Finite Group Databasebeta

← #11887645

Subgroups — #11887645

Order 1152.

916 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic
3C3×D4×C3⋊C8C211yesmaximal, characteristic
4#10591190C212yesmaximal, complemented
5#10591187C212yesmaximal, complemented
6#10591135C212yesmaximal, complemented
7C2×#63567C212yesmaximal, complemented
8#10590385C211yesmaximal, characteristic, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10#10590288C211yesmaximal, characteristic, complemented
11#10590284C211yesmaximal, characteristic, complemented
12#83640—31nomaximal
13#79448—31nomaximal
14C22×#634C2212yes—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3—21no—
17#64133C2212yes—
18#64097—21no—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×D4×Dic3—21no—
23C2×C3×C4⋊Dic3C2212yes—
24C3×#924C2212yes—
25C22×C3×C3⋊C8C2212yes—
26C3×#890—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#63567C2212yes—
38#63567C2212yes—
39#63567C2212yes—
40#63567C2211yescharacteristic
41#63567C2212yes—
42#63566C2211yescharacteristic
43C3×#554—31no—
44#5543D311yescharacteristic
45D4×Dic6—31no—
46D4×Dic6—31no—
47D4×Dic6—61no—
48C3×C8×D4—31no—
49#5116—32no—
50C2×#816—32no—
51#5093—31no—
52#5091—31no—
53#5051—32no—
54#5050—32no—
55#5031—31no—
56C4×#216—31no—
57D4×C3⋊C8D311yescharacteristic
58#4970—32no—
59C2×#810—32no—
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—24no—
70C2×#634—22no—
71C2×#634—42no—
72C2×#634C2312yes—
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—22no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4D411yescharacteristic
78C32×C22⋊C4D412yes—
79C32×C42C2311yescharacteristic
80#3757—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—22no—
86C4×C3⋊Dic3—21no—
87C3×#217—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
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×Dic6—32no—
103C22×Dic6—32no—
104C22×Dic6—62no—
105C22×C3×C8—32no—
106C3×C4⋊Q8—31no—
107C3×#125—61no—
108C3×C22⋊Q8—32no—
109C3×C22⋊Q8—62no—
110C3×C4×Q8—31no—
111C3×C4×D4—21no—
112C3×C4×D4—61no—
113C3×C4×D4C2×D311yescharacteristic
114C3×C4×D4C2×D311yescharacteristic
115C2×C3×C4⋊C4—32no—
116C2×#216—31no—
117C2×#216—32no—
118D4×Dic3—21no—
119D4×Dic3—62no—
120D4×Dic3—61no—
121D4×Dic3—61no—
122C2×C4⋊Dic3C2×D312yes—
123#924—32no—
124#924—32no—
125#924—62no—
126#924C2×D312yes—
127C22×C3⋊C8C2×D312yes—
128C2×Dic12—31no—
129C2×Dic12—32no—
130#890—21no—
131#888—62no—
132#888—61no—
133#888—61no—
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#830C2×D312yes—
151#818—31no—
152#818—32no—
153#816—31no—
154#816—32no—
155#816—32no—
156#816—31no—
157#816—32no—
158#816—32no—
159#810—31no—
160#810—32no—
161#810—32no—
162#810—32no—
163#810—32no—
164#807—31no—
165#807—32no—
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×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—44no—
180#634—21no—
181#634—22no—
182#634—22no—
183#634—44no—
184#634#4112yes—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—82no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6—81no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195#554—31no—
196D4×Q8—91no—
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—61no—
208C2×C3×D4—21no—
209C2×C3×D4D1211yescharacteristic
