Finite Group Databasebeta

← #11903793

Subgroups — #11903793

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595422C212yesmaximal, complemented
5#10595386C212yesmaximal
6#10594470C216yesmaximal, complemented
7#10594448C216yesmaximal, complemented
8#10593958C213yesmaximal, complemented
9#10593903C213yesmaximal, complemented
10C4×#3797C213yesmaximal, complemented
11#10593866C213yesmaximal, complemented
12Q8×#239—31nomaximal
13#87015—31nomaximal
14C2×#3832C2211yescharacteristic
15C2×#3797C2213yes—
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18#64102C2213yes—
19#64101C2213yes—
20C4×C4⋊(C3⋊D3)C2213yes—
21C42×C3⋊D3C2213yes—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×#890C2216yes—
25C3×#888C2216yes—
26C3×#869C2213yes—
27C3×#869C2213yes—
28C3×C4×Dic6C2213yes—
29C3×C4×Dic6C2213yes—
30#63918C2216yes—
31C4×#627C2216yes—
32#63900C2213yes—
33#63895C22112yes—
34#63894C2216yes—
35#63894C2216yes—
36#63888C22112yes—
37#63883C2216yes—
38C4×#624C2216yes—
39#63872C2216yes—
40#63871C2216yes—
41#63871C2216yes—
42#63869C2216yes—
43#63849C2216yes—
44#63843C2213yes—
45#63843C2216yes—
46#63843C2211yescharacteristic
47#63838C2216yes—
48C3×Q82—31no—
49C3×#557—31no—
50#5730—36no—
51#5730—33no—
52#5728—36no—
53#5728—33no—
54#5728—33no—
55#5727—33no—
56#5690—36no—
57#5688—36no—
58#5579—33no—
59Q8×D12—33no—
60C4×#239—31no—
61C4×#239—31no—
62C4×#239—32no—
63C4×#239—32no—
64C4×#239—61no—
65C4×D3×Q8—33no—
66C4×D3×Q8—33no—
67#5570—32no—
68#5570D311yescharacteristic, complemented
69#5569—32no—
70Q8×Dic6D311yescharacteristic, complemented
71C2×C32×Q8C2311yescharacteristic
72#3832Q818yescomplemented
73C2×C4⋊(C3⋊D3)C2313yes—
74C2×C4×C3⋊D3C2313yes—
75C2×C4×C3⋊D3C2313yes—
76C2×C4×C3⋊D3C2313yes—
77C2×C3×Dic6C2313yes—
78C2×C3×Dic6C2316yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×#627C2316yes—
81C2×#624C2316yes—
82C2×#624C2316yes—
83#3797—212no—
84C32×C4⋊C4C2313yes—
85C32×C42C2313yes—
86#3752C2316yes—
87C4⋊(C3⋊Dic3)C2313yes—
88C4×C3⋊Dic3C2311yescharacteristic
89C4×C3⋊Dic3C2313yes—
90C4×C3⋊Dic3C2313yes—
91C3×C4⋊Dic3C2316yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2316yes—
94C3×C4⋊Dic3C2313yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4C2316yes—
97C3×Dic3⋊C4C2316yes—
98C3×C4×Dic3C2316yes—
99C3×C4×Dic3C2316yes—
100#3724C2316yes—
101Dic3⋊Dic3C23112yes—
102Dic3⋊Dic3C2316yes—
103Dic3⋊Dic3C2312yes—
104#3722C23112yes—
105Dic32C2312yes—
106Dic32C2316yes—
107Q8×#41—91noSylow
108C2×#239—31no—
109C2×#239—31no—
110C2×#239—61no—
111C2×D3×Q8—33no—
112C2×D3×Q8—33no—
113C3×C4⋊Q8—36no—
114C3×C4⋊Q8—33no—
115C3×C4⋊Q8—33no—
116C3×#125—36no—
117C3×C4×Q8—21no—
118C3×C4×Q8—32no—
119C3×C4×Q8—32no—
120C3×C4×Q8—33no—
121C3×C4×Q8—33no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C2×D311yescharacteristic
124#946—36no—
125#946—36no—
126#946—312no—
127Q8×Dic3—31no—
