Finite Group Databasebeta

← C2×#10594046 #11903049

Subgroups — C2×#10594046 #11903049

Order 1152.

2461 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×C3×#877C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C22×#3724C211yesmaximal, characteristic, complemented
5C2×#63966C212yesmaximal
6C2×C4×#627C211yesmaximal, characteristic, complemented
7C2×#63874C211yesmaximal, characteristic, complemented
8C2×#63870C211yesmaximal, characteristic, complemented
9C2×#63868C212yesmaximal, complemented
10C2×#63867C212yesmaximal, complemented
11C2×#63865C211yesmaximal, characteristic, complemented
12#10594046C2116yesmaximal, direct product factor
13C2×#5531—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×#627C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64090C2218yes—
24C2×C3×#217C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C3×#877C22116yescomplemented
30#63982C2218yescomplemented
31C2×#3724C2211yescharacteristic
32C2×#3724C2212yes—
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2218yescomplemented
36#63966C22116yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×#3722C2212yes—
41C2×#3722C2212yes—
42C4×#627C2218yescomplemented
43#63874C2218yescomplemented
44#63870C2218yescomplemented
45#63868C22116yescomplemented
46#63867C22116yescomplemented
47#63865C2218yescomplemented
48C2×C3×#117—32no—
49C2×#929—32no—
50C22×Dic3⋊C4—32no—
51#5531—332no—
52C2×#898—32no—
53C2×#896—32no—
54C2×#889—32no—
55C2×#889—32no—
56C2×#886—32no—
57C2×#67⋊C4—32no—
58C2×#67⋊C4—61no—
59C2×#878—32no—
60C2×#877D312yescomplemented
61C2×#876—32no—
62C2×#872—32no—
63C2×#870—32no—
64C2×C4×Dic6—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C2×#638—24no—
70C2×#638C2314yes—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3C2314yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3C2314yes—
78C22×C3×Dic3—28no—
79C22×C3×Dic3C2318yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C2×#627—24no—
85C2×#627C2314yes—
86C32×C22⋊C4C2314yes—
87#3752C2314yes—
88#3750C2314yes—
89C4×C3⋊Dic3C2314yes—
90C3×#217C2318yes—
91C3×Dic3⋊C4C2318yes—
92C3×Dic3⋊C4C2318yes—
93C3×C4×Dic3C2318yes—
94C3×C4×Dic3C2318yes—
95#3724C2314yes—
96#3724C2318yes—
97#3724C2314yes—
98#3724C2314yes—
99Dic3⋊Dic3C2318yes—
100Dic3⋊Dic3C2318yes—
101Dic3⋊Dic3C2318yes—
102#3722C2318yes—
103#3722C2318yes—
104C2×#552—91noSylow
105C23×C3×C4—32no—
106C22×#67—32no—
107C22×#67—61no—
108C23×Dic3—32no—
109C23×Dic3—61no—
110C23×Dic3C2×D312yes—
111C22×C4×D3—32no—
112C22×C4×D3—61no—
113C22×Dic6—32no—
114C3×#117—316no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4C2×D312yes—
120C2×C3×C42—32no—
121C2×C3×C42—32no—
122C2×#217C2×D312yes—
123#929—316no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—61no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—316no—
143C2×Dic3⋊C4—61no—
144C2×Dic3⋊C4C2×D312yes—
145C2×Dic3⋊C4C2×D312yes—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3C2×D312yes—
149C2×C4×Dic3C2×D312yes—
150#898—316no—
151#896—316no—
152#889—316no—
153#889—316no—
154#886—316no—
155#67⋊C4—316no—
156#67⋊C4—68no—
157#878—316no—
158#877C2×D3116yescomplemented
159#876—316no—
160#872—316no—
161#870—316no—
162C4×Dic6—316no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32#4114yes—
166C23×C32C2412yes—
167C23×C32C2411yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3C2412yes—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2412yes—
175C2×C32×C4C2412yes—
176#638—28no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—28no—
180C2×C3⋊Dic3#4114yes—
181C2×C3⋊Dic3C2412yes—
