Finite Group Databasebeta

← C2×#10590989 #11867892

Subgroups — C2×#10590989 #11867892

Order 1152.

1065 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
1C2×#64118C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic, complemented
6C2×C3×#822C211yesmaximal, characteristic, complemented
7C2×#63561C211yesmaximal, characteristic, complemented
8#10590989C218yesmaximal, direct product factor
9C2×#4898—31nomaximal
10C2×#4748—31nomaximal
11C2×#3828C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64118—22no—
16#64118C2214yescomplemented
17C2×#3746—21no—
18C2×#3744—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63830—22no—
23#63830C2214yes—
24C2×#3716—21no—
25C2×#3716—21no—
26C2×#3716—22no—
27C2×#3716—21no—
28C2×#3716C2214yescomplemented
29C2×#3714—21no—
30C2×#3712—21no—
31#63817—22no—
32#63817C2214yescomplemented
33C2×#3710—21no—
34C3×#823C2214yescomplemented
35C3×#822C2214yescomplemented
36#63561C2214yescomplemented
37C22×#214—31no—
38C2×#932—31no—
39C2×#909—31no—
40C2×#909—31no—
41C2×#909—61no—
42C2×#908—31no—
43C2×#907—31no—
44C22×#204—31no—
45C2×#901—31no—
46C2×C3×#108—31no—
47C2×C3×#100—31no—
48C2×#824—31no—
49C2×#824—31no—
50C2×#823D311yescharacteristic, complemented
51C2×#822D311yescharacteristic, complemented
52#4898—38no—
53#4748—38no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57C22×C3⋊Dic3—21no—
58#3828—21no—
59#3828—21no—
60#3828D412yes—
61#3828C2312yes—
62C2×C4⋊(C3⋊D3)D411yescharacteristic
63C2×C4×C3⋊D3—21no—
64C2×#634—21no—
65C2×#634—21no—
66C2×#634—21no—
67C2×#634—21no—
68C2×#634—21no—
69C2×#634D411yescharacteristic
70C2×#634C2312yes—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80#3746—24no—
81#3744—24no—
82C3×#208—21no—
83C3×#208—21no—
84C3×#208C2312yes—
85C3×#208C2312yes—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8—21no—
88C2×C3×C3⋊C8D411yescharacteristic
89C2×C3×C3⋊C8D412yes—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92#3716—24no—
93#3716—24no—
94#3716—24no—
95#3714—24no—
96#3712—24no—
97#3710—24no—
98C2×#471—91noSylow
99C22×C3×D4—31no—
100C2×#235—31no—
101C2×#235—31no—
102C2×#235—61no—
103C22×D12C2×D311yescharacteristic
104C22×Dic6—31no—
105C22×Dic6—31no—
106C22×Dic6—61no—
107C2×C3×M16—21no—
108C2×C3×M16—31no—
109C2×C3×M16—31no—
110C2×C3×M16C2×D311yescharacteristic
111C2×C3×M16C2×D311yescharacteristic
112C22×C3×C8—31no—
113C2×#214—34no—
114C2×#214—61no—
115C2×#214—61no—
116C2×#214—61no—
117C2×#214—62no—
118#932—34no—
119#932—62no—
120C2×#213—61no—
121C2×#208C2×D311yescharacteristic
122C2×#208C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124#909—34no—
125#909—34no—
126#909—64no—
127#909—62no—
128#909—62no—
129#909—64no—
130#908—34no—
131#908—62no—
132#907—34no—
133#907—62no—
134C2×Dic12—61no—
135C2×Dic12—61no—
136C2×Dic12—62no—
137C2×D24—61no—
138C2×#204—34no—
139C2×#204—61no—
140C2×#204—61no—
141C2×#204—62no—
142C2×#204—61no—
143C2×#204—61no—
144C2×#204—62no—
145C2×#204—61no—
146#901—34no—
147#901—62no—
148C2×ΓL(1,𝔽25)—61no—
149C2×ΓL(1,𝔽25)—61no—
150C2×D3×C8—61no—
151C2×D3×C8—61no—
152C3×#108—34no—
153C3×#100—34no—
154#824—34no—
155#824—34no—
156#823C2×D314yescomplemented
157#822C2×D314yescomplemented
158C23×C32#4111yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3×D3—22no—
161C22×C3×D3—41no—
162C22×C3×D3—41no—
163C22×C3×D3—82no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4#4111yescharacteristic
169C2×C32×C4C2411yescharacteristic
170#638—22no—
171#638—22no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—41no—
175C2×C3⋊Dic3—41no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)C2×D412yes—
178C4×C3⋊D3—22no—
179C4×C3⋊D3—22no—
180#634—22no—
181#634—21no—
182#634—22no—
183#634—41no—
184#634—41no—
185#634C2×D412yes—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—41no—
189C3×D12—41no—
190C32×C8—22no—
191C3×C3⋊C8—22no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8C2×D412yes—
