Finite Group Databasebeta

← #11791405

Subgroups — #11791405

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595029C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#70358—31nomaximal
9#69867—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63978—21no—
18#63978—21no—
19C2×Dic3⋊Dic3—21no—
20#63911C411yescharacteristic, complemented
21C4×#626—21no—
22C4×#626—21no—
23#63866C411yescharacteristic, complemented
24#63864C411yescharacteristic, complemented
25#63860C411yescharacteristic, complemented
26#63652—22no—
27C3×#825—22no—
28C3×#815—21no—
29C3×C8×Dic3—21no—
30#63579—21no—
31#63570—22no—
32#63568—22no—
33#5832—31no—
34#5477—31no—
35C2×C3×#104—31no—
36C3×C4×M16—31no—
37C2×#837—31no—
38C2×#825—31no—
39C2×#825—31no—
40C2×#825—31no—
41C2×#825—31no—
42C2×#825—61no—
43C2×#825D311yescharacteristic, complemented
44Dic3×M16D311yescharacteristic, complemented
45C4×C4⋊Dic3—31no—
46C4×Dic3⋊C4—31no—
47C2×#805—31no—
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)C2×C411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634C2×C411yescharacteristic
58C2×C3×#67—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12C2×C411yescharacteristic
67C2×C3×C4×D3—21no—
68C2×C3×Dic6C2×C411yescharacteristic
69C2×#626—21no—
70C2×#626—21no—
71C32×M16—21no—
72C32×M16D412yescomplemented
73C2×C32×C8—21no—
74C4×C3⋊Dic3—21no—
75C4×C3⋊Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3C2×C411yescharacteristic
79C3×C4×Dic3C2×C411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3D411yescharacteristic
82C3×#208—21no—
83C3×#208D412yescomplemented
84C2×C3×C3⋊C8—21no—
85Dic3⋊Dic3—24no—
86Dic3⋊Dic3—21no—
87Dic3⋊Dic3—21no—
88#3722—21no—
89#3722—21no—
90(C2×D3)⋊Dic3—21no—
91(C2×D3)⋊Dic3—21no—
92#1980—91noSylow
93C2×C3×#41—31no—
94C2×#235—31no—
95C2×#235—31no—
96C2×#235—61no—
97C2×#235C2×D311yescharacteristic
98C2×C3×M16—21no—
99C2×C3×M16—31no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102C2×C3×C42—31no—
103C2×C3×C42—31no—
104#947—31no—
105#944—31no—
106#940—31no—
107#939—61no—
108#939—61no—
109#936—31no—
110#930—61no—
111#930—61no—
112C4×#67—61no—
113C4×#67—61no—
114C2×C4⋊Dic3—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3C2×D311yescharacteristic
120C2×C4×Dic3C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122#875—31no—
123#875—31no—
124#874—31no—
125C4×D12—61no—
126C4×D12—61no—
127#869—31no—
128C3×#104—62no—
129C3×#97—61no—
130C3×C4×C8—61no—
131#837—62no—
132C3⋊#95—61no—
133C3⋊#95—61no—
134#825—22no—
135#825—62no—
136#825—64no—
137#825—62no—
138#825—62no—
139#825—62no—
140#815—21no—
141C8×Dic3—21no—
142#805—62no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—21no—
145C22×C3×D3—21no—
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
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—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3C22⋊C411yescharacteristic
173C2×C3×Dic3C22⋊C411yescharacteristic
174C2×C3×Dic3C22⋊C411yescharacteristic
175C2×C3×Dic3C22⋊C411yescharacteristic
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—41no—
179C3×C4×D3—41no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182#626—42no—
183#626—42no—
184C32×C8—22no—
185C3×C3⋊C8—22no—
186#532—91no—
187C2×#104—31no—
188C2×#104—91no—
189C2×#104—91no—
190C2×#104—91no—
191C4×M16—31no—
192C4×C4⋊C4—91no—
193C3×#41—61no—
194C3×#41—61no—
195C3×#41—61no—
196C3×#41—61no—
197C2×C3×Q8—31no—
198C2×C3×D4—31no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C2×#67—61no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—121no—
213C22×Dic3—21no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—121no—
217C22×Dic3D1211yescharacteristic
218C22×Dic3D1211yescharacteristic
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223#235—62no—
224#235—62no—
225#235—61no—
226#235—61no—
227#235—61no—
228#235—61no—
229#235—61no—
230#235—61no—
231#235—61no—
232#235—61no—
233#235—121no—
234#235—121no—
235C2×D12—31no—
