Finite Group Databasebeta

← #11906006

Subgroups — #11906006

Order 1152.

4428 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×#64364C211yesmaximal, characteristic, complemented
3C32×#536C211yesmaximal, characteristic, complemented
4#10596303C211yesmaximal, characteristic, complemented
5C2×#64153C211yesmaximal, characteristic, complemented
6#10596195C212yesmaximal, complemented
7C3⋊D3×C4⋊Q8C212yesmaximal, complemented
8#10596146C212yesmaximal, complemented
9#10596139C212yesmaximal, complemented
10#10596126C218yesmaximal, complemented
11#10596103C214yesmaximal, complemented
12#10596102C214yesmaximal, complemented
13#10595997C211yesmaximal, characteristic, complemented
14#10595993C211yesmaximal, characteristic, complemented
15#86340—34nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×C32×Q8C2211yescharacteristic
18#64367—28no—
19#64364—28no—
20C2×#3832C2212yes—
21C2×#3832C2212yes—
22C2×Q8×C3⋊D3C2212yes—
23C2×Q8×C3⋊D3C2212yes—
24C2×Q8×C3⋊D3C2212yes—
25C2×#3830C2214yes—
26C2×#3830C2212yes—
27C2×#3828C2212yes—
28C2×#3828C2214yes—
29C2×#3828C2211yescharacteristic
30C2×#3828C2211yescharacteristic
31C22×#634C2212yes—
32C22×#634C2211yescharacteristic
33C32×C4⋊Q8C2212yes—
34C32×#124C2212yes—
35C32×#123C2214yes—
36C32×C22⋊Q8C2214yes—
37C32×#117C2211yescharacteristic
38#64156C2211yescharacteristic
39#64153C2214yes—
40#64153C2212yes—
41#64153C2212yes—
42#64153C2211yescharacteristic
43#64149C2211yescharacteristic
44#64148C2214yes—
45#64145C2211yescharacteristic
46C4×#638C2214yes—
47C2×#3750C2214yes—
48C2×C4×C3⋊Dic3C2211yescharacteristic
49#64106C2214yes—
50#64105C2218yes—
51#64103C2218yes—
52#64102C2212yes—
53C4⋊C4×C3⋊D3C2218yes—
54#64097C2218yes—
55#64096C2212yes—
56#64095C2214yes—
57#64093C2218yes—
58#64092C2218yes—
59#64090C2218yes—
60#64090C2214yes—
61#64087C2218yes—
62#64084C2212yes—
63#64081C2212yes—
64C42×C3⋊D3C2212yes—
65#64078C2212yes—
66C2×#1010—34no—
67C2×#1007—34no—
68C3×#536D314yescomplemented
69#5832—34no—
70C2×#944—34no—
71#5724—38no—
72D3×C4⋊Q8—38no—
73#5675—38no—
74#5668—38no—
75#5655—332no—
76#5632—316no—
77#5631—316no—
78#5526—34no—
79#5522—34no—
80C32×#41—24no—
81C2×C32×Q8—24no—
82C2×C32×Q8C2311yescharacteristic
83C2×C32×Q8C2312yes—
84C2×C32×Q8C2312yes—
85C2×C32×D4C2311yescharacteristic
86C2×C32×D4C2312yes—
87C22×C32×C4C2312yes—
88C22×C32×C4C2312yes—
89C22×C32×C4C2311yescharacteristic
90C2×#638C2314yes—
91C2×#638C2314yes—
92C2×#638C2312yes—
93C2×#638C2312yes—
94C22×C3⋊Dic3C2314yes—
95C22×C3⋊Dic3C2312yes—
96C22×C3⋊Dic3C2312yes—
