Finite Group Databasebeta

← #11792285

Subgroups — #11792285

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595043C211yesmaximal, characteristic
2C2×#63833C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6C2×C3×#805C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70393—31nomaximal
9#69694—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63978—22no—
18#63916—21no—
19#63909—21no—
20#63871—21no—
21#63857—21no—
22C2×#3719—21no—
23C2×#3718—21no—
24#63833—22no—
25#63833—22no—
26C2×#3717—21no—
27#63827—22no—
28#63827—22no—
29C2×#3715—21no—
30#63632—22no—
31C3×C3⋊#95—22no—
32C3×#805—22no—
33#5833—31no—
34C2×#951—31no—
35C2×#942—31no—
36C2×#942—31no—
37C2×#909—31no—
38#5510—31no—
39C2×C3×#104—31no—
40C3×#391—31no—
41#4929D311yescharacteristic, complemented
42C2×#805—31no—
43C2×#805—31no—
44C2×#805—61no—
45C2×#805D311yescharacteristic, complemented
46#4554—31no—
47#4530—31no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51#3828—21no—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634D411yescharacteristic
58C2×C3×#67—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D412yes—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C2×C3×D12D411yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6D412yescomplemented
74C2×#626—22no—
75C32×C42—21no—
76C32×C42—21no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×#208—21no—
83C3×#208D412yescomplemented
84C2×C3×C3⋊C8—21no—
85Dic3⋊Dic3—22no—
86#3722—22no—
87(C2×D3)⋊Dic3—22no—
88#3719—24no—
89#3718—24no—
90#3717—24no—
91#3715—24no—
92#2007—91noSylow
93C2×C3×#41—31no—
94C22×C3×Q8—31no—
95C2×#235—31no—
96C2×#235—31no—
97C2×#235—61no—
98C2×#235C2×D311yescharacteristic
99C22×Dic6C2×D311yescharacteristic
100C2×C3×M16—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C42—21no—
103C2×C3×C42C2×D311yescharacteristic
104C2×C3×C42C2×D311yescharacteristic
105#951—62no—
106#951—62no—
107#946—61no—
108C2×#216—61no—
109C2×#216—61no—
110C2×#216—61no—
111#942—62no—
112#942—62no—
113#942—62no—
114#942—62no—
115C2×#215—61no—
116C2×#215—61no—
117#939—62no—
118#938—61no—
119C2×#214—61no—
120#930—61no—
121#930—62no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123#924—61no—
124C2×#208—31no—
125C2×#208—31no—
126C2×#208—61no—
127C2×#208C2×D311yescharacteristic
128#909—62no—
129#909—62no—
130C2×Dic12—61no—
131C2×#204—61no—
132#897—61no—
133#897—61no—
134#895—61no—
135#895—61no—
136C3×#104—62no—
137C3×#95—62no—
138C3⋊#95—22no—
139#805—22no—
140#805—62no—
141#805—62no—
142#805—64no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—21no—
145C22×C3×D3—21no—
146C2×C32×C4—22no—
147C2×C32×C4—41no—
148C2×C32×C4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4111yescharacteristic
155#638—41no—
156#638—41no—
157C2×C3⋊Dic3—21no—
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—21no—
160C4×C3⋊D3—41no—
161C4×C3⋊D3—41no—
162#634—21no—
163#634—21no—
164C3×#67—41no—
165C3×#67—41no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—42no—
172C3×D12—21no—
173C3×D12—21no—
174C3×C4×D3—41no—
175C3×C4×D3—41no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—21no—
180C3×Dic6—41no—
181C3×Dic6—41no—
182#626—82no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185C2×#137—91no—
186C2×#137—91no—
187#537—91no—
188C2×#104—31no—
189C2×#104—91no—
190#391—31no—
191#343—91no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C3×#41—61no—
196C2×C3×Q8—32no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×D4—31no—
204C2×C3×D4—61no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—41no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—21no—
215C2×#67—62no—
216C2×#67—61no—
217C2×#67—61no—
218C2×#67—121no—
219C22×Dic3—21no—
220C22×Dic3#6712yes—
