Finite Group Databasebeta

← #11878731

Subgroups — #11878731

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic
2C2×#63866C211yesmaximal, characteristic, complemented
3#10592437C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591181C211yesmaximal, characteristic, complemented
7#10591174C211yesmaximal, characteristic, complemented
8#10590890C212yesmaximal, complemented
9#10590877C212yesmaximal, complemented
10#10590760C212yesmaximal, complemented
11#10590752C212yesmaximal, complemented
12#80034—31nomaximal
13#79312—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×#3804—21no—
17#64139C2211yescharacteristic
18C2×#3744C2212yes—
19C3×#930C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#204C2212yes—
22#63978—21no—
23C2×Dic3⋊Dic3—21no—
24C2×Dic3⋊Dic3—21no—
25#63918C2211yescharacteristic
26#63911C2211yescharacteristic
27#63894C2211yescharacteristic
28Dic3×D12C2211yescharacteristic
29#63880—21no—
30#63866—21no—
31#63866—21no—
32#63866C2212yes—
33#63866C2212yes—
34#63852—21no—
35C2×#3717C2212yes—
36C2×#3716C2212yes—
37C32×C22⋊C8C2211yescharacteristic
38#63643C2212yes—
39C3×#830C2211yescharacteristic
40C3×#816C2212yes—
41C3×Dic3⋊C8C2212yes—
42C3×C8×Dic3C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45C2×#944—31no—
46#5596—31no—
47#5477—31no—
48C2×#869—31no—
49C3×#448—31no—
50C3×#431—31no—
51#5227—31no—
52#5175—32no—
53#5162—32no—
54#5040—31no—
55#4841—32no—
56#4841—32no—
57#4818—32no—
58#4792—32no—
59#4738—31no—
60#4738—31no—
61#4738—31no—
62#4738—31no—
63#4738—61no—
64#4738D311yescharacteristic, complemented
65#4718D311yescharacteristic, complemented
66#4693—32no—
67#4681—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70C22×C3⋊Dic3—21no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×#634—21no—
73C2×#634—42no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×D12C2311yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6—42no—
82C2×C3×Dic6C2312yes—
83C2×#627—21no—
84C2×#626—21no—
85C2×#626—21no—
86C2×#624—21no—
87#3804—44no—
88C2×D3×Dic3—21no—
89C2×C32×C8C2312yes—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3744—42no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C3×#204—42no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—21no—
106#3722—21no—
107(C2×D3)⋊Dic3—21no—
108#3717—42no—
109#3716—42no—
110#3206—91noSylow
111C22×C3×Q8—31no—
112C2×#237—61no—
113C2×#235—61no—
114C22×Dic6—31no—
115C22×Dic6—31no—
116C22×Dic6—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×SD16—32no—
119C3×#121—31no—
120C2×C3×C42—31no—
121#944—32no—
122#944—32no—
123#944—61no—
124#944—61no—
125C2×#215—32no—
126#940—31no—
127#939—61no—
128D4×Dic3—31no—
129C2×#214—32no—
130#930—31no—
131#930—31no—
132#930—61no—
133#930—61no—
134#930C2×D311yescharacteristic
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3—61no—
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4—61no—
139C2×C4×Dic3C2×D311yescharacteristic
140C2×#204—32no—
141C2×#204—32no—
142C2×#204—32no—
143C2×#204—32no—
144C2×#204—62no—
145C2×#204C2×D312yes—
146#893—31no—
147#888—31no—
148#885—61no—
149#67⋊C4—61no—
150#875—61no—
151#874—31no—
152C4×D12—31no—
153C4×D12—31no—
154C4×D12—61no—
155#869—31no—
156#869—32no—
157#869—32no—
158#869—61no—
159#869—61no—
160C3×C4⋊C8—32no—
161C3×#103—32no—
162C3×C22⋊C8—21no—
163C3×C22⋊C8—31no—
164C3×C22⋊C8C2×D311yescharacteristic
165C3×C22⋊C8C2×D311yescharacteristic
166C3×C4×C8—32no—
167#835—32no—
168#830C2×D311yescharacteristic
169#816—32no—
170#816—32no—
171#816—32no—
172#816—32no—
173#816—62no—
174#816C2×D312yes—
175Dic3⋊C8C2×D312yes—
176C8×Dic3C2×D312yes—
177#810—32no—
178C23×C32C2×D411yescharacteristic
179C22×C3⋊D3—21no—
180C22×C3×D3—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—42no—
188C4⋊(C3⋊D3)—22no—
189#634—22no—
190#634—22no—
191#634—42no—
192C3×#67—42no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3SD1614yescomplemented
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203C3×Dic6—22no—
