Finite Group Databasebeta

← #11909789

Subgroups — #11909789

Order 1152.

2357 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595414C212yesmaximal, complemented
5#10595394C212yesmaximal, complemented
6#10594494C216yesmaximal, complemented
7#10594373C216yesmaximal, complemented
8#10593956C213yesmaximal, complemented
9#10593951C213yesmaximal, complemented
10#10593907C213yesmaximal, complemented
11#10593875C213yesmaximal, complemented
12#87043—31nomaximal
13#86776—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic
15C2×C3×#239C2212yes—
16C2×#3796C2216yes—
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2211yescharacteristic
19C4⋊C4×C3⋊D3C2213yes—
20#64096C2213yes—
21C42×C3⋊D3C2213yes—
22C4×#634C2213yes—
23C3×Q8×Dic3C2212yes—
24C3×#895C2216yes—
25C3×#888C2216yes—
26C3×#874C2213yes—
27C3×C4×D12C2213yes—
28C3×#869C2213yes—
29C3×C4×Dic6C2213yes—
30#63916C2216yes—
31#63916C2213yes—
32C4×#626C2216yes—
33#63898C2216yes—
34#63898C2216yes—
35Dic3×D12C2216yes—
36D3×C4⋊Dic3C2216yes—
37#63887C22112yes—
38#63884C22112yes—
39#63872C2213yes—
40#63871C2211yescharacteristic
41#63863C2213yes—
42#63863C2216yes—
43#63862C2216yes—
44#63860C2216yes—
45#63857C2216yes—
46#63855C2216yes—
47#63853C2216yes—
48C3×Q82—31no—
49C3×#550—31no—
50#5831—32no—
51#5827—32no—
52#5733—36no—
53#5730—33no—
54#5726—36no—
55#5725—33no—
56#5716—33no—
57#5713—33no—
58#5611—36no—
59#5603—36no—
60#5585—33no—
61#5580—33no—
62#5577D311yescharacteristic, complemented
63#5576—32no—
64#5574—32no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×D3×Q8—61no—
68Q8×Dic6D311yescharacteristic, complemented
69#5557—33no—
70#5543—33no—
71C2×C32×Q8C2311yescharacteristic
72Q8×C3⋊D3—24no—
73C2×C4×C3⋊D3C2313yes—
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×C4×C3⋊D3C2313yes—
76C2×#634C2313yes—
77C3×#239—28no—
78C2×C3×D12C2316yes—
79C2×C3×D12C2313yes—
80C2×C3×D12C2316yes—
81C2×C3×C4×D3C2316yes—
82C2×C3×Dic6C2311yescharacteristic
83C2×C3×Dic6C2316yes—
84C2×#626C2316yes—
85C2×D3×Dic3C23112yes—
86#3796—412no—
87C32×C4⋊C4C2313yes—
88C32×C42C2313yes—
89C4⋊(C3⋊Dic3)C2313yes—
90#3750C2316yes—
91C4×C3⋊Dic3C2313yes—
92C4×C3⋊Dic3C2313yes—
93C4×C3⋊Dic3C2313yes—
94C3×(C2×D3)⋊C4C2316yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2313yes—
98C3×Dic3⋊C4C2316yes—
99C3×C4×Dic3C2316yes—
100Dic3⋊Dic3C2316yes—
101Dic3⋊Dic3C2312yes—
102Dic3⋊Dic3C2316yes—
103#3722C2312yes—
104(C2×D3)⋊Dic3C2316yes—
105(C2×D3)⋊Dic3C2316yes—
106(C2×D3)⋊Dic3C23112yes—
107(C2×D3)⋊Dic3C2316yes—
108#3522—91noSylow
109C2×C3×#41—32no—
110C2×#239—36no—
111C2×#239C2×D312yes—
112C2×D3×Q8—31no—
113C2×D3×Q8—31no—
114C2×D3×Q8—61no—
115C2×#237—36no—
116C3×C4⋊Q8—36no—
117C3×C4⋊Q8—33no—
118C3×#127—33no—
119C3×#121—36no—
120C3×C4×Q8—21no—
121C3×C4×Q8—32no—
122C3×C4×Q8—33no—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C2×D311yescharacteristic
125C3×C4×D4—33no—
126#947—36no—