221#235—21no—
222#235—21no—
223#235—21no—
224#235—21no—
225#235—62no—
226#235—62no—
227#235—61no—
228#235—61no—
229#235—61no—
230#235—61no—
231#235—61no—
232#235—61no—
233#235—61no—
234#235—61no—
235#235—121no—
236#235—121no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12—62no—
241C2×D12D1211yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×Dic6—21no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—31no—
252C2×Dic6—31no—
253C2×Dic6—61no—
254C2×Dic6D1211yescharacteristic
255C2×Dic6D1212yescomplemented
256C3×M16—32no—
257C3×M16—61no—
258C2×C3×C8—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C42—22no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—41no—
267#217—62no—
268#216—64no—
269#216—64no—
270#216—64no—
271#215—64no—
272#215—64no—
273#214—64no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—62no—
280Dic3⋊C4—62no—
281#208—21no—
282#208—32no—
283#208—32no—
284#208—62no—
285#208—61no—
286#208—61no—
287#208—121no—
288#208#6712yescomplemented
289C2×C3⋊C8—21no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—121no—
293Dic12—64no—
294#204—64no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32#12011yescharacteristic
298C22×C32#12111yescharacteristic
299C22×C32#12711yescharacteristic
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C32×C4—42no—
307C32×C4#12011yescharacteristic
308C32×C4#12011yescharacteristic
309C32×C4#12111yescharacteristic
310C32×C4#12111yescharacteristic
311C3⋊Dic3—41no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41—91no—
317C22×Q8—31no—
318#137—182no—
319#137—182no—
320#137—182no—
321#137—182no—
322C2×Q16—181no—
323C2×Q16—181no—
324C2×SD16—181no—
325C2×SD16—181no—
326C2×M16—31no—
327C2×M16—91no—
328C22⋊Q8—181no—
329C22⋊Q8—181no—
330#121—181no—
331#121—181no—
332#121—182no—
333C2×C4⋊C4—31no—
334C2×C42D3211yescharacteristic
335#104—62no—
336#104—182no—
337#95—62no—
338C23×C3—21no—
339C23×C3—61no—
340C23×C3D3×D411yescharacteristic
341C23×C3C2×#6711yescharacteristic
342C22×D3—21no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—121no—
346C3×Q8—62no—
347C3×Q8—61no—
348C3×Q8—61no—
349C3×Q8—62no—
350C3×Q8—121no—
351C3×Q8—121no—
352C3×D4—61no—
353C3×D4—61no—
354C3×D4—121no—
355C3×D4—121no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—42no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—122no—
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4#23511yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391#67—41no—
392#67—41no—
393#67—122no—
394#67—122no—
395#67—121no—
396#67—121no—
397#67—121no—
398#67—121no—
399#67—242no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—42no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—121no—
409D12—21no—
410D12—21no—
411D12—62no—
412D12—61no—
413D12—61no—
414D12—61no—
415D12—61no—
416D12—121no—
417D12—242no—
418C4×D3—41no—
419C4×D3—41no—
420C4×D3—122no—
421C4×D3—122no—
422C4×D3—121no—
423C4×D3—121no—
424C4×D3—121no—
425C4×D3—121no—
426Dic6—22no—
427Dic6—22no—
428Dic6—21no—
429Dic6—21no—
430Dic6—41no—
431Dic6—41no—
432Dic6—62no—
433Dic6—61no—
434Dic6—61no—
435Dic6—61no—
436Dic6—61no—
437Dic6—121no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—62no—
441C3⋊C8—62no—
442C3⋊C8—122no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32#39211yescharacteristic
446C2×C32#45511yescharacteristic
447C2×C32#45611yescharacteristic
448C3⋊D3—81no—
449C3×D3—81no—
450#41—61no—
451#41—61no—
452#41—61no—
453#41—61no—
454#41—181no—
455#41—181no—
456#41—181no—
457#41—181no—
458C2×Q8—31no—
459C2×Q8—32no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×Q8—61no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—91no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—91no—
