Finite Group Databasebeta

← #11906042

Subgroups — #11906042

Order 1152.

3107 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2C4×#3828C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5#10594928C218yesmaximal, complemented
6#10594855C212yesmaximal, complemented
7#10593909C212yesmaximal, complemented
8#10593908C214yesmaximal, complemented
9#10593907C212yesmaximal, complemented
10#10593904C214yesmaximal, complemented
11#10593869C214yesmaximal, complemented
12#86243—31nomaximal
13#86214—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2212yes—
16C22×C3×Dic6C2212yes—
17C2×#3804C2218yes—
18C2×#3799C2214yes—
19C2×#3797C2214yes—
20#64297—216no—
21C2×#3796C2214yes—
22C2×D3×Dic6C2214yes—
23C2×C32×C42C2211yescharacteristic
24C4×#638C2214yes—
25#64135C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2212yes—
27#64081C2212yes—
28C42×C3⋊D3C2212yes—
29C4×#634C2212yes—
30C3×#930C2214yes—
31C2×C3×C4⋊Dic3C2214yes—
32C3×#875C2212yes—
33C3×#874C2211yescharacteristic
34C3×C4×D12C2214yes—
35C3×#869C2214yes—
36C3×#869C2212yes—
37C3×#869C2212yes—
38C3×#869C2211yescharacteristic
39#63961C2218yes—
40#63919C2218yes—
41#63916C2218yes—
42#63900C2218yes—
43#63899C22116yes—
44#63898C2218yes—
45#63873C2214yes—
46#63863C2214yes—
47#63856C2218yes—
48#63854C22116yes—
49C2×#1010—32no—
50C2×#1007—32no—
51C3×#532—31no—
52C2×C3×C4⋊Q8—31no—
53#5825—32no—
54#5816—32no—
55#5727—34no—
56#5726—34no—
57#5725—32no—
58#5724—34no—
59D3×C4⋊Q8—32no—
60D3×C4⋊Q8—32no—
61#5716—32no—
62#5675—34no—
63#5611—38no—
64#5551—34no—
65D4×Dic6—34no—
66#5507—38no—
67#5477D311yescharacteristic, complemented
68C4×#235—31no—
69C4×#235—31no—
70C4×#235—61no—
71C2×#869D311yescharacteristic, complemented
72C22×C32×C4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638C2312yes—
75#3828D418yescomplemented
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3C2314yes—
78C2×C4×C3⋊D3C2312yes—
79C2×#634C2311yescharacteristic
80C2×C3×#67C2314yes—
81C22×C3×Dic3C2314yes—
82C3×#235—28no—
83C2×C3×D12C2312yes—
84C2×C3×D12C2314yes—
85C2×C3×C4×D3C2314yes—
86C2×C3×Dic6—28no—
87C2×C3×Dic6C2314yes—
88C2×C3×Dic6C2314yes—
89C2×C3×Dic6C2312yes—
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×C42C2312yes—
100C32×C42C2311yescharacteristic
101C32×C42C2311yescharacteristic
102#3757C2312yes—
103#3752C2314yes—
104C4⋊(C3⋊Dic3)C2312yes—
105#3750C2314yes—
106C4×C3⋊Dic3C2314yes—
107C4×C3⋊Dic3C2312yes—
108C3×(C2×D3)⋊C4C2318yes—
109C3×C4⋊Dic3C2318yes—
110C3×C4⋊Dic3C2318yes—
111C3×C4⋊Dic3C2314yes—
112#3724C23116yes—
113(C2×D3)⋊Dic3C23116yes—
114#3499—91noSylow
115C2×C3×#41—32no—
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—31no—
127C2×#235—31no—
128C2×#235—38no—
129C2×#235—34no—
130C2×#235—61no—
131C2×#235C2×D312yes—
132C22×Dic6—34no—
133C22×Dic6C2×D312yes—
134C3×C4⋊Q8—31no—
135C3×C4⋊Q8—32no—
136C3×C4⋊Q8—32no—
137C3×C4⋊Q8—34no—
138C3×#127—31no—
139C3×#124—32no—
140C3×#121—34no—
141C3×C4×D4—34no—
142C2×C3×C4⋊C4—34no—
143C2×C3×C42—21no—
144C2×C3×C42C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146#947—34no—
