Finite Group Databasebeta

← C2×#10590394 #11858166

Subgroups — C2×#10590394 #11858166

Order 1152.

1709 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5C2×#63568C212yesmaximal, complemented
6#10590394C218yesmaximal, direct product factor
7C2×#4821—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×#3811—21no—
11C2×#3805—21no—
12#64306—22no—
13#64306—22no—
14#64306C414yescomplemented
15#64306C2214yes—
16C2×#3802C411yescharacteristic, complemented
17C2×C4×D32—21no—
18C2×#3798—21no—
19C2×#3797C411yescharacteristic, complemented
20C2×#3796C412yescomplemented
21C2×C32×C42C2211yescharacteristic, complemented
22C2×#3752—21no—
23C2×#3750—21no—
24C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
25#64081—22no—
26#64081C2214yescomplemented
27C2×C3×#208C2212yescomplemented
28C2×#3712—21no—
29#63818—22no—
30#63818C2214yescomplemented
31C2×#3710—21no—
32C3×#805C2218yescomplemented
33#63568C2218yescomplemented
34C2×D3×#41—32no—
35C2×D3×M16—32no—
36C2×#872—32no—
37C2×#872—61no—
38C2×C3×#104—32no—
39C2×#837—32no—
40C2×#825—32no—
41C2×#805D312yescomplemented
42#4821—316no—
43C23×C3⋊D3D411yescharacteristic
44C22×D32—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3C2×C411yescharacteristic
51C2×C4×C3⋊D3C2×C412yes—
52C2×C4×C3⋊D3D412yes—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3C2312yes—
57C2×C3×#67—22no—
58C3×#235—22no—
59C3×#235—22no—
60C3×#235C2×C414yes—
61C3×#235C2314yes—
62C2×C3×D12C2×C412yes—
63C2×C3×C4×D3—22no—
64C2×C3×Dic6C2×C412yes—
65#3811—24no—
66#3811—24no—
67C2×#627—21no—
68C2×#626—22no—
69C2×#625—21no—
70C2×#624—21no—
71#3805—24no—
72#3805—24no—
73C2×D3×Dic3—22no—
74#3802—22no—
75#3802C2×C414yescomplemented
76C4×D32—24no—
77C4×D32—24no—
78#3798—24no—
79#3798—24no—
80#3797—22no—
81#3797C2×C414yescomplemented
82#3796—24no—
83#3796C2×C418yescomplemented
84C32×C42—21no—
85C32×C42C2312yescomplemented
86#3752—24no—
87#3750—24no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3C2312yescomplemented
90C3×#208—22no—
91C3×#208C2314yescomplemented
92C2×C3×C3⋊C8—22no—
93#3712—24no—
94#3710—24no—
95C2×#421—91noSylow
96C2×C3×#41—32no—
97D3×#41—38no—
98D3×#41—38no—
99D3×#41—64no—
100D3×#41—64no—
101C2×#239—32no—
102C2×D3×Q8—32no—
103C2×#237—32no—
104C2×#237—62no—
105C2×D3×D4—32no—
106C2×D3×D4—62no—
107C2×#235—62no—
108C2×#235C2×D312yes—
109C22×C4×D3—32no—
110C22×C4×D3—61no—
111C22×C4×D3—62no—
112C2×C3×M16—32no—
113C2×C3×C42—21no—
114C2×C3×C42C2×D312yescomplemented
115C2×(C2×D3)⋊C4—62no—
116C2×(C2×D3)⋊C4—62no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—61no—
121C2×#208C2×D312yescomplemented
122D3×M16—38no—
123D3×M16—64no—
124C2×ΓL(1,𝔽25)—62no—
125C2×D3×C8—62no—
126#872—38no—
127#872—64no—
128#872—64no—
129#872—64no—
130C3×#104—38no—
131#837—38no—
132#825—38no—
133#805C2×D318yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—42no—
136C22×C3⋊D3C22⋊C411yescharacteristic
137C22×C3⋊D3C22⋊C411yescharacteristic