97#3832—28no—
98#3832—28no—
99Q8×C3⋊D3—28no—
100Q8×C3⋊D3—28no—
101Q8×C3⋊D3—28no—
102#3830—216no—
103#3830—28no—
104#3828—24no—
105#3828—216no—
106#3828—28no—
107#3828D418yescomplemented
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4⋊(C3⋊D3)C2314yes—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2314yes—
112C2×C4×C3⋊D3C2314yes—
113C2×C4×C3⋊D3C2314yes—
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2312yes—
117C2×#634—24no—
118C2×#634—28no—
119C2×#634C2311yescharacteristic
120C2×#634C2312yes—
121C2×#634C2314yes—
122C2×#634C2314yes—
123C2×#634C2312yes—
124C2×#634C2311yescharacteristic
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2318yes—
127C32×C22⋊C4C2318yes—
128C32×C22⋊C4C2312yes—
129C32×C42C2312yes—
130#3757C2314yes—
131#3752C2314yes—
132#3752C2318yes—
133#3752C2314yes—
134C4⋊(C3⋊Dic3)C2318yes—
135#3750C2314yes—
136#3750C2318yes—
137#3750C2318yes—
138#3750C2314yes—
139C4×C3⋊Dic3C2311yescharacteristic
140C4×C3⋊Dic3C2314yes—
141C4×C3⋊Dic3C2311yescharacteristic
142C4×C3⋊Dic3C2312yes—
143#3499—91noSylow
144C2×C3×#41C2×D314yes—
145C22×C3×Q8C2×D314yes—
146#1010—632no—
147#1007—632no—
148C2×#239—38no—
149C2×#239—38no—
150C2×D3×Q8—38no—
151C2×D3×Q8—38no—
152C2×D3×Q8—38no—
153C2×#237—316no—
154C2×#237—38no—
155C2×#235—34no—
156C2×#235—316no—
157C2×#235—34no—
158C2×#235—38no—
159C22×Dic6—38no—
160C22×Dic6—34no—
161C3×C4⋊Q8C2×D318yes—
162C3×#124C2×D318yes—
163C3×#123C2×D3116yes—
164C3×C22⋊Q8C2×D3116yes—
165C3×#117C2×D314yes—
166#947—34no—
167#944—316no—
168#944—38no—
169#944—38no—
170#944—34no—
171#940—34no—
172#939—316no—
173#936—34no—
174C4×#67—316no—
175C2×Dic3⋊C4—316no—
176C2×C4×Dic3—34no—
177#897—316no—
178#896—332no—
179#894—332no—
180#893—38no—
181D3×C4⋊C4—332no—
182#888—332no—
183#887—38no—
184#886—316no—
185#884—332no—
186#883—332no—
187#67⋊C4—332no—
188#67⋊C4—316no—
189#878—332no—
190#875—38no—
191#872—38no—
192C42×D3—38no—
193#869—38no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3⋊D3C2412yes—
197C22×C3⋊D3C2412yes—
198C32×Q8—22no—
199C32×Q8—24no—
200C32×Q8—24no—
201C32×D4—24no—
202C32×D4—22no—
203C2×C32×C4—24no—
204C2×C32×C4—24no—
205C2×C32×C4C2×D414yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2414yes—
208C2×C32×C4C2412yes—
209C2×C32×C4C2411yescharacteristic
210C2×C32×C4C2411yescharacteristic
211#638—24no—
212#638—28no—
213#638—28no—
214#638C2×D418yes—
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3—28no—
217C2×C3⋊Dic3—24no—
218C2×C3⋊Dic3C2412yes—
219C2×C3⋊Dic3C2414yes—
