Finite Group Databasebeta

← C2×#10594310 #11910199

Subgroups — C2×#10594310 #11910199

Order 1152.

2859 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64095C211yesmaximal, characteristic, complemented
2C2×C3×#884C212yesmaximal, complemented
3C2×#63983C211yesmaximal, characteristic, complemented
4C2×#63980C212yesmaximal, complemented
5C2×#63979C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×#63908C212yesmaximal, complemented
8C2×#63861C212yesmaximal, complemented
9C2×#63850C212yesmaximal, complemented
10#10594310C2116yesmaximal, direct product factor
11C2×#5620—32nomaximal
12C23×D32C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic, complemented
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yescomplemented
17C22×C3×D12C2212yes—
18C22×C3×C4×D3C2212yescomplemented
19C22×#626C2212yes—
20C22×#625C2212yes—
21C22×#625C2211yescharacteristic, complemented
22C2×C32×C22⋊C4C2211yescharacteristic, complemented
23C2×#3752C2212yes—
24C2×C4⋊(C3⋊Dic3)C2212yescomplemented
25#64095C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yescomplemented
28C3×#884C22116yescomplemented
29#63983C2218yescomplemented
30#63980C22116yescomplemented
31#63979C2218yescomplemented
32C2×#3724C2212yescomplemented
33C2×#3722C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C2×Dic32C2211yescharacteristic, complemented
38#63922C22116yescomplemented
39#63908C22116yescomplemented
40#63861C22116yescomplemented
41#63850C22116yescomplemented
42C2×C3×#121—32no—
43C2×#940—32no—
44C2×#939—32no—
45C2×#939—32no—
46C2×#938—32no—
47C2×#937—32no—
48C2×#937—32no—
49C2×#930—32no—
50C2×#929—32no—
51#5620—332no—
52C2×#898—32no—
53C2×#894—32no—
54C2×#886—32no—
55C2×#886—61no—
56C2×#884D312yescomplemented
57C2×#882—32no—
58C2×#879—32no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C23×C3×D3C2312yes—
63C22×D32—42no—
64C22×D32—44no—
65C22×D32C2314yes—
66C22×C32×C4C2312yes—
67C2×#638—42no—
68C2×#638C2314yes—
69C22×C3⋊Dic3—42no—
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2314yescomplemented
73C2×C3×#67—44no—
74C2×C3×#67—44no—
75C2×C3×#67C2318yes—
76C2×C3×#67C2318yescomplemented
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×C3×D12—44no—
80C2×C3×D12C2318yes—
81C2×C3×C4×D3—44no—
82C2×C3×C4×D3C2318yescomplemented
83C2×#626—44no—
84C2×#626C2318yes—
85C2×#625—44no—
86C2×#625—42no—
87C2×#625C2318yes—
88C2×#625C2314yescomplemented
89C32×C22⋊C4C2314yescomplemented
90#3752C2318yes—
91C4⋊(C3⋊Dic3)C2318yescomplemented
92C3×(C2×D3)⋊C4C2318yes—
93C3×Dic3⋊C4C2318yescomplemented
94#3724C2318yescomplemented
95#3722C2314yes—
96(C2×D3)⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yescomplemented
99Dic32C2314yescomplemented
100C2×#560—91noSylow
101C24×D3—32no—
102C22×C3×D4—32no—
103C22×C3×D4—32no—
104C22×C3×D4—32no—
105C23×C3×C4—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—32no—
111C22×#67—61no—
112C22×#67C2×D312yes—
113C22×#67C2×D312yescomplemented
114C23×Dic3—32no—
115C23×Dic3—61no—
116C22×D12—32no—
117C22×D12C2×D312yes—
118C22×C4×D3C2×D312yescomplemented
119C3×#121—316no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4C2×D312yescomplemented
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—32no—
127#940—316no—
128#939—316no—
129#939—316no—
130#938—316no—
131#937—316no—
132#937—316no—
133#930—316no—
134#929—316no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4C2×D312yes—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—62no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4C2×D312yescomplemented
149C2×C4×Dic3—32no—
150#898—316no—
151#894—316no—
152#886—316no—
153#886—68no—
154#884C2×D3116yescomplemented