138C22×C3⋊D3C22⋊C412yes—
139C22×C3⋊D3C2×D412yes—
140C22×C3×D3—22no—
141C2×D32—24no—
142C2×D32—44no—
143C2×C32×C4—22no—
144C2×C32×C4—42no—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153C2×C3⋊Dic3C22⋊C411yescharacteristic
154C2×C3⋊Dic3C22⋊C412yes—
155C2×C3⋊Dic3C22⋊C411yescharacteristic
156C2×C3⋊Dic3C2×D412yes—
157C4×C3⋊D3C22⋊C412yes—
158C4×C3⋊D3C22⋊C412yes—
159C4×C3⋊D3C22⋊C412yes—
160C4×C3⋊D3C22⋊C412yes—
161C4×C3⋊D3C22×C412yes—
162C4×C3⋊D3C22×C412yes—
163C4×C3⋊D3C2×D412yes—
164C4×C3⋊D3C2×D412yes—
165C3×#67—24no—
166C3×#67—24no—
167C2×C3×Dic3—22no—
168C3×D12—22no—
169C3×D12C22×C414yes—
170C3×C4×D3—24no—
171C3×C4×D3—24no—
172C3×Dic6—22no—
173C3×Dic6C22×C414yes—
174#627—24no—
175#626—28no—
176#625—24no—
177#624—24no—
178D3×Dic3—28no—
179C3×C3⋊C8—24no—
180C22×#41—91no—
181C22×M16—91no—
182C2×#117—91no—
183#421—98no—
184C2×#104—32no—
185C2×#104—92no—
186C23×D3—32no—
187C23×D3—61no—
188C23×D3—62no—
189C3×#41—34no—
190C3×#41—34no—
191C3×#41—62no—
192C3×#41—62no—
193C2×C3×Q8—32no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—62no—
200C22×C3×C4C22×D312yes—
201C2×#67—22no—
202C2×#67—62no—
203C2×#67—62no—
204C22×Dic3—32no—
205C22×Dic3—61no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209#239—38no—
210#239—64no—
211D3×Q8—38no—
212D3×Q8—64no—
213#237—38no—
214#237—64no—
215#237—68no—
216#237—68no—
217D3×D4—38no—
218D3×D4—64no—
219D3×D4—68no—
220D3×D4—68no—
221#235—22no—
222#235—22no—
223#235—68no—
224#235—68no—
225#235C4×D314yes—
226#235C22×D314yes—
227C2×D12—62no—
228C2×D12C4×D312yes—
229C2×C4×D3—22no—
230C2×C4×D3—32no—
231C2×C4×D3—32no—
232C2×C4×D3—34no—
233C2×C4×D3—34no—
234C2×C4×D3—32no—
235C2×C4×D3—32no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—68no—
247C2×C4×D3—68no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×Dic6—62no—
251C2×Dic6C4×D312yes—
252C3×M16—34no—
253C3×M16—62no—
254C2×C3×C8—62no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—22no—
258C3×C42C22×D314yescomplemented
259(C2×D3)⋊C4—68no—
260(C2×D3)⋊C4—68no—
261Dic3⋊C4—68no—
262Dic3⋊C4—68no—
263C4×Dic3—34no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267#208—22no—
268#208C22×D314yescomplemented
269C2×C3⋊C8—22no—
270ΓL(1,𝔽25)—68no—
271D3×C8—68no—
272C22×C32—22no—
273C22×C32C2×C22⋊C411yescharacteristic
274C22×C32C2×C22⋊C411yescharacteristic
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3C2×C22⋊C412yes—
281C2×C3⋊D3C2×C22⋊C412yes—
282C2×C3×D3—24no—
283C2×C3×D3—44no—
284D32—48no—
285C32×C4—42no—
286C32×C4C2×C22⋊C411yescharacteristic
287C32×C4C2×C22⋊C411yescharacteristic
288C32×C4C23×C411yescharacteristic
289C32×C4C22×D411yescharacteristic
290C3⋊Dic3—42no—
291C3⋊Dic3C2×C22⋊C412yes—
292C3⋊Dic3C2×C22⋊C412yes—
293C3×Dic3—24no—
294C2×#41—32no—
295C2×#41—92no—
296C2×#41—94no—
297C2×#41—94no—
298C2×#41—181no—
299C2×#41—181no—
300C2×#41—182no—
301C2×#41—182no—
302C22×Q8—91no—
303C22×D4—91no—
304C22×D4—181no—
