Finite Group Databasebeta

← #11895664

Subgroups — #11895664

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C4×#3719C211yesmaximal, characteristic, complemented
5#10590378C212yesmaximal, complemented
6#10590377C211yesmaximal, characteristic
7C4×#3716C212yesmaximal, complemented
8#10590301C211yesmaximal, characteristic, complemented
9#10590274C212yesmaximal, complemented
10#10590273C211yesmaximal, characteristic
11#10590271C212yesmaximal, complemented
12#83717—31nomaximal
13#79935—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64153—21no—
16#64098—22no—
17#64096—21no—
18#64079C2212yes—
19#64078C2211yescharacteristic
20C4×#634C2212yes—
21C4×#634C2211yescharacteristic
22C3×#947—21no—
23C3×#894—22no—
24C3×#893—21no—
25C3×#875C2212yes—
26C3×#874C2211yescharacteristic
27C3×C4×D12C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C2×#3719C2211yescharacteristic
30C2×#3716C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34C3×C4×C3⋊C8C2212yes—
35#63575C2211yescharacteristic
36#63573C2212yes—
37#63567C2211yescharacteristic
38#63566C2211yescharacteristic
39#63566C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63563C2212yes—
43C3×#559—31no—
44#5585D311yescharacteristic
45#5567—31no—
46#5567—31no—
47#5567—61no—
48C3×C8×Q8—31no—
49#5075—31no—
50#5070—31no—
51#5056—32no—
52#5054—32no—
53C4×#216—31no—
54Q8×C3⋊C8D311yescharacteristic, complemented
55#5020—31no—
56C4×#214—32no—
57#5009—32no—
58#4851—31no—
59#4848—31no—
60#4847—32no—
61#4845—32no—
62C4×Dic12—31no—
63#4697—32no—
64#4694—31no—
65C4×#204—32no—
66C2×C32×Q8D411yescharacteristic
67C2×#634—21no—
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—22no—
83#3750—22no—
84#3750—22no—
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96#3719—22no—
97#3716—24no—
98#3365—91noSylow
99C3×#127—31no—
100C3×#124—32no—
101C3×#124—61no—
102C3×#123—62no—
103C3×C4×Q8—21no—
104C3×C4×Q8—31no—
105C3×C4×Q8C2×D311yescharacteristic
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×D4—32no—
108C3×C4×D4—61no—
109#947—21no—
110#944—62no—
111#944—61no—
112#944—61no—
113C2×#216—31no—
114C2×#214—32no—
115C2×Dic12—31no—
116C2×#204—32no—
117#894—22no—
118#893—21no—
119#889—64no—
120#889—62no—
121#889—62no—
122#887—62no—
123#887—61no—
124#887—61no—
125#875C2×D312yes—
126#874C2×D311yescharacteristic
127C4×D12C2×D312yes—
128#870—32no—
129#870—32no—
130#870—62no—
131#869—31no—
132#869—31no—
133#869—61no—
134C4×Dic6—32no—
135C4×Dic6—31no—
136C4×Dic6—32no—
137C4×Dic6—31no—
138C4×Dic6—62no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×C4×C8—32no—
144C3×C4×C8—31no—
145#835—32no—
146#835—31no—
147#832—32no—
148#832—32no—
149#832—32no—
150#821—32no—
151#821—32no—
152#821—32no—
153#818—31no—
154#817—32no—
155#816—31no—
156#816—32no—
157#816—31no—
158#810—31no—
159#808—32no—
160#807—31no—
161C4⋊(C3⋊C8)C2×D312yes—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8C2×D312yes—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3—22no—
166C32×Q8—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175#634—21no—
176#634—42no—
177#634#4112yes—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—82no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—31no—
191#557—91no—
192#488—92no—
193#486—91no—
194#478—92no—
195#475—91no—
196#464—92no—
197#460—91no—
198C8×Q8—31no—
199C4×Q16—91no—
200C4×SD16—92no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8D1211yescharacteristic
204C2×C3×Q8#6711yescharacteristic
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×C3×C4—62no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×C4×D3—22no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—31no—
221C2×C3×C8—32no—
222C2×C3×C8—31no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4D1211yescharacteristic
228C3×C4⋊C4D1212yes—
229C3×C4⋊C4#6711yescharacteristic
230C3×C4⋊C4#6712yes—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C42—21no—
235C3×C42—22no—
236C3×C42—61no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D312yes—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D312yes—
241#216—62no—
242#214—64no—
243(C2×D3)⋊C4—22no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246C4⋊Dic3—31no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—31no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3C22×D311yescharacteristic
256Dic3⋊C4—21no—
257Dic3⋊C4—62no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—61no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—61no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269C4×Dic3—21no—
