Finite Group Databasebeta

← C2×#10590978 #11861059

Subgroups — C2×#10590978 #11861059

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2C2×#63829C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C2×C3×#822C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590978C218yesmaximal, direct product factor
9C2×#4894—31nomaximal
10C2×#4823—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15#64116—22no—
16#64116C2214yescomplemented
17C2×#3743—21no—
18C2×C8×C3⋊D3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3719C411yescharacteristic, complemented
23C2×#3717C411yescharacteristic, complemented
24#63829C414yescomplemented
25#63829C2214yes—
26C2×#3716C411yescharacteristic, complemented
27C2×#3714C411yescharacteristic, complemented
28C2×#3711—21no—
29#63815—22no—
30#63815C2214yescomplemented
31C2×D3×C3⋊C8—21no—
32C3×#825C2214yescomplemented
33C3×#822C2214yescomplemented
34#63570C2214yescomplemented
35#63554C2214yescomplemented
36C2×#950—31no—
37C2×#948—31no—
38C2×#907—31no—
39C2×#907—31no—
40C2×#907—31no—
41C2×#907—61no—
42C2×#904—31no—
43C2×C3×#108—31no—
44C2×C3×#104—31no—
45C2×#825—31no—
46C2×#825D311yescharacteristic, complemented
47C2×#822D311yescharacteristic, complemented
48C2×#815—31no—
49C2×#805—31no—
50C2×#803—31no—
51#4894—38no—
52#4823—38no—
53C22×C32×C4C2311yescharacteristic
54C2×#638—21no—
55#3828—21no—
56#3828—21no—
57#3828C2×C412yes—
58#3828C2312yes—
59C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×#634C2×C411yescharacteristic
62C2×C3×#67—21no—
63C22×C3×Dic3—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235C2×C412yes—
67C3×#235C2312yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2×C411yescharacteristic
71C32×M16—21no—
72C32×M16C2312yes—
73C2×C32×C8—21no—
74C2×C3⋊(C3⋊C8)D411yescharacteristic
75C2×C3⋊(C3⋊C8)D412yes—
76C2×C3⋊(C3⋊C8)D411yescharacteristic
77C2×C3⋊(C3⋊C8)C2312yes—
78#3743—24no—
79C8×C3⋊D3—24no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3C2312yes—
82C3×#208—21no—
83C3×#208C2312yes—
84C2×C3×C3⋊C8—21no—
85C2×C3×C3⋊C8C2×C411yescharacteristic
86C2×C3×C3⋊C8C2×C411yescharacteristic
87C2×C3×C3⋊C8C2×C412yes—
88C2×C3×C3⋊C8C2312yes—
89#3719C2×C414yescomplemented
90#3717C2×C414yescomplemented
91#3716C2×C414yescomplemented
92#3714C2×C414yescomplemented
93#3711—24no—
94D3×C3⋊C8—24no—
95C2×#444—91noSylow
96C2×C3×#41—31no—
97C2×#235—31no—
98C2×#235—31no—
99C2×#235—61no—
100C2×#235C2×D311yescharacteristic
101C2×C3×M16—21no—
102C2×C3×M16—31no—
103C2×C3×M16C2×D311yescharacteristic
104C2×C3×M16C2×D311yescharacteristic
105C22×C3×C8—31no—
106C2×C3×C42—31no—
107#950—34no—
108#950—34no—
109#948—34no—
110#948—62no—
111C2×#216—31no—
112C2×#215—31no—
113C2×#214—31no—
114C2×#213—31no—
115C2×C4×Dic3C2×D311yescharacteristic
116C2×#208—61no—
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123#907—34no—
124#907—34no—
125#907—34no—
126#907—64no—
127#907—62no—
128#907—62no—
129#907—62no—
130#907—64no—
131C2×Dic12—31no—
132#904—34no—
133#904—34no—
134C2×D24—31no—
135C2×#204—31no—
136C2×#204—31no—
137C2×ΓL(1,𝔽25)—61no—