220C2×C3⋊Dic3C2412yes—
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2412yes—
223C4⋊(C3⋊D3)—28no—
224C4⋊(C3⋊D3)—22no—
225C4⋊(C3⋊D3)C2×D414yes—
226C4×C3⋊D3—28no—
227C4×C3⋊D3—28no—
228C4×C3⋊D3—24no—
229C4×C3⋊D3—28no—
230C4×C3⋊D3—28no—
231C4×C3⋊D3C2×D418yes—
232#634—24no—
233#634—24no—
234#634—22no—
235#634—28no—
236#634—28no—
237#634C2×D414yes—
238C2×2−1+4—91no—
239C2×2−1+4—91no—
240D4×Q8—94no—
241#547—98no—
242#547—94no—
243#536—92no—
244#536—92no—
245#536—91no—
246#536C3⋊D311yescharacteristic, complemented
247#532—91no—
248#532—92no—
249C2×C4⋊Q8—91no—
250C2×C4⋊Q8—92no—
251C4×#41—91no—
252C3×#41—216no—
253C2×C3×Q8—216no—
254C2×C3×Q8C22×D318yes—
255C2×C3×Q8C22×D318yes—
256C2×C3×Q8C22×D314yes—
257C2×C3×D4C22×D314yes—
258C2×C3×D4C22×D318yes—
259C22×C3×C4C22×D318yes—
260C22×C3×C4C22×D318yes—
261C22×C3×C4C22×D314yes—
262C2×#67—38no—
263C2×#67—316no—
264C2×#67—316no—
265C2×#67—38no—
266C22×Dic3—316no—
267C22×Dic3—38no—
268C22×Dic3—38no—
269#239—632no—
270#239—632no—
271D3×Q8—632no—
272D3×Q8—632no—
273D3×Q8—632no—
274#237—632no—
275#237—664no—
276#235—332no—
277#235—632no—
278#235—664no—
279#235—616no—
280C2×D12—34no—
281C2×D12—34no—
282C2×D12—316no—
283C2×C4×D3—38no—
284C2×C4×D3—316no—
285C2×C4×D3—316no—
286C2×C4×D3—316no—
287C2×C4×D3—316no—
288C2×C4×D3—38no—
289C2×Dic6—34no—
290C2×Dic6—34no—
291C2×Dic6—38no—
292C2×Dic6—316no—
293C2×Dic6—316no—
294C2×Dic6—38no—
295C2×Dic6—632no—
296C2×Dic6—616no—
297C3×C4⋊C4C22×D318yes—
298C3×C4⋊C4C22×D3132yes—
299C3×C22⋊C4C22×D3132yes—
300C3×C22⋊C4C22×D318yes—
301C3×C42C22×D318yes—
302#217—316no—
303(C2×D3)⋊C4—316no—
304(C2×D3)⋊C4—332no—
305(C2×D3)⋊C4—316no—
306C4⋊Dic3—332no—
307Dic3⋊C4—316no—
308Dic3⋊C4—332no—
309Dic3⋊C4—332no—
310Dic3⋊C4—316no—
311C4×Dic3—34no—
312C4×Dic3—316no—
313C4×Dic3—34no—
314C4×Dic3—38no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—24no—
318C22×C32C22×D412yes—
319C22×C32C2511yescharacteristic
320C2×C3⋊D3—24no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—24no—
323C2×C3⋊D3C22×D414yes—
324C32×C4—22no—
325C32×C4—24no—
326C32×C4—24no—
327C32×C4C22×D412yes—
328C32×C4C22×D412yes—
329C3⋊Dic3—22no—
330C3⋊Dic3—24no—
331C3⋊Dic3—22no—
332C3⋊Dic3C22×D414yes—
333C3⋊Dic32−1+414yescomplemented
3342−1+4—188no—
3352−1+4—188no—
336C2×#41—92no—
337C2×#41—92no—
338C2×#41—92no—
339C2×#41—94no—
340C2×#41—91no—
341C2×#41—91no—
342C2×#41—92no—
343C2×#41—94no—
344C2×#41C2×C3⋊D311yescharacteristic
345C22×Q8—92no—
346C22×Q8—92no—
347C22×Q8—92no—
348C22×Q8—91no—
349C22×Q8—92no—
350C22×Q8C2×C3⋊D311yescharacteristic
