Finite Group Databasebeta

← C2×#10590931 #11867876

Subgroups — C2×#10590931 #11867876

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2C2×C3×#901C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic
5C2×C3×#819C211yesmaximal, characteristic, complemented
6C2×#63561C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#10590931C218yesmaximal, direct product factor
9C2×#5141—31nomaximal
10C2×#4898—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3744—21no—
16C2×#3744—21no—
17C2×#3744—22no—
18C2×#3744C2214yescomplemented
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#901—22no—
23C3×#901C2214yescomplemented
24C2×C3×ΓL(1,𝔽25)—21no—
25C2×C3×D3×C8—21no—
26C2×#3719—21no—
27C2×#3717—21no—
28#63831—22no—
29#63831C2214yescomplemented
30C2×#3716—21no—
31#63825—22no—
32#63825C2214yes—
33C2×#3714—21no—
34C3×#819C2214yescomplemented
35#63561C2214yescomplemented
36#63559C2214yescomplemented
37C2×C3×#131—31no—
38C2×#951—31no—
39C2×#949—31no—
40C2×#909—31no—
41C2×#908—31no—
42C22×#204—31no—
43C22×#204—31no—
44C22×#204—61no—
45C2×#901D311yescharacteristic, complemented
46C2×C3×#108—31no—
47#5141—38no—
48C2×#824—31no—
49C2×#824—31no—
50C2×#823—31no—
51C2×#823—31no—
52C2×#819D311yescharacteristic, complemented
53#4898—38no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634—21no—
66C2×#634—21no—
67C2×#634—21no—
68C2×#634C2312yes—
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235D412yes—
73C3×#235C2312yes—
74C2×C3×D12D411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C32×C8D411yescharacteristic
78C2×C32×C8D411yescharacteristic
79C2×C32×C8D412yes—
80C2×C32×C8C2312yes—
81#3744—24no—
82#3744—24no—
83C3×#208—21no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208C2312yes—
87C3×#208C2312yes—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8—21no—
92C3×ΓL(1,𝔽25)—24no—
93C3×D3×C8—24no—
94#3719—24no—
95#3717—24no—
96#3716—24no—
97#3714—24no—
98C2×#471—91noSylow
99C2×C3×#41—31no—
100C2×#235C2×D311yescharacteristic
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C22×Dic6—31no—
105C22×Dic6—31no—
106C22×Dic6—61no—
107C3×#131—34no—
108C3×#131—62no—
109C2×C3×M16—31no—
110C2×C3×M16—31no—
111C2×C3×M16—31no—
112C2×C3×M16—61no—
113C22×C3×C8—21no—
114C22×C3×C8—61no—
115C22×C3×C8C2×D311yescharacteristic
116C22×C3×C8C2×D311yescharacteristic
117#951—34no—
118#951—62no—
119#949—34no—
120#949—62no—
121C2×#216—61no—
122C2×#215—61no—
123C2×#214—61no—
124C2×#213—61no—
125C2×#208C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C2×#208C2×D311yescharacteristic
128#909—34no—
129#909—62no—
130#908—34no—
131#908—62no—
132C2×Dic12—61no—
133C2×D24—61no—
134C2×#204—34no—
135C2×#204—34no—
136C2×#204—64no—
137C2×#204—62no—
138C2×#204—62no—
139C2×#204—64no—
140C2×#204—61no—
141C2×#204—61no—
142C2×#204—61no—
143C2×#204—61no—
144C2×#204—62no—
145C2×#204—61no—
146C2×#204—61no—
147C2×#204—62no—
148#901—22no—
149#901C2×D314yescomplemented
150C2×ΓL(1,𝔽25)—21no—
151C2×D3×C8—21no—
152C3×#108—34no—
153#824—34no—
154#824—34no—
155#823—34no—
156#823—34no—
157#819C2×D314yescomplemented
158C23×C32#4111yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3⋊D3—41no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—82no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4#4111yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—41no—
172C2×C3⋊Dic3—41no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—41no—
176C4⋊(C3⋊D3)—41no—
177#634—22no—
178#634—22no—
179#634—41no—
180#634—41no—
181C3×#67—22no—
182C3×#67—22no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12C2×D412yes—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×Dic6—21no—
189C3×Dic6C2×D412yes—
190C32×C8C2×D412yes—
191C32×C8C2×D412yes—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C2×#137—91no—
196C2×AGL(1,ℤ/8)—91no—
197C22×SD16—91no—
198C2×#131—31no—
199#471—98no—
200C2×#108—31no—
201C2×#101—91no—
202C2×#100—91no—
203C23×D3—61no—
204C23×D3—61no—
