D29—42no—
109C22×D29C22⋊C411yescharacteristic
110C22×D29C22⋊C411yescharacteristic
111Q8×C29—21no—
112Q8×C29C22⋊C412yescomplemented
113D4×C29—22no—
114D4×C29—22no—
115D4×C29—21no—
116D4×C29C22⋊C412yescomplemented
117C2×C4×C29—21no—
118C2×C4×C29—22no—
119C2×C4×C29—22no—
120C2×C4×C29—22no—
121C2×C4×C29—41no—
122C2×C4×C29—41no—
123C2×C4×C29C22×C411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C22⋊D29—24no—
130C22⋊D29—24no—
131C22⋊D29—22no—
132C22⋊D29—22no—
133C2×Dic29—24no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—22no—
138C2×Dic29—41no—
139C2×Dic29—41no—
140C2×Dic29C22⋊C411yescharacteristic
141C2×Dic29C22⋊C411yescharacteristic
142D116—24no—
143D116—21no—
144D116C22⋊C412yescomplemented
145C4×D29—24no—
146C4×D29—24no—
147C4×D29—21no—
148C4×D29—21no—
149C4×D29—21no—
150C4×D29—21no—
151C4×D29—21no—
152C4×D29—21no—
153C4×D29—22no—
154C4×D29—22no—
155C4×D29—21no—
156C4×D29—21no—
157Dic58—24no—
158Dic58—21no—
159Dic58C22⋊C412yescomplemented
160C8×C29—41no—
161#6597—41no—
162#1789—291nomaximal, Sylow
163C22×C29—21no—
164C22×C29—21no—
165C22×C29—22no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29C2×C22⋊C411yescharacteristic
169C22×C29#12011yescharacteristic
170C22×C29#12011yescharacteristic
171C2×D29—21no—
172C2×D29—21no—
173C2×D29—21no—
174C2×D29—22no—
175C2×D29—21no—
176C2×D29—21no—
177C2×D29—42no—
178C2×D29—42no—
179C2×D29—48no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29#10412yescomplemented
183C4×C29—22no—
184C4×C29—42no—
185C4×C29C2×C22⋊C411yescharacteristic
186C4×C29C2×C22⋊C411yescharacteristic
187C4×C29#12011yescharacteristic
188C4×C29#12011yescharacteristic
189Dic29—21no—
190Dic29—22no—
191Dic29—21no—
192Dic29—42no—
193C22×#41—291no—
194C2×#104—291no—
195C2×#104—291no—
196C2×#104—291no—
197C2×#104D2911yescharacteristic, complemented
198#407—291no—
199C4×C22⋊C4—291no—
200C2×C29—21no—
201C2×C29—21no—
202C2×C29—42no—
203C2×C29#37911yescharacteristic
204C2×C29C2×#10411yescharacteristic
205C2×C29#42111yescharacteristic
206D29—22no—
207D29—41no—
208D29—42no—
209C2×#41—291no—
210C2×#41—291no—
211C2×#41—291no—
212C2×#41—581no—
213C2×#41—581no—
214C2×#41—582no—
215C2×#41—582no—
216C2×#41—582no—
217C2×#41—582no—
218C2×#41C2×D2911yescharacteristic
219C22×Q8—291no—
220C22×D4—291no—
221C22×D4—581no—
222C23×C4—291no—
223C23×C4—581no—
224C2×M16—291no—
225C2×M16C2×D2911yescharacteristic, complemented
226C2×C22⋊C4—581no—
227C2×C42—291no—
228C2×C42C2×D2911yescharacteristic, complemented
229#104—22no—
230#104—582no—
231#104—582no—
232#104—582no—
233C22⋊C8—581no—
234C22⋊C8—581no—
235#95—581no—
236C29#178911yescharacteristic, complemented, Sylow
237C24—291no—
238C24—581no—
239#41—21no—
240#41—21no—
241#41—292no—
242#41—292no—
243#41—584no—
244#41—584no—
245#41—582no—
246#41—584no—
247#41—584no—
248#41—582no—
249#41—582no—
250#41—582no—
251#41—581no—
252#41—581no—
253#41D11612yes—
254#41C22⋊D2912yes—
255C2×Q8—291no—
256C2×Q8—581no—
257C2×Q8—582no—
258C2×Q8—582no—
259C2×Q8C4×D2911yescharacteristic
260C2×D4—21no—
261C2×D4—291no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—582no—
265C2×D4—584no—
266C2×D4—584no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—582no—
270C2×D4C4×D2911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—291no—
