Finite Group Databasebeta

← #11898378

Subgroups — #11898378

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596055C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590386C211yesmaximal, characteristic, complemented
5C4×#3719C212yesmaximal, complemented
6#10590379C211yesmaximal, characteristic, complemented
7#10590378C212yesmaximal, complemented
8#10590370C212yesmaximal
9#10590368C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11C4×#3714C211yesmaximal, characteristic
12#83670—31nomaximal
13#79912—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16#64107—22no—
17#64101—21no—
18#64084C2212yes—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64078C2211yescharacteristic
21C4×#634C2212yes—
22C3×#946—21no—
23C3×#898—22no—
24C3×#892—21no—
25C3×#875C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3719C2212yes—
30C2×#3719C2212yes—
31C2×#3717C2212yes—
32C2×#3716C2212yes—
33C2×#3714C2211yescharacteristic
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×C4×C3⋊C8C2212yes—
38#63575C2211yescharacteristic
39#63567C2212yes—
40#63566C2212yes—
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43C3×#556—31no—
44#5584—31no—
45#5584—31no—
46#5584—61no—
47#5584D311yescharacteristic, complemented
48C3×C8×Q8—31no—
49#5092—31no—
50#5083—31no—
51#5059—32no—
52#5054—32no—
53C4×#216—32no—
54#5028—32no—
55Q8×C3⋊C8D311yescharacteristic, complemented
56#5019—31no—
57C4×#213—31no—
58#4845—32no—
59#4845—32no—
60#4841—31no—
61#4841—31no—
62#4699—31no—
63C4×Dic12—32no—
64#4696—32no—
65C4×D24—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4D412yes—
75C32×C42C2312yes—
76C32×C42C2311yescharacteristic
77#3752—21no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84C4×C3⋊Dic3—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96#3719—24no—
97#3719—42no—
98#3717—42no—
99#3716—42no—
100#3714—22no—
101#3393—91noSylow
102C3×C4⋊Q8—31no—
103C3×#126—62no—
104C3×#124—32no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—21no—
107C3×C4×Q8—32no—
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×D4—31no—
111C3×#117—61no—
112#946—21no—
113#946—62no—
114#946—61no—
115#946—61no—
116C2×#216—32no—
117C2×#216—32no—
118C2×#215—32no—
119C2×#214—32no—
120C2×#213—31no—
121C2×Dic12—32no—
122C2×Dic12—32no—
123C2×D24—31no—
124C2×#204—32no—
125C2×#204—32no—
126#898—22no—
127#898—64no—
128#898—62no—
129#898—62no—
130#892—21no—
131#892—62no—
132#892—61no—
133#892—61no—
134#875—32no—
135#875—32no—
136#875—62no—
137#875C2×D312yes—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—61no—
141C4×D12C2×D311yescharacteristic
142#869—31no—
143#869—31no—
144#869—61no—
145#869C2×D311yescharacteristic
146C4×Dic6—32no—
147C4×Dic6—32no—
148C4×Dic6—62no—
149C4×Dic6C2×D312yes—
150C3×C4⋊C8—31no—
151C3×C4⋊C8—32no—
152C3×C4×C8—31no—
153C3×C4×C8—32no—
154#835—32no—
155#832—31no—
156#821—31no—
157#821—31no—
158#818—31no—
159#816—32no—
160#816—32no—
161#810—32no—
162#809—31no—
163#807—31no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4⋊(C3⋊C8)C2×D312yes—
166C4×C3⋊C8C2×D311yescharacteristic
167C4×C3⋊C8C2×D312yes—
168C22×C3⋊D3—21no—
169C22×C3×D3—21no—
170C32×Q8—22no—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—21no—
180C4×C3⋊D3—42no—
181#634—22no—
182#634—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C3×D12—21no—
186C3×D12—21no—
187C3×C4×D3—42no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8#4112yes—
193#556—31no—
194#556—91no—
195#495—92no—
196#494—91no—
197#464—92no—
198#464—92no—
199#461—91no—
200#461—91no—
201C8×Q8—31no—
202C4×Q16—92no—
203C4×D8—91no—
204C2×C3×Q8—21no—
205C2×C3×Q8—32no—
206C2×C3×Q8D1211yescharacteristic
207C2×C3×Q8#6711yescharacteristic
208C2×C3×D4—31no—
209C22×C3×C4—61no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—62no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×Dic6—32no—
219C2×Dic6—32no—
220C2×Dic6—62no—
221C2×Dic6C22×D312yes—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C2×C3×C8—31no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4D1211yescharacteristic
232C3×C4⋊C4D1212yes—
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4#6712yes—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—61no—
237C3×C22⋊C4—62no—
238C3×C42—22no—
239C3×C42—21no—
240C3×C42—62no—
241C3×C42C22×D312yes—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D312yes—
244C3×C42C22×D311yescharacteristic
245#216—64no—
246#216—122no—
247#215—122no—
248#214—122no—
249#213—62no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—22no—
275Dic3⋊C4—64no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—22no—
279C4×Dic3—64no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D312yes—
284C2×C3⋊C8C22×D311yescharacteristic
285Dic12—64no—
286Dic12—122no—
287D24—62no—
288#204—122no—
289#204—122no—
290C22×C32C22×D411yescharacteristic