236C2×D12—31no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12C4×D311yescharacteristic
241C2×C4×D3—21no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—121no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C2×Dic6—61no—
248C2×Dic6C4×D311yescharacteristic
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—22no—
252C3×M16—32no—
253C3×M16—41no—
254C3×M16—61no—
255C3×M16D1212yescomplemented
256C3×M16#6712yescomplemented
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—41no—
260C2×C3×C8—61no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42—61no—
266C3×C42—61no—
267#217—61no—
268#217—61no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—64no—
278Dic3⋊C4—64no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283C4×Dic3—62no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—121no—
289C4×Dic3C4×D311yescharacteristic
290C4×Dic3C4×D311yescharacteristic
291C4×Dic3#6711yescharacteristic
292C4×Dic3#6711yescharacteristic
293#208—21no—
294#208D1212yescomplemented
295C2×C3⋊C8—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C2×C22⋊C411yescharacteristic
299C22×C32#12411yescharacteristic
300C22×C32#12711yescharacteristic
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C32×C4C4×D411yescharacteristic
308C32×C4C4×D411yescharacteristic
309C32×C4#12111yescharacteristic
310C32×C4#12111yescharacteristic
311C3⋊Dic3—42no—
312C3⋊Dic3—41no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3#10412yescomplemented
319C2×#41—31no—
320C2×#41—91no—
321C2×M16—31no—
322C2×M16D3211yescharacteristic
323C4⋊Q8—91no—
324#127—91no—
325#124—91no—
326#124—91no—
327#121—181no—
328#121—181no—
329C4×D4—181no—
330C4×D4—181no—
331C2×C4⋊C4—181no—
332C2×C42—31no—
333C2×C42—31no—
334C2×C42—91no—
335#104—62no—
336#104—182no—
337#104—182no—
338#104—182no—
339#97—61no—
340C4×C8—61no—
341#95—181no—
342C23×C3—21no—
343C23×C3—61no—
344C23×C3C2×D1211yescharacteristic
345C23×C3D3×D411yescharacteristic
346C22×D3—21no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—121no—
350C3×Q8—61no—
351C3×Q8—61no—
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—31no—
363C2×C3×C4—31no—
364C2×C3×C4—31no—
365C2×C3×C4—31no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—121no—
370C2×C3×C4—121no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4C2×C4×D311yescharacteristic
376C2×C3×C4C2×D1211yescharacteristic
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4#23511yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386#67—41no—
387#67—41no—
388#67—122no—
389#67—122no—
390#67—122no—
391#67—121no—
392#67—121no—
393#67—121no—
394#67—121no—
395#67—122no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—121no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3—121no—
410C2×Dic3—121no—
411C2×Dic3—122no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3(C2×D3)⋊C411yescharacteristic
415C2×Dic3(C2×D3)⋊C411yescharacteristic
416C2×Dic3(C2×D3)⋊C411yescharacteristic
417C2×Dic3(C2×D3)⋊C411yescharacteristic
418D12—21no—
419D12—21no—
420D12—62no—
421D12—61no—
422D12—61no—
423D12—61no—
424D12—61no—
425D12—121no—
426D12—122no—
427D12—122no—
428C4×D3—41no—
429C4×D3—41no—
430C4×D3—122no—
431C4×D3—122no—
432C4×D3—121no—
433C4×D3—121no—
434C4×D3—121no—
435C4×D3—121no—
436Dic6—21no—
437Dic6—21no—
438Dic6—62no—
439Dic6—61no—
440Dic6—61no—
441Dic6—61no—
442Dic6—61no—
443Dic6—121no—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—42no—
447C3×C8—62no—
448C3⋊C8—22no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32#39011yescharacteristic
452C2×C32C2×#10411yescharacteristic
453C2×C32#42111yescharacteristic
454C3⋊D3—81no—
455C3×D3—81no—
456#41—61no—
457#41—61no—
458#41—61no—
459#41—61no—
460#41—181no—
461#41—181no—
462#41—181no—
463#41—181no—
464C2×Q8—31no—
465C2×Q8—91no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—91no—
469C2×D4—181no—
470C2×D4—181no—
471C2×D4—181no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4C2×D3211yescharacteristic
479M16—21no—
480M16—32no—
481M16—61no—