155#882—316no—
156#879—316no—
157C23×C32—22no—
158C23×C32—24no—
159C23×C32C2412yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—24no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3C2412yes—
164C22×C3×D3—24no—
165C22×C3×D3—24no—
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—24no—
170C22×C3×D3C2414yes—
171C22×C3×D3C2414yes—
172C2×D32—44no—
173C2×D32—48no—
174C2×D32—416no—
175C2×C32×C4—24no—
176C2×C32×C4C2414yes—
177#638—44no—
178C2×C3⋊Dic3—24no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—44no—
181C2×C3⋊Dic3C2412yes—
182C2×C3⋊Dic3C2414yes—
183C3×#67—48no—
184C3×#67—48no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189C3×D12—48no—
190C3×C4×D3—48no—
191#626—48no—
192#625—48no—
193#625—44no—
194#560—916no—
195C2×#127—91no—
196C2×#126—92no—
197C2×#123—92no—
198C2×#123—91no—
199C2×#121—32no—
200C2×#121—92no—
201C2×#121—92no—
202C2×#120—92no—
203C2×#120—91no—
204C24×C3—21no—
205C24×C3—32no—
206C24×C3—32no—
207C24×C3C22×D312yes—
208C23×D3—32no—
209C23×D3—38no—
210C23×D3—61no—
211C23×D3—124no—
212C23×D3—124no—
213C23×D3—124no—
214C23×D3C22×D312yes—
215C23×D3C22×D312yes—
216C2×C3×D4—38no—
217C2×C3×D4—38no—
218C2×C3×D4—38no—
219C2×C3×D4—124no—
220C2×C3×D4—124no—
221C2×C3×D4—124no—
222C22×C3×C4—22no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—38no—
226C22×C3×C4—124no—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C2×#67—38no—
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—38no—
234C2×#67—44no—
235C2×#67—44no—
236C2×#67—64no—
237C2×#67—124no—
238C2×#67—124no—
239C2×#67—124no—
240C2×#67—124no—
241C2×#67—124no—
242C2×#67—124no—
243C2×#67C22×D318yes—
244C2×#67C22×D318yescomplemented
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—38no—
249C22×Dic3—64no—
250C22×Dic3—61no—
251C22×Dic3—62no—
252C22×Dic3—124no—
253C22×Dic3—124no—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D312yes—
256C2×D12—38no—
257C2×D12—44no—
258C2×D12—124no—
259C2×D12C22×D318yes—
260C2×C4×D3—44no—
261C2×C4×D3C22×D318yescomplemented
262C3×C4⋊C4—38no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—38no—
265C3×C22⋊C4C22×D318yescomplemented
266#217—38no—
267#217—38no—
268#217—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4—38no—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—68no—
276(C2×D3)⋊C4C22×D318yes—
277C4⋊Dic3—38no—
278C4⋊Dic3—38no—
279C4⋊Dic3—68no—
280Dic3⋊C4—38no—
281Dic3⋊C4—38no—
282Dic3⋊C4C22×D318yescomplemented
283C4×Dic3—38no—
284C22×C32—22no—
285C22×C32—24no—
286C22×C32—44no—
287C22×C32H(5,𝔽2)14yes—
288C22×C32H(5,𝔽2)12yes—
289C22×C32C2511yescharacteristic
290C2×C3⋊D3—24no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—44no—
293C2×C3×D3—24no—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—48no—
300C2×C3×D3—48no—
301D32—416no—
302C32×C4—24no—
303C3⋊Dic3—24no—
304C3⋊Dic3—22no—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C25—91no—
308C22×D4—32no—
309C22×D4—32no—
310C22×D4—32no—
311C22×D4—92no—
312C22×D4—92no—
313C22×D4—91no—
314C22×D4—91no—
315C23×C4—32no—
316C23×C4—91no—
317#127—98no—
318#126—916no—
319#123—916no—
320#123—98no—
321#121—316no—
322#121—916no—
323#121—916no—
324#120—916no—
325#120—98no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—92no—
328C2×C4⋊C4—92no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4D3211yescharacteristic, complemented
336C2×C42—91no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—34no—
344C23×C3—34no—
345C23×C3—44no—
346C23×C3—64no—
347C23×C3—64no—
348C23×C3—64no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3C23×D314yes—
353C23×C3C23×D312yes—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—34no—