128Q8×Dic3—31no—
129Q8×Dic3—36no—
130Q8×Dic3—33no—
131Q8×Dic3—31no—
132Q8×Dic3—61no—
133Q8×Dic3C2×D312yes—
134Q8×Dic3C2×D312yes—
135#897—36no—
136#897—36no—
137#897—312no—
138#896—312no—
139#896—312no—
140#893—33no—
141#893—33no—
142#893—36no—
143#893—36no—
144#893—63no—
145#892—33no—
146#892—33no—
147#892—36no—
148#892—36no—
149#892—63no—
150D3×C4⋊C4—33no—
151D3×C4⋊C4—33no—
152D3×C4⋊C4—36no—
153D3×C4⋊C4—36no—
154#890—36no—
155#890—36no—
156#890—36no—
157#890C2×D316yes—
158#888—36no—
159#888C2×D316yes—
160#887—36no—
161#887—33no—
162#887—31no—
163#887—36no—
164#887—36no—
165C4×D12—33no—
166C4×D12—33no—
167C4×D12—36no—
168C4×D12—36no—
169C4×D12—63no—
170C42×D3—33no—
171C42×D3—33no—
172C42×D3—36no—
173C42×D3—36no—
174C42×D3—63no—
175#870—36no—
176#869—36no—
177#869C2×D313yes—
178#869C2×D313yes—
179C4×Dic6—36no—
180C4×Dic6—36no—
181C4×Dic6C2×D313yes—
182C4×Dic6C2×D313yes—
183C22×C3⋊D3C2413yes—
184C32×Q8C2×Q814yescomplemented
185C2×C32×C4C2413yes—
186C2×C32×C4C2413yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3C2411yescharacteristic
189C2×C3⋊Dic3C2413yes—
190C2×C3⋊Dic3C2411yescharacteristic
191C4⋊(C3⋊D3)C2×Q8112yescomplemented
192C4×C3⋊D3—26no—
193C4×C3⋊D3—43no—
194C4×C3⋊D3C2×Q8112yescomplemented
195C2×C3×Dic3C2416yes—
196C2×C3×Dic3C2416yes—
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2412yes—
199C3×Dic6—26no—
200C3×Dic6—46no—
201C3×Dic6#4114yescomplemented
202#627—212no—
203#624—212no—
204#624—46no—
205Q82—31no—
206#557—31no—
207#557—92no—
208#554—93no—
209#554—96no—
210D4×Q8—93no—
211#533—96no—
212#533—93no—
213C4×#41—92no—
214C4×#41—91no—
215C2×C4×Q8—93no—
216C2×C3×Q8—21no—
217C2×C3×Q8—31no—
218C2×C3×Q8—33no—
219C2×C3×Q8—36no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C22×D311yescharacteristic
222#239—38no—
223#239—38no—
224#239—68no—
225D3×Q8—612no—
226D3×Q8—612no—
227C2×D12—33no—
228C2×D12—33no—
229C2×D12—63no—
230C2×C4×D3—33no—
231C2×C4×D3—33no—
232C2×C4×D3—33no—
233C2×C4×D3—33no—
234C2×C4×D3—36no—
235C2×C4×D3—36no—
236C2×C4×D3—33no—
237C2×C4×D3—33no—
238C2×C4×D3—36no—
239C2×C4×D3—36no—
240C2×C4×D3—63no—
241C2×C4×D3—63no—
242C2×C4×D3—63no—
243C2×Dic6—36no—
244C2×Dic6—36no—
245C2×Dic6C22×D313yes—
246C2×Dic6C22×D316yes—
247C2×Dic6C22×D311yescharacteristic
248C3×C4⋊C4—23no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—36no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4—33no—
253C3×C4⋊C4—36no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4—36no—
256C3×C4⋊C4C22×D313yes—
257C3×C4⋊C4C22×D313yes—
258C3×C42—23no—
259C3×C42—36no—
260C3×C42—36no—
261C3×C42C22×D313yes—
262C3×C42C22×D313yes—
263(C2×D3)⋊C4—36no—
264(C2×D3)⋊C4—36no—
265(C2×D3)⋊C4—312no—
266(C2×D3)⋊C4—312no—
267(C2×D3)⋊C4—66no—
268C4⋊Dic3—33no—
269C4⋊Dic3—33no—
270C4⋊Dic3—32no—
271C4⋊Dic3—36no—
272C4⋊Dic3—312no—
273C4⋊Dic3—63no—