351C4⋊Q8—91no—
352C4⋊Q8—92no—
353C4⋊Q8—92no—
354C4⋊Q8—94no—
355C4⋊Q8—98no—
356C4⋊Q8—92no—
357C4⋊Q8C2×C3⋊D312yes—
358#127—91no—
359#124—91no—
360#124—91no—
361#124—92no—
362#124C2×C3⋊D312yes—
363#123—98no—
364#123—98no—
365#123—94no—
366#123C2×C3⋊D314yes—
367C22⋊Q8—98no—
368C22⋊Q8—94no—
369C22⋊Q8—98no—
370C22⋊Q8C2×C3⋊D314yes—
371#121—94no—
372#121—98no—
373C4×Q8—92no—
374C4×D4—94no—
375C4×D4—92no—
376C4×D4—94no—
377C4×D4—98no—
378#117—92no—
379#117C2×C3⋊D311yescharacteristic
380C2×C4⋊C4—94no—
381C2×C4⋊C4—98no—
382C2×C42—91no—
383C2×C42—92no—
384C23×C3C23×D318yes—
385C23×C3C23×D314yes—
386C22×D3—38no—
387C22×D3—38no—
388C3×Q8—28no—
389C3×Q8—216no—
390C3×Q8—216no—
391C3×D4—216no—
392C3×D4—28no—
393C2×C3×C4—216no—
394C2×C3×C4—216no—
395C2×C3×C4D3×D4116yes—
396C2×C3×C4C23×D3116yes—
397C2×C3×C4C23×D3116yes—
398C2×C3×C4C23×D318yes—
399C2×C3×C4C23×D314yes—
400C2×C3×C4C23×D314yes—
401#67—332no—
402#67—632no—
403#67—632no—
404#67—616no—
405C2×Dic3—38no—
406C2×Dic3—38no—
407C2×Dic3—38no—
408C2×Dic3—316no—
409C2×Dic3—38no—
410C2×Dic3—632no—
411C2×Dic3—616no—
412C2×Dic3—616no—
413D12—316no—
414D12—632no—
415D12—68no—
416C4×D3—332no—
417C4×D3—632no—
418C4×D3—632no—
419C4×D3—632no—
420C4×D3—632no—
421C4×D3—616no—
422Dic6—316no—
423Dic6—632no—
424Dic6—632no—
425Dic6—616no—
426Dic6—616no—
427Dic6—68no—
428C2×C32—22no—
429C2×C32—42no—
430C2×C32C23×D411yescharacteristic
431C2×C32C2×2−1+412yes—
432C3⋊D3—24no—
433C3⋊D3—42no—
434#41—24no—
435#41—98no—
436#41—1816no—
437#41—188no—
438#41—188no—
439#41—188no—
440#41—1816no—
441#41—188no—
442#41—184no—
443C2×Q8—24no—
444C2×Q8—91no—
445C2×Q8—94no—
446C2×Q8—94no—
447C2×Q8—92no—
448C2×Q8—91no—
449C2×Q8—92no—
450C2×Q8—188no—
451C2×Q8—188no—
452C2×Q8—188no—
453C2×Q8—188no—
454C2×Q8—184no—
455C2×Q8C22×C3⋊D312yes—
456C2×Q8C22×C3⋊D311yescharacteristic
457C2×Q8C22×C3⋊D312yes—
458C2×D4—92no—
459C2×D4—94no—
460C2×D4—94no—
461C2×D4—92no—
462C2×D4—91no—
463C2×D4—94no—
464C2×D4—91no—
465C2×D4C22×C3⋊D312yes—
466C2×D4C22×C3⋊D311yescharacteristic
467C22×C4—92no—
468C22×C4—92no—
469C22×C4—92no—
470C22×C4—94no—
471C22×C4—94no—
472C22×C4—94no—
473C22×C4—94no—
474C22×C4—94no—
475C22×C4—92no—
476C22×C4C22×C3⋊D312yes—
477C22×C4C22×C3⋊D312yes—
478C22×C4C22×C3⋊D311yescharacteristic
479C4⋊C4—94no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—94no—
484C4⋊C4C22×C3⋊D318yes—
485C4⋊C4C22×C3⋊D312yes—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—98no—
490C22⋊C4C22×C3⋊D312yes—
491C22⋊C4C22×C3⋊D318yes—
492C42—91no—
