Finite Group Databasebeta

← #10950837

Subgroups — #10950837

Order 768.

520 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
1#79727C211yesmaximal, characteristic, complemented
2#79601C211yesmaximal, characteristic, complemented
3C3×C4×SD32C211yesmaximal, characteristic, complemented
4#71488C211yesmaximal, characteristic, complemented
5#71481C211yesmaximal, characteristic, complemented
6#70913C211yesmaximal, characteristic, complemented
7#70885C211yesmaximal, characteristic, complemented
8#69348C211yesmaximal, characteristic, complemented
9#69341C211yesmaximal, characteristic, complemented
10#69228C211yesmaximal, characteristic, complemented
11#69216C211yesmaximal, characteristic, complemented
12#69195C211yesmaximal, characteristic, complemented
13#69183C211yesmaximal, characteristic, complemented
14C4×D48C211yesmaximal, characteristic, complemented
15#69051C211yesmaximal, characteristic, complemented
16#33744—31nomaximal, Sylow
17#5582—21no—
18#5562—21no—
19C2×C3×SD32C2211yescharacteristic
20C3×C4×Q16C2211yescharacteristic
21C3×C4×D8C2211yescharacteristic
22#5191C2211yescharacteristic
23#5188C2211yescharacteristic
24C2×#828C2211yescharacteristic
25#5157C2211yescharacteristic
26#5151C2211yescharacteristic
27C2×#826C2211yescharacteristic
28#5026—21no—
29#5014—21no—
30C2×D48C2211yescharacteristic
31C2×#798C2211yescharacteristic
32C2×D3×C16C2211yescharacteristic
33#4883C2211yescharacteristic
34#4883C2211yescharacteristic
35#4878C2211yescharacteristic
36#4874C2211yescharacteristic
37#4812—21no—
38#4794—21no—
39#4782—21no—
40#4764—21no—
41C4×D24C2211yescharacteristic
42C4×D24C2211yescharacteristic
43#4689C2211yescharacteristic
44C3×#367C2211yescharacteristic
45C3×#358C2211yescharacteristic
46C3×#357C2211yescharacteristic
47C3×C4×C16C2211yescharacteristic
48#4564C2211yescharacteristic
49#4562C2211yescharacteristic
50#4509C2211yescharacteristic
51#4509C2211yescharacteristic
52#4504C2211yescharacteristic
53#4502C2211yescharacteristic
54Dic3×C16C2211yescharacteristic
55#4491C2211yescharacteristic
56#4491C2211yescharacteristic
57#4490C2211yescharacteristic
58#4489C2211yescharacteristic
59#4461C2211yescharacteristic
60#3176—31no—
61#3175—31no—
62#2255—31no—
63#2250—31no—
64#2242—31no—
65#2240—31no—
66#2220—31no—
67#2218—31no—
68#2217—31no—
69#2215—31no—
70#2177—31no—
71#2175—31no—
72C4×SD32D311yescharacteristic, complemented
73C4×D16—31no—
74#2108—31no—
75C2×C3×Q16C2311yescharacteristic
76C2×C3×D8C2311yescharacteristic
77C3×C4×Q8—21no—
78C3×C4×D4—21no—
79#947—21no—
80#946—21no—
81C2×#215—21no—
82#940—21no—
83#938—21no—
84C2×#213—21no—
85#930—41no—
86#929—41no—
87C2×D24C2311yescharacteristic
88C2×D24C2311yescharacteristic
89C2×ΓL(1,𝔽25)D411yescharacteristic
90C2×D3×C8C2311yescharacteristic
91#896—41no—
92#895—21no—
93#895—21no—
94#894—41no—
95#890—21no—
96#888—21no—
97#884—41no—
98#883—41no—
99#876—41no—
100#875—41no—
101C4×D12—21no—
102C4×D12—21no—
103#872D411yescharacteristic
104C3×SD32—22no—
105C2×C3×C16C2311yescharacteristic
106C2×C3×C16C2311yescharacteristic
107C3×#107C2311yescharacteristic
108C3×#107C2311yescharacteristic
109C3×#103—21no—
110C3×#102—21no—
111C3×C4×C8C2311yescharacteristic
112#835—21no—
113#832—21no—
114#828—22no—
115#826—22no—
116#821—21no—
117#821—21no—
118#818C2311yescharacteristic
119#818C2311yescharacteristic
120#815D411yescharacteristic
121C8×Dic3C2311yescharacteristic
122C2×C3⋊C16C2311yescharacteristic
123C2×C3⋊C16C2311yescharacteristic
124#809—21no—
125#809—21no—
126#808—21no—
127#807—21no—
128#803D411yescharacteristic
129D48—22no—
130#798—22no—
131D3×C16—22no—
132#542—61no—
133#540—61no—