270C4×Dic3—64no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—61no—
274C4×Dic3—62no—
275C4×Dic3—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279Dic12—62no—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—22no—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—22no—
292C3⋊Dic3—42no—
293C3⋊Dic3—41no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C2×Q16—91no—
297C2×SD16—92no—
298C4⋊Q8—91no—
299C4⋊Q8—181no—
300#127—31no—
301#125—92no—
302#125—182no—
303#124—32no—
304#124—61no—
305#123—62no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—91no—
309C4×Q8—181no—
310C4×Q8D3211yescharacteristic
311C4×D4—32no—
312C4×D4—61no—
313#107—91no—
314#106—92no—
315C4⋊C8—31no—
316C4⋊C8—32no—
317#103—91no—
318#103—91no—
319#103—92no—
320#102—92no—
321#102—92no—
322#102—92no—
323C4×C8—32no—
324C4×C8—31no—
325C23×C3—62no—
326C22×D3—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—42no—
330C3×Q8—61no—
331C3×Q8—61no—
332C3×D4—62no—
333C3×D4—62no—
334C3×D4—122no—
335C3×D4—241no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—242no—
344C2×C3×C4C2×D1212yes—
345C2×C3×C4C2×D1212yes—
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—62no—
360C2×Dic3—64no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365D12—22no—
366D12—22no—
367D12—42no—
368D12—81no—
369C4×D3—82no—
370Dic6—21no—
371Dic6—21no—
372Dic6—32no—
373Dic6—32no—
374Dic6—62no—
375Dic6—62no—
376Dic6—61no—
377Dic6—61no—
378Dic6—124no—
379Dic6—122no—
380Dic6—122no—
381C3×C8—62no—
382C3×C8—61no—
383C3×C8—61no—
384C3⋊C8—21no—
385C3⋊C8—22no—
386C3⋊C8—21no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C2×Q8—31no—
392C2×Q8—91no—
393C2×Q8—181no—
394C2×Q8#62611yescharacteristic
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C22×C4—62no—
399Q16—182no—
400SD16—184no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—32no—
404C4⋊C4—31no—
405C4⋊C4—61no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C4⋊C4—181no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—181no—
413C4⋊C4#62611yescharacteristic
414C4⋊C4#62612yes—
415C22⋊C4—62no—
416C22⋊C4—62no—
417C22⋊C4—62no—
418C42—61no—
419C42—182no—
420C42—181no—
421C42C2×D3212yes—
422C42C2×D3211yescharacteristic
423C22×C3—21no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C22×D1211yescharacteristic
428C22×C3C22×#6711yescharacteristic
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—41no—
444C3×C4—121no—
445C3×C4—121no—
446C3×C4#90412yes—
447C3×C4#95012yes—
448C3×C4#100711yescharacteristic
449C3×C4D3×#4111yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—41no—
453Dic3—41no—
454Dic3—64no—
455Dic3—62no—
456Dic3—62no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460Dic3—121no—
461Dic3—122no—
462Dic3—121no—
463C32#336511yescharacteristic, complemented, Sylow
464C23—62no—
465Q8—22no—
466Q8—61no—
467Q8—61no—
468Q8—92no—
469Q8—181no—
470Q8—362no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—182no—
480C2×C4—242no—
481C2×C4C2×#62612yes—
482C2×C4C2×#62612yes—
483C2×C4C2×#62611yescharacteristic
484C2×C4C2×#62611yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—61no—
487C8—62no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—242no—
493C2×C3#557611yescharacteristic
494C2×C3C2×#90411yescharacteristic
495C2×C3#575111yescharacteristic
496C2×C3C2×#95011yescharacteristic
497C2×C3#583111yescharacteristic
498C2×C3#583611yescharacteristic
499D3—82no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22C22×#62611yescharacteristic
504C4—22no—
505C4—21no—
506C4—22no—
507C4—121no—
508C4—121no—
509C4—182no—
510C4—361no—
511C4—362no—
512C4#6382912yes—
513C4#6431511yescharacteristic
514C4#6431911yescharacteristic
515C3—21no—
516C3#7993511yescharacteristic, complemented
517C3#8371711yescharacteristic, complemented
518C2—242no—
519C2C2×#6382911yescharacteristic
520C2#1059541411yescharacteristic
521C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4×Q8D32
hypocenterC32#3365
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. #10596038C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. C4×#3719C2semidirect
5. #10590378C2semidirect
7. C4×#3716C2semidirect
8. #10590301C2semidirect
9. #10590274C2semidirect
11. #10590271C2semidirect
54. Q8×C3⋊C8D3semidirect
463. C32#3365semidirect
516. C3#79935semidirect
517. C3#83717semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55852
C3×Q8×C3⋊C82
C4×#37192
#105903782
#105903772
C4×#37162
#105903012
#105902742
#105902732
#105902712
#837173
#799353