Finite Group Databasebeta

← #34111672

Subgroups — #34111672

Order 20096.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097797C211yesmaximal, characteristic, complemented
2C2×#19097791C211yesmaximal, characteristic, complemented
3#23757944C211yesmaximal, characteristic, complemented
4#23757663C211yesmaximal, characteristic, complemented
5#23757521C211yesmaximal, characteristic, complemented
6#23757507C211yesmaximal, characteristic, complemented
7#23757492C211yesmaximal, characteristic, complemented
8#23757468C211yesmaximal, characteristic, complemented
9#23757433C211yesmaximal, characteristic, complemented
10#23757418C211yesmaximal, characteristic, complemented
11#23757416C211yesmaximal, characteristic, complemented
12#23757407C211yesmaximal, characteristic, complemented
13#23757373C211yesmaximal, characteristic, complemented
14#23757345C211yesmaximal, characteristic, complemented
15#546×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578954C2211yescharacteristic, complemented
18#19097797—24no—
19#19097791—24no—
20C2×#14578944C2211yescharacteristic, complemented
21C2×#14578942C2211yescharacteristic
22C2×#14578942C2211yescharacteristic
23C2×#14578941C2211yescharacteristic, complemented
24C2×#14578941C2211yescharacteristic, complemented
25C2×#14578939C2211yescharacteristic
26C2×#14578939C2211yescharacteristic
27C2×#14578939C2211yescharacteristic
28C2×#14578939C2211yescharacteristic
29C2×#14578938C2211yescharacteristic
30C22×#11929434C2211yescharacteristic, complemented
31#19097768C2211yescharacteristic, complemented
32#19097767—21no—
33#19097745C2211yescharacteristic
34#19097745C2211yescharacteristic, complemented
35#19097744—21no—
36#19097744—21no—
37C4×Dic314C2211yescharacteristic, complemented
38#19097733—21no—
39#19097704C2211yescharacteristic, complemented
40C4⋊#11929434C2211yescharacteristic, complemented
41#19097695C2211yescharacteristic, complemented
42#19097694C2211yescharacteristic, complemented
43#19097692C2211yescharacteristic
44#19097692C2211yescharacteristic
45#19097691C2211yescharacteristic, complemented
46#19097691C2211yescharacteristic, complemented
47C22⋊#11929434C2211yescharacteristic
48C22⋊#11929434C2211yescharacteristic, complemented
49#19097682C2211yescharacteristic, complemented
50C2×#41×C157C2211yescharacteristic
51C22×D4×C157C2211yescharacteristic
52#124×C157C2211yescharacteristic
53#123×C157—21no—
54C22⋊Q8×C157C2211yescharacteristic
55#121×C157—21no—
56#121×C157C2211yescharacteristic
57#120×C157—21no—
58C4×D4×C157C2211yescharacteristic
59C4×D4×C157C2211yescharacteristic
60C2×C22⋊C4×C157—21no—
61#14578954—22no—
62#14578954—22no—
63#14578954—41no—
64#14578954—41no—
65C2×Dic314C2311yescharacteristic
66C2×D628—21no—
67C2×D628—21no—
68C2×D628C2311yescharacteristic
69C2×D628C2311yescharacteristic
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76#14578944—22no—
77#14578942—22no—
78#14578942D414yescomplemented
79#14578941—22no—
80#14578941—41no—
81#14578939—22no—
82#14578939—22no—
83#14578939—22no—
84#14578939—41no—
85#14578938—22no—
86C2×#11929434—22no—
87C2×#11929434C2311yescharacteristic
88C2×#11929434C2311yescharacteristic
89C2×#11929434C2311yescharacteristic
90C2×#11929434C2311yescharacteristic
91C4⋊Dic157C2311yescharacteristic
92#14578933—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157—21no—
96C24×C157—21no—
97#41×C157—22no—
98#41×C157—41no—
99C2×Q8×C157C2311yescharacteristic
100C2×D4×C157—22no—
101C2×D4×C157—21no—
102C2×D4×C157—21no—
103C2×D4×C157—21no—
104C2×D4×C157—41no—
105C2×D4×C157D411yescharacteristic
106C2×D4×C157C2311yescharacteristic
107C2×D4×C157C2311yescharacteristic
