Finite Group Databasebeta

← #11906041

Subgroups — #11906041

Order 1152.

3107 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2#10595948C211yesmaximal, characteristic, complemented
3C3×C4×#235C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5#10594906C218yesmaximal, complemented
6#10594866C212yesmaximal, complemented
7#10593970C212yesmaximal, complemented
8#10593903C214yesmaximal, complemented
9#10593896C214yesmaximal, complemented
10#10593893C214yesmaximal, complemented
11D3×#869C212yesmaximal, complemented
12#86214—31nomaximal
13#85827—31nomaximal
14C2×#3828C2212yes—
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×#3804C2218yes—
18C2×#3799C2214yes—
19C2×#3797C2214yes—
20#64297—216no—
21C2×#3796C2214yes—
22C2×D3×Dic6C2214yes—
23C2×C32×C42C2211yescharacteristic
24#64139C2214yes—
25#64084C2212yes—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2214yes—
28#64078C2211yescharacteristic
29C3×C4×#67C2214yes—
30C3×#926C2211yescharacteristic
31C2×C3×C4⋊Dic3C2214yes—
32C3×C4×D12C2212yes—
33C3×#872C2212yes—
34C3×C42×D3C2212yes—
35C3×#869C2212yes—
36C3×#869C2212yes—
37C3×#869C2214yes—
38C3×C4×Dic6C2212yes—
39#63966C2218yes—
40#63918C2218yes—
41#63909C2218yes—
42#63895C22116yes—
43#63894C2218yes—
44#63890C22116yes—
45D3×C4⋊Dic3C2218yes—
46#63871C2218yes—
47#63866C2214yes—
48#63864C2214yes—
49C2×#1010—32no—
50C2×#1007—32no—
51C2×C3×C4⋊Q8—31no—
52C3×C4×#41—31no—
53#5816—32no—
54#5727—34no—
55#5726—34no—
56#5725—32no—
57#5724—34no—
58D3×C4⋊Q8—32no—
59Q8×D12—34no—
60#5555—38no—
61#5555—34no—
62#5526—32no—
63#5526—34no—
64#5507—38no—
65#5477—31no—
66#5477—31no—
67#5477—32no—
68#5477—61no—
69C4×#235D311yescharacteristic, complemented
70C2×#869—32no—
71C2×#869D311yescharacteristic, complemented
72C22×C32×C4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638C2314yes—
75#3828—28no—
76C2×C4⋊(C3⋊D3)C2312yes—
77C2×C4⋊(C3⋊D3)C2314yes—
78C2×C4×C3⋊D3C2314yes—
79C2×#634C2312yes—
80C2×C3×#67C2312yes—
81C22×C3×Dic3C2314yes—
82C3×#235D418yescomplemented
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3C2314yes—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6—28no—
87C2×C3×Dic6C2314yes—
88C2×C3×Dic6C2314yes—
89C2×C3×Dic6C2311yescharacteristic
90C2×#627C2318yes—
91C2×#626C2318yes—
92C2×#624C2318yes—
93#3804—232no—
94C2×D3×Dic3C2318yes—
95#3799—216no—
96#3797—216no—
97#3796—216no—
98D3×Dic6—216no—
99C32×C42C2311yescharacteristic
100C32×C42C2312yes—
101C32×C42C2311yescharacteristic
102#3752C2318yes—
103C4⋊(C3⋊Dic3)C2314yes—
104C3×#217C2312yes—
105C3×(C2×D3)⋊C4C2314yes—
106C3×C4⋊Dic3C2318yes—
107C3×C4⋊Dic3C2318yes—
108C3×C4⋊Dic3C2312yes—
109C3×Dic3⋊C4C2314yes—
110C3×C4×Dic3C2312yes—
111C3×C4×Dic3C2314yes—
112Dic3⋊Dic3C23116yes—
113#3722C23116yes—
114#3499—91noSylow
115C2×C3×#41—31no—
116C22×C3×Q8—32no—
117#1010—616no—
118#1007—616no—
119C2×#239—34no—
120C2×#239—34no—
121C2×D3×Q8—34no—
122C2×D3×Q8—34no—
123C2×D3×Q8—34no—
124C2×#237—38no—
125C2×#237—34no—
126C2×#235—32no—
127C2×#235—32no—
128C2×#235—38no—
129C2×#235—34no—
130C2×#235—62no—
131C2×#235C2×D311yescharacteristic
132C22×Dic6—34no—
133C22×Dic6C2×D312yes—
134C3×C4⋊Q8—32no—