210C2×C3×D4#6711yescharacteristic
211C22×C3×C4—22no—
212C22×C3×C4—62no—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C22×Dic3—22no—
216C22×Dic3—64no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C2×Dic6—21no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—32no—
223C2×Dic6—32no—
224C2×Dic6—61no—
225C2×Dic6—62no—
226C2×Dic6—64no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—124no—
232C2×Dic6—122no—
233C2×Dic6—122no—
234C2×Dic6—124no—
235C2×Dic6C22×D311yescharacteristic
236C2×C3×C8—31no—
237C2×C3×C8—31no—
238C2×C3×C8—32no—
239C2×C3×C8—122no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4D1211yescharacteristic
248C3×C4⋊C4#6711yescharacteristic
249C3×C22⋊C4—22no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4D1212yes—
252C3×C22⋊C4#6712yes—
253C3×C42—21no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C22×D311yescharacteristic
257#217—22no—
258#217—64no—
259#217—62no—
260#217—62no—
261#216—62no—
262#216—122no—
263C4⋊Dic3—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D312yes—
276Dic3⋊C4—21no—
277Dic3⋊C4—22no—
278Dic3⋊C4—62no—
279Dic3⋊C4—64no—
280Dic3⋊C4—61no—
281Dic3⋊C4—62no—
282Dic3⋊C4—61no—
283Dic3⋊C4—62no—
284C4×Dic3—21no—
285C4×Dic3—62no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C2×C3⋊C8—42no—
289C2×C3⋊C8C22×D311yescharacteristic
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D312yes—
292Dic12—62no—
293Dic12—122no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32C2×Q1614yes—
297C22×C32C22×D411yescharacteristic
298C32×C4—22no—
299C32×C4—21no—
300C32×C4C2×Q1612yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4H(5,𝔽2)11yescharacteristic
303C3⋊Dic3—22no—
304C3⋊Dic3—42no—
305C3⋊Dic3—41no—
306C3×Dic3—41no—
307C3×Dic3—42no—
308C3×Dic3—41no—
309C22×Q8—92no—
310C2×Q16—91no—
311C2×Q16—92no—
312C22×C8—32no—
313C4⋊Q8—31no—
314C4⋊Q8—91no—
315C4⋊Q8—181no—
316#125—61no—
317C22⋊Q8—32no—
318C22⋊Q8—62no—
319C22⋊Q8—92no—
320C22⋊Q8—182no—
321C4×Q8—31no—
322C4×Q8—91no—
323C4×D4—61no—
324C4×D4—181no—
325C4×D4D3211yescharacteristic
326C2×C4⋊C4—32no—
327#107—91no—
328#107—92no—
329C4⋊C8—31no—
330#103—91no—
331#103—92no—
332#103—92no—
333#103—92no—
334#103—92no—
335#103—91no—
336C22⋊C8—32no—
337C4×C8—31no—
338C23×C3—22no—
339C23×C3C2×D1212yes—
340C23×C3C2×#6712yes—
341C3×Q8—61no—
342C3×Q8—61no—
343C3×Q8—241no—
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—21no—
354C2×C3×C4—22no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—242no—
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4C2×D1212yes—
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4C2×#6712yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—62no—
376C2×Dic3—64no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—82no—
382C2×Dic3—124no—
383C2×Dic3—124no—
384C2×Dic3—128no—
385Dic6—21no—
386Dic6—21no—
387Dic6—32no—
388Dic6—32no—
389Dic6—62no—
390Dic6—62no—
391Dic6—61no—
392Dic6—61no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—62no—
397Dic6—81no—
398Dic6—122no—
399Dic6—122no—
400Dic6—124no—
401Dic6—124no—
402Dic6—128no—
403C3×C8—61no—
404C3×C8—62no—
405C3×C8—61no—
406C3⋊C8—21no—
407C3⋊C8—22no—
408C3⋊C8—21no—
409C2×C32—24no—
410C2×C32#54611yescharacteristic
411C2×C32C22×Q1611yescharacteristic
412C2×C32#57711yescharacteristic