138C2×ΓL(1,𝔽25)—61no—
139C2×ΓL(1,𝔽25)—61no—
140C2×ΓL(1,𝔽25)—62no—
141C2×D3×C8—61no—
142C2×D3×C8—61no—
143C2×D3×C8—61no—
144C2×D3×C8—62no—
145C3×#108—34no—
146C3×#104—34no—
147#825—34no—
148#825C2×D314yescomplemented
149#822C2×D314yescomplemented
150#815—34no—
151#805—34no—
152#803—34no—
153C23×C32#4111yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3×D3—21no—
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C22×C411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C2×C32×C4C2411yescharacteristic
162#638—22no—
163#638—22no—
164C2×C3⋊Dic3—21no—
165C4⋊(C3⋊D3)—21no—
166C4⋊(C3⋊D3)C22×C412yes—
167C4×C3⋊D3—22no—
168C4×C3⋊D3—22no—
169#634—21no—
170#634C22×C412yes—
171C3×#67—22no—
172C3×#67—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C3×D12—21no—
177C3×D12C22×C412yes—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—21no—
181C3×Dic6C22×C412yes—
182C32×C8—22no—
183C3⋊(C3⋊C8)C2×D412yes—
184C3⋊(C3⋊C8)C2×D412yes—
185C3×C3⋊C8—22no—
186C3×C3⋊C8C22×C412yes—
187C3×C3⋊C8C22×C412yes—
188C2×#135—91no—
189C2×#131—91no—
190C2×#131—91no—
191#444—98no—
192C2×#108—31no—
193C2×#104—31no—
194C2×#104—91no—
195C2×#97—91no—
196C3×#41—32no—
197C3×#41—32no—
198C3×#41—61no—
199C3×#41—61no—
200C2×C3×Q8—31no—
201C2×C3×D4—31no—
202C2×C3×D4—61no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—21no—
209C2×#67—62no—
210C2×#67—61no—
211C2×#67—61no—
212C22×Dic3—21no—
213#235—21no—
214#235—21no—
215#235—32no—
216#235—32no—
217#235—32no—
218#235—32no—
219#235—62no—
220#235—62no—
221#235—62no—
222#235—62no—
223#235—61no—
224#235—61no—
225#235—61no—
226#235—61no—
227#235C4×D312yes—
228#235C22×D312yes—
229C2×D12—31no—
230C2×D12—31no—
231C2×D12—61no—
232C2×D12C4×D311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—62no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×Dic6—31no—
238C2×Dic6—31no—
239C2×Dic6—61no—
240C2×Dic6C4×D311yescharacteristic
241C3×M16—22no—
242C3×M16—21no—
243C3×M16—21no—
244C3×M16—22no—
245C3×M16—32no—
246C3×M16—61no—
247C3×M16C22×D312yes—
248C3×M16C22×D312yes—
249C2×C3×C8—22no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—31no—
253C2×C3×C8—31no—
254C2×C3×C8—32no—
255C2×C3×C8—32no—
256C2×C3×C8—61no—
257C3×C42—32no—
258C3×C42—61no—
259#216—34no—
260#215—34no—
261#214—34no—
262#213—34no—
263C4×Dic3—21no—
264C4×Dic3C22×D312yes—
265#208—21no—
266#208—64no—
267#208C22×D312yes—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—64no—
282C2×C3⋊C8C4×D311yescharacteristic
283C2×C3⋊C8C4×D311yescharacteristic
284C2×C3⋊C8C4×D312yes—
285C2×C3⋊C8C22×D312yes—
286Dic12—34no—
287D24—34no—
288#204—34no—
289#204—34no—
290ΓL(1,𝔽25)—64no—
291ΓL(1,𝔽25)—64no—
292ΓL(1,𝔽25)—64no—
293ΓL(1,𝔽25)—68no—
294D3×C8—64no—
295D3×C8—64no—
296D3×C8—64no—
297D3×C8—68no—
298C22×C32—22no—
299C22×C32C4×D411yescharacteristic
300C22×C32C4×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—42no—
304C2×C3×D3—22no—
305C2×C3×D3—42no—
306C32×C4C4×D411yescharacteristic
307C32×C4C4×D411yescharacteristic
308C32×C4C23×C411yescharacteristic
309C32×C4C22×D411yescharacteristic
