Finite Group Databasebeta

← #11887644

Subgroups — #11887644

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3C3×D4×C3⋊C8C211yesmaximal, characteristic
4#10591187C212yesmaximal, complemented
5#10591186C212yesmaximal, complemented
6#10591103C212yesmaximal, complemented
7C2×#63566C212yesmaximal, complemented
8#10590388C211yesmaximal, characteristic, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10#10590287C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#83551—31nomaximal
13#79448—31nomaximal
14C22×C3×Dic6C2212yes—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3—21no—
17C2×C4⋊(C3⋊Dic3)C2212yes—
18#64133C2212yes—
19#64099—21no—
20#64087—22no—
21#64078C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×D4×Dic3—21no—
24C3×#924C2212yes—
25C22×C3×C3⋊C8C2212yes—
26C3×#888—21no—
27C3×#878—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C2×#3719C2211yescharacteristic
31C2×#3719C2212yes—
32C3×#830C2212yes—
33C3×C4⋊(C3⋊C8)C2211yescharacteristic
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2212yes—
36#63575C2211yescharacteristic
37#63567C2211yescharacteristic
38#63566C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63566C2211yescharacteristic
42#63566C2212yes—
43C3×D4×Q8—31no—
44#5543—31no—
45#5543—31no—
46#5543—61no—
47D4×Dic6D311yescharacteristic
48C3×C8×D4—31no—
49#5228—32no—
50C2×#835—32no—
51#5116—32no—
52C2×#816—32no—
53#5090—31no—
54#5079—31no—
55#5051—32no—
56#5044—32no—
57C4×#216—31no—
58#5021—31no—
59D4×C3⋊C8D311yescharacteristic
60#4850—31no—
61#4849—31no—
62#4739—32no—
63#4722—32no—
64C4×Dic12—31no—
65#4681—31no—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634C2311yescharacteristic
71C22×C3×Dic3—22no—
72C2×C3×Dic6—24no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—42no—
75C2×C3×Dic6C2312yes—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4D411yescharacteristic
78C32×C22⋊C4D412yes—
79C32×C42C2311yescharacteristic
80#3757—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—21no—
86#3750—22no—
87C4×C3⋊Dic3—21no—
88C3×#217—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8—42no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3719—22no—
100#3719—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C22×Dic6C2×D312yes—
104C22×C3×C8—32no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×C22⋊Q8—32no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—31no—
110C3×C4×D4—21no—
111C3×C4×D4—61no—
112C3×C4×D4C2×D311yescharacteristic
113C3×C4×D4C2×D311yescharacteristic
114C2×#216—31no—
115C2×#216—32no—
116D4×Dic3—21no—
117D4×Dic3—62no—
118D4×Dic3—61no—
119D4×Dic3—61no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—62no—
123#924—32no—
124#924—32no—
125#924—62no—
126#924C2×D312yes—
127C22×C3⋊C8C2×D312yes—
128C2×Dic12—31no—
129C2×Dic12—32no—
130#890—62no—
131#890—61no—
132#890—61no—
133#888—21no—
134#878—22no—
135#878—64no—
136#878—62no—
137#878—62no—
138#869—31no—
139#869—31no—
140#869—61no—
141#869C2×D311yescharacteristic
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—31no—
147C3×C22⋊C8—32no—
148C3×C4×C8—31no—
149#835—31no—
150#835—32no—
151#835—32no—
152#835—32no—
153#835—32no—
154#830C2×D312yes—
155#818—31no—
156#818—32no—
157#816—32no—
158#816—32no—
159#816—31no—
160#816—32no—
161#816—32no—
162#816—31no—
163#810—31no—
164#807—32no—
165#807—31no—
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C4×C3⋊C8C2×D311yescharacteristic
168C23×C32C2×D412yes—
169C32×D4Q1614yescomplemented
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—82no—