182C2×C3⋊Dic3C2412yes—
183C2×C3⋊Dic3C2412yes—
184C4×C3⋊D3—28no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—216no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194#627—28no—
195#552—916no—
196C2×#126—92no—
197C2×#125—92no—
198C2×#125—91no—
199C2×#123—92no—
200C2×C22⋊Q8—91no—
201C2×C22⋊Q8—91no—
202C2×C4×Q8—91no—
203C2×C4×D4—91no—
204C2×#117—32no—
205C2×#117—91no—
206C22×C4⋊C4—91no—
207C24×C3—21no—
208C24×C3C22×D312yes—
209C23×D3—32no—
210C23×D3—61no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—38no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—68no—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C2×#67—38no—
222C2×#67—64no—
223C2×#67—68no—
224C2×#67—68no—
225C22×Dic3—28no—
226C22×Dic3—32no—
227C22×Dic3—38no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—64no—
233C22×Dic3—61no—
234C22×Dic3—68no—
235C22×Dic3—124no—
236C22×Dic3C22×D318yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C2×C4×D3—38no—
242C2×C4×D3—64no—
243C2×C4×D3—68no—
244C2×C4×D3—124no—
245C2×Dic6—38no—
246C2×Dic6—68no—
247C3×C4⋊C4—38no—
248C3×C4⋊C4—38no—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—38no—
251C3×C22⋊C4C22×D318yes—
252C3×C42—38no—
253C3×C42—38no—
254#217C22×D318yes—
255(C2×D3)⋊C4—38no—
256(C2×D3)⋊C4—38no—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—64no—
261C4⋊Dic3—38no—
262C4⋊Dic3—38no—
263C4⋊Dic3—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—38no—
273Dic3⋊C4—64no—
274Dic3⋊C4C22×D318yes—
275Dic3⋊C4C22×D318yes—
276C4×Dic3—38no—
277C4×Dic3—64no—
278C4×Dic3C22×D318yes—
279C4×Dic3C22×D318yes—
280C22×C32—28no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32C2×#4114yes—
284C22×C32C2×#4112yes—
285C22×C32C2×#4112yes—
286C22×C322−1+412yes—
287C22×C32C2511yescharacteristic
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—44no—
292C32×C4—22no—
293C32×C4—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3C2×#4114yes—
297C3×Dic3—24no—
298C3×Dic3—24no—
299C3×Dic3—24no—
300C3×Dic3—24no—
301C22×Q8—91no—
302C22×D4—91no—
303C23×C4—32no—
304C23×C4—91no—
305C23×C4—91no—
306#126—916no—
307#125—916no—
308#125—98no—
309#123—916no—
310C22⋊Q8—98no—
311C22⋊Q8—98no—
312C4×Q8—98no—
313C4×D4—98no—
314#117—316no—
315#117—98no—
316C2×C4⋊C4—32no—
317C2×C4⋊C4—32no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—98no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—92no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4D3211yescharacteristic
332C2×C42—32no—
333C2×C42—32no—
334C2×C42—91no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—24no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3#23518yes—
343C23×C3C23×D314yes—
344C23×C3C23×D312yes—
345C22×D3—34no—
346C22×D3—62no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—122no—
352C22×D3—122no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—34no—
358C2×C3×C4—34no—
359C2×C3×C4—34no—
360C2×C3×C4—34no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—616no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4—64no—
367C2×C3×C4—64no—
368C2×C3×C4C23×D314yes—
369C2×C3×C4C23×D314yes—
370#67—616no—
371#67—616no—
372C2×Dic3—216no—
373C2×Dic3—24no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—38no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—616no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—128no—
390C2×Dic3—122no—
391C2×Dic3C23×D314yes—
392C2×Dic3C23×D314yes—
393C2×Dic3C23×D314yes—
394C2×Dic3C23×D314yes—
395C4×D3—616no—
396C4×D3—128no—
397Dic6—616no—
398C2×C32—24no—
399C2×C32#55214yescomplemented