493C42—91no—
494C42—94no—
495C42—92no—
496C42C22×C3⋊D312yes—
497C22×C3—28no—
498C22×C3—28no—
499C22×C3—216no—
500C22×C3C2×D3×D418yes—
501C22×C3C24×D314yes—
502C2×D3—316no—
503C2×D3—616no—
504C2×D3—68no—
505C2×D3—616no—
506C3×C4—28no—
507C3×C4—216no—
508C3×C4—216no—
509C3×C4C2×D3×D418yes—
510C3×C4C2×D3×D418yes—
511Dic3—316no—
512Dic3—316no—
513Dic3—68no—
514Dic3—616no—
515Dic3—68no—
516C32#349911yescharacteristic, complemented, Sylow
517C23—92no—
518C23—92no—
519C23C23×C3⋊D312yes—
520C23C23×C3⋊D311yescharacteristic
521Q8—24no—
522Q8—24no—
523Q8—22no—
524Q8—94no—
525Q8—188no—
526Q8—188no—
527Q8—184no—
528Q8—182no—
529Q8—184no—
530D4—24no—
531D4—22no—
532D4—98no—
533D4—94no—
534D4—188no—
535D4—188no—
536D4—188no—
537D4—184no—
538D4—182no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—98no—
544C2×C4—92no—
545C2×C4—92no—
546C2×C4—94no—
547C2×C4—188no—
548C2×C4—188no—
549C2×C4—188no—
550C2×C4—188no—
551C2×C4—188no—
552C2×C4—184no—
553C2×C4—184no—
554C2×C4—184no—
555C2×C4D4×C3⋊D314yes—
556C2×C4C23×C3⋊D314yes—
557C2×C4C23×C3⋊D312yes—
558C2×C4C23×C3⋊D314yes—
559C2×C4C23×C3⋊D311yescharacteristic
560C2×C4C23×C3⋊D311yescharacteristic
561C2×C3—28no—
562C2×C3—48no—
563C2×C3C22×D3×D414yes—
564C2×C3D3×2−1+418yes—
565D3—616no—
566D3—128no—
567C22—22no—
568C22—22no—
569C22—24no—
570C22—94no—
571C22—184no—
572C22—182no—
573C22—184no—
574C22C2×D4×C3⋊D312yes—
575C22C24×C3⋊D311yescharacteristic
576C4—22no—
577C4—24no—
578C4—24no—
579C4—94no—
580C4—94no—
581C4—182no—
582C4—184no—
583C4—182no—
584C4C2×D4×C3⋊D312yes—
585C4C2×D4×C3⋊D312yes—
586C3#8634014yescomplemented
587C2—22no—
588C2—42no—
589C2—184no—
590C2—362no—
591C2C22×D4×C3⋊D311yescharacteristic
592C2C3⋊D3×2−1+412yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#536C2
hypercenter#536C3⋊D3
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×#64364C2semidirect
3. C32×#536C2semidirect
4. #10596303C2semidirect
5. C2×#64153C2semidirect
6. #10596195C2semidirect
7. C3⋊D3×C4⋊Q8C2semidirect
8. #10596146C2semidirect
9. #10596139C2semidirect
10. #10596126C2semidirect
11. #10596103C2semidirect
12. #10596102C2semidirect
13. #10595997C2semidirect
14. #10595993C2semidirect
68. C3×#536D3semidirect
107. #3828D4semidirect
246. #536C3⋊D3semidirect
333. C3⋊Dic32−1+4semidirect
516. C32#3499semidirect
586. C3#86340semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×#643642
C32×#5362
#105963032
C2×#641532
#105961952
C3⋊D3×C4⋊Q82
#105961462
#105961392
#105961262
#105961032
#105961022
#105959972
#105959932
#863403