180#634—21no—
181#634—21no—
182#634—81no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—44no—
187C3×Dic6—21no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6—44no—
191C3×Dic6#4112yes—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195#554—91no—
196D4×Q8—31no—
197#487—91no—
198#484—92no—
199#477—91no—
200#467—92no—
201#462—91no—
202#451—92no—
203C4×Q16—91no—
204C8×D4—31no—
205C2×#103—92no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×Q8—64no—
209C2×C3×Q8—62no—
210C2×C3×Q8—122no—
211C2×C3×D4—21no—
212C2×C3×D4D1211yescharacteristic
213C2×C3×D4#6711yescharacteristic
214C22×C3×C4—22no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D312yes—
218C22×Dic3—22no—
219C22×Dic3—64no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C2×Dic6—24no—
223C2×Dic6—22no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—42no—
227C2×Dic6—61no—
228C2×Dic6—62no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6C22×D312yes—
232C2×Dic6C22×D311yescharacteristic
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C2×C3×C8—32no—
236C2×C3×C8—122no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4D1211yescharacteristic
244C3×C4⋊C4#6711yescharacteristic
245C3×C22⋊C4—22no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4D1212yes—
248C3×C22⋊C4#6712yes—
249C3×C42—21no—
250C3×C42—61no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—22no—
254#217—64no—
255#217—62no—
256#217—62no—
257#216—62no—
258#216—122no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—31no—
262C4⋊Dic3—32no—
263C4⋊Dic3—31no—
264C4⋊Dic3—32no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—64no—
269C4⋊Dic3—61no—
270C4⋊Dic3—62no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—21no—
275Dic3⋊C4—22no—
276Dic3⋊C4—62no—
277Dic3⋊C4—64no—
278Dic3⋊C4—61no—
279Dic3⋊C4—62no—
280Dic3⋊C4—61no—
281Dic3⋊C4—62no—
282C4×Dic3—21no—
283C4×Dic3—62no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C2×C3⋊C8—42no—
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D312yes—
290Dic12—62no—
291Dic12—122no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32C2×Q1614yes—
295C22×C32C22×D411yescharacteristic
296C32×C4—22no—
297C32×C4—21no—
298C32×C4C2×Q1612yes—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3⋊Dic3—41no—
302C3⋊Dic3—42no—
303C3⋊Dic3—41no—
304C3×Dic3—22no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C22×Q8—32no—
308C2×Q16—91no—
309C2×Q16—92no—
310C22×C8—32no—
311C4⋊Q8—31no—
312C4⋊Q8—61no—
313C4⋊Q8—91no—
314#125—181no—
315C22⋊Q8—32no—
316C22⋊Q8—62no—
317C22⋊Q8—92no—
318C22⋊Q8—182no—
319C4×Q8—31no—
320C4×Q8—91no—
321C4×D4—61no—
322C4×D4—181no—
323C4×D4D3211yescharacteristic
324C2×C4⋊C4—92no—
325#107—91no—
326#107—92no—
327C4⋊C8—31no—
328#103—91no—
329#103—91no—
330#103—92no—
331#103—92no—
332#103—92no—
333#103—92no—
334C22⋊C8—32no—
335C4×C8—31no—
336C23×C3—22no—
337C23×C3C2×D1212yes—
338C23×C3C2×#6712yes—
339C3×Q8—32no—
340C3×Q8—61no—
341C3×Q8—62no—
342C3×Q8—62no—
343C3×Q8—124no—
344C3×D4—24no—
345C3×D4Dic1214yescomplemented
346C3×D4#21614yescomplemented
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—124no—
361C2×C3×C4C2×D1212yes—
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6712yes—
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—44no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—64no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—62no—
382C2×Dic3—242no—
383C2×Dic3—242no—
384C2×Dic3—244no—
385Dic6—21no—
386Dic6—22no—
387Dic6—22no—
388Dic6—44no—
389Dic6—61no—