205C23×D3—121no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C2×C3×Q8—31no—
211C2×C3×D4—31no—
212C2×C3×D4—61no—
213C22×C3×C4—21no—
214C22×C3×C4—61no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C2×#67—21no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—121no—
221#235—21no—
222#235—21no—
223#235D1212yes—
224#235C22×D312yes—
225C2×D12—32no—
226C2×D12—32no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—121no—
241C2×D12—121no—
242C2×D12—121no—
243C2×D12D1211yescharacteristic
244C2×C4×D3—21no—
245C2×Dic6—32no—
246C2×Dic6—32no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6—61no—
260C2×Dic6—121no—
261C2×Dic6—121no—
262C2×Dic6—121no—
263C2×Dic6D1211yescharacteristic
264C3×M16—32no—
265C3×M16—32no—
266C3×M16—32no—
267C3×M16—61no—
268C3×M16—61no—
269C3×M16—61no—
270C3×M16—64no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—22no—
274C2×C3×C8—22no—
275C2×C3×C8—61no—
276C2×C3×C8—61no—
277C2×C3×C8—61no—
278C2×C3×C8—64no—
279C2×C3×C8D1211yescharacteristic
280C2×C3×C8D1211yescharacteristic
281C2×C3×C8D1212yes—
282C2×C3×C8#6711yescharacteristic
283C2×C3×C8#6711yescharacteristic
284C2×C3×C8#6712yes—
285C2×C3×C8C22×D312yes—
286C2×C3×C8C22×D312yes—
287#216—64no—
288#215—64no—
289#214—64no—
290#213—64no—
291#208—21no—
292#208—21no—
293#208—21no—
294#208C22×D312yes—
295#208C22×D312yes—
296#208C22×D312yes—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300Dic12—64no—
301D24—64no—
302#204—68no—
303#204—68no—
304#204—64no—
305#204—64no—
306#204—64no—
307#204—64no—
308#204—64no—
309#204—64no—
310ΓL(1,𝔽25)—24no—
311D3×C8—24no—
312C22×C32—22no—
313C22×C32#12111yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C2×C3⋊D3—42no—
317C2×C3⋊D3—82no—
318C2×C3⋊D3—82no—
319C2×C3⋊D3—82no—
320C2×C3×D3—22no—
321C2×C3×D3—42no—
322C32×C4#12111yescharacteristic
323C32×C4#12111yescharacteristic
324C32×C4C22×D411yescharacteristic
325C32×C4C22×D411yescharacteristic
326C3⋊Dic3—42no—
327C3×Dic3—22no—
328C2×#41—31no—
329C22×Q8—91no—
330C22×D4—91no—
331#137—94no—
332#137—182no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)—182no—
335C2×Q16—181no—
336C2×SD16—94no—
337C2×SD16—181no—
338C2×SD16—181no—
339C2×SD16—181no—
340C2×SD16—181no—
341C2×SD16—182no—
342C2×D8—181no—
343#131—34no—
344#131—62no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—31no—
348C2×M16—61no—
349C22×C8—61no—
350C22×C8D3211yescharacteristic
351#108—34no—
352#101—94no—
353#100—94no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3#23511yescharacteristic
357C23×C3#23911yescharacteristic
358C22×D3—21no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—121no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—244no—
369C22×D3—242no—
370C22×D3—242no—
371C3×Q8—32no—
372C3×Q8—61no—
373C3×D4—32no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—61no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4C2×D1211yescharacteristic
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4#23511yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23911yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—22no—
399#67—22no—
400C2×Dic3—21no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410D12—21no—
411D12—64no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—62no—
416D12—122no—
417D12—122no—
418D12—122no—
419D12—121no—
420D12—121no—
421D12—121no—
422D12—121no—
423D12C2×D1212yes—
424C4×D3—22no—
425C4×D3—22no—
426Dic6—21no—
427Dic6—64no—
428Dic6—62no—
429Dic6—62no—
430Dic6—62no—
431Dic6—62no—
432Dic6—122no—
433Dic6—122no—
434Dic6—122no—
435Dic6—121no—
436Dic6—121no—
437Dic6—121no—
438Dic6—121no—
439Dic6C2×D1212yes—
440C3×C8—22no—
441C3×C8—22no—
442C3×C8—62no—
443C3×C8—62no—
444C3×C8—62no—
445C3×C8C2×D1212yes—
446C3×C8C2×D1212yes—
447C3×C8C2×#6712yes—
448C3×C8C2×#6712yes—
449C3⋊C8—22no—
450C3⋊C8—22no—
451C3⋊C8—22no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32#47112yescomplemented
455C2×C32C2×#12111yescharacteristic
456C3⋊D3—82no—
457C3×D3—42no—
458C24—181no—
459#41—32no—
460#41—32no—