413C2×Q8—31no—
414C2×Q8—61no—
415C2×Q8—91no—
416C2×Q8—92no—
417C2×Q8—184no—
418C2×Q8—182no—
419C2×Q8—362no—
420C2×D4#62611yescharacteristic
421C22×C4—62no—
422C22×C4—182no—
423C22×C4C2×D3212yes—
424Q16—182no—
425Q16—362no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8—32no—
429C2×C8—122no—
430C4⋊C4—31no—
431C4⋊C4—32no—
432C4⋊C4—62no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—62no—
436C4⋊C4—91no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—182no—
440C4⋊C4—181no—
441C4⋊C4#62611yescharacteristic
442C22⋊C4—62no—
443C22⋊C4—182no—
444C22⋊C4#62612yes—
445C42—61no—
446C42—181no—
447C42C2×D3211yescharacteristic
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—24no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3C2×Dic1214yes—
457C22×C3C2×#21614yes—
458C22×C3C22×D1211yescharacteristic
459C22×C3C22×#6711yescharacteristic
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—41no—
469C3×C4—121no—
470C3×C4—122no—
471C3×C4—121no—
472C3×C4C2×Dic1212yes—
473C3×C4C2×#21612yes—
474C3×C4#100411yescharacteristic
475C3×C4D3×#4111yescharacteristic
476C3×C4D3×#4111yescharacteristic
477C3×C4#100911yescharacteristic
478Dic3—41no—
479Dic3—42no—
480Dic3—41no—
481Dic3—64no—
482Dic3—62no—
483Dic3—62no—
484Dic3—124no—
485Dic3—122no—
486Dic3—121no—
487Dic3—122no—
488Dic3—122no—
489Dic3—121no—
490C32#329911yescharacteristic, complemented, Sylow
491C23C2×#62612yes—
492Q8—61no—
493Q8—61no—
494Q8—92no—
495Q8—181no—
496Q8—182no—
497Q8—182no—
498Q8—241no—
499Q8—364no—
500D4#371914yescomplemented
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—62no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—182no—
509C2×C4—242no—
510C2×C4—364no—
511C2×C4C2×#62611yescharacteristic
512C2×C4C2×#62612yes—
513C2×C4C2×#62611yescharacteristic
514C2×C4C22×D3211yescharacteristic
515C8—61no—
516C8—61no—
517C8—62no—
518C2×C3—24no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—44no—
524C2×C3#555411yescharacteristic
525C2×C3C22×Dic1211yescharacteristic
526C2×C3#575111yescharacteristic
527C2×C3C22×#21611yescharacteristic
528C2×C3#582911yescharacteristic
529C2×C3#583611yescharacteristic
530C22—22no—
531C22—22no—
532C22C2×#371914yes—
533C22C22×#62611yescharacteristic
534C4—21no—
535C4—22no—
536C4—121no—
537C4—122no—
538C4—121no—
539C4—182no—
540C4—361no—
541C4—362no—
542C4C2×#371912yes—
543C4#6431211yescharacteristic
544C4#6431411yescharacteristic
545C3—21no—
546C3#7944811yescharacteristic, complemented
547C3#8364011yescharacteristic, complemented
548C2—24no—
549C2C22×#371911yescharacteristic
550C2#1059525411yescharacteristic
551C2#1059544711yescharacteristic
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. #10591190C2semidirect
5. #10591187C2semidirect
6. #10591135C2semidirect
7. C2×#63567C2semidirect
8. #10590385C2semidirect
9. C4×#3719C2semidirect
10. #10590288C2semidirect
11. #10590284C2semidirect
169. C32×D4Q16semidirect
345. C3×D4Dic12semidirect
346. C3×D4#216semidirect
490. C32#3299semidirect
500. D4#3719semidirect
546. C3#79448semidirect
547. C3#83640semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55432
C3×D4×C3⋊C82
#105911902
#105911872
#105911352
C2×#635672
#105903852
C4×#37192
#105902882
#105902842
#836403
#794483