Finite Group Databasebeta

← #11792280

Subgroups — #11792280

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
1C2×C3×#909C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5#10591221C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#72110—31nomaximal
9#69009—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#909—22no—
18C3×#909—22no—
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21#63978—22no—
22#63916—21no—
23#63909—21no—
24#63871—21no—
25#63857—21no—
26C2×#3719—21no—
27#63833—22no—
28#63833—22no—
29C2×#3717—21no—
30#63652—22no—
31#63579—22no—
32#63568—22no—
33C2×C3×#137—31no—
34#5833—31no—
35C2×#942—31no—
36C2×#909—31no—
37C2×#909D311yescharacteristic, complemented
38#5510—31no—
39C2×#837—31no—
40#5229—31no—
41C2×#825—31no—
42C2×#825—31no—
43C2×#825—31no—
44C2×#825—61no—
45#4973—31no—
46C3×#343—31no—
47#4554D311yescharacteristic, complemented
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C22×C3⋊Dic3—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×M16—21no—
76C32×M16D412yescomplemented
77C2×C32×C8—21no—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×#208—21no—
83C3×#208D412yescomplemented
84C2×C3×C3⋊C8—21no—
85C3×Dic12—24no—
86C3×#204—24no—
87Dic3⋊Dic3—22no—
88#3722—22no—
89(C2×D3)⋊Dic3—22no—
90#3719—24no—
91#3717—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
100C3×#137—62no—
101C3×#137—62no—
102C2×C3×Q16—61no—
103C2×C3×SD16—61no—
104C2×C3×M16—21no—
105C2×C3×M16—31no—
106C2×C3×M16C2×D311yescharacteristic
107C2×C3×M16C2×D311yescharacteristic
108C2×C3×C4⋊C4—31no—
109#946—61no—
110C2×#216—61no—
111#942—62no—
112#942—62no—
113C2×#215—61no—
114#939—62no—
115#938—61no—
116#930—61no—
117#930—62no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119#924—61no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—61no—
123C2×#208C2×D311yescharacteristic
124#909—22no—
125#909—22no—
126#909—62no—
127#909—62no—
128C2×Dic12—21no—
129C2×Dic12—61no—
130C2×#204—21no—
131C2×#204—61no—
132#897—61no—
133#897—61no—
134#895—61no—
135#895—61no—
136#837—62no—
137C3⋊#95—62no—
138C3⋊#95—62no—
139#825—64no—
140#825—62no—
141#825—62no—
142#825—62no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—21no—
145C22×C3×D3—21no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152#638—41no—
153#638—41no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—41no—
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—
183C32×C8—22no—
184C3×C3⋊C8—22no—
185C2×#137—31no—
186C2×#137—91no—
187#537—91no—
188C2×#104—91no—
189C2×#104—91no—
190#391—91no—
191#343—31no—
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—32no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—21no—
212C2×#67—62no—
213C2×#67—61no—
214C2×#67—61no—
215C2×#67—121no—
216C22×Dic3—21no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—121no—
220C22×Dic3D1212yes—
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×D12#6711yescharacteristic
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×Dic6#6711yescharacteristic
255C2×Dic6#6712yescomplemented
256C3×Q16—64no—
257C3×SD16—64no—
258C3×M16—21no—
259C3×M16—21no—
260C3×M16—22no—
261C3×M16—32no—
262C3×M16—41no—
263C3×M16—61no—
264C3×M16D1212yescomplemented
265C3×M16#6712yescomplemented
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—41no—
269C2×C3×C8—61no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272#217—62no—
273#216—64no—
274#215—64no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—62no—
281Dic3⋊C4—62no—
282C4×Dic3—62no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—121no—
288#208—21no—
289#208D1212yescomplemented
290C2×C3⋊C8—21no—
291Dic12—24no—
292Dic12—64no—
293#204—24no—
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#12011yescharacteristic
307C32×C4#12011yescharacteristic
308C32×C4#12111yescharacteristic
309C32×C4#12111yescharacteristic
310C3⋊Dic3—42no—
311C3⋊Dic3—41no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41—91no—
317C22×Q8—31no—
318#137—62no—
319#137—62no—
320#137—182no—
321#137—182no—
322C2×Q16—61no—
323C2×Q16—181no—
324C2×SD16—61no—
325C2×SD16—181no—
326C2×M16—31no—
327C2×M16D3211yescharacteristic
328C22⋊Q8—181no—
329C22⋊Q8—181no—
330#121—181no—
331#121—181no—
332#121—182no—
333C2×C4⋊C4—31no—
334C2×C42—91no—
335#104—182no—
336#104—182no—
337#95—182no—
