Finite Group Databasebeta

← #11787787

Subgroups — #11787787

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10591231C211yesmaximal, characteristic, complemented
4#10591111C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10589389C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8#71817—31nomaximal
9#68777—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#930—22no—
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#875C411yescharacteristic, complemented
19C3×#875C411yescharacteristic, complemented
20C3×#874C411yescharacteristic, complemented
21C3×C4×D12—22no—
22C3×#869C411yescharacteristic, complemented
23#63815—22no—
24#63814—22no—
25D3×#208—22no—
26#63580—22no—
27#63569—22no—
28#63568—22no—
29C3×#532—31no—
30#5819—31no—
31#5745—31no—
32#5477D311yescharacteristic
33#5240—31no—
34#5236—31no—
35#5236—31no—
36#5139—31no—
37#5006—31no—
38#5005—31no—
39C3×#339—31no—
40#4523—31no—
41#4523—31no—
42#4523—61no—
43#4523D311yescharacteristic, complemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12—22no—
57C2×C3×D12C2×C411yescharacteristic
58C2×C3×D12C2×C411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3D412yes—
61C2×C3×Dic6C2×C411yescharacteristic
62C2×C3×Dic6C2×C411yescharacteristic
63C32×C42—21no—
64C32×C42C2×C411yescharacteristic
65C32×C42C2×C411yescharacteristic
66#3757—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4×C3⋊Dic3—21no—
69#3748—21no—
70#3748D412yescomplemented
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3—21no—
77C3×C4×Dic3—21no—
78C3×#208—21no—
79C3×#208D412yescomplemented
80C2×C3×C3⋊C8—21no—
81#3711—24no—
82D3×C3⋊C8—24no—
83#1884—91noSylow
84C2×C3×#41—31no—
85C2×C3×#41—31no—
86C2×#235C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C2×C3×M16—31no—
89C3×C4⋊Q8—31no—
90C3×#127—31no—
91C3×#124—31no—
92C3×#124—31no—
93C3×#121—62no—
94C3×C4×D4—62no—
95C3×#117—31no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99#948—62no—
100#948—62no—
101#930—22no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—62no—
110C2×#208C2×D311yescharacteristic
111#907—62no—
112D3×M16—62no—
113#901—62no—
114#875Dic311yescharacteristic, complemented
115#875Dic311yescharacteristic, complemented
116#874Dic311yescharacteristic, complemented
117C4×D12—22no—
118#869Dic311yescharacteristic, complemented
119#837—62no—
120#837—62no—
121#834—62no—
122#825—62no—
123#806—62no—
124#805—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3C22⋊C412yes—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—42no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—41no—
138C3×#67—22no—
139C3×#67—22no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3C22⋊C412yes—
145C3×D12—21no—
146C3×D12—21no—
147C3×D12—21no—
148C3×D12—21no—
149C3×D12—44no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—41no—
153C3×C4×D3—41no—
154C3×Dic6—21no—
155C3×Dic6—21no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158C3⋊(C3⋊C8)—22no—
159C3×C3⋊C8—22no—
160#568—91no—
161#532—31no—
162#421—91no—
163#421—91no—
164#410—91no—
165#339—31no—
166#339—91no—
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×Q8—31no—
177C2×C3×D4—32no—
178C2×C3×D4—31no—
179C2×C3×D4—31no—
180C2×C3×D4—62no—
181C2×C3×D4—61no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4—41no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C2×#67#6712yes—
192#235—21no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200C2×D12—22no—
201C2×D12C2×Dic311yescharacteristic
202C2×D12C2×Dic311yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3#6712yes—
205C2×Dic6C2×Dic311yescharacteristic
206C2×Dic6C2×Dic311yescharacteristic
207C3×M16—32no—
208C3×M16—61no—
209C2×C3×C8—61no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—61no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—61no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—41no—
220C3×C42—61no—
221C3×C42C4×D311yescharacteristic
222C3×C42C4×D311yescharacteristic
223C3×C42C2×Dic311yescharacteristic
224C3×C42C2×Dic311yescharacteristic
225#217—21no—
226#217—61no—
227#217—61no—
228#217—121no—
229(C2×D3)⋊C4—22no—
230(C2×D3)⋊C4—22no—
231C4⋊Dic3—22no—
232C4⋊Dic3—21no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4×Dic3—21no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—121no—
240#208—21no—
241#208—32no—
242#208—32no—
243#208—62no—
244#208—64no—
245#208—61no—
246#208—61no—
247#208—121no—
248#208D1212yescomplemented
249C2×C3⋊C8—21no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254ΓL(1,𝔽25)—64no—
255D3×C8—64no—
256C22×C32—41no—
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12111yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C32×C4—22no—
265C32×C4—41no—
266C32×C4C4×D411yescharacteristic
267C32×C4C4×D411yescharacteristic
268C32×C4#12011yescharacteristic
269C32×C4#12311yescharacteristic
270C3⋊Dic3—81no—
271C3×Dic3—22no—
272C3×Dic3—41no—
273C3×Dic3—81no—
274C2×#41—31no—
275C2×#41—31no—
276#131—182no—
277#131—182no—