127#947—33no—
128#946—312no—
129#946—31no—
130Q8×Dic3—31no—
131Q8×Dic3—31no—
132Q8×Dic3—61no—
133Q8×Dic3C2×D312yes—
134#938—33no—
135#938—36no—
136#936—33no—
137#936—36no—
138#936—36no—
139#935—312no—
140D4×Dic3—36no—
141D4×Dic3—36no—
142D4×Dic3—36no—
143C4×#67—36no—
144#926—36no—
145C2×C4⋊Dic3—36no—
146#924—36no—
147#898—36no—
148#897—36no—
149#897—31no—
150#895—33no—
151#895—36no—
152#895C2×D316yes—
153#894—312no—
154#894—36no—
155#893—36no—
156#893—36no—
157D3×C4⋊C4—36no—
158D3×C4⋊C4—33no—
159D3×C4⋊C4—33no—
160D3×C4⋊C4—63no—
161#890—33no—
162#890—33no—
163#888C2×D316yes—
164#887—33no—
165#887—33no—
166#887—63no—
167#883—36no—
168#879—36no—
169#878—312no—
170#875—36no—
171#874C2×D313yes—
172C4×D12—36no—
173C4×D12—36no—
174C4×D12C2×D313yes—
175#872—36no—
176C42×D3—33no—
177C42×D3—33no—
178C42×D3—63no—
179#869C2×D313yes—
180C4×Dic6—33no—
181C4×Dic6—33no—
182C4×Dic6—63no—
183C4×Dic6C2×D313yes—
184C22×C3⋊D3C2411yescharacteristic
185C22×C3×D3C2416yes—
186C32×Q8#4114yescomplemented
187C2×C32×C4C2413yes—
188C2×C32×C4C2413yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3C2411yescharacteristic
191C2×C3⋊Dic3C2413yes—
192C2×C3⋊Dic3C2413yes—
193C4×C3⋊D3—26no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—26no—
196#634—26no—
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2416yes—
199C2×C3×Dic3C2412yes—
200C3×D12—212no—
201C3×D12—26no—
202C3×D12—46no—
203C3×C4×D3—212no—
204C3×Dic6—22no—
205C3×Dic6—46no—
206#626—212no—
207D3×Dic3—412no—
208#559—93no—
209Q82—31no—
210#554—93no—
211#550—31no—
212#548—92no—
213#547—96no—
214#542—96no—
215#532—93no—
216#529—93no—
217#520—92no—
218C2×C4×Q8—91no—
219C3×#41—68no—
220C2×C3×Q8—21no—
221C2×C3×Q8—31no—
222C2×C3×Q8—36no—
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×D4—33no—
226C2×C3×D4—36no—
227C2×C3×D4—36no—
228C22×C3×C4—36no—
229C2×#67—36no—
230C22×Dic3—312no—
231#239—28no—
232#239—1212no—
233D3×Q8—68no—
234D3×Q8—64no—
235D3×Q8—64no—
236#237—1212no—
237C2×D12—36no—
238C2×D12C22×D316yes—
239C2×D12C22×D313yes—
240C2×D12C22×D316yes—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—33no—
244C2×C4×D3—33no—
245C2×C4×D3—33no—
246C2×C4×D3—33no—
247C2×C4×D3—312no—
248C2×C4×D3—61no—
249C2×C4×D3—63no—
250C2×C4×D3—63no—
251C2×C4×D3C22×D316yes—
252C2×Dic6—33no—
253C2×Dic6—33no—
254C2×Dic6—63no—
255C2×Dic6C22×D311yescharacteristic
256C2×Dic6C22×D316yes—
257C3×C4⋊C4—23no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—33no—
260C3×C4⋊C4—36no—
261C3×C4⋊C4—36no—
262C3×C4⋊C4C22×D313yes—
263C3×C4⋊C4C22×D313yes—
264C3×C22⋊C4—36no—
265C3×C42—23no—
266C3×C42—36no—
267C3×C42C22×D313yes—
268C3×C42C22×D313yes—
269#217—312no—
270#217—36no—
271#217—36no—
272#217—36no—
273(C2×D3)⋊C4—36no—
274(C2×D3)⋊C4—36no—
275(C2×D3)⋊C4—36no—
276(C2×D3)⋊C4—312no—
277(C2×D3)⋊C4—32no—
278(C2×D3)⋊C4—32no—
279(C2×D3)⋊C4C22×D316yes—
280C4⋊Dic3—33no—
281C4⋊Dic3—33no—
282C4⋊Dic3—36no—