147#946—38no—
148#944—34no—
149#944—34no—
150#938—38no—
151#936—34no—
152#935—38no—
153D4×Dic3—38no—
154#930C2×D314yes—
155#929—38no—
156C4×#67—34no—
157C4×#67—34no—
158C4×#67—64no—
159#926—31no—
160#926—31no—
161#926—61no—
162C2×C4⋊Dic3C2×D314yes—
163#924—38no—
164#896—316no—
165#895—38no—
166#894—316no—
167#893—38no—
168D3×C4⋊C4—38no—
169D3×C4⋊C4—38no—
170#888—38no—
171#888—38no—
172#883—316no—
173#878—316no—
174#875C2×D312yes—
175#874C2×D311yescharacteristic
176C4×D12—32no—
177C4×D12—32no—
178C4×D12—62no—
179C4×D12C2×D314yes—
180#872—32no—
181#872—32no—
182#872—62no—
183C42×D3—32no—
184C42×D3—32no—
185C42×D3—62no—
186#869C2×D312yes—
187#869C2×D312yes—
188#869C2×D311yescharacteristic
189#869C2×D314yes—
190C4×Dic6—32no—
191C4×Dic6—32no—
192C4×Dic6—62no—
193C23×C32C2411yescharacteristic
194C22×C3⋊D3C2412yes—
195C22×C3×D3C2414yes—
196C2×C32×C4—24no—
197C2×C32×C4C2×D414yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2411yescharacteristic
200C2×C32×C4C2411yescharacteristic
201C2×C32×C4C2412yes—
202#638C2×D418yes—
203C2×C3⋊Dic3C2414yes—
204C2×C3⋊Dic3C2412yes—
205C4⋊(C3⋊D3)C2×D414yes—
206C4×C3⋊D3—28no—
207C4×C3⋊D3C2×D418yes—
208#634C2×D414yes—
209C3×#67—28no—
210C2×C3×Dic3—28no—
211C2×C3×Dic3C2418yes—
212C2×C3×Dic3C2414yes—
213C3×D12—24no—
214C3×D12—28no—
215C3×C4×D3—28no—
216C3×Dic6—28no—
217C3×Dic6—28no—
218C3×Dic6—24no—
219#627—216no—
220#626—216no—
221#624—216no—
222D3×Dic3—216no—
223C2×2−1+4—92no—
224D4×Q8—94no—
225#547—98no—
226#547—94no—
227#536—94no—
228#536—92no—
229#532—31no—
230#532—92no—
231C2×C4⋊Q8—31no—
232C2×C4⋊Q8—92no—
233C4×#41—91no—
234C3×#41—68no—
235C2×C3×Q8—32no—
236C2×C3×Q8—34no—
237C2×C3×Q8—34no—
238C2×C3×Q8—68no—
239C2×C3×D4—34no—
240C2×C3×D4—34no—
241C2×C3×D4—32no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—34no—
245C22×C3×C4—34no—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—32no—
251C2×#67—32no—
252C2×#67—38no—
253C2×#67—62no—
254C2×#67C22×D314yes—
255C22×Dic3—38no—
256C22×Dic3C22×D314yes—
257#239—616no—
258#239—616no—
259D3×Q8—616no—
260D3×Q8—616no—
261D3×Q8—616no—
262#237—616no—
263#237—632no—
264#235—28no—
265#235—38no—
266#235—38no—
267#235—68no—
268#235—616no—
269#235—632no—
270C2×D12—31no—
271C2×D12—31no—
272C2×D12—38no—
273C2×D12—61no—
274C2×D12C22×D314yes—
275C2×D12C22×D312yes—
276C2×C4×D3—32no—
277C2×C4×D3—32no—
278C2×C4×D3—38no—
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—38no—
282C2×C4×D3—38no—
283C2×C4×D3—62no—
284C2×C4×D3—64no—
285C2×C4×D3C22×D314yes—
286C2×Dic6—28no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—38no—
290C2×Dic6—38no—
291C2×Dic6—61no—
292C2×Dic6—616no—
293C2×Dic6C22×D314yes—
294C2×Dic6C22×D314yes—
295C2×Dic6C22×D312yes—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4—38no—
299C3×C22⋊C4—38no—
300C3×C42—22no—
301C3×C42—21no—
302C3×C42—21no—
303C3×C42C22×D312yes—
304C3×C42C22×D312yes—
305C3×C42C22×D311yescharacteristic
306C3×C42C22×D311yescharacteristic
307C3×C42C22×D311yescharacteristic
