Finite Group Databasebeta

← C2×#10594476 #11903023

Subgroups — C2×#10594476 #11903023

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×#64102C211yesmaximal, characteristic
2C2×C3×#889C212yesmaximal, complemented
3C2×#63900C211yesmaximal, characteristic, complemented
4C2×#63897C212yesmaximal
5C2×#63874C211yesmaximal, characteristic, complemented
6C2×#63870C211yesmaximal, characteristic, complemented
7C2×#63865C211yesmaximal, characteristic, complemented
8C2×#63865C211yesmaximal, characteristic, complemented
9C2×#63848C212yesmaximal, complemented
10C2×#63838C211yesmaximal, characteristic, complemented
11C2×#63836C212yesmaximal, complemented
12#10594476C2116yesmaximal, direct product factor
13C2×#5693—32nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#627C2211yescharacteristic
18C22×#624C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64102C2218yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C3×#889C22116yescomplemented
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2212yes—
36C2×#3722C2212yes—
37C2×#3722C2212yes—
38C2×Dic32C2212yes—
39#63900C2218yescomplemented
40#63897C22116yes—
41#63874C2218yescomplemented
42#63870C2218yescomplemented
43#63865C2218yescomplemented
44#63865C2218yescomplemented
45#63848C22116yescomplemented
46#63838C2218yescomplemented
47#63836C22116yescomplemented
48C2×C3×#125—32no—
49#5693—332no—
50C2×#898—32no—
51C2×#898—32no—
52C2×#896—32no—
53C2×#896—32no—
54C2×#894—32no—
55C2×#894—32no—
56C2×#893—32no—
57C2×#893—61no—
58C2×#892—32no—
59C2×D3×C4⋊C4—32no—
60C2×#889—32no—
61C2×#889D312yescomplemented
62C2×#887—32no—
63C2×#872—32no—
64C2×#872—32no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4⋊(C3⋊D3)—24no—
73C2×C4⋊(C3⋊D3)C2314yes—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3—24no—
76C2×C4×C3⋊D3C2314yes—
77C2×C4×C3⋊D3C2314yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#627—24no—
83C2×#627C2314yes—
84C2×#624—28no—
85C2×#624C2318yes—
86C32×C4⋊C4C2314yes—
87#3752C2314yes—
88#3752C2314yes—
89C4×C3⋊Dic3C2314yes—
90C3×C4⋊Dic3C2318yes—
91C3×Dic3⋊C4C2318yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94C3×Dic3⋊C4C2318yes—
95C3×C4×Dic3C2318yes—
96#3724C2314yes—
97#3724C2314yes—
98#3724C2314yes—
99Dic3⋊Dic3C2318yes—
100#3722C2318yes—
101#3722C2318yes—
102#3722C2318yes—
103Dic32C2318yes—
104C2×#552—91noSylow
105C22×D12—32no—
106C22×D12—61no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×Dic6—32no—
114C3×#125—316no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4C2×D312yes—
122C2×C3×C42—32no—
123C2×(C2×D3)⋊C4—32no—
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—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3C2×D312yes—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4C2×D312yes—
140C2×Dic3⋊C4C2×D312yes—
141C2×Dic3⋊C4C2×D312yes—
142C2×Dic3⋊C4C2×D312yes—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3C2×D312yes—
148#898—316no—
149#898—316no—
150#896—316no—
151#896—316no—
152#894—316no—
153#894—316no—
154#893—316no—
155#893—68no—
156#892—316no—
157D3×C4⋊C4—316no—
158#889—316no—
159#889C2×D3116yescomplemented
160#887—316no—
161#872—316no—
162#872—316no—
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3#4114yes—
170C22×C3⋊D3C2412yes—
171C22×C3⋊D3C2412yes—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4C2412yes—
176C2×C32×C4C2412yes—