305C23×C4—91no—
306C23×C4—181no—
307C2×M16—32no—
308C2×M16—94no—
309C2×M16—181no—
310C2×M16—182no—
311C22×C8—181no—
312#117—94no—
313#117—182no—
314C2×C4⋊C4—181no—
315C2×C22⋊C4—181no—
316C2×C42—91no—
317C2×C42D3211yescharacteristic, complemented
318#104—38no—
319#104—98no—
320C23×C3—21no—
321C23×C3—62no—
322C23×C3D3×D412yes—
323C22×D3—22no—
324C22×D3—32no—
325C22×D3—32no—
326C22×D3—34no—
327C22×D3—34no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—68no—
333C22×D3—128no—
334C22×D3—124no—
335C22×D3—124no—
336C3×Q8—34no—
337C3×Q8—62no—
338C3×D4—34no—
339C3×D4—64no—
340C3×D4—64no—
341C3×D4—62no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—44no—
351C2×C3×C4—44no—
352C2×C3×C4—62no—
353C2×C3×C4—64no—
354C2×C3×C4—64no—
355C2×C3×C4C2×C4×D312yes—
356C2×C3×C4C2×C4×D312yes—
357C2×C3×C4D3×D412yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4D3×D412yes—
360C2×C3×C4C23×D312yes—
361#67—24no—
362#67—24no—
363#67—68no—
364#67—68no—
365C2×Dic3—22no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—68no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—124no—
378C2×Dic3—124no—
379D12—22no—
380D12—68no—
381D12C2×C4×D314yes—
382C4×D3—24no—
383C4×D3—24no—
384C4×D3—34no—
385C4×D3—34no—
386C4×D3—34no—
387C4×D3—34no—
388C4×D3—34no—
389C4×D3—34no—
390C4×D3—34no—
391C4×D3—34no—
392C4×D3—62no—
393C4×D3—62no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—68no—
401C4×D3—68no—
402Dic6—22no—
403Dic6—68no—
404Dic6C2×C4×D314yes—
405C3×C8—64no—
406C3⋊C8—24no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32#42112yescomplemented
410C2×C32C22×C22⋊C411yescharacteristic
411C3⋊D3—22no—
412C3⋊D3—22no—
413C3×D3—44no—
414C24—91no—
415C24—181no—
416#41—34no—
417#41—34no—
418#41—62no—
419#41—62no—
420#41—98no—
421#41—184no—
422#41—184no—
423#41—184no—
424#41—184no—
425#41—184no—
426C2×Q8—32no—
427C2×Q8—94no—
428C2×Q8—181no—
429C2×Q8—182no—
430C2×D4—32no—
431C2×D4—62no—
432C2×D4—94no—
433C2×D4—182no—
434C2×D4—182no—
435C2×D4—181no—
436C2×D4—184no—
437C2×D4—184no—
438C22×C4—21no—
439C22×C4—62no—
440C22×C4—91no—
441C22×C4—92no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—92no—
445C22×C4—92no—
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—92no—
449C22×C4—184no—
450C22×C4—184no—
451C22×C4—181no—
452C22×C4—182no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455M16—34no—
456M16—62no—
457M16—184no—
458C2×C8—62no—
459C2×C8—184no—
460C4⋊C4—184no—
461C22⋊C4—184no—
462C42—21no—
463C42—92no—
464C42—181no—
465C42C2×D3212yescomplemented
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—64no—
472C22×C3—124no—
473C22×C3D3×C22⋊C412yes—
474C22×C3D3×C22⋊C412yes—
475C22×C3C2×D3×D412yes—
476C2×D3—24no—
477C2×D3—34no—
478C2×D3—34no—
479C2×D3—44no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—1216no—
487C2×D3—124no—
488C2×D3—124no—
489C2×D3—124no—
490C2×D3—124no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—44no—