390Dic6—61no—
391Dic6—61no—
392Dic6—61no—
393Dic6—121no—
394Dic6—121no—
395Dic6—241no—
396Dic6—241no—
397Dic6—242no—
398Dic6#23712yes—
399C3×C8—61no—
400C3×C8—62no—
401C3×C8—61no—
402C3⋊C8—21no—
403C3⋊C8—22no—
404C3⋊C8—21no—
405C2×C32—24no—
406C2×C32#54611yescharacteristic
407C2×C32C22×Q1611yescharacteristic
408C2×C32#57711yescharacteristic
409C2×Q8—31no—
410C2×Q8—32no—
411C2×Q8—64no—
412C2×Q8—62no—
413C2×Q8—91no—
414C2×Q8—122no—
415C2×Q8—181no—
416C2×D4#62611yescharacteristic
417C22×C4—62no—
418C22×C4—182no—
419C22×C4C2×D3212yes—
420Q16—182no—
421Q16—362no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—122no—
426C4⋊C4—31no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—62no—
430C4⋊C4—61no—
431C4⋊C4—91no—
432C4⋊C4—92no—
433C4⋊C4—182no—
434C4⋊C4—181no—
435C4⋊C4—181no—
436C4⋊C4—182no—
437C4⋊C4#62611yescharacteristic
438C22⋊C4—62no—
439C22⋊C4—182no—
440C22⋊C4#62612yes—
441C42—61no—
442C42—181no—
443C42C2×D3211yescharacteristic
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—24no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3C2×Dic1214yes—
453C22×C3C2×#21614yes—
454C22×C3C22×D1211yescharacteristic
455C22×C3C22×#6711yescharacteristic
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—42no—
465C3×C4—62no—
466C3×C4—121no—
467C3×C4—122no—
468C3×C4C2×Dic1212yes—
469C3×C4C2×#21612yes—
470C3×C4C2×#23711yescharacteristic
471C3×C4#100411yescharacteristic
472C3×C4#100411yescharacteristic
473C3×C4D3×#4111yescharacteristic
474Dic3—22no—
475Dic3—42no—
476Dic3—41no—
477Dic3—122no—
478Dic3—124no—
479Dic3—122no—
480Dic3—122no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—122no—
485Dic3—121no—
486C32#329911yescharacteristic, complemented, Sylow
487C23C2×#62612yes—
488Q8—32no—
489Q8—61no—
490Q8—62no—
491Q8—62no—
492Q8—124no—
493Q8—181no—
494Q8—181no—
495Q8—721no—
496D4#371914yescomplemented
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—124no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—182no—
506C2×C4—722no—
507C2×C4C2×#62611yescharacteristic
508C2×C4C2×#62612yes—
509C2×C4C2×#62611yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—61no—
512C8—61no—
513C8—62no—
514C2×C3—24no—
515C2×C3—24no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—44no—
520C2×C3#555411yescharacteristic
521C2×C3C22×Dic1211yescharacteristic
522C2×C3#575111yescharacteristic
523C2×C3#580611yescharacteristic
524C2×C3C22×#21611yescharacteristic
525C2×C3#583711yescharacteristic
526C22—22no—
527C22—22no—
528C22C2×#371914yes—
529C22C22×#62611yescharacteristic
530C4—21no—
531C4—22no—
532C4—62no—
533C4—121no—
534C4—122no—
535C4—361no—
536C4—362no—
537C4—361no—
538C4C2×#371912yes—
539C4D3×#23711yescharacteristic
540C4#6431311yescharacteristic
541C3—21no—
542C3#7944811yescharacteristic, complemented
543C3#8355111yescharacteristic, complemented
544C2—24no—
545C2C22×#371911yescharacteristic
546C2#1059524611yescharacteristic
547C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10591187C2semidirect
5. #10591186C2semidirect
6. #10591103C2semidirect
7. C2×#63566C2semidirect
8. #10590388C2semidirect
9. C4×#3719C2semidirect
10. #10590287C2semidirect
11. #10590283C2semidirect
169. C32×D4Q16semidirect
345. C3×D4Dic12semidirect
346. C3×D4#216semidirect
486. C32#3299semidirect
496. D4#3719semidirect
542. C3#79448semidirect
543. C3#83551semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×D4×Dic62
C3×D4×C3⋊C82
#105911872
#105911862
#105911032
C2×#635662
#105903882
C4×#37192
#105902872
#105902832
#835513
#794483