177C2×C32×C4C2412yes—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3#4114yes—
180C2×C3⋊Dic3C2412yes—
181C2×C3⋊Dic3C2412yes—
182C4⋊(C3⋊D3)—28no—
183C4×C3⋊D3—28no—
184C4×C3⋊D3—28no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193#627—28no—
194#624—216no—
195#552—916no—
196C2×#126—92no—
197C2×#125—32no—
198C2×#125—91no—
199C2×#123—92no—
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—
207C23×D3—32no—
208C23×D3—32no—
209C23×D3—61no—
210C23×D3—61no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C2×D12—38no—
230C2×D12—64no—
231C2×D12—68no—
232C2×D12—68no—
233C2×C4×D3—38no—
234C2×C4×D3—38no—
235C2×C4×D3—38no—
236C2×C4×D3—38no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—68no—
240C2×C4×D3—68no—
241C2×C4×D3—68no—
242C2×C4×D3—68no—
243C2×C4×D3—124no—
244C2×C4×D3—124no—
245C2×Dic6—38no—
246C2×Dic6—68no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—38no—
249C3×C4⋊C4—38no—
250C3×C4⋊C4—38no—
251C3×C4⋊C4—38no—
252C3×C4⋊C4—38no—
253C3×C4⋊C4C22×D318yes—
254C3×C42—38no—
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—38no—
261(C2×D3)⋊C4—38no—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—38no—
266C4⋊Dic3C22×D318yes—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4C22×D318yes—
272Dic3⋊C4C22×D318yes—
273Dic3⋊C4C22×D318yes—
274Dic3⋊C4C22×D318yes—
275C4×Dic3—38no—
276C4×Dic3—38no—
277C4×Dic3—38no—
278C4×Dic3—64no—
279C4×Dic3C22×D318yes—
280C22×C32C2×#4112yes—
281C22×C32C2×#4112yes—
282C22×C322−1+412yes—
283C22×C32C2511yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—28no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—44no—
291C2×C3⋊D3C2×#4114yes—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—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—92no—
304C23×C4—91no—
305C23×C4—91no—
306#126—916no—
307#125—316no—
308#125—98no—
309#123—916no—
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—32no—
319C2×C4⋊C4—32no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—98no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4D3211yescharacteristic
327C2×C22⋊C4—92no—
328C2×C22⋊C4—92no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C42—32no—
333C2×C42—92no—
334C2×C42—91no—
335C23×C3—21no—
336C23×C3C23×D312yes—
337C22×D3—38no—
338C22×D3—34no—
339C22×D3—34no—
340C22×D3—64no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—122no—
352C22×D3—122no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—34no—
361C2×C3×C4—34no—
362C2×C3×C4—34no—
363C2×C3×C4—34no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—64no—
367C2×C3×C4—64no—
368C2×C3×C4—64no—
369C2×C3×C4—64no—
370C2×C3×C4C23×D314yes—
371C2×C3×C4C23×D314yes—
372C2×C3×C4C23×D314yes—
373C2×Dic3—24no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—38no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—64no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—64no—
384C2×Dic3—122no—
385C2×Dic3C23×D314yes—
386C2×Dic3C23×D314yes—
387C2×Dic3C23×D314yes—
388C2×Dic3C23×D314yes—
389D12—616no—
390D12—616no—
391C4×D3—616no—
392C4×D3—616no—
393C4×D3—616no—
394C4×D3—616no—
395C4×D3—128no—
396C4×D3—128no—
397Dic6—616no—
398C2×C32#55214yescomplemented
399C2×C32C22×#4111yescharacteristic
400C2×C32C22×#4111yescharacteristic
401C2×C32C2×2−1+411yescharacteristic
402C3⋊D3—24no—
403C3⋊D3—42no—
404C24—91no—
405C24—91no—
406C2×Q8—94no—
407C2×Q8—184no—