108C22×C4×C157—21no—
109C22×C4×C157—21no—
110C22×C4×C157C2311yescharacteristic
111C22×C4×C157C2311yescharacteristic
112C4⋊C4×C157—21no—
113C4⋊C4×C157D411yescharacteristic
114C4⋊C4×C157C2311yescharacteristic
115C22⋊C4×C157—21no—
116C22⋊C4×C157—21no—
117C22⋊C4×C157—21no—
118C22⋊C4×C157—21no—
119C22⋊C4×C157—21no—
120C22⋊C4×C157D411yescharacteristic
121C22⋊C4×C157D411yescharacteristic
122C42×C157C2311yescharacteristic
123C22×D157—21no—
124C22×D157—21no—
125Dic314—21no—
126Dic314C2×D412yes—
127D628—21no—
128D628—21no—
129D628—21no—
130D628—21no—
131D628—42no—
132D628—81no—
133C22⋊D157—42no—
134C22⋊D157—42no—
135C22⋊D157—81no—
136C22⋊D157—81no—
137C2×Dic157—21no—
138C2×Dic157—21no—
139C4×D157—42no—
140C4×D157—42no—
141#11929434—21no—
142#11929434—21no—
143#11929434—21no—
144#11929434C2×D412yes—
145C23×C157—21no—
146C23×C157—21no—
147C23×C157—42no—
148C23×C157—42no—
149C23×C157—81no—
150C23×C157C2×D411yescharacteristic
151C23×C157C2×D411yescharacteristic
152Q8×C157—21no—
153Q8×C157—21no—
154D4×C157—21no—
155D4×C157—21no—
156D4×C157—21no—
157D4×C157—41no—
158D4×C157—42no—
159D4×C157—42no—
160D4×C157—81no—
161D4×C157C2×D412yes—
162C2×C4×C157—21no—
163C2×C4×C157—21no—
164C2×C4×C157—21no—
165C2×C4×C157—21no—
166C2×C4×C157—21no—
167C2×C4×C157—21no—
168C2×C4×C157—42no—
169C2×C4×C157—81no—
170C2×C4×C157C2×D411yescharacteristic
171C2×C4×C157C2×D411yescharacteristic
172C2×C4×C157C2×D411yescharacteristic
173C2×C4×C157C2×D411yescharacteristic
174C2×C4×C157C2411yescharacteristic
175C22×C157—21no—
176C22×C157—21no—
177C22×C157—22no—
178C22×C157—21no—
179C22×C157—21no—
180C22×C157—21no—
181C22×C157—21no—
182C22×C157—41no—
183C22×C157—41no—
184C22×C157—41no—
185C22×C157—41no—
186C22×C157—41no—
187C22×C157—84no—
188C22×C157C22×D411yescharacteristic
189C2×D157—41no—
190C2×D157—41no—
191C2×D157—41no—
192C2×D157—41no—
193C2×D157—41no—
194C2×D157—41no—
195C4×C157—21no—
196C4×C157—21no—
197C4×C157—21no—
198C4×C157—21no—
199C4×C157—41no—
200C4×C157—41no—
201C4×C157C22×D411yescharacteristic
202C4×C157H(5,𝔽2)11yescharacteristic
203Dic157—22no—
204Dic157—41no—
205C2×C157—41no—
206C2×C157—41no—
207C2×C157—42no—
208C2×C157—81no—
209C2×C157D4211yescharacteristic
210C2×C157#57511yescharacteristic
211C2×C157#57611yescharacteristic
212D157—81no—
213D157—81no—
214C157#326811yescharacteristic, complemented, Sylow
215#3268—1571nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1571no—
217C2×#135—1571no—
218#550—1571no—
219#546D15711yescharacteristic, complemented
220#496—1571no—
221#468—1571no—
222#466—1571no—
223#464—1571no—
224#459—1571no—
225#452—1571no—
226#449—1571no—
227#449—1571no—
228#447—1571no—
229#440—1571no—
230#435—1571no—
231C2×#41—1571no—
232C2×#41—1571no—
233C2×#41C2×D15711yescharacteristic
234C22×D4C2×D15711yescharacteristic
235AGL(1,ℤ/8)—3144no—
236#135—3144no—
237C2×Q16—1571no—
238C2×SD16—1571no—
239C2×SD16—1571no—
240C2×SD16—1571no—
241C2×SD16—1571no—
242C2×D8—1571no—
243C2×D8—1571no—
244C2×D8—1571no—
245C2×D8—1571no—
246C2×M16—1571no—
247C22×C8—1571no—
248#127—3141no—
249#127—1571no—
250#124C2×D15711yescharacteristic
251#123—21no—
252C22⋊Q8C2×D15711yescharacteristic
253#121—21no—
254#121—3141no—
255#121—3141no—
256#121—1571no—
257#121—1571no—
258#121C2×D15711yescharacteristic
259#120—21no—
260C4×Q8—1571no—
261C4×D4—3141no—
262C4×D4C2×D15711yescharacteristic
263C4×D4C2×D15711yescharacteristic
264C2×C22⋊C4—21no—
265#107—1571no—
266C4⋊C8—1571no—
267#103—1571no—
268#103—1571no—
269#102—1571no—
270#102—1571no—
271#102—1571no—
272#102—1571no—
273C22⋊C8—1571no—
274C22⋊C8—1571no—
275#97—1571no—
276C24—21no—
277#41—22no—