310C3⋊Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C2×#41—31no—
314C2×#41—91no—
315#135—94no—
316#135—94no—
317C2×Q16—91no—
318C2×SD16—91no—
319C2×SD16—91no—
320C2×D8—91no—
321#131—94no—
322#131—94no—
323#131—182no—
324#131—182no—
325C2×M16—31no—
326C2×M16—181no—
327C2×M16—181no—
328C2×M16D3211yescharacteristic
329C22×C8—31no—
330C22×C8—91no—
331C22×C8—181no—
332C22×C8—181no—
333C2×C42—31no—
334#108—34no—
335#104—34no—
336#104—94no—
337#97—94no—
338C23×C3—21no—
339C23×C3—61no—
340C23×C3#23711yescharacteristic
341C23×C3#23911yescharacteristic
342C22×D3—21no—
343C22×D3—62no—
344C22×D3—61no—
345C22×D3—61no—
346C3×Q8—32no—
347C3×Q8—61no—
348C3×D4—32no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—61no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—122no—
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×C4×D311yescharacteristic
366C2×C3×C4C2×C4×D311yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4#23911yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375#67—22no—
376#67—22no—
377#67—64no—
378#67—64no—
379#67—62no—
380#67—62no—
381#67—62no—
382#67—62no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—42no—
386C2×Dic3—62no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389D12—21no—
390D12—32no—
391D12—32no—
392D12—62no—
393D12—62no—
394D12—61no—
395D12—61no—
396D12C2×C4×D312yes—
397C4×D3—22no—
398C4×D3—22no—
399C4×D3—64no—
400C4×D3—64no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—62no—
404C4×D3—62no—
405Dic6—21no—
406Dic6—32no—
407Dic6—32no—
408Dic6—62no—
409Dic6—62no—
410Dic6—61no—
411Dic6—61no—
412Dic6C2×C4×D312yes—
413C3×C8—24no—
414C3×C8—22no—
415C3×C8—22no—
416C3×C8—32no—
417C3×C8—32no—
418C3×C8—62no—
419C3⋊C8—22no—
420C3⋊C8—32no—
421C3⋊C8—32no—
422C3⋊C8—32no—
423C3⋊C8—32no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8C2×C4×D312yes—
427C3⋊C8C2×C4×D312yes—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32#44412yescomplemented
431C2×C32C2×C4×D411yescharacteristic
432C3⋊D3—42no—
433C3×D3—42no—
434#41—32no—
435#41—32no—
436#41—61no—
437#41—61no—
438#41—92no—
439#41—92no—
440#41—181no—
441#41—181no—
442C2×Q8—31no—
443C2×Q8—91no—
444C2×D4—31no—
445C2×D4—61no—
446C2×D4—91no—
447C2×D4—181no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—181no—
451C22×C4C2×D3211yescharacteristic
452Q16—94no—
453SD16—94no—
454SD16—94no—
455D8—94no—
456M16—21no—
457M16—32no—
458M16—61no—
459M16—184no—
460M16—184no—
461M16C2×D3212yes—
462C2×C8—21no—
463C2×C8—32no—
464C2×C8—31no—
465C2×C8—31no—
466C2×C8—32no—
467C2×C8—61no—
468C2×C8—92no—
469C2×C8—92no—
470C2×C8—91no—
471C2×C8—91no—
472C2×C8—184no—
473C2×C8—184no—
474C42—32no—
475C42—61no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—42no—
482C22×C3—62no—
483C22×C3—122no—
484C22×C3#67⋊C411yescharacteristic
485C22×C3#67⋊C411yescharacteristic
486C22×C3#89311yescharacteristic
487C22×C3#89311yescharacteristic
488C22×C3C2×#23711yescharacteristic
489C22×C3C2×#23911yescharacteristic
490C2×D3—22no—
491C2×D3—42no—
