Finite Group Databasebeta

← C2×#10594224 #11901669

Subgroups — C2×#10594224 #11901669

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×C3×#885C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic
5C2×#63969C212yesmaximal, complemented
6C2×C4×#627C211yesmaximal, characteristic, complemented
7C2×#63915C211yesmaximal, characteristic, complemented
8C2×#63902C211yesmaximal, characteristic, complemented
9C2×#63887C212yesmaximal, complemented
10C2×#63873C211yesmaximal, characteristic, complemented
11C2×#63859C212yesmaximal, complemented
12#10594224C2116yesmaximal, direct product factor
13C2×#5669—32nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#627C2211yescharacteristic
18C22×#625C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64086C2218yescomplemented
27C2×C3×#217C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C3×#885C22116yescomplemented
32#63982C2218yescomplemented
33#63980C2218yes—
34#63969C22116yescomplemented
35C2×#3724C2212yes—
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C4×#627C2218yescomplemented
43#63915C2218yescomplemented
44#63902C2218yescomplemented
45#63887C22116yescomplemented
46#63873C2218yescomplemented
47#63859C22116yescomplemented
48C2×C3×#124—32no—
49C2×#946—32no—
50C2×#944—32no—
51C2×#939—32no—
52C2×#935—32no—
53#5669—332no—
54C2×#885—32no—
55C2×#885D312yescomplemented
56C2×#883—32no—
57C2×#67⋊C4—32no—
58C2×#879—32no—
59C2×#878—32no—
60C2×#878—32no—
61C2×#877—32no—
62C2×#877—61no—
63C2×#876—32no—
64C2×C4×Dic6—32no—
65C24×C32C2311yescharacteristic
66C23×C3×D3C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—24no—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2314yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C2×C3×#67—44no—
76C2×C3×#67C2318yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×Dic6—44no—
81C2×C3×Dic6C2318yes—
82C2×#627—24no—
83C2×#627C2314yes—
84C2×#625—24no—
85C2×#625C2314yes—
86C2×D3×Dic3—44no—
87C2×D3×Dic3C2318yes—
88C32×C22⋊C4C2314yes—
89#3757C2314yes—
90#3750C2314yes—
91#3750C2314yes—
92C4×C3⋊Dic3C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×#217C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×C4×Dic3C2318yes—
98#3724C2318yes—
99#3724C2314yes—
100#3724C2314yes—
101Dic3⋊Dic3C2318yes—
102Dic3⋊Dic3C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105C2×#542—91noSylow
106C22×C3×Q8—32no—
107C22×C3×D4—32no—
108C22×#67—32no—
109C22×#67C2×D312yes—
110C23×Dic3—32no—
111C23×Dic3—32no—
112C23×Dic3—61no—
113C22×C4×D3—32no—
114C22×Dic6—32no—
115C22×Dic6C2×D312yes—
116C3×#124—316no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4C2×D312yes—
122C2×C3×C42—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—61no—
127C2×#217C2×D312yes—
128#946—316no—
129#944—316no—
130#939—316no—
131#935—316no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—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⋊C4—32no—
146C2×Dic3⋊C4—61no—
147C2×Dic3⋊C4—61no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3C2×D312yes—
153#885—316no—
154#885C2×D3116yescomplemented
155#883—316no—
156#67⋊C4—316no—
157#879—316no—
158#878—316no—
159#878—316no—
160#877—316no—
161#877—68no—
162#876—316no—
163C4×Dic6—316no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32C2412yes—
168C23×C32C2411yescharacteristic
169C22×C3×D3—24no—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3C2414yes—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4C2412yes—
176C2×C32×C4C2412yes—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—28no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3#4114yes—