400C2×C32C22×#4111yescharacteristic
401C2×C32C22×#4111yescharacteristic
402C2×C32C2×2−1+411yescharacteristic
403C3⋊D3—42no—
404C24—91no—
405C24C2×D3211yescharacteristic
406C2×Q8—94no—
407C2×Q8—184no—
408C2×D4—94no—
409C2×D4—184no—
410C22×C4—38no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—68no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—94no—
421C22×C4—184no—
422C22×C4—184no—
423C22×C4C2×D3211yescharacteristic
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—38no—
426C4⋊C4—38no—
427C4⋊C4—94no—
428C4⋊C4—94no—
429C4⋊C4—98no—
430C4⋊C4—94no—
431C4⋊C4—98no—
432C4⋊C4—98no—
433C4⋊C4—98no—
434C4⋊C4—94no—
435C22⋊C4—38no—
436C22⋊C4—98no—
437C22⋊C4—98no—
438C22⋊C4—94no—
439C22⋊C4C2×D3214yes—
440C42—38no—
441C42—38no—
442C42—94no—
443C22×C3—24no—
444C22×C3—24no—
445C22×C3—216no—
446C22×C3—22no—
447C22×C3—24no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—48no—
454C22×C3C2×#23518yes—
455C22×C3C2×#23514yes—
456C22×C3D3×#4114yes—
457C22×C3#101014yes—
458C22×C3C24×D312yes—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—128no—
466C2×D3—128no—
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—64no—
472C3×C4—64no—
473C3×C4—64no—
474C3×C4—64no—
475Dic3—24no—
476Dic3—24no—
477Dic3—24no—
478Dic3—24no—
479Dic3—38no—
480Dic3—64no—
481Dic3—64no—
482Dic3—64no—
483Dic3—64no—
484Dic3—122no—
485C32C2×#55211yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—92no—
489C23—182no—
490C23—182no—
491C23—182no—
492C23#379814yes—
493C23C22×D3212yes—
494C23C22×D3211yescharacteristic
495Q8—188no—
496D4—188no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—34no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—34no—
503C2×C4—616no—
504C2×C4—64no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—64no—
508C2×C4—94no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—188no—
513C2×C4—188no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4C22×D3212yes—
517C2×C4C22×D3212yes—
518C2×C3—28no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—24no—
523C2×C3—44no—
524C2×C3#553118yescomplemented
525C2×C3C22×#23512yes—
526C2×C3C2×D3×#4112yes—
527C2×C3C2×#101012yes—
528D3—124no—
529D3—124no—
530C22—22no—
531C22—22no—
532C22—28no—
533C22—182no—
534C22—182no—
535C22—182no—
536C22—364no—
537C22C2×#379814yes—
538C22C2×#379812yes—
539C22#6430912yes—
540C22#6431212yes—
541C22C23×D3211yescharacteristic
542C4—22no—
543C4—22no—
544C4—64no—
545C4—64no—
546C4—64no—
547C4—64no—
548C4—94no—
549C4—182no—
550C4—182no—
551C3—21no—
552C3C2×#553112yescomplemented
553C2—24no—
554C2—362no—
555C2#1059404614yesdirect product factor
556C2C22×#379811yescharacteristic
557C2C2×#6430911yescharacteristic
558C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#877C2semidirect
3. C2×#63982C2semidirect
4. C22×#3724C2semidirect
6. C2×C4×#627C2semidirect
7. C2×#63874C2semidirect
8. C2×#63870C2semidirect
9. C2×#63868C2semidirect
10. C2×#63867C2semidirect
11. C2×#63865C2semidirect
12. #10594046C2direct (N × H)
29. C3×#877C22semidirect
30. #63982C22semidirect
35. C2×#3724C22semidirect
42. C4×#627C22semidirect
43. #63874C22semidirect
44. #63870C22semidirect
45. #63868C22semidirect
46. #63867C22semidirect
47. #63865C22semidirect
60. C2×#877D3semidirect
158. #877C2×D3semidirect
399. C2×C32#552semidirect
485. C32C2×#552semidirect
524. C2×C3#5531semidirect
552. C3C2×#5531semidirect
555. C2#10594046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C3×#8772
C2×#639822
C22×#37242
C2×#639662
C2×C4×#6272
C2×#638742
C2×#638702
C2×#638682
C2×#638672
C2×#638652
#105940462
C2×#55313