492C2×D3—64no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—124no—
496C2×D3—122no—
497C2×D3—122no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—62no—
503C3×C4—122no—
504C3×C4#67⋊C411yescharacteristic
505C3×C4#67⋊C411yescharacteristic
506C3×C4#89311yescharacteristic
507C3×C4#89311yescharacteristic
508C3×C4C22×C4×D311yescharacteristic
509C3×C4C22×C4×D311yescharacteristic
510C3×C4C2×D3×D411yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512Dic3—22no—
513Dic3—42no—
514Dic3—64no—
515Dic3—62no—
516Dic3—62no—
517C32C2×#44411yescharacteristic, complemented, Sylow
518C23—61no—
519C23—181no—
520C23#379611yescharacteristic
521Q8—32no—
522Q8—61no—
523Q8—92no—
524Q8—181no—
525D4—32no—
526D4—62no—
527D4—62no—
528D4—61no—
529D4—92no—
530D4—182no—
531D4—182no—
532D4—181no—
533C2×C4—61no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4#379611yescharacteristic
542C2×C4C4×D3211yescharacteristic
543C2×C4C4×D3211yescharacteristic
544C2×C4#381111yescharacteristic
545C2×C4#381111yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—22no—
548C8—32no—
549C8—32no—
550C8—62no—
551C8—92no—
552C8—92no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—41no—
560C2×C3—41no—
561C2×C3—122no—
562C2×C3#482312yescomplemented
563C2×C3#489412yescomplemented
564C2×C3C2×#67⋊C411yescharacteristic
565C2×C3C2×#89311yescharacteristic
566D3—42no—
567D3—124no—
568D3—122no—
569D3—122no—
570C22—22no—
571C22—62no—
572C22—122no—
573C22—182no—
574C22—362no—
575C22#6388111yescharacteristic
576C22#6388111yescharacteristic
577C22C2×#379611yescharacteristic
578C4—62no—
579C4—122no—
580C4—182no—
581C4#6388111yescharacteristic
582C4#6388111yescharacteristic
583C4C2×C4×D3211yescharacteristic
584C4C2×#381111yescharacteristic
585C3—21no—
586C3C2×#482311yescharacteristic, complemented
587C3C2×#489411yescharacteristic, complemented
588C2—21no—
589C2—21no—
590C2—122no—
591C2—362no—
592C2#1059097812yesdirect product factor
593C2C2×#6388111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#444
LCSG ▷ 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
1. C2×#64116C2semidirect
3. C2×#63815C2semidirect
4. C2×C3×#825C2semidirect
5. C2×C3×#822C2semidirect
6. C2×#63570C2semidirect
7. C2×#63554C2semidirect
8. #10590978C2direct (N × H)
16. #64116C22semidirect
22. C2×#3719C4semidirect
23. C2×#3717C4semidirect
24. #63829C4semidirect
26. C2×#3716C4semidirect
27. C2×#3714C4semidirect
30. #63815C22semidirect
32. C3×#825C22semidirect
33. C3×#822C22semidirect
34. #63570C22semidirect
35. #63554C22semidirect
46. C2×#825D3semidirect
47. C2×#822D3semidirect
89. #3719C2×C4semidirect
90. #3717C2×C4semidirect
91. #3716C2×C4semidirect
92. #3714C2×C4semidirect
148. #825C2×D3semidirect
149. #822C2×D3semidirect
430. C2×C32#444semidirect
517. C32C2×#444semidirect
562. C2×C3#4823semidirect
563. C2×C3#4894semidirect
586. C3C2×#4823semidirect
587. C3C2×#4894semidirect
592. C2#10590978direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#638292
C2×#638152
C2×C3×#8252
C2×C3×#8222
C2×#635702
C2×#635542
#105909782
C2×#48943
C2×#48233