204C3×Dic6—22no—
205C3×Dic6—42no—
206#627—42no—
207#626—42no—
208#626—42no—
209#624—42no—
210D3×Dic3—42no—
211C32×C8—22no—
212C3×C3⋊C8—22no—
213#532—91no—
214C2×C4⋊Q8—91no—
215#492—92no—
216#487—92no—
217#461—92no—
218#461—92no—
219#448—31no—
220#448—91no—
221#448—91no—
222#448—91no—
223#431—31no—
224C2×C3×Q8—32no—
225C2×C3×Q8—61no—
226C2×C3×Q8—122no—
227C2×C3×D4—31no—
228C2×C3×D4—61no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C2×#67—61no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—121no—
241C22×Dic3—21no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—121no—
246C22×Dic3D1211yescharacteristic
247C22×Dic3D1211yescharacteristic
248#237—124no—
249#235—124no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×Dic6—21no—
260C2×Dic6—32no—
261C2×Dic6—32no—
262C2×Dic6—42no—
263C2×Dic6—62no—
264C2×Dic6—61no—
265C2×Dic6—61no—
266C2×Dic6—61no—
267C2×Dic6—61no—
268C2×Dic6—121no—
269C2×Dic6—122no—
270C2×Dic6—122no—
271C2×Dic6—124no—
272C2×Dic6C22×D312yes—
273C3×SD16—122no—
274C2×C3×C8—22no—
275C2×C3×C8—32no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—31no—
279C3×C22⋊C4—61no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284#217—61no—
285#215—122no—
286#214—122no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—121no—
294C4⋊Dic3—31no—
295C4⋊Dic3—31no—
296C4⋊Dic3—61no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3—62no—
300C4⋊Dic3—62no—
301C4⋊Dic3—61no—
302C4⋊Dic3C22×D311yescharacteristic
303Dic3⋊C4—61no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308C4×Dic3D1211yescharacteristic
309C4×Dic3D1211yescharacteristic
310C4×Dic3C22×D311yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C2×C3⋊C8C22×D312yes—
313#204—42no—
314#204—122no—
315#204—122no—
316#204—124no—
317#204—122no—
318#204—122no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32C2×SD1612yes—
322C22×C32C22×D411yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4H(5,𝔽2)12yes—
331C3⋊Dic3—42no—
332C3⋊Dic3—41no—
333C3×Dic3—21no—
334C3×Dic3—42no—
335C3×Dic3—41no—
336C3×Dic3C2×SD1612yes—
337C3×Dic3C2×SD1612yes—
338C3×Dic3#13712yes—
339C2×#41—181no—
340C22×Q8—31no—
341C22×Q8—91no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×SD16—92no—
345C2×SD16—92no—
346C4⋊Q8—91no—
347C4⋊Q8—92no—
348C4⋊Q8—92no—
349C4⋊Q8—181no—
350C4⋊Q8—181no—
351#127—91no—
352#124—181no—
353#121—31no—
354#121—91no—
355#121—181no—
356C4×D4—91no—
357C4×D4—91no—
358C4×D4—181no—
359C2×C4⋊C4—181no—
360C2×C4⋊C4—181no—
361C2×C42—31no—
362C4⋊C8—32no—
363#103—32no—
364#103—92no—
365#103—92no—
366#103—92no—
367C22⋊C8—31no—
368C22⋊C8D3211yescharacteristic
369C4×C8—32no—
370C23×C3—21no—
371C23×C3—61no—
372C23×C3C2×D1211yescharacteristic
373C23×C3D3×D411yescharacteristic
374C22×D3—21no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—121no—
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×D4—62no—
382C3×D4—122no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—34no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—42no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—122no—
397C2×C3×C4C2×D1211yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—42no—
402#67—122no—
403#67—122no—
404#67—122no—
405#67—122no—
406#67—242no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—42no—
411C2×Dic3—62no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—121no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—124no—
420C2×Dic3—122no—
421C2×Dic3#20414yescomplemented
422C2×Dic3C2×D1211yescharacteristic
423C2×Dic3C2×D1211yescharacteristic
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426D12—22no—
427D12—62no—
428D12—62no—
429D12—122no—
430D12—122no—
431D12—122no—
432C4×D3—122no—
433C4×D3—122no—
434C4×D3—122no—
435Dic6—22no—
436Dic6—22no—
437Dic6—42no—
438Dic6—64no—
439Dic6—62no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—122no—
444Dic6—122no—
445Dic6—122no—
446Dic6—122no—
447Dic6—124no—
