Finite Group Databasebeta

← #11887665

Subgroups — #11887665

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593960C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic
6#10590949C212yesmaximal, complemented
7#10590851C212yesmaximal, complemented
8#10590682C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590287C211yesmaximal, characteristic, complemented
12#80491—31nomaximal
13#79448—31nomaximal
14C2×D3×Dic6C2212yes—
15#64078C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C2×C3×Dic12C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63919—21no—
23#63899—22no—
24#63898—21no—
25#63896—22no—
26Dic3×D12—21no—
27D3×C4⋊Dic3C2212yes—
28#63869—21no—
29#63856C2212yes—
30#63856C2212yes—
31C2×#3719C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33#63645C2212yes—
34#63643C2212yes—
35C3×(C2×D3)⋊C8C2212yes—
36C3×#816C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2212yes—
41#63566C2212yes—
42#63566C2211yescharacteristic
43#5727—31no—
44#5579—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×#462—31no—
48C3×C8×D4—31no—
49#5188—32no—
50#5186—32no—
51#5116—32no—
52C2×#816—32no—
53#5079—31no—
54C4×#216—31no—
55#4850—31no—
56#4850—31no—
57#4850—61no—
58#4849D311yescharacteristic, complemented
59#4834D311yescharacteristic
60#4811—32no—
61D3×#103—32no—
62#4739—32no—
63#4722—32no—
64C4×Dic12—31no—
65#4681—31no—
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6C2311yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—24no—
76D3×Dic6—42no—
77C2×C32×C8C2312yes—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—21no—
83C4×C3⋊Dic3—21no—
84C3×(C2×D3)⋊C4D412yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×Dic12—42no—
94C3×D3×C8—42no—
95#3724—22no—
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3719—22no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C22×Dic6—32no—
104C2×C3×Q16—32no—
105C22×C3×C8—32no—
106C3×C4⋊Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—31no—
109#946—32no—
110#946—32no—
111C2×#216—31no—
112D4×Dic3—61no—
113D4×Dic3—61no—
114C2×C4⋊Dic3—32no—
115#924—32no—
116#924—32no—
117C2×Dic12—31no—
118C2×Dic12C2×D312yes—
119C2×D3×C8C2×D312yes—
120#896—62no—
121#896—62no—
122#893—61no—
123D3×C4⋊C4—32no—
124#890—61no—
125#888—61no—
126#888—61no—
127#878—62no—
128#878—62no—
129C4×D12—61no—
130C4×D12C2×D311yescharacteristic
131#870—61no—
132#869—31no—
133#869—31no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6C2×D311yescharacteristic
140C3×C4⋊C8—21no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C2×D311yescharacteristic
143C3×#103—32no—
144C3×C22⋊C8—32no—
145C3×C4×C8—31no—
146#835—32no—
147#835—31no—
148#835—32no—
149(C2×D3)⋊C8C2×D312yes—
150#818—32no—
151#818—32no—
152#818—31no—
153#818—62no—
154#816—32no—
155#816—32no—
156#816—31no—
157#816—32no—
158#816—32no—
159#816—31no—
160#816—62no—
161#816C2×D312yes—
162#810—31no—
163#807—31no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—22no—
172#634—21no—
173#634—81no—
174#634#4112yes—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×Dic6—21no—
183C3×Dic6—22no—
184C3×Dic6—21no—
185C3×Dic6—22no—
186#627—44no—
187D3×Dic3—44no—
188D3×Dic3—82no—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—91no—
193D4×Q8—91no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—31no—
199#451—92no—
200C4×Q16—91no—
201C8×D4—31no—
202C2×#103—92no—
203C2×C3×Q8—32no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C22×C3×C4—32no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209D3×Q8—64no—
210D3×Q8—122no—
211C2×D12D1211yescharacteristic
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3C22×D312yes—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—64no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D311yescharacteristic
227C3×Q16—122no—
228C2×C3×C8—22no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—122no—
232C2×C3×C8C22×D312yes—
233C2×C3×C8C22×D312yes—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—32no—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#217—62no—
246#216—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4D1212yes—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—31no—
253C4⋊Dic3—32no—
254C4⋊Dic3—31no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—121no—