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C32×C4—22no—
298C32×C4—22no—
299C32×C4—21no—
300C32×C4#13512yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4H(5,𝔽2)11yescharacteristic
303C3⋊Dic3—42no—
304C3⋊Dic3—41no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C2×Q16—92no—
308C2×Q16—92no—
309C2×SD16—92no—
310C2×SD16—92no—
311C2×D8—91no—
312C4⋊Q8—31no—
313C4⋊Q8—91no—
314#126—62no—
315#126—182no—
316#124—32no—
317#124—92no—
318C22⋊Q8—61no—
319C22⋊Q8—181no—
320C4×Q8—32no—
321C4×Q8—92no—
322C4×Q8D3211yescharacteristic
323C4×D4—31no—
324C4×D4—91no—
325#117—61no—
326#117—181no—
327#107—91no—
328C4⋊C8—31no—
329C4⋊C8—32no—
330#103—92no—
331#103—92no—
332#102—91no—
333#102—91no—
334C4×C8—31no—
335C4×C8—32no—
336C23×C3—61no—
337C22×D3—21no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—61no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—42no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—61no—
347C3×D4—61no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—122no—
356C2×C3×C4C2×D1212yes—
357C2×C3×C4C2×D1212yes—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—62no—
369C2×Dic3—64no—
370C2×Dic3—61no—
371C2×Dic3—62no—
372C2×Dic3—61no—
373C2×Dic3—62no—
374D12—21no—
375D12—21no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—121no—
381D12—121no—
382C4×D3—42no—
383C4×D3—124no—
384C4×D3—122no—
385C4×D3—122no—
386Dic6—22no—
387Dic6—22no—
388Dic6—62no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—122no—
393Dic6—122no—
394C3×C8—32no—
395C3×C8—62no—
396C3×C8—61no—
397C3⋊C8—22no—
398C3⋊C8—21no—
399C3⋊C8#23912yes—
400C2×C32#55011yescharacteristic
401C2×C32C2×#13511yescharacteristic
402C2×C32#57811yescharacteristic
403C3⋊D3—81no—
404C3×D3—81no—
405C2×Q8—32no—
406C2×Q8—92no—
407C2×Q8#62611yescharacteristic
408C2×D4—31no—
409C2×D4—91no—
410C22×C4—61no—
411C22×C4—181no—
412Q16—184no—
413Q16—362no—
414SD16—362no—
415SD16—362no—
416D8—182no—
417C2×C8—31no—
418C2×C8—31no—
419C2×C8—32no—
420C4⋊C4—31no—
421C4⋊C4—61no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—181no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C4⋊C4#62611yescharacteristic
429C4⋊C4#62612yes—
430C22⋊C4—62no—
431C22⋊C4—61no—
432C22⋊C4—62no—
433C22⋊C4—182no—
434C22⋊C4—181no—
435C22⋊C4—182no—
436C42—62no—
437C42—182no—
438C42C2×D3211yescharacteristic
439C42C2×D3212yes—
440C22×C3—21no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3C22×D1211yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—41no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—42no—
468C3×C4—42no—
469C3×C4—41no—
470C3×C4—121no—
471C3×C4—122no—
472C3×C4#90412yes—
473C3×C4#95012yes—
474C3×C4C2×#23911yescharacteristic
475C3×C4D3×#4111yescharacteristic
476C3×C4#100911yescharacteristic
477C3×C4#100911yescharacteristic
478Dic3—41no—
479Dic3—42no—
480Dic3—124no—
481Dic3—122no—
482Dic3—121no—
483Dic3—121no—
484Dic3—122no—
485Dic3—122no—
486C32#339311yescharacteristic, complemented, Sylow
487C23—61no—
488C23—181no—
489Q8—22no—
490Q8—62no—
491Q8—62no—
492Q8—182no—
493Q8—182no—
494D4—61no—
495D4—61no—
496D4—181no—
497D4—181no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—122no—
501C2×C4—181no—
502C2×C4—182no—
503C2×C4—362no—
504C2×C4C2×#62612yes—
505C2×C4C2×#62611yescharacteristic
506C2×C4C2×#62612yes—
507C2×C4C2×#62611yescharacteristic
508C2×C4C22×D3211yescharacteristic
509C8—32no—
510C8—62no—
511C8—61no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—241no—
516C2×C3#557711yescharacteristic
517C2×C3C2×#90411yescharacteristic
518C2×C3#575311yescharacteristic
519C2×C3C2×#95011yescharacteristic
520C2×C3#583411yescharacteristic
521C2×C3#583811yescharacteristic
522D3—81no—
523D3—242no—
524D3—241no—
525D3—241no—
526C22—121no—
527C22—121no—
528C22—121no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22C22×#62611yescharacteristic
533C4—22no—
534C4—21no—
535C4—22no—
536C4—122no—
537C4—121no—
538C4—362no—
539C4—361no—
540C4#6382912yes—
541C4D3×#23911yescharacteristic
542C4#6432011yescharacteristic
543C3—21no—
544C3#7991211yescharacteristic, complemented
545C3#8367011yescharacteristic, complemented
546C2—241no—
547C2—721no—
548C2C2×#6382911yescharacteristic
549C2#1059541011yescharacteristic
550C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4×Q8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. C3×#5584C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. #10590386C2semidirect
5. C4×#3719C2semidirect
6. #10590379C2semidirect
7. #10590378C2semidirect
9. #10590368C2semidirect
10. #10590365C2semidirect
47. #5584D3semidirect
55. Q8×C3⋊C8D3semidirect
486. C32#3393semidirect
544. C3#79912semidirect
545. C3#83670semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×#55842
C3×Q8×C3⋊C82
#105903862
C4×#37192
#105903792
#105903782
#105903702
#105903682
#105903652
C4×#37142
#836703
#799123