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D313yes—
276C4⋊Dic3C22×D316yes—
277C4⋊Dic3C22×D316yes—
278C4⋊Dic3C22×D316yes—
279Dic3⋊C4—32no—
280Dic3⋊C4—36no—
281Dic3⋊C4—36no—
282Dic3⋊C4—36no—
283Dic3⋊C4—312no—
284Dic3⋊C4C22×D316yes—
285Dic3⋊C4C22×D316yes—
286C4×Dic3—33no—
287C4×Dic3—33no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—33no—
291C4×Dic3—33no—
292C4×Dic3—32no—
293C4×Dic3—32no—
294C4×Dic3—36no—
295C4×Dic3—36no—
296C4×Dic3—61no—
297C4×Dic3—63no—
298C4×Dic3—63no—
299C4×Dic3C22×D316yes—
300C4×Dic3C22×D316yes—
301C22×C32C2511yescharacteristic
302C2×C3⋊D3—23no—
303C2×C3⋊D3—23no—
304C2×C3⋊D3C22×Q816yes—
305C32×C4—23no—
306C32×C4C22×Q816yes—
307C32×C4C2×#4112yes—
308C3⋊Dic3—21no—
309C3⋊Dic3—23no—
310C3⋊Dic3C22×Q812yes—
311C3×Dic3—26no—
312C3×Dic3—22no—
313C3×Dic3—26no—
314C3×Dic3C2×#4114yes—
315C2×#41—91no—
316C22×Q8—93no—
317C4⋊Q8—36no—
318C4⋊Q8—33no—
319C4⋊Q8—33no—
320C4⋊Q8—96no—
321#125—36no—
322#125—96no—
323#125—96no—
324C22⋊Q8—912no—
325C22⋊Q8—96no—
326C22⋊Q8—912no—
327C22⋊Q8—96no—
328C4×Q8—32no—
329C4×Q8—32no—
330C4×Q8—33no—
331C4×Q8—33no—
332C4×Q8—96no—
333C4×Q8—96no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—96no—
337C4×Q8—91no—
338C4×Q8D3211yescharacteristic
339C4×D4—96no—
340C4×D4—96no—
341C4×D4—93no—
342C4×D4—93no—
343#117—96no—
344#117—93no—
345C2×C4⋊C4—93no—
346C2×C4⋊C4—96no—
347C2×C42—96no—
348C2×C42—93no—
349C22×D3—33no—
350C22×D3—33no—
351C22×D3—63no—
352C3×Q8—24no—
353C3×Q8—34no—
354C3×Q8—66no—
355C3×Q8—126no—
356C3×Q8D3×Q814yescomplemented
357C3×Q8D3×Q814yescomplemented
358C2×C3×C4—23no—
359C2×C3×C4—21no—
360C2×C3×C4—23no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—36no—
364C2×C3×C4—36no—
365C2×C3×C4C23×D313yes—
366C2×C3×C4C23×D313yes—
367C2×C3×C4C23×D313yes—
368C2×C3×C4C23×D313yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—31no—
374C2×Dic3—31no—
375C2×Dic3—33no—
376C2×Dic3—33no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—63no—
380C2×Dic3C23×D312yes—
381C2×Dic3C23×D316yes—
382C2×Dic3C23×D316yes—
383C2×Dic3C23×D312yes—
384D12—312no—
385D12—312no—
386D12—612no—
387C4×D3—312no—
388C4×D3—312no—
389C4×D3—612no—
390C4×D3—612no—
391C4×D3—66no—
392C4×D3—66no—
393C4×D3—612no—
394C4×D3—126no—
395C4×D3—126no—
396C4×D3—126no—
397C4×D3—123no—
398C4×D3—123no—
399C4×D3—126no—
400Dic6—26no—
401Dic6—46no—
402Dic6—612no—
403Dic6—612no—
404Dic6#23914yescomplemented
405C2×C32C23×Q811yescharacteristic
406C2×C32C22×#4111yescharacteristic
407C2×C32#58511yescharacteristic
408C3⋊D3—26no—
409#41—98no—
410C2×Q8—31no—
411C2×Q8—33no—
412C2×Q8—36no—
413C2×Q8—96no—
414C2×Q8—1812no—
415C2×Q8C2×D3211yescharacteristic
416C2×D4—93no—
417C22×C4—96no—
418C22×C4—96no—
419C22×C4—93no—
420C22×C4—93no—
421C22×C4—93no—
422C4⋊C4—31no—
423C4⋊C4—36no—
424C4⋊C4—36no—
425C4⋊C4—33no—
426C4⋊C4—36no—
427C4⋊C4—36no—
428C4⋊C4—36no—
429C4⋊C4—92no—