262C4⋊Dic3D1211yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—121no—
273C4×Dic3—21no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—121no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279Dic12—42no—
280Dic12—62no—
281D3×C8—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—21no—
287C32×C4C2×Q1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C4H(5,𝔽2)11yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—42no—
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—92no—
298C2×Q16—32no—
299C2×Q16—91no—
300C22×C8—32no—
301C4⋊Q8—31no—
302C4⋊Q8—91no—
303C4⋊Q8—181no—
304#125—181no—
305C22⋊Q8—92no—
306C22⋊Q8—92no—
307C22⋊Q8—182no—
308C22⋊Q8—182no—
309C4×Q8—31no—
310C4×Q8—91no—
311C4×D4—31no—
312C4×D4—181no—
313C4×D4—181no—
314C2×C4⋊C4—92no—
315#107—91no—
316#107—92no—
317C4⋊C8D3211yescharacteristic
318#103—32no—
319#103—91no—
320#103—92no—
321#103—91no—
322#103—92no—
323#103—92no—
324C22⋊C8—32no—
325C4×C8—31no—
326C23×C3—32no—
327C22×D3C2×D1212yes—
328C3×Q8—61no—
329C3×Q8—62no—
330C3×Q8—61no—
331C3×Q8—62no—
332C3×D4—34no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3—242no—
362C2×Dic3C2×D1212yes—
363D12Dic1214yescomplemented
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—124no—
367C4×D3—242no—
368Dic6—21no—
369Dic6—22no—
370Dic6—21no—
371Dic6—22no—
372Dic6—32no—
373Dic6—32no—
374Dic6—62no—
375Dic6—61no—
376Dic6—61no—
377Dic6—121no—
378Dic6—124no—
379Dic6—124no—
380Dic6—241no—
381Dic6—241no—
382Dic6—242no—
383C3×C8—22no—
384C3×C8—22no—
385C3×C8—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—32no—
395C2×Q8—31no—
396C2×Q8—91no—
397C2×Q8—182no—
398C2×Q8—184no—
399C2×Q8—181no—
400C2×Q8—362no—
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—182no—
404C22×C4—182no—
405Q16—122no—
406Q16—182no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—122no—
410C2×C8C2×D3212yes—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C22⋊C4—32no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C42—61no—
427C42—181no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C22×D1211yescharacteristic
434C22×C3C2×D3×D411yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×Dic1214yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—121no—
446C3×C4—122no—
447C3×C4—121no—
448C3×C4C2×Dic1212yes—
449C3×C4D3×Q1612yes—
450C3×C4#100411yescharacteristic
451C3×C4#100411yescharacteristic
452C3×C4D3×#4111yescharacteristic
453C3×C4D3×#4111yescharacteristic
454Dic3—22no—
455Dic3—41no—
456Dic3—42no—
457Dic3—41no—
458Dic3—62no—
459Dic3—62no—
460Dic3—122no—
461Dic3—122no—
462Dic3—121no—
463Dic3—122no—
464Dic3—121no—
465Dic3—242no—
466Dic3—241no—
467C32#329911yescharacteristic, complemented, Sylow
468C23—32no—
469Q8—61no—
470Q8—62no—
471Q8—61no—
472Q8—62no—
473Q8—92no—
474Q8—181no—
475Q8—364no—
476Q8—721no—
477D4—34no—
478C2×C4—32no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—182no—
487C2×C4—364no—
488C2×C4—722no—
489C2×C4D3×D1211yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—22no—
493C8—61no—
494C8—61no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3#555411yescharacteristic
500C2×C3#561211yescharacteristic
501C2×C3C22×Dic1211yescharacteristic
502C2×C3#575111yescharacteristic
503C2×C3C2×D3×Q1611yescharacteristic
504C2×C3#577811yescharacteristic
505D3—24no—
506C22—34no—
507C22—62no—
508C22—62no—
509C22C2×D3×D1211yescharacteristic
510C4—21no—
511C4—62no—
512C4—122no—
513C4—121no—
514C4—121no—
515C4—182no—
516C4—362no—
517C4—361no—
518C4D3×Dic1212yes—
519C4#6431311yescharacteristic
520C4#6431911yescharacteristic
521C3—21no—
522C3#7944811yescharacteristic, complemented
523C3#8049111yescharacteristic, complemented
524C2—64no—
525C2#1059463011yescharacteristic
526C2C2×D3×Dic1211yescharacteristic
527C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592549C2semidirect
4. C3×#4849C2semidirect
6. #10590949C2semidirect
7. #10590851C2semidirect
8. #10590682C2semidirect
9. D3×#816C2semidirect
10. C4×#3719C2semidirect
11. #10590287C2semidirect
58. #4849D3semidirect
179. C3×D12Q16semidirect
363. D12Dic12semidirect
467. C32#3299semidirect
522. C3#79448semidirect
523. C3#80491semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105939042
#105925492
C3×#48492
C3×#48342
#105909492
#105908512
#105906822
D3×#8162
C4×#37192
#105902872
#804913
#794483