283C4⋊Dic3—36no—
284C4⋊Dic3—32no—
285C4⋊Dic3—63no—
286C4⋊Dic3C22×D313yes—
287C4⋊Dic3C22×D316yes—
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—36no—
290Dic3⋊C4—36no—
291Dic3⋊C4—32no—
292Dic3⋊C4—36no—
293Dic3⋊C4—36no—
294Dic3⋊C4—66no—
295Dic3⋊C4C22×D316yes—
296C4×Dic3—33no—
297C4×Dic3—33no—
298C4×Dic3—33no—
299C4×Dic3—33no—
300C4×Dic3—33no—
301C4×Dic3—33no—
302C4×Dic3—63no—
303C4×Dic3—63no—
304C4×Dic3—63no—
305C4×Dic3C22×D316yes—
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—21no—
308C2×C3⋊D3—21no—
309C2×C3⋊D3H(5,𝔽2)12yes—
310C2×C3×D3—26no—
311C2×C3×D3—26no—
312C2×C3×D3—26no—
313C32×C4—23no—
314C32×C4C2×#4116yes—
315C32×C42−1+412yes—
316C3⋊Dic3—23no—
317C3⋊Dic3—21no—
318C3⋊Dic3—23no—
319C3×Dic3—22no—
320C3×Dic3—26no—
321C3×Dic3—22no—
322C2×#41—32no—
323C2×#41—96no—
324C22×Q8—91no—
325C4⋊Q8—36no—
326C4⋊Q8—33no—
327#127—33no—
328#126—96no—
329#125—93no—
330#124—96no—
331#124—93no—
332#124—96no—
333#123—96no—
334#123—912no—
335C22⋊Q8—912no—
336C22⋊Q8—96no—
337C22⋊Q8—91no—
338#121—36no—
339#121—93no—
340#121—96no—
341C4×Q8—32no—
342C4×Q8—33no—
343C4×Q8—91no—
344C4×Q8—93no—
345C4×Q8—93no—
346C4×Q8D3211yescharacteristic
347C4×D4—33no—
348C4×D4—96no—
349C4×D4—96no—
350C4×D4—96no—
351C4×D4—96no—
352#117—96no—
353C2×C4⋊C4—96no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C23×C3—36no—
357C22×D3—31no—
358C22×D3—31no—
359C22×D3—61no—
360C22×D3C23×D316yes—
361C3×Q8—24no—
362C3×Q8—62no—
363C3×Q8—126no—
364C3×Q8#23714yescomplemented
365C3×Q8#23914yescomplemented
366C3×D4—612no—
367C3×D4—66no—
368C3×D4—126no—
369C2×C3×C4—21no—
370C2×C3×C4—23no—
371C2×C3×C4—23no—
372C2×C3×C4—32no—
373C2×C3×C4—36no—
374C2×C3×C4—32no—
375C2×C3×C4—612no—
376C2×C3×C4C23×D313yes—
377C2×C3×C4C23×D313yes—
378C2×C3×C4C23×D313yes—
379C2×C3×C4C23×D313yes—
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—612no—
383C2×Dic3—31no—
384C2×Dic3—31no—
385C2×Dic3—33no—
386C2×Dic3—33no—
387C2×Dic3—33no—
388C2×Dic3—33no—
389C2×Dic3—61no—
390C2×Dic3—63no—
391C2×Dic3—63no—
392C2×Dic3—1212no—
393C2×Dic3C23×D312yes—
394C2×Dic3C23×D316yes—
395C2×Dic3C23×D312yes—
396D12—212no—
397D12—26no—
398D12—46no—
399D12—612no—
400C4×D3—212no—
401C4×D3—66no—
402C4×D3—66no—
403C4×D3—64no—
404C4×D3—612no—
405C4×D3—66no—
406C4×D3—66no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—126no—
410C4×D3—1212no—
411Dic6—22no—
412Dic6—46no—
413Dic6—612no—
414Dic6—66no—
415Dic6—66no—
416C2×C32C22×#4111yescharacteristic
417C2×C32C2×H(5,𝔽2)11yescharacteristic
418C2×C32C2×2−1+411yescharacteristic
419C3⋊D3—22no—
420C3×D3—46no—
421#41—68no—
422#41—3612no—
423C2×Q8—31no—
424C2×Q8—36no—
425C2×Q8—93no—
426C2×Q8—184no—
427C2×Q8C2×D3211yescharacteristic
428C2×D4—33no—
429C2×D4—36no—
430C2×D4—36no—
431C2×D4—96no—
432C22×C4—36no—
433C22×C4—912no—
434C22×C4—91no—
435C22×C4—93no—
436C22×C4—93no—
437C4⋊C4—36no—
438C4⋊C4—31no—
439C4⋊C4—33no—
440C4⋊C4—36no—