278C2×M16—31no—
279C2×M16—91no—
280C2×M16—182no—
281C4⋊Q8—31no—
282#127—31no—
283#124—31no—
284#124—31no—
285#121—62no—
286C4×D4—62no—
287#117—31no—
288#117—91no—
289C2×C42D3211yescharacteristic
290#104—182no—
291#104—182no—
292#99—182no—
293C23×C3—21no—
294C23×C3—32no—
295C23×C3—61no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—21no—
299C22×D3#21712yes—
300C3×Q8—61no—
301C3×Q8—61no—
302C3×Q8—61no—
303C3×Q8—61no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—61no—
307C3×D4—61no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—124no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—44no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—61no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4#23711yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4#23911yescharacteristic
345C2×C3×C4C22×Dic311yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347#67—22no—
348#67—22no—
349#67—41no—
350#67—41no—
351C2×Dic3—21no—
352C2×Dic3—41no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3#21712yes—
357D12—21no—
358D12—21no—
359D12—21no—
360D12—21no—
361D12—44no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—41no—
365C4×D3—41no—
366Dic6—21no—
367Dic6—21no—
368Dic6—21no—
369Dic6—21no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32#38611yescharacteristic
379C3×D3—42no—
380C3×D3—81no—
381#41—61no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—61no—
386#41—61no—
387#41—61no—
388#41—61no—
389C2×Q8—31no—
390C2×Q8—31no—
391C2×D4—32no—
392C2×D4—31no—
393C2×D4—31no—
394C2×D4—62no—
395C2×D4—61no—
396C22×C4—21no—
397C22×C4—32no—
398C22×C4—61no—
399C22×C4C2×D3211yescharacteristic
400M16—32no—
401M16—61no—
402M16—92no—
403M16—184no—
404M16—181no—
405C2×C8—61no—
406C2×C8—184no—
407C2×C8—181no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—181no—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—61no—
414C22⋊C4—181no—
415C42—21no—
416C42—61no—
417C42—181no—
418C42D3×Dic311yescharacteristic
419C42D3×Dic311yescharacteristic
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—42no—
426C22×C3—62no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3D3×C22⋊C411yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3#89511yescharacteristic
433C22×C3#93911yescharacteristic
434C22×C3#93911yescharacteristic
435C22×C3C2×#21711yescharacteristic
436C2×D3—22no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—62no—
451C3×C4—121no—
452C3×C4—241no—
453C3×C4C4×D1211yescharacteristic
454C3×C4#88211yescharacteristic
455C3×C4#89311yescharacteristic
456C3×C4#89411yescharacteristic
457C3×C4D4×Dic311yescharacteristic
458C3×C4D4×Dic311yescharacteristic
459C3×C4#93511yescharacteristic
460C3×C4#93711yescharacteristic
461Dic3—22no—
462Dic3—41no—
463Dic3—81no—
464Dic3—242no—
465Dic3—241no—
466Dic3—241no—
467C32#188411yescharacteristic, complemented, Sylow
468C23—32no—
469C23—61no—
470C23D3×#6711yescharacteristic
471Q8—61no—
472Q8—61no—
473Q8—61no—
474Q8—61no—
475D4—62no—
476D4—62no—
477D4—61no—
478D4—61no—
479D4—61no—
480D4—61no—
481D4—124no—
482D4—121no—
483D4—121no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—32no—
487C2×C4—42no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—361no—
495C2×C4#379511yescharacteristic
496C2×C4#379611yescharacteristic
497C2×C4D3×D1211yescharacteristic
498C2×C4#380211yescharacteristic
499C2×C4C2×D3×Dic311yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C8—62no—
502C8—182no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—122no—
514C2×C3—241no—
515C2×C3#466511yescharacteristic
516C2×C3#522011yescharacteristic
517D3—42no—
518D3—81no—
519C22—41no—
520C22—62no—
521C22—122no—
522C22—122no—
523C22—121no—
524C22#6388511yescharacteristic
525C22#6388611yescharacteristic
526C22D3×#21711yescharacteristic
527C4—22no—
528C4—41no—
529C4—62no—
530C4—121no—
531C4—241no—
532C4—721no—
533C4#6388411yescharacteristic
534C4Dic3×D1211yescharacteristic
535C4#6389811yescharacteristic
536C4#6392211yescharacteristic
537C3—21no—
538C3#6877711yescharacteristic, complemented
539C3#7181711yescharacteristic, complemented
540C2—21no—
541C2—21no—
542C2—21no—
543C2—122no—
544C2—241no—
545C2#1059137611yescharacteristic
subgroupG/H
centerC4#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#386
prime radicalC3×#5477C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10591231C2semidirect
4. #10591111C2semidirect
5. #10591110C2semidirect
6. #10589389C2semidirect
7. C3×#4523C2semidirect
18. C3×#875C4semidirect
19. C3×#875C4semidirect
20. C3×#874C4semidirect
22. C3×#869C4semidirect
43. #4523D3semidirect
70. #3748D4semidirect
79. C3×#208D4semidirect
114. #875Dic3semidirect
115. #875Dic3semidirect
116. #874Dic3semidirect
118. #869Dic3semidirect
248. #208D12semidirect
467. C32#1884semidirect
538. C3#68777semidirect
539. C3#71817semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
#105947762
#105912312
#105911112
#105911102
#105893892
C3×#45232
#718173
#687773