194C3×C3⋊C8C2×D412yes—
195C2×#137—91no—
196C2×AGL(1,ℤ/8)—91no—
197C22×SD16—91no—
198C2×#131—91no—
199#471—98no—
200C2×#108—31no—
201C2×#101—91no—
202C2×#100—31no—
203C24×C3—61no—
204C23×D3—21no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C22×C3×C4—21no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—61no—
215C2×#67—61no—
216C2×#67—121no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—121no—
220#235—32no—
221#235—32no—
222#235—32no—
223#235—32no—
224#235—62no—
225#235—62no—
226#235—61no—
227#235—61no—
228#235—61no—
229#235—61no—
230#235—121no—
231#235—121no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12C22×D312yes—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—121no—
244C2×Dic6—31no—
245C2×Dic6—31no—
246C2×Dic6—32no—
247C2×Dic6—32no—
248C2×Dic6—61no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
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—61no—
261C2×Dic6—61no—
262C2×Dic6—121no—
263C2×Dic6—121no—
264C2×Dic6—121no—
265C3×M16—22no—
266C3×M16—21no—
267C3×M16—21no—
268C3×M16—22no—
269C3×M16—32no—
270C3×M16—32no—
271C3×M16—61no—
272C3×M16—61no—
273C3×M16C22×D312yes—
274C3×M16C22×D312yes—
275C2×C3×C8—22no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—31no—
279C2×C3×C8—31no—
280C2×C3×C8—32no—
281C2×C3×C8—32no—
282C2×C3×C8—61no—
283C2×C3×C8—61no—
284#214—64no—
285#214—64no—
286#214—64no—
287#213—64no—
288#208—21no—
289#208—21no—
290#208C22×D312yes—
291#208C22×D312yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8D1211yescharacteristic
295C2×C3⋊C8D1211yescharacteristic
296C2×C3⋊C8D1212yes—
297C2×C3⋊C8C22×D312yes—
298Dic12—64no—
299Dic12—64no—
300Dic12—68no—
301D24—64no—
302#204—64no—
303#204—64no—
304#204—68no—
305#204—64no—
306#204—64no—
307#204—64no—
308ΓL(1,𝔽25)—64no—
309ΓL(1,𝔽25)—64no—
310D3×C8—64no—
311D3×C8—64no—
312C22×C32—22no—
313C22×C32#12111yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C2×C3⋊D3—22no—
317C2×C3⋊D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—82no—
320C2×C3×D3—82no—
321C2×C3×D3—82no—
322C32×C4#12111yescharacteristic
323C32×C4#12111yescharacteristic
324C32×C4C22×D411yescharacteristic
325C32×C4C22×D411yescharacteristic
326C3⋊Dic3—22no—
327C3⋊Dic3—42no—
328C2×#41—91no—
329C22×Q8—91no—
330C22×D4—31no—
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—182no—
341C2×SD16—181no—
342C2×D8—181no—
343#131—94no—
344#131—182no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—181no—
348C2×M16D3211yescharacteristic
349C22×C8—31no—
350C22×C8—181no—
351#108—34no—
352#101—94no—
353#100—34no—
354C23×C3—21no—
355C23×C3—62no—
356C23×C3—121no—
357C23×C3—121no—
358C23×C3—242no—
359C23×C3#23511yescharacteristic
360C23×C3#23911yescharacteristic
361C22×D3—22no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—82no—
367C22×D3—121no—
368C3×D4—62no—
369C3×D4—62no—
370C3×D4—121no—
371C3×D4—121no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23911yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—62no—
391#67—62no—
392#67—62no—
393#67—62no—
394#67—122no—
395#67—122no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408D12—22no—
409D12—22no—
410D12—32no—
411D12—32no—
412D12—41no—
413D12—41no—
414D12—62no—
415D12—61no—
416D12—61no—
417D12—121no—
418C4×D3—62no—
419C4×D3—62no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—122no—
423C4×D3—122no—
424Dic6—32no—
425Dic6—32no—
426Dic6—62no—
427Dic6—61no—
428Dic6—61no—
429Dic6—64no—
430Dic6—62no—
431Dic6—62no—
432Dic6—62no—
433Dic6—62no—
434Dic6—122no—
435Dic6—121no—
436Dic6—122no—
437Dic6—122no—
438Dic6—121no—
439Dic6—121no—
440Dic6—121no—
441Dic6—121no—
442C3×C8—24no—
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—32no—
446C3×C8—32no—
447C3×C8—62no—
448C3×C8—62no—
449C3⋊C8—22no—
450C3⋊C8—22no—
451C3⋊C8C2×D1212yes—
452C3⋊C8C2×D1212yes—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32#47112yescomplemented
