Finite Group Databasebeta

← #11887667

Subgroups — #11887667

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593956C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic
6#10590952C212yesmaximal, complemented
7#10590852C212yesmaximal, complemented
8#10590684C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590288C211yesmaximal, characteristic, complemented
12#81119—31nomaximal
13#79448—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2212yes—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918—21no—
23#63898—21no—
24#63893—22no—
25Dic3×D12—21no—
26D3×C4⋊Dic3C2212yes—
27#63887—22no—
28#63872—21no—
29#63857C2212yes—
30#63857C2212yes—
31C2×#3719C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33#63643C2212yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×#818C2212yes—
36C3×#816C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63567C2211yescharacteristic
42#63566C2211yescharacteristic
43#5730—31no—
44Q8×D12—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×#477—31no—
48C3×C8×D4—31no—
49#5116—32no—
50C2×#816—32no—
51#5093—31no—
52C4×#216—31no—
53#4887—32no—
54#4884—32no—
55#4850D311yescharacteristic, complemented
56#4849—31no—
57#4849—31no—
58#4849—61no—
59#4834D311yescharacteristic
60#4809—32no—
61D3×#103—32no—
62#4739—32no—
63#4722—32no—
64C4×Dic12—31no—
65#4681—31no—
66C2×#634C2312yes—
67C2×#634C2311yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
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)—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84#3746—42no—
85C3×(C2×D3)⋊C4D412yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×D3×C8—42no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—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—
104C22×C3×C8—32no—
105C3×C4⋊Q8—31no—
106C3×C4×Q8—31no—
107C3×C4×D4—31no—
108#946—62no—
109C2×#216—31no—
110D4×Dic3—61no—
111D4×Dic3—61no—
112C2×C4⋊Dic3—32no—
113#924—32no—
114#924—32no—
115C2×Dic12—31no—
116C2×Dic12—32no—
117C2×Dic12—32no—
118C2×Dic12—62no—
119C2×D3×C8C2×D312yes—
120#897—32no—
121#897—32no—
122#897—62no—
123#893—61no—
124D3×C4⋊C4—32no—
125#890—61no—
126#890—61no—
127#888—61no—
128#878—62no—
129#878—62no—
130C4×D12—61no—
131C4×D12C2×D311yescharacteristic
132#869—31no—
133#869—31no—
134#869—61no—
135#869—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#107—32no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8C2×D311yescharacteristic
144C3×C4⋊C8C2×D311yescharacteristic
145C3×#103—32no—
146C3×C22⋊C8—32no—
147C3×C4×C8—31no—
148#835—31no—
149(C2×D3)⋊C8C2×D312yes—
150#818—31no—
151#818C2×D312yes—
152#816—31no—
153#816—32no—
154#816—32no—
155#816—32no—
156#816—32no—
157#816—31no—
158#816—62no—
159#816C2×D312yes—
160#810—32no—
161#810—31no—
162#810—32no—
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—22no—
171C2×C3⋊Dic3—21no—
172#634—21no—
173#634—21no—
174#634—22no—
175#634—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C3×D12Q1614yescomplemented
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×Dic6—21no—
184C3×Dic6—81no—
185C3×Dic6#4112yes—
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—31no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—91no—
201C8×D4—31no—
202C2×#103—92no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
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—21no—
216C2×Dic6—32no—
217C2×Dic6—31no—
218C2×Dic6—32no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6—62no—
222C2×Dic6—64no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—122no—
226C2×Dic6C22×D311yescharacteristic
227C2×C3×C8—22no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C2×C3×C8—122no—
231C2×C3×C8C22×D312yes—
232C2×C3×C8C22×D312yes—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C22⋊C4—32no—
239C3×C42—21no—
240C3×C42—61no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#217—62no—
245#216—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4D1212yes—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—121no—
261C4⋊Dic3—121no—
262C4⋊Dic3D1211yescharacteristic
263C4⋊Dic3C22×D312yes—
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—62no—
271Dic3⋊C4—121no—
272C4×Dic3—21no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—121no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278Dic12—62no—
279Dic12—122no—
280Dic12—122no—
281Dic12—124no—
282D3×C8—42no—
283C22×C32C22×D411yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3C2×Q1614yes—