182C2×C3⋊Dic3C2412yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
185C2×C3⋊Dic3C2412yes—
186C3×#67—48no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193C3×Dic6—48no—
194#627—28no—
195#625—28no—
196D3×Dic3—48no—
197#542—916no—
198C2×C4⋊Q8—91no—
199C2×#126—92no—
200C2×#124—32no—
201C2×#124—91no—
202C2×#123—92no—
203C2×C22⋊Q8—91no—
204C2×C22⋊Q8—92no—
205C2×#121—91no—
206C2×C4×Q8—91no—
207C2×C4×D4—91no—
208C2×#117—91no—
209C24×C3—21no—
210C24×C3—32no—
211C24×C3C22×D312yes—
212C23×D3C22×D312yes—
213C2×C3×Q8—38no—
214C2×C3×Q8—124no—
215C2×C3×D4—38no—
216C2×C3×D4—124no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C2×#67—38no—
225C2×#67—44no—
226C2×#67—68no—
227C2×#67C22×D318yes—
228C22×Dic3—32no—
229C22×Dic3—38no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—38no—
234C22×Dic3—64no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—68no—
240C22×Dic3—68no—
241C22×Dic3—124no—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×C4×D3—38no—
246C2×C4×D3—124no—
247C2×Dic6—38no—
248C2×Dic6—44no—
249C2×Dic6—68no—
250C2×Dic6C22×D318yes—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—38no—
253C3×C22⋊C4—38no—
254C3×C22⋊C4—38no—
255C3×C22⋊C4C22×D318yes—
256C3×C42—38no—
257#217—38no—
258#217—38no—
259#217—38no—
260#217—64no—
261#217C22×D318yes—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4C22×D318yes—
265(C2×D3)⋊C4C22×D318yes—
266C4⋊Dic3—38no—
267C4⋊Dic3—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—38no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4—38no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278C4×Dic3—38no—
279C4×Dic3—38no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C4×Dic3C22×D318yes—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32—22no—
286C22×C32—44no—
287C22×C32C2×#4112yes—
288C22×C32H(5,𝔽2)12yes—
289C22×C322−1+412yes—
290C22×C32C2511yescharacteristic
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—48no—
295C32×C4—22no—
296C32×C4—22no—
297C3⋊Dic3—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3C2×#4114yes—
301C3×Dic3—24no—
302C3×Dic3—24no—
303C3×Dic3—24no—
304C22×Q8—32no—
305C22×Q8—91no—
306C22×D4—32no—
307C22×D4—91no—
308C23×C4—92no—
309C23×C4—91no—
310C4⋊Q8—98no—
311#126—916no—
312#124—316no—
313#124—98no—
314#123—916no—
315C22⋊Q8—98no—
316C22⋊Q8—916no—
317#121—98no—
318C4×Q8—98no—
319C4×D4—98no—
320#117—98no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—91no—
334C2×C22⋊C4D3211yescharacteristic
335C2×C42—32no—
336C2×C42—91no—
337C2×C42—91no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—34no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—64no—
348C23×C3—64no—
349C23×C3—64no—
350C23×C3C23×D314yes—
351C23×C3C23×D312yes—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3C23×D314yes—
356C3×Q8—128no—
357C3×D4—128no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—34no—
363C2×C3×C4—34no—
364C2×C3×C4—34no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—64no—
368C2×C3×C4—64no—
369C2×C3×C4—64no—
370C2×C3×C4C23×D314yes—
371C2×C3×C4C23×D314yes—
372#67—48no—
373#67—616no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—24no—
377C2×Dic3—38no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—616no—
388C2×Dic3—616no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3—128no—
396C2×Dic3C23×D314yes—
397C2×Dic3C23×D314yes—
398C2×Dic3C23×D314yes—
399C4×D3—128no—
400Dic6—48no—
401Dic6—616no—
402C2×C32—42no—
403C2×C32#54214yescomplemented
404C2×C32C22×#4111yescharacteristic
405C2×C32C2×H(5,𝔽2)11yescharacteristic