482M16#62612yescomplemented
483C2×C8—21no—
484C2×C8—61no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4—184no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—31no—
496C42—61no—
497C42—61no—
498C42—181no—
499C42—181no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—121no—
510C22×C3—121no—
511C22×C3—121no—
512C22×C3#87411yescharacteristic
513C22×C3#87511yescharacteristic
514C22×C3D3×C22⋊C411yescharacteristic
515C22×C3#88511yescharacteristic
516C22×C3C2×(C2×D3)⋊C411yescharacteristic
517C22×C3#94011yescharacteristic
518C2×D3—41no—
519C2×D3—41no—
520C2×D3—41no—
521C2×D3—122no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—241no—
529C2×D3—241no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—32no—
535C3×C4—61no—
536C3×C4—61no—
537C3×C4—61no—
538C3×C4—122no—
539C3×C4—121no—
540C3×C4C4×D1211yescharacteristic
541C3×C4C4×D1211yescharacteristic
542C3×C4#67⋊C411yescharacteristic
543C3×C4#88411yescharacteristic
544C3×C4C4×#6711yescharacteristic
545C3×C4#93011yescharacteristic
546C3×C4#93011yescharacteristic
547C3×C4#93911yescharacteristic
548Dic3—21no—
549Dic3—21no—
550Dic3—21no—
551Dic3—42no—
552Dic3—41no—
553Dic3—122no—
554Dic3—122no—
555Dic3—122no—
556Dic3—124no—
557Dic3—121no—
558Dic3—121no—
559Dic3#82512yescomplemented
560C32#198011yescharacteristic, complemented, Sylow
561C23—61no—
562C23—181no—
563C23D3×D1211yescharacteristic
564Q8—61no—
565Q8—61no—
566Q8—181no—
567Q8—181no—
568D4—61no—
569D4—61no—
570D4—121no—
571D4—121no—
572D4—181no—
573D4—181no—
574D4—362no—
575D4—362no—
576D4—361no—
577D4—361no—
578C2×C4—31no—
579C2×C4—31no—
580C2×C4—31no—
581C2×C4—31no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—121no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—121no—
589C2×C4—121no—
590C2×C4—182no—
591C2×C4—181no—
592C2×C4—361no—
593C2×C4—361no—
594C2×C4—361no—
595C2×C4—361no—
596C2×C4#379811yescharacteristic
597C2×C4C4×D3211yescharacteristic
598C2×C4D3×D1211yescharacteristic
599C2×C4#380411yescharacteristic
600C2×C4C2×#62611yescharacteristic
601C2×C4D3×#6711yescharacteristic
602C8—22no—
603C8—62no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—241no—
614C2×C3D3×#10411yescharacteristic
615C2×C3#482111yescharacteristic
616C2×C3#493911yescharacteristic
617C2×C3#495711yescharacteristic
618C2×C3C2×#82511yescharacteristic
619C2×C3#513911yescharacteristic
620D3—81no—
621D3—242no—
622D3—241no—
623D3—241no—
624C22—21no—
625C22—21no—
626C22—121no—
627C22—121no—
628C22—121no—
629C22—361no—
630C22—361no—
631C22—361no—
632C22#6385211yescharacteristic
633C22#6391111yescharacteristic
634C22D3×(C2×D3)⋊C411yescharacteristic
635C4—32no—
636C4—61no—
637C4—61no—
638C4—61no—
639C4—122no—
640C4—121no—
641C4—362no—
642C4—361no—
643C4#6388011yescharacteristic
644C4C4×#62611yescharacteristic
645C4#6390611yescharacteristic
646C4#6397811yescharacteristic
647C3—21no—
648C3#6986711yescharacteristic, complemented
649C3#7035811yescharacteristic, complemented
650C2—21no—
651C2—21no—
652C2—241no—
653C2—721no—
654C2D3×#82511yescharacteristic
655C2#1059100511yescharacteristic
656C2#1059138311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595029C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63652C2semidirect
3. C2×C3×#825C2semidirect
4. C3×Dic3×M16C2semidirect
5. C4×Dic3⋊Dic3C2semidirect
6. C2×#63570C2semidirect
7. C2×#63568C2semidirect
20. #63911C4semidirect
23. #63866C4semidirect
24. #63864C4semidirect
25. #63860C4semidirect
43. C2×#825D3semidirect
44. Dic3×M16D3semidirect
72. C32×M16D4semidirect
83. C3×#208D4semidirect
255. C3×M16D12semidirect
256. C3×M16#67semidirect
294. #208D12semidirect
318. C3×Dic3#104semidirect
482. M16#626semidirect
559. Dic3#825semidirect
560. C32#1980semidirect
648. C3#69867semidirect
649. C3#70358semidirect

Maximal subgroups

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

subgroupindex
#105950292
C2×#636522
C2×C3×#8252
C3×Dic3×M162
C4×Dic3⋊Dic32
C2×#635702
C2×#635682
#703583
#698673