134C2×SD32—31no—
135C2×SD32C2×D311yescharacteristic
136C2×D16—31no—
137C2×D16—31no—
138C2×M32—31no—
139C22×C16—31no—
140#500—31no—
141#499—31no—
142#495—31no—
143#493—31no—
144#490—61no—
145#489—61no—
146#469—61no—
147#468—61no—
148#467—31no—
149#466—31no—
150#466—31no—
151#466—31no—
152#442—61no—
153#440—61no—
154C4×Q16C2×D311yescharacteristic
155C4×D8—31no—
156C4×D8—31no—
157C4×D8C2×D311yescharacteristic
158#405—31no—
159#367—31no—
160#367C2×D311yescharacteristic
161#366—31no—
162#366—31no—
163#358—31no—
164#358C2×D311yescharacteristic
165#357—31no—
166#357—31no—
167#357—31no—
168#357—31no—
169#357—31no—
170#357C2×D311yescharacteristic
171#346—31no—
172#346—31no—
173C4×C16—31no—
174C4×C16C2×D311yescharacteristic
175C2×C3×Q8—21no—
176C2×C3×D4—21no—
177C22×C3×C4—41no—
178C2×#67—41no—
179C2×#67—41no—
180C2×#67—41no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—41no—
184C2×D12—41no—
185C2×C4×D3—41no—
186C2×C4×D3—41no—
187C2×C4×D3C2×D411yescharacteristic
188C2×Dic6—41no—
189C3×Q16—21no—
190C3×Q16—21no—
191C3×D8—21no—
192C3×D8—21no—
193C2×C3×C8C2×D411yescharacteristic
194C2×C3×C8C2411yescharacteristic
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—41no—
198C3×C22⋊C4—41no—
199C3×C42—41no—
200C3×C42C2×D411yescharacteristic
201#217—41no—
202#215—42no—
203#213—42no—
204(C2×D3)⋊C4—41no—
205(C2×D3)⋊C4—41no—
206(C2×D3)⋊C4—41no—
207(C2×D3)⋊C4—41no—
208(C2×D3)⋊C4—41no—
209(C2×D3)⋊C4—41no—
210(C2×D3)⋊C4—41no—
211(C2×D3)⋊C4D811yescharacteristic
212(C2×D3)⋊C4D811yescharacteristic
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—41no—
216Dic3⋊C4—41no—
217Dic3⋊C4—41no—
218Dic3⋊C4—41no—
219Dic3⋊C4D811yescharacteristic
220Dic3⋊C4D811yescharacteristic
221C4×Dic3C2×D411yescharacteristic
222C2×C3⋊C8C2×D411yescharacteristic
223C2×C3⋊C8C2×D411yescharacteristic
224D24—21no—
225D24—21no—
226D24—21no—
227D24—21no—
228ΓL(1,𝔽25)—22no—
229D3×C8—21no—
230D3×C8—21no—
231C3×C16—21no—
232C3×C16#4112yes—
233C3⋊C16—21no—
234C3⋊C16#4112yes—
235C2×Q16C22×D311yescharacteristic
236C2×SD16—61no—
237C2×D8—31no—
238C2×D8—31no—
239C2×D8—61no—
240C2×D8C22×D311yescharacteristic
241C2×M16—31no—
242C22×C8—31no—
243C4⋊Q8—61no—
244#127—61no—
245#126—121no—
246#125—61no—
247#124—61no—
248#124—121no—
249#123—121no—
250#123—121no—
251#123—121no—
252C22⋊Q8—61no—
253C22⋊Q8—121no—
254#121—61no—
255#121—61no—
256#121—61no—
257#121—121no—
258#121—121no—
259C4×Q8—21no—
260C4×D4—21no—
261C4×D4—61no—
262C4×D4—61no—
263#117—31no—
264SD32—22no—
265SD32—62no—
266D16—62no—
267D16—62no—
268M32—62no—
269C2×C16—31no—
270C2×C16—31no—
271C2×C16—62no—
272C2×C16C22×D311yescharacteristic
273C2×C16C22×D311yescharacteristic
274#107—31no—
275#107—31no—
276#107—61no—
277#107C22×D311yescharacteristic
278#107C22×D311yescharacteristic
279#106—61no—
280#103—21no—
281#103—61no—
282#102—21no—
283#102—61no—
284#102—61no—
285#102—61no—
286#102—61no—
287#102—61no—
288#97—31no—
289#97—31no—
290C4×C8—31no—
291C4×C8C22×D311yescharacteristic
292C23×C3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3C2×D811yescharacteristic
296C3×Q8—41no—
297C3×Q8—41no—
298C3×D4—41no—
299C3×D4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—161no—
304C2×C3×C4C2×D811yescharacteristic
305C2×C3×C4C2×D811yescharacteristic
306C2×C3×C4C22×D411yescharacteristic
307#67—161no—
308#67—161no—
309#67—161no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3C2×D811yescharacteristic
313C2×Dic3C2×D811yescharacteristic
314C2×Dic3C2×D811yescharacteristic
315D12—41no—
316D12—41no—
317D12—41no—
318D12—41no—
319D12—161no—
320D12—161no—
321C4×D3—21no—
322C4×D3—21no—
323C4×D3—161no—
324C4×D3—161no—
325Dic6—161no—
326C3×C8—21no—