338C23×C3—21no—
339C23×C3—61no—
340C23×C3C2×D1211yescharacteristic
341C23×C3D3×D411yescharacteristic
342C22×D3—21no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—121no—
346C3×Q8—62no—
347C3×Q8—62no—
348C3×Q8—61no—
349C3×Q8—61no—
350C3×Q8—121no—
351C3×Q8—121no—
352C3×D4—61no—
353C3×D4—61no—
354C3×D4—121no—
355C3×D4—121no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—122no—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4#23911yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382#67—41no—
383#67—41no—
384#67—122no—
385#67—122no—
386#67—121no—
387#67—121no—
388#67—121no—
389#67—121no—
390#67—242no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—42no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—122no—
407C2×Dic3—121no—
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—21no—
428Dic6—22no—
429Dic6—21no—
430Dic6—41no—
431Dic6—41no—
432Dic6—62no—
433Dic6—61no—
434Dic6—61no—
435Dic6—61no—
436Dic6—61no—
437Dic6—121no—
438C3×C8—22no—
439C3×C8—22no—
440C3×C8—42no—
441C3×C8—62no—
442C3⋊C8—22no—
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—32no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477Q16—64no—
478Q16—184no—
479SD16—64no—
480SD16—184no—
481M16—21no—
482M16—32no—
483M16—61no—
484M16#62612yescomplemented
485C2×C8—21no—
486C2×C8—61no—
487C4⋊C4—61no—
488C4⋊C4—61no—
489C4⋊C4—182no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C42—181no—
493C42—181no—
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#87411yescharacteristic
507C22×C3#88211yescharacteristic
508C22×C3#89511yescharacteristic
509C22×C3#93711yescharacteristic
510C22×C3#93911yescharacteristic
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—121no—
529C3×C4—122no—
530C3×C4—122no—
531C3×C4#88211yescharacteristic
532C3×C4#88211yescharacteristic
533C3×C4#89511yescharacteristic
534C3×C4#89511yescharacteristic
535C3×C4#93711yescharacteristic
536C3×C4#93811yescharacteristic
537C3×C4#93911yescharacteristic
538C3×C4#95311yescharacteristic
539Dic3—42no—
540Dic3—41no—
541Dic3—42no—
542Dic3—122no—
543Dic3—122no—
544Dic3—122no—
545Dic3—124no—
546Dic3—121no—
547Dic3—121no—
548C32#200711yescharacteristic, complemented, Sylow
549C23—61no—
550C23—181no—
551C23D3×D1211yescharacteristic
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—62no—
570C2×C4—62no—
571C2×C4—61no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4—121no—
576C2×C4—122no—
577C2×C4—182no—
578C2×C4—181no—
579C2×C4—361no—
580C2×C4—361no—
581C2×C4—361no—
582C2×C4—361no—
583C2×C4#379611yescharacteristic
584C2×C4D3×D1211yescharacteristic
585C2×C4#380211yescharacteristic
586C2×C4C2×#62611yescharacteristic
587C2×C4D3×#6711yescharacteristic
588C2×C4D3×#6711yescharacteristic
589C8—22no—
590C8—62no—
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#467111yescharacteristic
602C2×C3#474611yescharacteristic
603C2×C3#475211yescharacteristic
604C2×C3#520211yescharacteristic
605C2×C3#520511yescharacteristic
606C2×C3#522311yescharacteristic
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#6388611yescharacteristic
620C22#6391111yescharacteristic
621C22#6392211yescharacteristic
622C4—122no—
623C4—121no—
624C4—122no—
625C4—362no—
626C4—361no—
627C4#6388611yescharacteristic
628C4#6391611yescharacteristic
629C4#6392211yescharacteristic
630C4#6397711yescharacteristic
631C3—21no—
632C3#6900911yescharacteristic, complemented
633C3#7211011yescharacteristic, complemented
634C2—21no—
635C2—21no—
636C2—241no—
637C2—721no—
638C2#1059101211yescharacteristic
639C2#1059101811yescharacteristic
640C2#1059139111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radical#10595043C2
hypercenterC2×M16D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
3. C2×#63833C2semidirect
4. C2×#63652C2semidirect
5. #10591221C2semidirect
6. C2×#63568C2semidirect
7. C3×#4554C2semidirect
37. C2×#909D3semidirect
47. #4554D3semidirect
73. C2×C3×Dic6D4semidirect
76. C32×M16D4semidirect
83. C3×#208D4semidirect
255. C2×Dic6#67semidirect
264. C3×M16D12semidirect
265. C3×M16#67semidirect
289. #208D12semidirect
484. M16#626semidirect
548. C32#2007semidirect
632. C3#69009semidirect
633. C3#72110semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105950432
C2×#638332
C2×#636522
#105912212
C2×#635682
C3×#45542
#721103
#690093