135C3×C4⋊Q8—32no—
136C3×C4⋊Q8—34no—
137C3×C4×Q8—32no—
138C3×C4×D4—34no—
139C3×C4×D4—32no—
140C3×#117—31no—
141C3×#117—32no—
142C2×C3×C4⋊C4—34no—
143C2×C3×C42—21no—
144C2×C3×C42—32no—
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C2×D311yescharacteristic
147#947—34no—
148#946—38no—
149#944—34no—
150#930—34no—
151#930—34no—
152#930—38no—
153#930—64no—
154#929—38no—
155C4×#67C2×D314yes—
156#926C2×D311yescharacteristic
157C2×C4⋊Dic3—38no—
158C2×C4⋊Dic3C2×D314yes—
159#897—38no—
160#897—316no—
161#896—316no—
162#895—38no—
163#894—316no—
164#893—38no—
165D3×C4⋊C4—38no—
166#888—38no—
167#886—38no—
168#886—316no—
169#875—34no—
170#875—32no—
171#875—32no—
172#875—62no—
173#874—31no—
174#874—31no—
175#874—61no—
176C4×D12—34no—
177C4×D12—34no—
178C4×D12—38no—
179C4×D12—64no—
180C4×D12C2×D312yes—
181#872C2×D312yes—
182C42×D3C2×D312yes—
183#869—34no—
184#869—31no—
185#869—31no—
186#869—38no—
187#869—61no—
188#869C2×D312yes—
189#869C2×D312yes—
190#869C2×D314yes—
191C4×Dic6C2×D312yes—
192C23×C32C2411yescharacteristic
193C22×C3⋊D3C2414yes—
194C22×C3×D3C2412yes—
195C2×C32×C4—24no—
196C2×C32×C4C2×D414yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2411yescharacteristic
200C2×C32×C4C2412yes—
201#638—28no—
202C2×C3⋊Dic3C2414yes—
203C4⋊(C3⋊D3)—24no—
204C4⋊(C3⋊D3)—28no—
205C4×C3⋊D3—28no—
206#634—24no—
207C3×#67C2×D418yes—
208C2×C3×Dic3—28no—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2418yes—
211C2×C3×Dic3C2412yes—
212C3×D12C2×D414yes—
213C3×C4×D3—28no—
214C3×C4×D3C2×D418yes—
215C3×Dic6—28no—
216C3×Dic6—28no—
217C3×Dic6C2×D414yes—
218#627—216no—
219#626—216no—
220#624—216no—
221D3×Dic3—216no—
222C2×2−1+4—92no—
223D4×Q8—94no—
224#547—98no—
225#547—94no—
226#536—94no—
227#536—92no—
228#532—92no—
229#532—91no—
230C2×C4⋊Q8—31no—
231C2×C4⋊Q8—92no—
232C4×#41—31no—
233C3×#41—38no—
234C2×C3×Q8—31no—
235C2×C3×Q8—34no—
236C2×C3×Q8—34no—
237C2×C3×Q8—68no—
238C2×C3×D4—32no—
239C2×C3×D4—31no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—32no—
243C22×C3×C4—34no—
244C22×C3×C4—34no—
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—34no—
250C2×#67—34no—
251C2×#67—38no—
252C2×#67—64no—
253C2×#67C22×D312yes—
254C22×Dic3—38no—
255C22×Dic3C22×D314yes—
256#239—616no—
257#239—616no—
258D3×Q8—616no—
259D3×Q8—616no—
260D3×Q8—616no—
261#237—616no—
262#237—632no—
263#235—616no—
264#235—68no—
265#235—68no—
266#235—632no—
267#235—128no—
268#235D1218yescomplemented
269C2×D12—38no—
270C2×D12—34no—
271C2×D12—34no—
272C2×D12—32no—
273C2×D12—32no—
274C2×D12—64no—
275C2×D12—62no—
276C2×D12C22×D311yescharacteristic
277C2×C4×D3—38no—
278C2×C4×D3—34no—
279C2×C4×D3—34no—
280C2×C4×D3—38no—
281C2×C4×D3—38no—
282C2×C4×D3—64no—
283C2×C4×D3C22×D314yes—
284C2×C4×D3C22×D312yes—
285C2×Dic6—28no—
286C2×Dic6—32no—
287C2×Dic6—32no—
288C2×Dic6—38no—
289C2×Dic6—38no—
290C2×Dic6—62no—
291C2×Dic6—616no—
292C2×Dic6C22×D314yes—
293C2×Dic6C22×D314yes—
294C2×Dic6C22×D311yescharacteristic
295C3×C4⋊C4—38no—
296C3×C4⋊C4—38no—
297C3×C4⋊C4—34no—
298C3×C4⋊C4—32no—
299C3×C22⋊C4—32no—
300C3×C22⋊C4—34no—
301C3×C42—21no—
302C3×C42—22no—
303C3×C42—21no—
304C3×C42—34no—
305C3×C42—32no—