287C32×C4—21no—
288C32×C4C2×Q1612yes—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3⋊Dic3—41no—
292C3⋊Dic3—42no—
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C22×Q8—92no—
299C2×Q16—91no—
300C2×Q16—92no—
301C22×C8—32no—
302C4⋊Q8—31no—
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#125—181no—
306C22⋊Q8—92no—
307C22⋊Q8—92no—
308C22⋊Q8—182no—
309C22⋊Q8—182no—
310C4×Q8—31no—
311C4×Q8—91no—
312C4×D4—31no—
313C4×D4—181no—
314C4×D4—181no—
315C2×C4⋊C4—92no—
316#107—32no—
317#107—91no—
318C4⋊C8D3211yescharacteristic
319#103—32no—
320#103—92no—
321#103—91no—
322#103—92no—
323#103—91no—
324#103—92no—
325C22⋊C8—32no—
326C4×C8—31no—
327C23×C3—32no—
328C22×D3C2×D1212yes—
329C3×Q8—32no—
330C3×Q8—61no—
331C3×Q8—241no—
332C3×D4—34no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
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—62no—
354C2×Dic3—61no—
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—62no—
370Dic6—61no—
371Dic6—62no—
372Dic6—61no—
373Dic6—62no—
374Dic6—61no—
375Dic6—62no—
376Dic6—61no—
377Dic6—62no—
378Dic6—81no—
379Dic6—121no—
380Dic6—122no—
381Dic6—122no—
382Dic6—124no—
383Dic6—124no—
384Dic6#23912yes—
385C3×C8—22no—
386C3×C8—22no—
387C3×C8—42no—
388C3×C8—61no—
389C3×C8—61no—
390C3⋊C8—21no—
391C3⋊C8—21no—
392C2×C32#54611yescharacteristic
393C2×C32C22×Q1611yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—24no—
396C2×Q8—31no—
397C2×Q8—61no—
398C2×Q8—92no—
399C2×Q8—91no—
400C2×Q8—182no—
401C2×Q8—184no—
402C2×Q8—362no—
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—182no—
406C22×C4—182no—
407Q16—182no—
408Q16—362no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—122no—
412C2×C8C2×D3212yes—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—31no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—91no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C22⋊C4—32no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C42—61no—
429C42—181no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—34no—
433C22×C3—62no—
434C22×C3—62no—
435C22×C3C22×D1211yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—22no—
438C2×D3—22no—
439C2×D3C2×Dic1214yes—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—122no—
449C3×C4—121no—
450C3×C4C2×Dic1212yes—
451C3×C4D3×Q1612yes—
452C3×C4#100411yescharacteristic
453C3×C4C2×#23911yescharacteristic
454C3×C4D3×#4111yescharacteristic
455C3×C4#100911yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—42no—
459Dic3—41no—
460Dic3—122no—
461Dic3—121no—
462Dic3—121no—
463Dic3—122no—
464Dic3—121no—
465Dic3—122no—
466Dic3—121no—
467Dic3—242no—
468Dic3—241no—
469C32#329911yescharacteristic, complemented, Sylow
470C23—32no—
471Q8—32no—
472Q8—61no—
473Q8—181no—
474Q8—182no—
475Q8—181no—
476Q8—182no—
477Q8—241no—
478Q8—364no—
479D4—34no—
480C2×C4—32no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—182no—
489C2×C4—364no—
490C2×C4—722no—
491C2×C4D3×D1211yescharacteristic
492C2×C4D3×D1211yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—22no—
495C8—61no—
496C8—61no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#555411yescharacteristic
502C2×C3#563011yescharacteristic
503C2×C3C22×Dic1211yescharacteristic
504C2×C3#575111yescharacteristic
505C2×C3C2×D3×Q1611yescharacteristic
506C2×C3#577511yescharacteristic
507D3—24no—
508C22—34no—
509C22—62no—
510C22—62no—
511C22C2×D3×D1211yescharacteristic
512C4—21no—
513C4—62no—
514C4—62no—
515C4—122no—
516C4—121no—
517C4—362no—
518C4—361no—
519C4—361no—
520C4D3×Dic1212yes—
521C4#6431411yescharacteristic
522C4D3×#23911yescharacteristic
523C3—21no—
524C3#7944811yescharacteristic, complemented
525C3#8111911yescharacteristic, complemented
526C2—64no—
527C2#1059462911yescharacteristic
528C2C2×D3×Dic1211yescharacteristic
529C2#1059471311yescharacteristic
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. #10592548C2semidirect
4. C3×#4850C2semidirect
6. #10590952C2semidirect
7. #10590852C2semidirect
8. #10590684C2semidirect
9. D3×#816C2semidirect
10. C4×#3719C2semidirect
11. #10590288C2semidirect
55. #4850D3semidirect
180. C3×D12Q16semidirect
363. D12Dic12semidirect
469. C32#3299semidirect
524. C3#79448semidirect
525. C3#81119semidirect

Maximal subgroups

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

subgroupindex
#105939562
Dic6×D122
#105925482
C3×#48502
C3×#48342
#105909522
#105908522
#105906842
D3×#8162
C4×#37192
#105902882
#811193
#794483