Finite Group Databasebeta

← #11868741

Subgroups — #11868741

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592720C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591557C212yesmaximal
6#10591547C212yesmaximal, complemented
7#10590581C212yesmaximal
8#10590543C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic
10#10590285C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#82431—31nomaximal
13#81011—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×Q8×Dic3C2211yescharacteristic
18C3×D3×C4⋊C4—21no—
19C3×D3×C4⋊C4C2211yescharacteristic
20C3×#887—21no—
21C3×#887C2211yescharacteristic
22C3×C42×D3—21no—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63869C2212yes—
28#63857—21no—
29#63856—21no—
30#63844—21no—
31Dic3×Dic6—21no—
32#63841C2212yes—
33C2×#3711C2212yes—
34#63662C2212yes—
35#63634C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#835C2212yes—
38C3×#808C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63574C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63566C2212yes—
44#63565C2212yes—
45C2×C3×C4×Q8—31no—
46#5728—31no—
47C4×D3×Q8D311yescharacteristic
48#5470—31no—
49C3×#475—31no—
50#5225—32no—
51#5094—31no—
52#5022—32no—
53#5022—32no—
54#5021—31no—
55#5021—31no—
56#5021—31no—
57#5021—61no—
58#5020—31no—
59#5020D311yescharacteristic, complemented
60#4964—32no—
61#4924—31no—
62#4861—32no—
63#4857—32no—
64#4850—31no—
65#4837—31no—
66#4802—32no—
67#4796—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634—21no—
70C3×D3×Q8—22no—
71C3×D3×Q8Q814yescomplemented
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#3724—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104Dic32—22no—
105#3711—24no—
106#3078—91noSylow
107C22×C3×Q8—31no—
108C2×D3×Q8C2×D311yescharacteristic
109C3×C4⋊Q8—31no—
110C3×C4×Q8—21no—
111C3×C4×Q8—31no—
112C3×C4×Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×Q8—61no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C2×D311yescharacteristic
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—61no—
120C2×C3×C42—31no—
121C2×C3×C42—61no—
122#946—61no—
123Q8×Dic3—61no—
124Q8×Dic3C2×D311yescharacteristic
125#926—32no—
126#924—61no—
127#924—61no—
128C2×#208—32no—
129C2×ΓL(1,𝔽25)—32no—
130#897—61no—
131#892—32no—
132D3×C4⋊C4—21no—
133D3×C4⋊C4C2×D311yescharacteristic
134#890—32no—
135#887—21no—
136#887—61no—
137#887C2×D311yescharacteristic
138C42×D3—21no—
139C42×D3C2×D311yescharacteristic
140#870—32no—
141#869—31no—
142#869—31no—
143#869—61no—
144#869C2×D311yescharacteristic
145C4×Dic6—21no—
146C4×Dic6—61no—
147C4×Dic6—61no—
148C4×Dic6C2×D311yescharacteristic
149C3×#106—32no—
150C3×C4⋊C8—31no—
151C3×#103—32no—
152#835—32no—
153#835—32no—
154#835—32no—
155#835—32no—
156#835—62no—
157#835C2×D312yes—
158#818—32no—
159#816—32no—
160Dic3⋊C8—32no—
161#810—32no—
162#808—32no—
163#808—32no—
164#808C2×D312yes—
165#807—32no—
166#807—32no—
167#807—32no—
168#807—62no—
169C4⋊(C3⋊C8)—31no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—32no—
172C4⋊(C3⋊C8)—61no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8C2×Q812yes—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183#634—42no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C3×C4×D3—24no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—42no—
194C3×C4×D3C2×Q812yes—
195C3×C4×D3#4112yes—
196C3×Dic6—21no—
197C3×Dic6—24no—
198C3×Dic6—42no—
199C3×Dic6C2×Q812yes—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202#533—91no—
203C2×C4×Q8—31no—
204#479—92no—
205#479—92no—
206#477—91no—
207#477—91no—
208#475—31no—
209#475—91no—
210#428—92no—
211#423—91no—
212#419—92no—
213C2×C3×Q8—21no—
214C2×C3×Q8—34no—
215C2×C3×Q8—31no—
216C2×C3×Q8—61no—
217C2×C3×Q8—62no—
218C2×C3×Q8—61no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C22×D311yescharacteristic
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226D3×Q8—22no—
227D3×Q8Dic614yescomplemented
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3#6711yescharacteristic
231C2×C4×D3#6711yescharacteristic
232C2×C4×D3C22×D311yescharacteristic
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6C22×D311yescharacteristic
239C2×C3×C8—32no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—41no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42—31no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—41no—
260C3×C42—61no—
261C3×C42—61no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C22×D311yescharacteristic
265#217—62no—
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—121no—
276C4⋊Dic3C22×D311yescharacteristic
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—21no—
279Dic3⋊C4—21no—
280Dic3⋊C4—21no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3#6711yescharacteristic
290C4×Dic3#6711yescharacteristic
291C4×Dic3C22×D311yescharacteristic
292#208—64no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—62no—
296C2×C3⋊C8C22×D312yes—
297ΓL(1,𝔽25)—64no—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—21no—