278#41—41no—
279#41—3142no—
280#41—3142no—
281#41—6281no—
282#41—6281no—
283C2×Q8—1571no—
284C2×Q8C22×D15711yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—3141no—
291C2×D4—3141no—
292C2×D4—3141no—
293C2×D4—3141no—
294C2×D4—3141no—
295C2×D4—3141no—
296C2×D4—1571no—
297C2×D4—1571no—
298C2×D4C22⋊D15711yescharacteristic
299C2×D4C22×D15711yescharacteristic
300C2×D4C22×D15711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—3141no—
304C22×C4—3141no—
305C22×C4C22×D15711yescharacteristic
306C22×C4C22×D15711yescharacteristic
307Q16—3142no—
308SD16—3142no—
309SD16—3142no—
310SD16—6281no—
311SD16—1574no—
312D8—3142no—
313D8—3142no—
314D8—3142no—
315D8—6281no—
316M16—3142no—
317C2×C8—3142no—
318C2×C8—1571no—
319C2×C8—1571no—
320C2×C8—1571no—
321C2×C8—1571no—
322C4⋊C4—21no—
323C4⋊C4—3141no—
324C4⋊C4—1571no—
325C4⋊C4C22⋊D15711yescharacteristic
326C4⋊C4C22×D15711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—3141no—
333C22⋊C4—3141no—
334C22⋊C4C22⋊D15711yescharacteristic
335C22⋊C4C22⋊D15711yescharacteristic
336C42—3141no—
337C42C22×D15711yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—3141no—
344C23—3141no—
345C23C2×C22⋊D15711yescharacteristic
346C23C2×C22⋊D15711yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—3141no—
350Q8—1572no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—3141no—
359D4—3141no—
360D4—3141no—
361D4—3141no—
362D4—6282no—
363D4—6282no—
364D4—6282no—
365D4—12561no—
366D4—12561no—
367D4—12561no—
368D4D4×D15712yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—3141no—
378C2×C4—3141no—
379C2×C4—6282no—
380C2×C4—6282no—
381C2×C4C2×C22⋊D15711yescharacteristic
382C2×C4C2×C22⋊D15711yescharacteristic
383C2×C4C2×C22⋊D15711yescharacteristic
384C2×C4C2×C22⋊D15711yescharacteristic
385C2×C4C23×D15711yescharacteristic
386C8—3141no—
387C8—3141no—
388C8—3141no—
389C8—1572no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—6281no—
404C22—6281no—
405C22—6281no—
406C22—6281no—
407C22—6281no—
408C22—6281no—
409C22C22×C22⋊D15711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—3142no—
417C4—6281no—
418C4C2×D4×D15711yescharacteristic
419C4#1909781611yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—12561no—
425C2—12561no—
426C2D4×C22⋊D15711yescharacteristic
427C2#2375807111yescharacteristic
428C2#2375807611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#546×C157C2
socleC22×C157C22×D4
hypercenter#546D157
hypocenterC157#3268
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#19097797C2semidirect
2. C2×#19097791C2semidirect
3. #23757944C2semidirect
4. #23757663C2semidirect
5. #23757521C2semidirect
6. #23757507C2semidirect
7. #23757492C2semidirect
8. #23757468C2semidirect
9. #23757433C2semidirect
10. #23757418C2semidirect
11. #23757416C2semidirect
12. #23757407C2semidirect
13. #23757373C2semidirect
14. #23757345C2semidirect
15. #546×C157C2semidirect
17. C2×#14578954C22semidirect
20. C2×#14578944C22semidirect
23. C2×#14578941C22semidirect
24. C2×#14578941C22semidirect
30. C22×#11929434C22semidirect
31. #19097768C22semidirect
34. #19097745C22semidirect
37. C4×Dic314C22semidirect
39. #19097704C22semidirect
40. C4⋊#11929434C22semidirect
41. #19097695C22semidirect
42. #19097694C22semidirect
45. #19097691C22semidirect
46. #19097691C22semidirect
48. C22⋊#11929434C22semidirect
49. #19097682C22semidirect
78. #14578942D4semidirect
214. C157#3268semidirect
219. #546D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
C2×#190977912
#237579442
#237576632
#237575212
#237575072
#237574922
#237574682
#237574332
#237574182
#237574162
#237574072
#237573732
#237573452
#546×C1572
#3268157