308C3×C42C22×D311yescharacteristic
309#217—32no—
310#217—32no—
311#217—316no—
312#217—62no—
313(C2×D3)⋊C4—316no—
314(C2×D3)⋊C4—34no—
315(C2×D3)⋊C4—34no—
316(C2×D3)⋊C4—64no—
317(C2×D3)⋊C4C22×D318yes—
318C4⋊Dic3—32no—
319C4⋊Dic3—32no—
320C4⋊Dic3—62no—
321C4⋊Dic3C22×D318yes—
322C4⋊Dic3C22×D318yes—
323C4⋊Dic3C22×D314yes—
324Dic3⋊C4—34no—
325Dic3⋊C4—34no—
326Dic3⋊C4—316no—
327Dic3⋊C4—316no—
328Dic3⋊C4—64no—
329C4×Dic3—34no—
330C4×Dic3—34no—
331C4×Dic3—32no—
332C4×Dic3—32no—
333C4×Dic3—64no—
334C4×Dic3—62no—
335C22×C32—22no—
336C22×C32C22×D412yes—
337C22×C32C2511yescharacteristic
338C2×C3⋊D3—24no—
339C2×C3⋊D3C22×D414yes—
340C2×C3×D3—24no—
341C2×C3×D3—28no—
342C32×C4—22no—
343C32×C4C22×D412yes—
344C32×C4C22×D412yes—
345C32×C42−1+414yescomplemented
346C3⋊Dic3—24no—
347C3⋊Dic3C22×D414yes—
348C3×Dic3—28no—
349C3×Dic3—24no—
3502−1+4—1816no—
351C2×#41—32no—
352C2×#41—98no—
353C2×#41—94no—
354C2×#41—94no—
355C2×#41—91no—
356C22×Q8—32no—
357C22×Q8—94no—
358C22×Q8—94no—
359C4⋊Q8—32no—
360C4⋊Q8—32no—
361C4⋊Q8—34no—
362C4⋊Q8—31no—
363C4⋊Q8—98no—
364C4⋊Q8—94no—
365#127—31no—
366#124—32no—
367#124—94no—
368#123—916no—
369#123—98no—
370C22⋊Q8—916no—
371C22⋊Q8—98no—
372#121—34no—
373#121—98no—
374C4×Q8—92no—
375C4×D4—34no—
376C4×D4—98no—
377C4×D4—94no—
378C4×D4—92no—
379#117—91no—
380#117—92no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—98no—
383C2×C42—92no—
384C2×C42D3211yescharacteristic
385C23×C3—21no—
386C23×C3—34no—
387C23×C3C23×D311yescharacteristic
388C23×C3C23×D311yescharacteristic
389C22×D3—32no—
390C22×D3—32no—
391C22×D3—62no—
392C22×D3C23×D314yes—
393C3×Q8—64no—
394C3×Q8—68no—
395C3×Q8—68no—
396C3×D4—68no—
397C3×D4—64no—
398C3×D4—68no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—34no—
407C2×C3×C4—38no—
408C2×C3×C4—44no—
409C2×C3×C4—68no—
410C2×C3×C4—68no—
411C2×C3×C4D3×D414yes—
412C2×C3×C4D3×D414yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C23×D312yes—
420C2×C3×C4C23×D312yes—
421#67—28no—
422#67—38no—
423#67—38no—
424#67—68no—
425#67—616no—
426C2×Dic3—28no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—34no—
430C2×Dic3—34no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—616no—
434C2×Dic3C23×D314yes—
435C2×Dic3C23×D318yes—
436D12—24no—
437D12—28no—
438D12—34no—
439D12—34no—
440D12—64no—
441D12—616no—
442C4×D3—28no—
443C4×D3—38no—
444C4×D3—38no—
445C4×D3—68no—
446C4×D3—616no—
447C4×D3—616no—
448C4×D3—616no—
449C4×D3—68no—
450C4×D3—68no—
451C4×D3—128no—
452Dic6—28no—
453Dic6—28no—
454Dic6—24no—
455Dic6—34no—
456Dic6—34no—
457Dic6—64no—
458Dic6—616no—
459Dic6—616no—
460C2×C32—22no—
461C2×C32C23×D411yescharacteristic
462C2×C32C2×2−1+412yes—
463C3⋊D3—24no—
464C3×D3—44no—
465#41—68no—
466#41—98no—
467#41—1832no—
468#41—1816no—
469#41—1816no—
470C2×Q8—34no—
471C2×Q8—32no—
472C2×Q8—34no—
473C2×Q8—68no—
474C2×Q8—98no—
475C2×Q8—91no—
476C2×Q8—1816no—
477C2×Q8—1816no—
478C2×D4—34no—
479C2×D4—34no—
480C2×D4—32no—
481C2×D4—98no—
482C2×D4—92no—
483C2×D4—91no—
484C22×C4—34no—
485C22×C4—34no—
486C22×C4—98no—
487C22×C4—98no—