406C2×C32C2×2−1+411yescharacteristic
407C3×D3—44no—
408C24—32no—
409C24C2×D3211yescharacteristic
410C2×Q8—38no—
411C2×Q8—94no—
412C2×Q8—124no—
413C2×Q8—184no—
414C2×D4—38no—
415C2×D4—94no—
416C2×D4—124no—
417C2×D4—184no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—98no—
422C22×C4—91no—
423C22×C4—94no—
424C22×C4—91no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—184no—
428C22×C4—364no—
429C22×C4C2×D3211yescharacteristic
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—94no—
432C4⋊C4—94no—
433C4⋊C4—98no—
434C4⋊C4—98no—
435C4⋊C4—98no—
436C4⋊C4—94no—
437C4⋊C4—94no—
438C22⋊C4—38no—
439C22⋊C4—38no—
440C22⋊C4—38no—
441C22⋊C4—98no—
442C22⋊C4—98no—
443C22⋊C4—94no—
444C22⋊C4C2×D3214yes—
445C42—38no—
446C42—94no—
447C42—94no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—48no—
459C22×C3—48no—
460C22×C3—64no—
461C22×C3—64no—
462C22×C3—64no—
463C22×C3—128no—
464C22×C3#100414yes—
465C22×C3D3×#4114yes—
466C22×C3#101014yes—
467C22×C3C24×D312yes—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—48no—
472C3×C4—24no—
473C3×C4—24no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—64no—
479Dic3—24no—
480Dic3—24no—
481Dic3—24no—
482Dic3—38no—
483Dic3—64no—
484Dic3—64no—
485Dic3—64no—
486Dic3—64no—
487Dic3—64no—
488Dic3—122no—
489Dic3—122no—
490C32C2×#54211yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—22no—
494C23—34no—
495C23—64no—
496C23—64no—
497C23—64no—
498C23C22×D3212yes—
499C23C22×D3211yescharacteristic
500Q8—128no—
501Q8—188no—
502D4—128no—
503D4—188no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—34no—
509C2×C4—64no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—94no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—188no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—368no—
522C2×C4C22×D3212yes—
523C2×C4C22×D3212yes—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—24no—
528C2×C3—44no—
529C2×C3—44no—
530C2×C3—124no—
531C2×C3#566918yescomplemented
532C2×C3C2×#100412yes—
533C2×C3C2×D3×#4112yes—
534C2×C3C2×#101012yes—
535D3—44no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—44no—
540C22—64no—
541C22—64no—
542C22—64no—
543C22—128no—
544C22#6430612yes—
545C22#6430912yes—
546C22#6431312yes—
547C22C23×D3211yescharacteristic
548C4—22no—
549C4—22no—
550C4—64no—
551C4—64no—
552C4—64no—
553C4—94no—
554C4—182no—
555C4—182no—
556C4—182no—
557C3—21no—
558C3C2×#566912yescomplemented
559C2—42no—
560C2—124no—
561C2#1059422414yesdirect product factor
562C2C2×#6430611yescharacteristic
563C2C2×#6430911yescharacteristic
564C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63980C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64086C2semidirect
2. C2×C3×#885C2semidirect
3. C2×#63982C2semidirect
5. C2×#63969C2semidirect
6. C2×C4×#627C2semidirect
7. C2×#63915C2semidirect
8. C2×#63902C2semidirect
9. C2×#63887C2semidirect
10. C2×#63873C2semidirect
11. C2×#63859C2semidirect
12. #10594224C2direct (N × H)
26. #64086C22semidirect
31. C3×#885C22semidirect
32. #63982C22semidirect
34. #63969C22semidirect
42. C4×#627C22semidirect
43. #63915C22semidirect
44. #63902C22semidirect
45. #63887C22semidirect
46. #63873C22semidirect
47. #63859C22semidirect
55. C2×#885D3semidirect
154. #885C2×D3semidirect
403. C2×C32#542semidirect
490. C32C2×#542semidirect
531. C2×C3#5669semidirect
558. C3C2×#5669semidirect
561. C2#10594224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640862
C2×C3×#8852
C2×#639822
C2×#639802
C2×#639692
C2×C4×#6272
C2×#639152
C2×#639022
C2×#638872
C2×#638732
C2×#638592
#105942242
C2×#56693