327C3×C8C2×#4111yescharacteristic
328C3×C8C2×#4111yescharacteristic
329C3⋊C8—21no—
330C3⋊C8#13512yes—
331C2×Q8—21no—
332C2×Q8—121no—
333C2×D4—21no—
334C2×D4—61no—
335C2×D4—61no—
336C2×D4—121no—
337C2×D4—121no—
338C2×D4—121no—
339C2×D4—121no—
340C2×D4—121no—
341C22×C4—31no—
342C22×C4—41no—
343C22×C4—121no—
344C22×C4—121no—
345Q16—21no—
346Q16—21no—
347SD16—122no—
348D8—21no—
349D8—21no—
350D8—61no—
351D8—61no—
352D8—61no—
353D8—61no—
354D8—122no—
355M16—62no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8D3×D411yescharacteristic
361C2×C8C23×D311yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—31no—
365C4⋊C4—31no—
366C4⋊C4—41no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—121no—
370C4⋊C4—121no—
371C4⋊C4—121no—
372C4⋊C4—121no—
373C22⋊C4—31no—
374C22⋊C4—31no—
375C22⋊C4—41no—
376C22⋊C4—121no—
377C22⋊C4—121no—
378C22⋊C4—121no—
379C22⋊C4—121no—
380C22⋊C4—121no—
381C22⋊C4—121no—
382C22⋊C4—121no—
383C22⋊C4—121no—
384C42—31no—
385C42—41no—
386C42D3×D411yescharacteristic
387C16—21no—
388C16—32no—
389C16—61no—
390C16#23512yes—
391C22×C3—81no—
392C22×C3—81no—
393C22×C3—81no—
394C22×C3C22×D811yescharacteristic
395C2×D3—21no—
396C2×D3—21no—
397C2×D3—21no—
398C2×D3—81no—
399C2×D3—81no—
400C2×D3—81no—
401C2×D3—81no—
402C2×D3—81no—
403C2×D3—81no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—81no—
407C3×C4—81no—
408C3×C4—81no—
409C3×C4#53211yescharacteristic
410C3×C4C2×#13511yescharacteristic
411Dic3—21no—
412Dic3—21no—
413Dic3—21no—
414Dic3—81no—
415Dic3—81no—
416C23—31no—
417C23—41no—
418C23—121no—
419C23—121no—
420Q8—41no—
421Q8—41no—
422Q8—481no—
423D4—41no—
424D4—41no—
425D4—121no—
426D4—121no—
427D4—121no—
428D4—121no—
429D4—481no—
430D4—481no—
431D4—481no—
432D4—481no—
433D4—481no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—161no—
445C2×C4—481no—
446C2×C4—481no—
447C2×C4D3×D811yescharacteristic
448C2×C4D3×D811yescharacteristic
449C2×C4C2×D3×D411yescharacteristic
450C8—21no—
451C8—32no—
452C8—61no—
453C8C2×#23511yescharacteristic
454C8D3×#4111yescharacteristic
455C2×C3—161no—
456C2×C3#316911yescharacteristic
457C2×C3#341511yescharacteristic
458C2×C3#341611yescharacteristic
459D3—41no—
460D3—161no—
461D3—161no—
462C22—61no—
463C22—61no—
464C22—61no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—241no—
469C22—241no—
470C22—241no—
471C22—241no—
472C22—241no—
473C22—241no—
474C22C2×D3×D811yescharacteristic
475C4—21no—
476C4—21no—
477C4—61no—
478C4—61no—
479C4—61no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—241no—
484C4—241no—
485C4#554811yescharacteristic
486C4D3×#13511yescharacteristic
487C3#3374411yescharacteristic, complemented, Sylow
488C2—121no—
489C2—161no—
490C2—481no—
491C2—481no—
492C2#7959811yescharacteristic
493C2#8202411yescharacteristic
494C2#8203111yescharacteristic
subgroupG/H
centerC22C2×D3×D8
commutator, cosocleC2×C3×C8C24
FrattiniC2×C8C23×D3
FittingC3×C4×SD32C2
socleC22×C3C22×D8
hypercenterC4×SD32D3
hypocenterC3#33744
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #79727C2semidirect
2. #79601C2semidirect
3. C3×C4×SD32C2semidirect
4. #71488C2semidirect
5. #71481C2semidirect
6. #70913C2semidirect
7. #70885C2semidirect
8. #69348C2semidirect
9. #69341C2semidirect
10. #69228C2semidirect
11. #69216C2semidirect
12. #69195C2semidirect
13. #69183C2semidirect
14. C4×D48C2semidirect
15. #69051C2semidirect
72. C4×SD32D3semidirect
487. C3#33744semidirect

Maximal subgroups

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

subgroupindex
#797272
#796012
C3×C4×SD322
#714882
#714812
#709132
#708852
#693482
#693412
#692282
#692162
#691952
#691832
C4×D482
#690512
#337443