430C4⋊C4—96no—
431C4⋊C4—96no—
432C4⋊C4—912no—
433C4⋊C4—93no—
434C4⋊C4C2×D3213yes—
435C22⋊C4—912no—
436C22⋊C4—96no—
437C42—36no—
438C42—36no—
439C42—92no—
440C42—96no—
441C42—91no—
442C42—93no—
443C42—93no—
444C42C2×D3213yes—
445C22×C3—21no—
446C22×C3C24×D311yescharacteristic
447C22×C3C24×D311yescharacteristic
448C2×D3—36no—
449C2×D3—36no—
450C2×D3—66no—
451C2×D3—63no—
452C2×D3—63no—
453C2×D3—63no—
454C2×D3—63no—
455C2×D3—123no—
456C2×D3—123no—
457C3×C4—23no—
458C3×C4—23no—
459C3×C4—26no—
460C3×C4—22no—
461C3×C4—34no—
462C3×C4—43no—
463C3×C4—66no—
464C3×C4—62no—
465C3×C4—66no—
466C3×C4C2×D3×Q816yes—
467C3×C4C2×D3×Q816yes—
468C3×C4C2×#23912yes—
469C3×C4D3×#4112yes—
470Dic3—26no—
471Dic3—26no—
472Dic3—22no—
473Dic3—32no—
474Dic3—32no—
475Dic3—62no—
476Dic3—62no—
477Dic3—63no—
478Dic3—63no—
479Dic3—61no—
480Dic3—61no—
481Dic3—123no—
482Dic3C2×#23914yes—
483C32Q8×#4111yescharacteristic, complemented, Sylow
484C23—93no—
485Q8—34no—
486Q8—66no—
487Q8—126no—
488Q8—1812no—
489Q8#379714yescomplemented
490D4—912no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—36no—
494C2×C4—36no—
495C2×C4—91no—
496C2×C4—912no—
497C2×C4—91no—
498C2×C4—93no—
499C2×C4—1812no—
500C2×C4—186no—
501C2×C4—363no—
502C2×C4—366no—
503C2×C4C22×D3213yes—
504C2×C4C22×D3213yes—
505C2×C4C22×D3211yescharacteristic
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3C22×D3×Q811yescharacteristic
510C2×C3C22×D3×Q811yescharacteristic
511C2×C3C22×#23911yescharacteristic
512C2×C3C2×D3×#4111yescharacteristic
513C2×C3#596611yescharacteristic
514C2×C3#596811yescharacteristic
515D3—66no—
516D3—66no—
517D3—126no—
518C22—96no—
519C22—183no—
520C22—183no—
521C22C23×D3211yescharacteristic
522C4—23no—
523C4—34no—
524C4—66no—
525C4—62no—
526C4—66no—
527C4—92no—
528C4—183no—
529C4—181no—
530C4C2×#379716yes—
531C4D3×#23912yes—
532C3—21no—
533C3#8701511yescharacteristic, complemented
534C3Q8×#23911yescharacteristic, complemented
535C2—186no—
536C2C22×#379711yescharacteristic
537C2C2×D3×#23911yescharacteristic
538C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3832C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595422C2semidirect
6. #10594470C2semidirect
7. #10594448C2semidirect
8. #10593958C2semidirect
9. #10593903C2semidirect
10. C4×#3797C2semidirect
11. #10593866C2semidirect
68. #5570D3semidirect
70. Q8×Dic6D3semidirect
72. #3832Q8semidirect
184. C32×Q8C2×Q8semidirect
191. C4⋊(C3⋊D3)C2×Q8semidirect
194. C4×C3⋊D3C2×Q8semidirect
201. C3×Dic6#41semidirect
356. C3×Q8D3×Q8semidirect
357. C3×Q8D3×Q8semidirect
404. Dic6#239semidirect
483. C32Q8×#41semidirect
489. Q8#3797semidirect
533. C3#87015semidirect
534. C3Q8×#239semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×#55702
C3×Q8×Dic62
#105954222
#105953862
#105944702
#105944482
#105939582
#105939032
C4×#37972
#105938662
Q8×#2393
#870153