408C2×D4—94no—
409C2×D4—184no—
410C22×C4—32no—
411C22×C4—32no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—98no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—94no—
419C22×C4—184no—
420C22×C4—184no—
421C22×C4—188no—
422C22×C4C2×D3211yescharacteristic
423C22×C4C2×D3211yescharacteristic
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—38no—
426C4⋊C4—38no—
427C4⋊C4—38no—
428C4⋊C4—38no—
429C4⋊C4—38no—
430C4⋊C4—94no—
431C4⋊C4—94no—
432C4⋊C4—94no—
433C4⋊C4—98no—
434C4⋊C4C2×D3214yes—
435C22⋊C4—98no—
436C22⋊C4—98no—
437C22⋊C4—98no—
438C22⋊C4—94no—
439C22⋊C4—94no—
440C42—38no—
441C42—98no—
442C42—94no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3#100714yes—
448C22×C3D3×#4114yes—
449C22×C3D3×#4114yes—
450C22×C3C24×D312yes—
451C2×D3—38no—
452C2×D3—64no—
453C2×D3—616no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—64no—
459C2×D3—64no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—128no—
464C2×D3—122no—
465C2×D3—128no—
466C2×D3—128no—
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—42no—
472C3×C4—42no—
473C3×C4—64no—
474C3×C4—64no—
475C3×C4—64no—
476C3×C4—64no—
477Dic3—24no—
478Dic3—24no—
479Dic3—24no—
480Dic3—24no—
481Dic3—38no—
482Dic3—64no—
483Dic3—64no—
484Dic3—122no—
485C32C2×#55211yescharacteristic, complemented, Sylow
486C23—94no—
487C23—92no—
488C23—92no—
489C23—182no—
490C23—182no—
491C23—182no—
492C23—182no—
493C23—182no—
494C23C22×D3211yescharacteristic
495Q8—188no—
496D4—188no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—64no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—64no—
508C2×C4—94no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—188no—
512C2×C4—188no—
513C2×C4—1816no—
514C2×C4—182no—
515C2×C4C22×D3212yes—
516C2×C4C22×D3212yes—
517C2×C4C22×D3212yes—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—24no—
522C2×C3#569318yescomplemented
523C2×C3C2×#100712yes—
524C2×C3C2×D3×#4112yes—
525C2×C3C2×D3×#4112yes—
526D3—68no—
527D3—124no—
528D3—124no—
529D3—124no—
530C22—94no—
531C22—182no—
532C22—182no—
533C22—188no—
534C22—182no—
535C22—182no—
536C22—182no—
537C22—364no—
538C22#6430612yes—
539C22#6431212yes—
540C22#6431612yes—
541C22C23×D3211yescharacteristic
542C4—22no—
543C4—22no—
544C4—22no—
545C4—64no—
546C4—64no—
547C4—64no—
548C4—64no—
549C4—94no—
550C4—182no—
551C3—21no—
552C3C2×#569312yescomplemented
553C2—184no—
554C2—362no—
555C2#1059447614yesdirect product factor
556C2C2×#6430611yescharacteristic
557C2C2×#6431211yescharacteristic
558C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#889C2semidirect
3. C2×#63900C2semidirect
5. C2×#63874C2semidirect
6. C2×#63870C2semidirect
7. C2×#63865C2semidirect
8. C2×#63865C2semidirect
9. C2×#63848C2semidirect
10. C2×#63838C2semidirect
11. C2×#63836C2semidirect
12. #10594476C2direct (N × H)
30. C3×#889C22semidirect
39. #63900C22semidirect
41. #63874C22semidirect
42. #63870C22semidirect
43. #63865C22semidirect
44. #63865C22semidirect
45. #63848C22semidirect
46. #63838C22semidirect
47. #63836C22semidirect
61. C2×#889D3semidirect
159. #889C2×D3semidirect
398. C2×C32#552semidirect
485. C32C2×#552semidirect
522. C2×C3#5693semidirect
552. C3C2×#5693semidirect
555. C2#10594476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8892
C2×#639002
C2×#638972
C2×#638742
C2×#638702
C2×#638652
C2×#638482
C2×#638382
C2×#638362
#105944762
C2×#56933