Finite Group Databasebeta

← C2×#10595120 #11903056

Subgroups — C2×#10595120 #11903056

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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#935C212yesmaximal
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C22×#3724C211yesmaximal, characteristic, complemented
6C2×#63957C211yesmaximal, characteristic, complemented
7C2×#63956C212yesmaximal, complemented
8C2×#63955C212yesmaximal, complemented
9#10595120C2116yesmaximal, direct product factor
10C2×#63870C211yesmaximal, characteristic, complemented
11C2×#63845C212yesmaximal, complemented
12C2×#63838C211yesmaximal, characteristic, complemented
13C2×#5650—32nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×#627C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21D4×C3⋊Dic3C2218yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×#935C22116yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30#63982C2218yescomplemented
31#63982C2218yescomplemented
32C2×#3724C2212yes—
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2218yescomplemented
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40#63957C2218yescomplemented
41#63956C22116yescomplemented
42#63955C22116yescomplemented
43C2×Dic32C2212yes—
44C2×Dic32C2212yes—
45#63870C2218yescomplemented
46#63845C22116yescomplemented
47#63838C2218yescomplemented
48C2×C3×#123—32no—
49C2×#935D312yes—
50C2×D4×Dic3—32no—
51C2×D4×Dic3—61no—
52C2×#926—32no—
53C22×Dic3⋊C4—32no—
54#5650—332no—
55C2×#890—32no—
56C2×#889—32no—
57C2×#889—32no—
58C2×#887—32no—
59C2×#879—32no—
60C2×#879—32no—
61C2×#878—32no—
62C2×#878—32no—
63C2×#877—32no—
64C2×#877—32no—
65C24×C32C2311yescharacteristic
66C24×C32C2311yescharacteristic
67C2×C32×D4—24no—
68C2×C32×D4C2314yes—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2314yes—
75C22×C3⋊Dic3C2314yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3×Dic3—28no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2318yes—
84C2×#627—24no—
85C2×#627C2314yes—
86#3757C2314yes—
87#3757C2314yes—
88C4⋊(C3⋊Dic3)C2314yes—
89C4×C3⋊Dic3C2314yes—
90C3×#217C2318yes—
91C3×#217C2318yes—
92C3×#217C2318yes—
93C3×Dic3⋊C4C2318yes—
94C3×Dic3⋊C4C2318yes—
95#3724C2314yes—
96#3724C2318yes—
97#3724C2314yes—
98#3724C2314yes—
99Dic3⋊Dic3C2318yes—
100Dic3⋊Dic3C2318yes—
101Dic3⋊Dic3C2318yes—
102Dic32C2318yes—
103Dic32C2318yes—
104C2×#552—91noSylow
105C22×C3×D4—21no—
106C22×C3×D4C2×D312yes—
107C23×C3×C4—32no—
108C23×Dic3—32no—
109C23×Dic3—32no—
110C23×Dic3—61no—
111C23×Dic3—61no—
112C23×Dic3C2×D312yes—
113C22×Dic6—32no—
114C3×#123—316no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—61no—
123C2×#217—61no—
124C2×#217C2×D312yes—
125C2×#217C2×D312yes—
126C2×#217C2×D312yes—
127#935C2×D3116yes—
128D4×Dic3—316no—
129D4×Dic3—68no—
130#926—316no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—61no—
136C2×Dic3⋊C4—316no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4C2×D312yes—
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—32no—
152C2×C4×Dic3—61no—
153#890—316no—
154#889—316no—
155#889—316no—
156#887—316no—
157#879—316no—
158#879—316no—
159#878—316no—
160#878—316no—
161#877—316no—
162#877—316no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32#4114yes—
169C23×C32C2412yes—
170C23×C32C2412yes—
171C23×C32C2411yescharacteristic
172C32×D4—28no—
173C2×C32×C4—22no—
174C2×C32×C4C2412yes—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—28no—
179C2×C3⋊Dic3—28no—
180C2×C3⋊Dic3#4114yes—
181C2×C3⋊Dic3C2412yes—
182C2×C3⋊Dic3C2412yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
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—91no—
198C2×#125—92no—
199C2×#123—32no—
200C2×C22⋊Q8—91no—
201C2×C22⋊Q8—91no—
202C2×C4×Q8—91no—
203C2×C4×D4—91no—
204C2×#117—91no—
205C2×#117—92no—
206C22×C4⋊C4—91no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3C22×D312yes—
210C24×C3C22×D312yes—
211C2×C3×D4—28no—
212C2×C3×D4—28no—
213C2×C3×D4—24no—
214C2×C3×D4C22×D318yes—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—38no—
221C22×C3×C4—68no—
222C22×C3×C4C22×D312yes—
223C22×Dic3—28no—
224C22×Dic3—32no—
225C22×Dic3—38no—
226C22×Dic3—38no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—64no—
235C22×Dic3—64no—
236C22×Dic3—68no—
237C22×Dic3—68no—
238C22×Dic3—124no—
239C22×Dic3—124no—
240C22×Dic3C22×D318yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×Dic6—38no—
246C2×Dic6—68no—
247C3×C4⋊C4—38no—
248C3×C4⋊C4—38no—
249C3×C22⋊C4—38no—
250C3×C22⋊C4—38no—
251C3×C22⋊C4—38no—
252#217—38no—
253#217—38no—
254#217—64no—
255#217—64no—
256#217C22×D318yes—
257#217C22×D318yes—
258#217C22×D318yes—
259C4⋊Dic3—38no—
260C4⋊Dic3—38no—
261C4⋊Dic3—38no—
262C4⋊Dic3—38no—
263C4⋊Dic3—64no—
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⋊C4C22×D318yes—
273Dic3⋊C4C22×D318yes—
274C4×Dic3—38no—
275C4×Dic3—38no—
276C4×Dic3—38no—
277C4×Dic3—38no—
278C4×Dic3—38no—
279C4×Dic3—64no—
280C22×C32—22no—