274C22×C4—291no—
275C22×C4—291no—
276C22×C4—291no—
277C22×C4—291no—
278C22×C4—581no—
279C22×C4—581no—
280C22×C4—584no—
281C22×C4—584no—
282C22×C4—581no—
283C22×C4—581no—
284C22×C4—581no—
285C22×C4—581no—
286C22×C4—581no—
287C22×C4—581no—
288C22×C4—581no—
289C22×C4C22×D2911yescharacteristic
290M16—21no—
291M16—21no—
292M16—581no—
293M16—581no—
294C2×C8—21no—
295C2×C8—581no—
296C22⋊C4—584no—
297C42—21no—
298C42—21no—
299C42—581no—
300C42—581no—
301C23—21no—
302C23—291no—
303C23—291no—
304C23—582no—
305C23—584no—
306C23—581no—
307C23—581no—
308C23—581no—
309C23—1161no—
310C23—1162no—
311C23—1162no—
312C23D4×D2911yescharacteristic
313Q8—21no—
314Q8—292no—
315Q8—584no—
316Q8—581no—
317Q8#9078112yescomplemented
318D4—22no—
319D4—22no—
320D4—21no—
321D4—292no—
322D4—584no—
323D4—584no—
324D4—584no—
325D4—582no—
326D4—582no—
327D4—581no—
328D4#9078112yescomplemented
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—291no—
336C2×C4—291no—
337C2×C4—584no—
338C2×C4—584no—
339C2×C4—584no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—581no—
345C2×C4—581no—
346C2×C4—581no—
347C2×C4—582no—
348C2×C4—581no—
349C2×C4—581no—
350C2×C4—581no—
351C2×C4—581no—
352C2×C4—582no—
353C2×C4—582no—
354C2×C4—1161no—
355C2×C4—1161no—
356C2×C4C2×C4×D2911yescharacteristic
357C2×C4C2×D11611yescharacteristic
358C2×C4D4×D2911yescharacteristic
359C2×C4D4×D2911yescharacteristic
360C2×C4D4×D2911yescharacteristic
361C2×C4C2×C22⋊D2911yescharacteristic
362C8—41no—
363C8—1161no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—292no—
370C22—581no—
371C22—581no—
372C22—582no—
373C22—581no—
374C22—581no—
375C22—581no—
376C22—1162no—
377C22—1162no—
378C22—1168no—
379C22—1161no—
380C22—1161no—
381C22C22⋊C4×D2911yescharacteristic
382C22#1174524411yescharacteristic
383C22#1174529911yescharacteristic
384C4—22no—
385C4—42no—
386C4—581no—
387C4—581no—
388C4—582no—
389C4—1162no—
390C4C22⋊C4×D2911yescharacteristic
391C4#1174524411yescharacteristic
392C4C2×#9078111yescharacteristic
393C4#1174529911yescharacteristic
394C2—21no—
395C2—21no—
396C2—42no—
397C2—582no—
398C2—1161no—
399C2—1162no—
400C2#1427101811yescharacteristic
401C2#104×D2911yescharacteristic
402C2#1427117811yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×#104C2
socleC22×C29C2×C22⋊C4
prime radicalC2×#41×D29C2
cosocleC22×C4×C29C23
hypercenterC2×#104D29
hypocenterC29#1789
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11745153C2semidirect
3. C2×#11745185C2semidirect
4. C2×#11745173C2semidirect
5. #14271126C2semidirect
6. C4×#90781C2semidirect
7. C2×C29×#104C2semidirect
13. C2×#90809C4semidirect
14. C2×Q8×D29C4semidirect
16. C2×#90807C4semidirect
18. C2×D4×D29C4semidirect
23. C2×M16×C29C22semidirect
24. C2×C42×C29C22semidirect
26. C2×C4×Dic29C22semidirect
27. C2×#90777C22semidirect
112. Q8×C29C22⋊C4semidirect
116. D4×C29C22⋊C4semidirect
144. D116C22⋊C4semidirect
159. Dic58C22⋊C4semidirect
182. C2×D29#104semidirect
197. C2×#104D29semidirect
225. C2×M16C2×D29semidirect
228. C2×C42C2×D29semidirect
236. C29#1789semidirect
317. Q8#90781semidirect
328. D4#90781semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D292
C2×#117451532
C2×#117451852
C2×#117451732
#142711262
C4×#907812
C2×C29×#1042
#178929