306C3×C42C22×D312yes—
307C3×C42C22×D311yescharacteristic
308C3×C42C22×D311yescharacteristic
309C3×C42C22×D312yes—
310C3×C42C22×D311yescharacteristic
311C3×C42C22×D311yescharacteristic
312#217C22×D312yes—
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4—38no—
315(C2×D3)⋊C4—316no—
316(C2×D3)⋊C4—316no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4C22×D314yes—
319C4⋊Dic3—34no—
320C4⋊Dic3—34no—
321C4⋊Dic3—316no—
322C4⋊Dic3—64no—
323C4⋊Dic3C22×D312yes—
324C4⋊Dic3C22×D318yes—
325C4⋊Dic3C22×D318yes—
326Dic3⋊C4—316no—
327Dic3⋊C4C22×D314yes—
328C4×Dic3C22×D314yes—
329C4×Dic3C22×D312yes—
330C22×C32—22no—
331C22×C32C22×D412yes—
332C22×C32C2511yescharacteristic
333C2×C3⋊D3—24no—
334C2×C3⋊D3—28no—
335C2×C3×D3—24no—
336C2×C3×D3C22×D414yes—
337C32×C4—22no—
338C32×C4C22×D412yes—
339C32×C4C22×D412yes—
340C32×C42−1+414yescomplemented
341C3⋊Dic3—24no—
342C3×Dic3—28no—
343C3×Dic3—24no—
344C3×Dic3C22×D414yes—
3452−1+4—1816no—
346C2×#41—31no—
347C2×#41—98no—
348C2×#41—94no—
349C2×#41—94no—
350C2×#41—92no—
351C22×Q8—32no—
352C22×Q8—94no—
353C22×Q8—94no—
354C4⋊Q8—32no—
355C4⋊Q8—32no—
356C4⋊Q8—34no—
357C4⋊Q8—98no—
358C4⋊Q8—94no—
359C4⋊Q8—91no—
360#127—91no—
361#124—94no—
362#124—92no—
363#123—916no—
364#123—98no—
365C22⋊Q8—916no—
366C22⋊Q8—98no—
367#121—98no—
368#121—94no—
369C4×Q8—32no—
370C4×D4—34no—
371C4×D4—32no—
372C4×D4—98no—
373C4×D4—94no—
374#117—31no—
375#117—32no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—98no—
378C2×C42—32no—
379C2×C42D3211yescharacteristic
380C23×C3—21no—
381C23×C3—32no—
382C23×C3C23×D311yescharacteristic
383C23×C3C23×D311yescharacteristic
384C22×D3—34no—
385C22×D3—34no—
386C22×D3—64no—
387C22×D3C23×D312yes—
388C3×Q8—34no—
389C3×Q8—68no—
390C3×Q8—68no—
391C3×D4—38no—
392C3×D4—34no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—32no—
401C2×C3×C4—38no—
402C2×C3×C4—38no—
403C2×C3×C4—34no—
404C2×C3×C4—44no—
405C2×C3×C4—68no—
406C2×C3×C4—68no—
407C2×C3×C4C2×D1214yes—
408C2×C3×C4D3×D414yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417#67—616no—
418#67—68no—
419#67—68no—
420#67—128no—
421#67C2×D1218yes—
422C2×Dic3—28no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—64no—
426C2×Dic3—616no—
427C2×Dic3C23×D314yes—
428C2×Dic3C23×D318yes—
429C2×Dic3C23×D312yes—
430D12—616no—
431D12—64no—
432D12—64no—
433D12—68no—
434D12—68no—
435D12—128no—
436D12—124no—
437D12C2×D1214yes—
438C4×D3—28no—
439C4×D3—616no—
440C4×D3—616no—
441C4×D3—68no—
442C4×D3—68no—
443C4×D3—616no—
444C4×D3—128no—
445C4×D3C2×D1218yes—
446Dic6—28no—
447Dic6—28no—
448Dic6—616no—
449Dic6—64no—
450Dic6—64no—
451Dic6—616no—
452Dic6—124no—
453Dic6C2×D1214yes—
454C2×C32—22no—
455C2×C32C23×D411yescharacteristic
456C2×C32C2×2−1+412yes—
457C3⋊D3—44no—
458C3×D3—24no—
459#41—38no—
460#41—1816no—
461#41—1832no—
462#41—1816no—
463#41—188no—
464C2×Q8—31no—
465C2×Q8—34no—
466C2×Q8—34no—
467C2×Q8—68no—
468C2×Q8—98no—
469C2×Q8—92no—
470C2×Q8—1816no—
471C2×Q8—1816no—
472C2×D4—32no—
473C2×D4—31no—
474C2×D4—98no—
475C2×D4—94no—
476C2×D4—94no—
477C2×D4—92no—
478C22×C4—32no—
479C22×C4—34no—
480C22×C4—34no—
481C22×C4—98no—
482C22×C4—98no—
483C22×C4—94no—