441C4⋊C4—96no—
442C4⋊C4—92no—
443C4⋊C4—96no—
444C4⋊C4—93no—
445C4⋊C4—96no—
446C4⋊C4C2×D3213yes—
447C22⋊C4—36no—
448C22⋊C4—92no—
449C22⋊C4—96no—
450C22⋊C4—96no—
451C22⋊C4—912no—
452C22⋊C4—96no—
453C42—36no—
454C42—93no—
455C42—93no—
456C42—93no—
457C42C2×D3213yes—
458C22×C3—21no—
459C22×C3—66no—
460C22×C3—66no—
461C22×C3—66no—
462C22×C3C24×D311yescharacteristic
463C22×C3C24×D311yescharacteristic
464C2×D3—26no—
465C2×D3—26no—
466C2×D3—26no—
467C2×D3—32no—
468C2×D3—32no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—61no—
473C2×D3—61no—
474C2×D3—61no—
475C2×D3—61no—
476C3×C4—23no—
477C3×C4—23no—
478C3×C4—26no—
479C3×C4—22no—
480C3×C4—43no—
481C3×C4—62no—
482C3×C4—62no—
483C3×C4—66no—
484C3×C4C2×#23716yes—
485C3×C4C2×#23916yes—
486C3×C4#100712yes—
487C3×C4#101012yes—
488Dic3—22no—
489Dic3—22no—
490Dic3—26no—
491Dic3—66no—
492Dic3—62no—
493Dic3—63no—
494Dic3—63no—
495Dic3—61no—
496Dic3—61no—
497Dic3—63no—
498Dic3—63no—
499Dic3—123no—
500C32#352211yescharacteristic, complemented, Sylow
501C23—36no—
502C23—91no—
503Q8—62no—
504Q8—126no—
505Q8—186no—
506Q8#379614yescomplemented
507D4—612no—
508D4—66no—
509D4—126no—
510D4—1812no—
511C2×C4—32no—
512C2×C4—36no—
513C2×C4—32no—
514C2×C4—612no—
515C2×C4—91no—
516C2×C4—93no—
517C2×C4—93no—
518C2×C4—186no—
519C2×C4—186no—
520C2×C4—182no—
521C2×C4—3612no—
522C2×C4C22×D3213yes—
523C2×C4C22×D3213yes—
524C2×C4C22×D3211yescharacteristic
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—126no—
529C2×C3C22×#23711yescharacteristic
530C2×C3C22×#23911yescharacteristic
531C2×C3C2×#100711yescharacteristic
532C2×C3C2×#101011yescharacteristic
533C2×C3D3×H(5,𝔽2)11yescharacteristic
534C2×C3D3×H(5,𝔽2)11yescharacteristic
535D3—46no—
536D3—64no—
537D3—62no—
538D3—62no—
539C22—66no—
540C22—66no—
541C22—66no—
542C22—92no—
543C22—181no—
544C22—181no—
545C22C23×D3211yescharacteristic
546C4—23no—
547C4—62no—
548C4—62no—
549C4—66no—
550C4—183no—
551C4—181no—
552C4—183no—
553C4C2×#379616yes—
554C4#6431512yes—
555C3—21no—
556C3#8677611yescharacteristic, complemented
557C3#8704311yescharacteristic, complemented
558C2—126no—
559C2—182no—
560C2C22×#379611yescharacteristic
561C2C2×#6431511yescharacteristic
562C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5577C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595414C2semidirect
5. #10595394C2semidirect
6. #10594494C2semidirect
7. #10594373C2semidirect
8. #10593956C2semidirect
9. #10593951C2semidirect
10. #10593907C2semidirect
11. #10593875C2semidirect
62. #5577D3semidirect
68. Q8×Dic6D3semidirect
186. C32×Q8#41semidirect
364. C3×Q8#237semidirect
365. C3×Q8#239semidirect
500. C32#3522semidirect
506. Q8#3796semidirect
556. C3#86776semidirect
557. C3#87043semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55772
C3×Q8×Dic62
#105954142
#105953942
#105944942
#105943732
#105939562
#105939512
#105939072
#105938752
#870433
#867763