496C3×C4—44no—
497C3×C4—64no—
498C3×C4D3×C22⋊C412yes—
499C3×C4D3×C22⋊C412yes—
500C3×C4C22×C4×D312yes—
501C3×C4C2×D3×D412yes—
502Dic3—24no—
503Dic3—34no—
504Dic3—34no—
505Dic3—62no—
506Dic3—62no—
507Dic3—124no—
508Dic3—124no—
509C32C2×#42111yescharacteristic, complemented, Sylow
510C23—62no—
511C23—91no—
512C23—91no—
513C23—92no—
514C23—92no—
515C23—184no—
516C23—362no—
517C23—364no—
518C23#381111yescharacteristic
519Q8—34no—
520Q8—62no—
521Q8—184no—
522D4—34no—
523D4—64no—
524D4—64no—
525D4—62no—
526D4—188no—
527D4—184no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—64no—
533C2×C4—92no—
534C2×C4—91no—
535C2×C4—91no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—92no—
544C2×C4—92no—
545C2×C4—184no—
546C2×C4—188no—
547C2×C4—182no—
548C2×C4—362no—
549C2×C4C4×D3211yescharacteristic
550C2×C4C4×D3211yescharacteristic
551C2×C4#380211yescharacteristic
552C2×C4#380211yescharacteristic
553C2×C4#381111yescharacteristic
554C2×C4C22×D3211yescharacteristic
555C8—64no—
556C2×C3—22no—
557C2×C3—22no—
558C2×C3—22no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—124no—
563C2×C3#482114yescomplemented
564C2×C3C2×D3×C22⋊C412yes—
565D3—44no—
566D3—64no—
567D3—64no—
568D3—122no—
569D3—122no—
570C22—22no—
571C22—64no—
572C22—92no—
573C22—92no—
574C22—124no—
575C22—182no—
576C22—182no—
577C22—362no—
578C22—362no—
579C22—368no—
580C22#6392111yescharacteristic
581C22#6392111yescharacteristic
582C22C2×#381111yescharacteristic
583C4—42no—
584C4—64no—
585C4—92no—
586C4—92no—
587C4—362no—
588C4#6392111yescharacteristic
589C4#6392111yescharacteristic
590C4C2×C4×D3211yescharacteristic
591C4C2×#380211yescharacteristic
592C3—21no—
593C3C2×#482112yescomplemented
594C2—21no—
595C2—21no—
596C2—124no—
597C2—182no—
598C2—182no—
599C2#1059039412yesdirect product factor
600C2C2×#6392111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#64081C2semidirect
3. C2×#63818C2semidirect
4. C2×C3×#805C2semidirect
5. C2×#63568C2semidirect
6. #10590394C2direct (N × H)
14. #64306C4semidirect
16. C2×#3802C4semidirect
19. C2×#3797C4semidirect
20. C2×#3796C4semidirect
21. C2×C32×C42C22semidirect
24. C2×C4×C3⋊Dic3C22semidirect
26. #64081C22semidirect
27. C2×C3×#208C22semidirect
30. #63818C22semidirect
32. C3×#805C22semidirect
33. #63568C22semidirect
41. C2×#805D3semidirect
75. #3802C2×C4semidirect
81. #3797C2×C4semidirect
83. #3796C2×C4semidirect
85. C32×C42C23semidirect
89. C4×C3⋊Dic3C23semidirect
91. C3×#208C23semidirect
114. C2×C3×C42C2×D3semidirect
121. C2×#208C2×D3semidirect
133. #805C2×D3semidirect
258. C3×C42C22×D3semidirect
268. #208C22×D3semidirect
317. C2×C42D32semidirect
409. C2×C32#421semidirect
465. C42C2×D32semidirect
509. C32C2×#421semidirect
563. C2×C3#4821semidirect
593. C3C2×#4821semidirect
599. C2#10590394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#640812
C2×#638182
C2×C3×#8052
C2×#635682
#105903942
C2×#48213