484C22×C4C2×D3212yes—
485C22×C4C2×D3211yescharacteristic
486C4⋊C4—38no—
487C4⋊C4—38no—
488C4⋊C4—34no—
489C4⋊C4—32no—
490C4⋊C4—916no—
491C4⋊C4—94no—
492C22⋊C4—32no—
493C22⋊C4—34no—
494C22⋊C4—916no—
495C22⋊C4—98no—
496C42—32no—
497C42—34no—
498C42C2×D3211yescharacteristic
499C42C2×D3211yescharacteristic
500C42C2×D3212yes—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—34no—
506C22×C3—42no—
507C22×C3—64no—
508C22×C3C22×D1212yes—
509C22×C3C2×D3×D412yes—
510C22×C3C24×D311yescharacteristic
511C22×C3C24×D311yescharacteristic
512C2×D3—24no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—68no—
516C2×D3—68no—
517C2×D3—124no—
518C2×D3—128no—
519C2×D3C22×D1214yes—
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—24no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—34no—
526C3×C4—42no—
527C3×C4—68no—
528C3×C4—64no—
529C3×C4C22×D1212yes—
530C3×C4C22×D1212yes—
531C3×C4C2×D3×D412yes—
532C3×C4C2×D3×D412yes—
533C3×C4#100714yescomplemented
534C3×C4#101014yescomplemented
535Dic3—28no—
536Dic3—24no—
537Dic3—64no—
538Dic3—64no—
539Dic3—124no—
540Dic3C22×D1214yes—
541C32#349911yescharacteristic, complemented, Sylow
542C23—32no—
543C23—94no—
544C23C22×D3211yescharacteristic
545Q8—34no—
546Q8—68no—
547Q8—68no—
548Q8—1816no—
549Q8—184no—
550D4—38no—
551D4—34no—
552D4—1816no—
553D4—188no—
554D4—188no—
555D4—184no—
556C2×C4—24no—
557C2×C4—32no—
558C2×C4—38no—
559C2×C4—34no—
560C2×C4—38no—
561C2×C4—68no—
562C2×C4—68no—
563C2×C4—94no—
564C2×C4—1816no—
565C2×C4—1816no—
566C2×C4—188no—
567C2×C4D3×D1214yes—
568C2×C4C22×D3212yes—
569C2×C4C22×D3212yes—
570C2×C4C22×D3211yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C2×C3—22no—
573C2×C3—22no—
574C2×C3—22no—
575C2×C3—21no—
576C2×C3—42no—
577C2×C3—64no—
578C2×C3C23×D1211yescharacteristic
579C2×C3C22×D3×D411yescharacteristic
580C2×C3C2×#100712yes—
581C2×C3C2×#101012yes—
582D3—24no—
583D3—124no—
584D3—124no—
585D3—244no—
586C22—22no—
587C22—34no—
588C22—64no—
589C22—188no—
590C22—184no—
591C22C2×D3×D1212yes—
592C22C23×D3211yescharacteristic
593C4—22no—
594C4—34no—
595C4—64no—
596C4—68no—
597C4—184no—
598C4#6429714yescomplemented
599C4C2×D3×D1212yes—
600C4C2×D3×D1212yes—
601C3—21no—
602C3#8582711yescharacteristic, complemented
603C3#8621411yescharacteristic, complemented
604C2—22no—
605C2—64no—
606C2—364no—
607C2C2×#6429712yes—
608C2C22×D3×D1211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64297C2semidirect
2. #10595948C2semidirect
3. C3×C4×#235C2semidirect
4. C2×C3×#869C2semidirect
5. #10594906C2semidirect
6. #10594866C2semidirect
7. #10593970C2semidirect
8. #10593903C2semidirect
9. #10593896C2semidirect
10. #10593893C2semidirect
11. D3×#869C2semidirect
69. C4×#235D3semidirect
71. C2×#869D3semidirect
82. C3×#235D4semidirect
268. #235D12semidirect
340. C32×C42−1+4semidirect
533. C3×C4#1007semidirect
534. C3×C4#1010semidirect
541. C32#3499semidirect
598. C4#64297semidirect
602. C3#85827semidirect
603. C3#86214semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
#105959482
C3×C4×#2352
C2×C3×#8692
#105949062
#105948662
#105939702
#105939032
#105938962
#105938932
D3×#8692
#862143
#858273