456C2×C32C2×#12111yescharacteristic
457C3⋊D3—42no—
458C3×D3—82no—
459C24—61no—
460#41—92no—
461#41—92no—
462#41—181no—
463#41—181no—
464C2×Q8—92no—
465C2×Q8—91no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C2×Q8—181no—
470C2×Q8—181no—
471C2×D4—32no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—91no—
478C2×D4—181no—
479C22×C4—181no—
480C22×C4—181no—
481C22×C4C2×D3211yescharacteristic
482Q16—184no—
483SD16—184no—
484SD16—184no—
485SD16—184no—
486SD16—184no—
487D8—184no—
488M16—21no—
489M16—32no—
490M16—32no—
491M16—61no—
492M16—61no—
493M16—184no—
494M16C2×D3212yes—
495C2×C8—21no—
496C2×C8—32no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—32no—
500C2×C8—61no—
501C2×C8—61no—
502C2×C8—184no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—42no—
509C22×C3—122no—
510C22×C3—242no—
511C22×C3—242no—
512C22×C3—242no—
513C22×C3#88411yescharacteristic
514C22×C3#88411yescharacteristic
515C22×C3#89511yescharacteristic
516C22×C3#89511yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3C2×#23911yescharacteristic
519C2×D3—42no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—82no—
523C2×D3—82no—
524C2×D3—82no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—242no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4#88411yescharacteristic
534C3×C4#88411yescharacteristic
535C3×C4#89511yescharacteristic
536C3×C4#89511yescharacteristic
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541Dic3—62no—
542Dic3—62no—
543Dic3—122no—
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—62no—
549C23—121no—
550C23—121no—
551C23—181no—
552C23—242no—
553C23#379911yescharacteristic
554Q8—92no—
555Q8—181no—
556Q8—182no—
557Q8—182no—
558Q8—361no—
559Q8—361no—
560D4—62no—
561D4—62no—
562D4—92no—
563D4—121no—
564D4—121no—
565D4—182no—
566D4—182no—
567D4—181no—
568C2×C4—181no—
569C2×C4—182no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4#379911yescharacteristic
575C2×C4D3×D1211yescharacteristic
576C2×C4D3×D1211yescharacteristic
577C2×C4#381111yescharacteristic
578C2×C4#381111yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—22no—
581C8—32no—
582C8—32no—
583C8—62no—
584C8—62no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—242no—
594C2×C3#474812yescomplemented
595C2×C3#489812yescomplemented
596C2×C3C2×#88411yescharacteristic
597C2×C3C2×#89511yescharacteristic
598D3—82no—
599D3—122no—
600D3—122no—
601D3—242no—
602C22—22no—
603C22—122no—
604C22—182no—
605C22—242no—
606C22—242no—
607C22—242no—
608C22—362no—
609C22#6391011yescharacteristic
610C22#6391011yescharacteristic
611C22C2×#379911yescharacteristic
612C4—182no—
613C4—362no—
614C4#6391011yescharacteristic
615C4#6391011yescharacteristic
616C4C2×D3×D1211yescharacteristic
617C4C2×#381111yescharacteristic
618C3—21no—
619C3C2×#474811yescharacteristic, complemented
620C3C2×#489811yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—242no—
624C2—362no—
625C2#1059098912yesdirect product factor
626C2C2×#6391011yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC2×M16D32
hypocenterC32C2×#471
LCSG ▷ C2×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×#64118C2semidirect
3. C22×#3716C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#823C2semidirect
6. C2×C3×#822C2semidirect
7. C2×#63561C2semidirect
8. #10590989C2direct (N × H)
16. #64118C22semidirect
28. C2×#3716C22semidirect
32. #63817C22semidirect
34. C3×#823C22semidirect
35. C3×#822C22semidirect
36. #63561C22semidirect
50. C2×#823D3semidirect
51. C2×#822D3semidirect
156. #823C2×D3semidirect
157. #822C2×D3semidirect
455. C2×C32#471semidirect
547. C32C2×#471semidirect
594. C2×C3#4748semidirect
595. C2×C3#4898semidirect
619. C3C2×#4748semidirect
620. C3C2×#4898semidirect
625. C2#10590989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641182
C2×#638302
C22×#37162
C2×#638172
C2×C3×#8232
C2×C3×#8222
C2×#635612
#105909892
C2×#48983
C2×#47483