281C22×C32—28no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32—22no—
286C22×C32—44no—
287C22×C32C2×#4114yes—
288C22×C32C2×#4112yes—
289C22×C32C2×#4112yes—
290C22×C322−1+412yes—
291C22×C32C2511yescharacteristic
292C32×C4—22no—
293C3⋊Dic3—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×D4D3211yescharacteristic
303C23×C4—32no—
304C23×C4—91no—
305C23×C4—91no—
306#126—916no—
307#125—98no—
308#125—916no—
309#123—316no—
310C22⋊Q8—98no—
311C22⋊Q8—98no—
312C4×Q8—98no—
313C4×D4—98no—
314#117—98no—
315#117—916no—
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—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C42—92no—
333C2×C42—92no—
334C2×C42—91no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—24no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3#23718yes—
350C23×C3C23×D314yes—
351C23×C3C23×D314yes—
352C23×C3C23×D312yes—
353C3×D4—216no—
354C3×D4—216no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—22no—
358C2×C3×C4—34no—
359C2×C3×C4—34no—
360C2×C3×C4—34no—
361C2×C3×C4—34no—
362C2×C3×C4—616no—
363C2×C3×C4—64no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4—64no—
367C2×C3×C4C23×D314yes—
368C2×Dic3—216no—
369C2×Dic3—24no—
370C2×Dic3—24no—
371C2×Dic3—24no—
372C2×Dic3—24no—
373C2×Dic3—38no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—34no—
378C2×Dic3—64no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—616no—
384C2×Dic3—616no—
385C2×Dic3—64no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—128no—
389C2×Dic3—128no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3C23×D314yes—
394C2×Dic3C23×D314yes—
395C2×Dic3C23×D314yes—
396C2×Dic3C23×D314yes—
397Dic6—616no—
398C2×C32—24no—
399C2×C32—42no—
400C2×C32#55214yescomplemented
401C2×C32C22×#4111yescharacteristic
402C2×C32C22×#4111yescharacteristic
403C2×C32C2×2−1+411yescharacteristic
404C24C2×D3211yescharacteristic
405C24C2×D3211yescharacteristic
406C2×Q8—94no—
407C2×Q8—184no—
408C2×D4—24no—
409C2×D4C2×D3214yes—
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—94no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—184no—
423C22×C4—184no—
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—38no—
437C22⋊C4—38no—
438C22⋊C4—94no—
439C22⋊C4—94no—
440C42—98no—
441C42—98no—
442C42—94no—
443C22×C3—216no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—24no—
454C22×C3—21no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—48no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—48no—
461C22×C3—48no—
462C22×C3C2×#23718yes—
463C22×C3C2×#23714yes—
464C22×C3D3×#4114yes—
465C22×C3#101014yes—
466C22×C3C24×D312yes—
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—64no—
470C3×C4—64no—
471C3×C4—64no—
472C3×C4—64no—
473Dic3—24no—
474Dic3—24no—
475Dic3—24no—
476Dic3—24no—
477Dic3—38no—
478Dic3—64no—
479Dic3—64no—
480Dic3—64no—
481Dic3—64no—
482Dic3—122no—
483Dic3—122no—
484Dic3—122no—
485C32C2×#55211yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23#380514yes—
492C23C22×D3212yes—
493C23C22×D3212yes—
494C23C22×D3211yescharacteristic
495Q8—188no—
496D4—28no—
497C2×C4—22no—
498C2×C4—34no—
499C2×C4—34no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—64no—
503C2×C4—64no—
504C2×C4—616no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—94no—
508C2×C4—92no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—188no—
513C2×C4—188no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4C22×D3212yes—
518C2×C3—28no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—44no—
524C2×C3—44no—
525C2×C3—44no—
526C2×C3#565018yescomplemented
527C2×C3C22×#23712yes—
528C2×C3C2×D3×#4112yes—
529C2×C3C2×#101012yes—
530C22—28no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—44no—
537C22#6430912yes—
538C22#6431212yes—
539C22C2×#380514yes—
540C22C2×#380512yes—
541C22C23×D3211yescharacteristic
542C4—22no—
543C4—64no—
544C4—64no—
545C4—64no—
546C4—64no—
547C4—94no—
548C4—182no—
549C4—182no—
550C4—182no—
551C3—21no—
552C3C2×#565012yescomplemented
553C2—24no—
554C2—42no—
555C2#1059512014yesdirect product factor
556C2C2×#6430911yescharacteristic
557C2C2×#6431211yescharacteristic
558C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C2×#63982C2semidirect
4. C2×#63982C2semidirect
5. C22×#3724C2semidirect
6. C2×#63957C2semidirect
7. C2×#63956C2semidirect
8. C2×#63955C2semidirect
9. #10595120C2direct (N × H)
10. C2×#63870C2semidirect
11. C2×#63845C2semidirect
12. C2×#63838C2semidirect
30. #63982C22semidirect
31. #63982C22semidirect
36. C2×#3724C22semidirect
40. #63957C22semidirect
41. #63956C22semidirect
42. #63955C22semidirect
45. #63870C22semidirect
46. #63845C22semidirect
47. #63838C22semidirect
400. C2×C32#552semidirect
485. C32C2×#552semidirect
526. C2×C3#5650semidirect
552. C3C2×#5650semidirect
555. C2#10595120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9352
C2×#639822
C22×#37242
C2×#639572
C2×#639562
C2×#639552
#105951202
C2×#638702
C2×#638452
C2×#638382
C2×#56503