488C22×C4—92no—
489C22×C4—94no—
490C22×C4C2×D3212yes—
491C22×C4C2×D3211yescharacteristic
492C4⋊C4—38no—
493C4⋊C4—38no—
494C4⋊C4—34no—
495C4⋊C4—916no—
496C4⋊C4—94no—
497C4⋊C4—92no—
498C22⋊C4—38no—
499C22⋊C4—916no—
500C22⋊C4—92no—
501C22⋊C4—94no—
502C42—92no—
503C42—94no—
504C42C2×D3211yescharacteristic
505C42C2×D3211yescharacteristic
506C42C2×D3212yes—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—64no—
513C22×C3—68no—
514C22×C3C2×D3×D412yes—
515C22×C3C2×D3×D412yes—
516C22×C3C24×D311yescharacteristic
517C22×C3C24×D311yescharacteristic
518C2×D3—24no—
519C2×D3—28no—
520C2×D3—34no—
521C2×D3—34no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—124no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—24no—
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—42no—
532C3×C4—64no—
533C3×C4—68no—
534C3×C4C2×D3×D412yes—
535C3×C4C2×D3×D412yes—
536C3×C4C2×D3×D412yes—
537C3×C4C2×D3×D412yes—
538C3×C4#100714yescomplemented
539C3×C4#101014yescomplemented
540Dic3—28no—
541Dic3—24no—
542Dic3—34no—
543Dic3—34no—
544Dic3—64no—
545Dic3—64no—
546Dic3—64no—
547Dic3—124no—
548C32#349911yescharacteristic, complemented, Sylow
549C23—34no—
550C23—92no—
551C23C22×D3211yescharacteristic
552Q8—68no—
553Q8—68no—
554Q8—64no—
555Q8—94no—
556Q8—1816no—
557D4—68no—
558D4—68no—
559D4—64no—
560D4—98no—
561D4—94no—
562D4—1816no—
563C2×C4—24no—
564C2×C4—34no—
565C2×C4—38no—
566C2×C4—68no—
567C2×C4—68no—
568C2×C4—92no—
569C2×C4—98no—
570C2×C4—94no—
571C2×C4—1816no—
572C2×C4—1816no—
573C2×C4—188no—
574C2×C4#380214yes—
575C2×C4C22×D3212yes—
576C2×C4C22×D3212yes—
577C2×C4C22×D3211yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—42no—
584C2×C3—124no—
585C2×C3C22×D3×D411yescharacteristic
586C2×C3C22×D3×D411yescharacteristic
587C2×C3C2×#100712yes—
588C2×C3C2×#101012yes—
589D3—44no—
590D3—64no—
591D3—64no—
592D3—124no—
593C22—22no—
594C22—68no—
595C22—64no—
596C22—94no—
597C22—184no—
598C22C2×#380212yes—
599C22C23×D3211yescharacteristic
600C4—22no—
601C4—64no—
602C4—68no—
603C4—94no—
604C4—184no—
605C4#6429714yescomplemented
606C4C2×#380212yes—
607C4C2×#380212yes—
608C3—21no—
609C3#8621411yescharacteristic, complemented
610C3#8624311yescharacteristic, complemented
611C2—22no—
612C2—124no—
613C2—184no—
614C2C2×#6429712yes—
615C2C22×#380211yescharacteristic
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. C4×#3828C2semidirect
3. C3×#5477C2semidirect
4. C2×C3×#869C2semidirect
5. #10594928C2semidirect
6. #10594855C2semidirect
7. #10593909C2semidirect
8. #10593908C2semidirect
9. #10593907C2semidirect
10. #10593904C2semidirect
11. #10593869C2semidirect
67. #5477D3semidirect
71. C2×#869D3semidirect
75. #3828D4semidirect
345. C32×C42−1+4semidirect
538. C3×C4#1007semidirect
539. C3×C4#1010semidirect
548. C32#3499semidirect
605. C4#64297semidirect
609. C3#86214semidirect
610. C3#86243semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
C4×#38282
C3×#54772
C2×C3×#8692
#105949282
#105948552
#105939092
#105939082
#105939072
#105939042
#105938692
#862433
#862143