469C2×D4—182no—
470C2×D4—181no—
471C22×C4—21no—
472C22×C4—32no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477Q16—184no—
478Q16—184no—
479SD16—184no—
480SD16—184no—
481M16—32no—
482M16—61no—
483M16—92no—
484M16—181no—
485C2×C8—61no—
486C2×C8—181no—
487C4⋊C4—61no—
488C4⋊C4—61no—
489C4⋊C4—182no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C42—21no—
493C42—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3—121no—
506C22×C3#88211yescharacteristic
507C22×C3#88411yescharacteristic
508C22×C3#93011yescharacteristic
509C22×C3#93711yescharacteristic
510C22×C3#94011yescharacteristic
511C22×C3#94011yescharacteristic
512C2×D3—41no—
513C2×D3—41no—
514C2×D3—41no—
515C2×D3—122no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—241no—
523C2×D3—241no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—42no—
529C3×C4—42no—
530C3×C4—44no—
531C3×C4—121no—
532C3×C4—122no—
533C3×C4—122no—
534C3×C4#88211yescharacteristic
535C3×C4#88211yescharacteristic
536C3×C4#88211yescharacteristic
537C3×C4#88411yescharacteristic
538C3×C4#88411yescharacteristic
539C3×C4#88411yescharacteristic
540C3×C4#93011yescharacteristic
541C3×C4#93711yescharacteristic
542Dic3—42no—
543Dic3—41no—
544Dic3—42no—
545Dic3—122no—
546Dic3—121no—
547Dic3—121no—
548C32#200711yescharacteristic, complemented, Sylow
549C23—61no—
550C23—181no—
551C23D3×#6711yescharacteristic
552Q8—61no—
553Q8—62no—
554Q8—62no—
555Q8—61no—
556Q8—121no—
557Q8—121no—
558Q8—181no—
559Q8—181no—
560D4—61no—
561D4—61no—
562D4—121no—
563D4—121no—
564D4—181no—
565D4—181no—
566D4—361no—
567D4—361no—
568D4—722no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—61no—
575C2×C4—121no—
576C2×C4—121no—
577C2×C4—121no—
578C2×C4—121no—
579C2×C4—122no—
580C2×C4—181no—
581C2×C4—361no—
582C2×C4—361no—
583C2×C4#379811yescharacteristic
584C2×C4D3×D1211yescharacteristic
585C2×C4D3×D1211yescharacteristic
586C2×C4#380211yescharacteristic
587C2×C4D3×#6711yescharacteristic
588C2×C4#381111yescharacteristic
589C8—62no—
590C8—182no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—241no—
601C2×C3#482511yescharacteristic
602C2×C3#482611yescharacteristic
603C2×C3#496011yescharacteristic
604C2×C3#496011yescharacteristic
605C2×C3#506111yescharacteristic
606C2×C3#509511yescharacteristic
607D3—81no—
608D3—242no—
609D3—241no—
610D3—241no—
611C22—21no—
612C22—21no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22—361no—
617C22—361no—
618C22—361no—
619C22#6390611yescharacteristic
620C22#6392211yescharacteristic
621C22#6397911yescharacteristic
622C4—42no—
623C4—121no—
624C4—122no—
625C4—122no—
626C4—361no—
627C4#6390611yescharacteristic
628C4#6391211yescharacteristic
629C4#6392211yescharacteristic
630C4#6392311yescharacteristic
631C3—21no—
632C3#6969411yescharacteristic, complemented
633C3#7039311yescharacteristic, complemented
634C2—21no—
635C2—21no—
636C2—241no—
637C2—721no—
638C2#1059039611yescharacteristic
639C2#1059039911yescharacteristic
640C2#1059139311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radical#10595043C2
hypercenterC2×C42D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63833C2semidirect
3. C2×#63827C2semidirect
4. C2×#63632C2semidirect
5. C3×#4929C2semidirect
6. C2×C3×#805C2semidirect
7. #10589167C2semidirect
41. #4929D3semidirect
45. C2×#805D3semidirect
73. C2×C3×Dic6D4semidirect
78. #3748D4semidirect
83. C3×#208D4semidirect
255. C2×Dic6D12semidirect
288. #208#67semidirect
548. C32#2007semidirect
632. C3#69694semidirect
633. C3#70393semidirect

Maximal subgroups

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

subgroupindex
#105950432
C2×#638332
C2×#638272
C2×#636322
C3×#49292
C2×C3×#8052
#105891672
#703933
#696943