448Dic6—122no—
449C3×C8—22no—
450C3×C8—22no—
451C3×C8—42no—
452C3×C8—62no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32#53511yescharacteristic
456C2×C32C22×SD1611yescharacteristic
457C2×C32C2×#13711yescharacteristic
458C3⋊D3—81no—
459C3×D3—81no—
460#41—364no—
461C2×Q8—32no—
462C2×Q8—61no—
463C2×Q8—92no—
464C2×Q8—122no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—362no—
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—91no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—181no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—61no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481SD16—122no—
482SD16—362no—
483SD16—362no—
484SD16—362no—
485C2×C8—32no—
486C2×C8C2×D3212yes—
487C4⋊C4—31no—
488C4⋊C4—91no—
489C4⋊C4—182no—
490C4⋊C4—182no—
491C4⋊C4—182no—
492C4⋊C4—182no—
493C4⋊C4—181no—
494C22⋊C4—61no—
495C22⋊C4—181no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—31no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—121no—
511C22×C3—121no—
512C22×C3—121no—
513C22×C3C2×#20412yes—
514C22×C3D3×SD1612yes—
515C22×C3C22×D1211yescharacteristic
516C22×C3C2×D3×D411yescharacteristic
517C2×D3—41no—
518C2×D3—41no—
519C2×D3—41no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—241no—
527C2×D3—241no—
528C2×D3—241no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—32no—
533C3×C4—32no—
534C3×C4—32no—
535C3×C4—41no—
536C3×C4—61no—
537C3×C4—121no—
538C3×C4—122no—
539C3×C4#100412yes—
540C3×C4#100912yes—
541Dic3—21no—
542Dic3—41no—
543Dic3—42no—
544Dic3—124no—
545Dic3—121no—
546Dic3—121no—
547Dic3—122no—
548Dic3—122no—
549Dic3—241no—
550Dic3C2×#20412yes—
551Dic3C2×#20412yes—
552Dic3#90912yes—
553C32#320611yescharacteristic, complemented, Sylow
554C23—61no—
555C23—181no—
556C23D3×D1211yescharacteristic
557Q8—62no—
558Q8—62no—
559Q8—122no—
560Q8—182no—
561Q8—182no—
562Q8—362no—
563Q8—362no—
564D4—62no—
565D4—122no—
566D4—182no—
567D4—362no—
568D4—362no—
569D4—362no—
570C2×C4—22no—
571C2×C4—31no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—34no—
575C2×C4—31no—
576C2×C4—62no—
577C2×C4—61no—
578C2×C4—62no—
579C2×C4—122no—
580C2×C4—181no—
581C2×C4—182no—
582C2×C4—362no—
583C2×C4—362no—
584C2×C4—362no—
585C2×C4D3×D1211yescharacteristic
586C2×C4C22×D3211yescharacteristic
587C8—22no—
588C8—62no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—42no—
595C2×C3—241no—
596C2×C3#552511yescharacteristic
597C2×C3#559211yescharacteristic
598C2×C3C22×#20411yescharacteristic
599C2×C3C2×#90911yescharacteristic
600C2×C3C2×D3×SD1611yescharacteristic
601C2×C3D3×#13711yescharacteristic
602D3—81no—
603D3—241no—
604D3—241no—
605D3—481no—
606C22—21no—
607C22—21no—
608C22—121no—
609C22—121no—
610C22—121no—
611C22—361no—
612C22—361no—
613C22—361no—
614C22D3×#20412yes—
615C22C2×D3×D1211yescharacteristic
616C4—21no—
617C4—32no—
618C4—32no—
619C4—32no—
620C4—61no—
621C4—122no—
622C4—121no—
623C4—362no—
624C4—361no—
625C4#6431412yes—
626C3—21no—
627C3#7931211yescharacteristic, complemented
628C3#8003411yescharacteristic, complemented
629C2—22no—
630C2—241no—
631C2—721no—
632C2#1059408011yescharacteristic
633C2C2×D3×#20411yescharacteristic
634C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594910C2
hypercenterC22⋊C8D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63866C2semidirect
3. #10592437C2semidirect
4. C3×#4738C2semidirect
5. C3×#4718C2semidirect
6. #10591181C2semidirect
7. #10591174C2semidirect
8. #10590890C2semidirect
9. #10590877C2semidirect
10. #10590760C2semidirect
11. #10590752C2semidirect
64. #4738D3semidirect
65. #4718D3semidirect
197. C2×C3×Dic3SD16semidirect
421. C2×Dic3#204semidirect
553. C32#3206semidirect
627. C3#79312semidirect
628. C3#80034semidirect

Maximal subgroups

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

subgroupindex
#105949102
C2×#638662
#105924372
C3×#47382
C3×#47182
#105911812
#105911742
#105908902
#105908772
#105907602
#105907522
#800343
#793123