461#41—61no—
462#41—61no—
463C2×Q8—31no—
464C2×Q8—92no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C2×Q8—181no—
470C2×D4—31no—
471C2×D4—61no—
472C2×D4—92no—
473C2×D4—181no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C22×C4—61no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481Q16—184no—
482SD16—184no—
483SD16—184no—
484SD16—184no—
485SD16—184no—
486D8—184no—
487M16—32no—
488M16—32no—
489M16—32no—
490M16—61no—
491M16—61no—
492M16—61no—
493M16—64no—
494C2×C8—61no—
495C2×C8—61no—
496C2×C8—61no—
497C2×C8—64no—
498C2×C8#62611yescharacteristic
499C2×C8#62611yescharacteristic
500C2×C8#62612yes—
501C2×C8C2×D3212yes—
502C22×C3—24no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—62no—
509C22×C3—122no—
510C22×C3#89511yescharacteristic
511C22×C3#89511yescharacteristic
512C22×C3#93011yescharacteristic
513C22×C3#93011yescharacteristic
514C22×C3C2×#23511yescharacteristic
515C22×C3C2×#23911yescharacteristic
516C2×D3—22no—
517C2×D3—42no—
518C2×D3—124no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—244no—
522C2×D3—244no—
523C2×D3—242no—
524C2×D3—242no—
525C2×D3—244no—
526C2×D3—242no—
527C2×D3—242no—
528C2×D3—242no—
529C2×D3—242no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—62no—
535C3×C4#89511yescharacteristic
536C3×C4#89511yescharacteristic
537C3×C4#93011yescharacteristic
538C3×C4#93011yescharacteristic
539C3×C4C22×D1211yescharacteristic
540C3×C4C22×D1211yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C22×#6711yescharacteristic
543Dic3—22no—
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—61no—
549C23—182no—
550C23—361no—
551C23—361no—
552C23—722no—
553C23#379911yescharacteristic
554Q8—32no—
555Q8—61no—
556Q8—182no—
557Q8—182no—
558Q8—361no—
559Q8—361no—
560D4—32no—
561D4—62no—
562D4—62no—
563D4—61no—
564D4—182no—
565D4—182no—
566D4—361no—
567D4—361no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—182no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4#379911yescharacteristic
575C2×C4D3×D1211yescharacteristic
576C2×C4D3×D1211yescharacteristic
577C2×C4C2×#62611yescharacteristic
578C2×C4C2×#62611yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—62no—
581C8—62no—
582C8—62no—
583C8C2×#62612yes—
584C8C2×#62612yes—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—22no—
593C2×C3—122no—
594C2×C3#489812yescomplemented
595C2×C3#514112yescomplemented
596C2×C3C2×#89511yescharacteristic
597C2×C3C2×#93011yescharacteristic
598D3—42no—
599D3—244no—
600D3—242no—
601D3—242no—
602C22—22no—
603C22—62no—
604C22—122no—
605C22—362no—
606C22—722no—
607C22—722no—
608C22—722no—
609C22#6390911yescharacteristic
610C22#6390911yescharacteristic
611C22C2×#379911yescharacteristic
612C4—62no—
613C4—362no—
614C4#6390911yescharacteristic
615C4#6390911yescharacteristic
616C4C2×D3×D1211yescharacteristic
617C4C22×#62611yescharacteristic
618C3—21no—
619C3C2×#489811yescharacteristic, complemented
620C3C2×#514111yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—122no—
624C2—722no—
625C2#1059093112yesdirect product factor
626C2C2×#6390911yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×#63825C2
hypercenterC22×C8D32
hypocenterC32C2×#471
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
1. C22×#3744C2semidirect
2. C2×C3×#901C2semidirect
3. C2×#63831C2semidirect
5. C2×C3×#819C2semidirect
6. C2×#63561C2semidirect
7. C2×#63559C2semidirect
8. #10590931C2direct (N × H)
18. C2×#3744C22semidirect
23. C3×#901C22semidirect
29. #63831C22semidirect
34. C3×#819C22semidirect
35. #63561C22semidirect
36. #63559C22semidirect
45. C2×#901D3semidirect
52. C2×#819D3semidirect
149. #901C2×D3semidirect
157. #819C2×D3semidirect
454. C2×C32#471semidirect
547. C32C2×#471semidirect
594. C2×C3#4898semidirect
595. C2×C3#5141semidirect
619. C3C2×#4898semidirect
620. C3C2×#5141semidirect
625. C2#10590931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C3×#9012
C2×#638312
C2×#638252
C2×C3×#8192
C2×#635612
C2×#635592
#105909312
C2×#51413
C2×#48983