300C2×C3×D3—21no—
301C2×C3×D3C22⋊Q812yes—
302C32×C4—22no—
303C32×C4—21no—
304C32×C4—41no—
305C32×C4#13712yes—
306C32×C4C22×Q811yescharacteristic
307C32×C4C2×#4111yescharacteristic
308C3⋊Dic3—42no—
309C3×Dic3—22no—
310C3×Dic3—21no—
311C3×Dic3—21no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3C22⋊Q812yes—
315C22×Q8—31no—
316C2×M16—92no—
317C4⋊Q8—31no—
318C4⋊Q8—91no—
319#125—92no—
320C22⋊Q8—181no—
321C22⋊Q8—181no—
322C4×Q8—31no—
323C4×Q8—31no—
324C4×Q8—31no—
325C4×Q8—61no—
326C4×Q8—61no—
327C4×Q8—181no—
328C4×Q8—181no—
329C4×Q8D3211yescharacteristic
330#117—92no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—61no—
333C2×C42—31no—
334C2×C42—61no—
335#107—92no—
336#107—92no—
337#106—32no—
338#106—92no—
339C4⋊C8—31no—
340C4⋊C8—92no—
341C4⋊C8—91no—
342#103—32no—
343#103—92no—
344#103—92no—
345#103—92no—
346C23×C3—31no—
347C22×D3C2×#6711yescharacteristic
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—22no—
351C3×Q8—32no—
352C3×Q8—41no—
353C3×Q8—64no—
354C3×Q8—61no—
355C3×Q8—122no—
356C3×Q8C2×Dic612yes—
357C3×Q8D3×Q812yes—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—31no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—31no—
369C2×C3×C4—31no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—64no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4—121no—
378C2×C3×C4—122no—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3C2×#6711yescharacteristic
392C2×Dic3C2×#6711yescharacteristic
393C2×Dic3C2×#6711yescharacteristic
394C4×D3—24no—
395C4×D3—22no—
396C4×D3—41no—
397C4×D3—42no—
398C4×D3C2×Dic612yes—
399C4×D3#23512yes—
400Dic6—21no—
401Dic6—24no—
402Dic6—42no—
403Dic6—122no—
404Dic6—122no—
405Dic6—242no—
406Dic6C2×Dic612yes—
407C3×C8—62no—
408C3⋊C8—22no—
409C3⋊C8—62no—
410C3⋊C8—62no—
411C3⋊C8—122no—
412C2×C32C2×C22⋊Q811yescharacteristic
413C2×C32C2×#13711yescharacteristic
414C2×C32#57511yescharacteristic
415C3×D3—22no—
416C2×Q8—34no—
417C2×Q8—31no—
418C2×Q8—61no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×Q8—181no—
422C2×Q8C2×D3211yescharacteristic
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—61no—
427C22×C4—61no—
428M16—184no—
429C2×C8—32no—
430C2×C8—92no—
431C4⋊C4—21no—
432C4⋊C4—32no—
433C4⋊C4—31no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—92no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—181no—
443C4⋊C4C2×D3211yescharacteristic
444C22⋊C4—182no—
445C42—21no—
446C42—31no—
447C42—31no—
448C42—31no—
449C42—61no—
450C42—61no—
451C42—61no—
452C42—182no—
453C42C2×D3211yescharacteristic
454C22×C3—21no—
455C22×C3—32no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C22×#6711yescharacteristic
460C2×D3—21no—
461C2×D3—21no—
462C2×D3#92412yes—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—32no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—61no—
476C3×C4—61no—
477C3×C4—62no—
478C3×C4—81no—
479C3×C4—121no—
480C3×C4—122no—
481C3×C4#91512yes—
482C3×C4#94212yes—
483C3×C4C22×Dic611yescharacteristic
484C3×C4C2×#23511yescharacteristic
485C3×C4C2×D3×Q811yescharacteristic
486C3×C4D3×#4111yescharacteristic
487Dic3—22no—
488Dic3—21no—
489Dic3—21no—
490Dic3—42no—
491Dic3—41no—
492Dic3—122no—
493Dic3—122no—
494Dic3—242no—
495Dic3#92412yes—
496C32#307811yescharacteristic, complemented, Sylow
497C23—31no—
498Q8—21no—
499Q8—32no—
500Q8—64no—
501Q8—61no—
502Q8—122no—
503Q8—362no—
504Q8D3×Dic612yes—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—31no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—31no—
511C2×C4—31no—
512C2×C4—64no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—121no—
518C2×C4—122no—
519C2×C4—182no—
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—62no—
524C8—182no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—62no—
529C2×C3D3×C22⋊Q811yescharacteristic
530C2×C3C2×#91511yescharacteristic
531C2×C3#577711yescharacteristic
532C2×C3C2×#92411yescharacteristic
533C2×C3C2×#94211yescharacteristic
534C2×C3#582211yescharacteristic
535D3—22no—
536C22—32no—
537C22—61no—
538C22—61no—
539C22C2×D3×#6711yescharacteristic
540C4—22no—
541C4—21no—
542C4—32no—
543C4—41no—
544C4—61no—
545C4—62no—
546C4—61no—
547C4—122no—
548C4—121no—
549C4—362no—
550C4#6394612yes—
551C4C2×D3×Dic611yescharacteristic
552C4D3×#23511yescharacteristic
553C3—21no—
554C3#8101111yescharacteristic, complemented
555C3#8243111yescharacteristic, complemented
556C2—62no—
557C2D3×#92411yescharacteristic
558C2C2×#6394611yescharacteristic
559C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592720C2semidirect
4. C3×#5020C2semidirect
6. #10591547C2semidirect
8. #10590543C2semidirect
10. #10590285C2semidirect
11. #10590283C2semidirect
59. #5020D3semidirect
71. C3×D3×Q8Q8semidirect
227. D3×Q8Dic6semidirect
496. C32#3078semidirect
554. C3#81011semidirect
555. C3#82431semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
#105938592
#105927202
C3×#50202
#105915572
#105915472
#105905812
#105905432
#105903362
#105902852
#105902832
#824313
#810113