361C22×D3—62no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—122no—
366C22×D3—124no—
367C22×D3—128no—
368C22×D3—128no—
369C22×D3—128no—
370C22×D3—1232no—
371C22×D3C23×D314yes—
372C22×D3C23×D314yes—
373C3×D4—128no—
374C3×D4—128no—
375C3×D4—128no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—44no—
382C2×C3×C4—64no—
383C2×C3×C4—64no—
384C2×C3×C4—128no—
385C2×C3×C4C23×D314yes—
386C2×C3×C4C23×D314yes—
387#67—48no—
388#67—48no—
389#67—128no—
390#67—128no—
391#67—128no—
392#67—128no—
393#67—128no—
394#67—128no—
395C2×Dic3—24no—
396C2×Dic3—24no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—62no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—124no—
406C2×Dic3—122no—
407C2×Dic3—128no—
408C2×Dic3—128no—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D314yes—
411D12—48no—
412D12—128no—
413C4×D3—48no—
414C2×C32—42no—
415C2×C32#56014yescomplemented
416C2×C32C2×H(5,𝔽2)12yes—
417C2×C32C2×H(5,𝔽2)11yescharacteristic
418C3⋊D3—42no—
419C3×D3—44no—
420C3×D3—44no—
421C24—32no—
422C24—32no—
423C24—94no—
424C24—91no—
425C24—362no—
426C24—364no—
427C24C2×D3211yescharacteristic
428C2×D4—38no—
429C2×D4—38no—
430C2×D4—38no—
431C2×D4—98no—
432C2×D4—98no—
433C2×D4—94no—
434C2×D4—94no—
435C2×D4—124no—
436C2×D4—124no—
437C2×D4—124no—
438C2×D4—364no—
439C2×D4—362no—
440C2×D4—364no—
441C2×D4—362no—
442C22×C4—32no—
443C22×C4—32no—
444C22×C4—38no—
445C22×C4—91no—
446C22×C4—92no—
447C22×C4—94no—
448C22×C4—124no—
449C22×C4—362no—
450C22×C4C2×D3212yes—
451C4⋊C4—38no—
452C4⋊C4—98no—
453C4⋊C4—98no—
454C22⋊C4—38no—
455C22⋊C4—94no—
456C22⋊C4—98no—
457C22⋊C4—98no—
458C22⋊C4—98no—
459C22⋊C4—98no—
460C22⋊C4C2×D3214yescomplemented
461C42—94no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—24no—
466C22×C3—22no—
467C22×C3—24no—
468C22×C3—21no—
469C22×C3—44no—
470C22×C3—48no—
471C22×C3—48no—
472C22×C3—64no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—64no—
477C22×C3—64no—
478C22×C3—128no—
479C22×C3—128no—
480C22×C3#100414yes—
481C22×C3#100414yes—
482C22×C3#100914yes—
483C22×C3C24×D312yes—
484C2×D3—24no—
485C2×D3—24no—
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—48no—
491C2×D3—48no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—122no—
496C2×D3—124no—
497C2×D3—1232no—
498C2×D3—128no—
499C2×D3—244no—
500C3×C4—24no—
501C3×C4—24no—
502C3×C4—44no—
503C3×C4—64no—
504C3×C4—64no—
505Dic3—24no—
506Dic3—24no—
507Dic3—64no—
508Dic3—64no—
509Dic3—64no—
510Dic3—124no—
511Dic3—122no—
512C32C2×#56011yescharacteristic, complemented, Sylow
513C23—22no—
514C23—24no—
515C23—34no—
516C23—34no—
517C23—64no—
518C23—64no—
519C23—64no—
520C23—64no—
521C23—64no—
522C23—64no—
523C23—92no—
524C23—182no—
525C23—184no—
526C23—364no—
527C23—368no—
528C23—3616no—
529C23C22×D3212yes—
530C23C22×D3211yescharacteristic
531D4—128no—
532D4—128no—
533D4—128no—
534D4—368no—
535D4—364no—
536D4—368no—
537D4—364no—
538C2×C4—24no—
539C2×C4—34no—
540C2×C4—34no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—92no—
544C2×C4—94no—
545C2×C4—128no—
546C2×C4—184no—
547C2×C4—182no—
548C2×C4—364no—
549C2×C4C22×D3214yes—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—44no—
554C2×C3—44no—
555C2×C3—124no—
556C2×C3—124no—
557C2×C3#562018yescomplemented
558C2×C3C2×#100412yes—
559C2×C3C2×#100412yes—
560C2×C3C2×#100912yes—
561D3—44no—
562D3—44no—
563D3—124no—
564D3—242no—
565C22—22no—
566C22—24no—
567C22—44no—
568C22—64no—
569C22—64no—
570C22—64no—
571C22—64no—
572C22—64no—
573C22—64no—
574C22—128no—
575C22—128no—
576C22—182no—
577C22—184no—
578C22—3616no—
579C22—364no—
580C22#6430812yes—
581C22#6431314yes—
582C22C23×D3211yescharacteristic
583C4—24no—
584C4—64no—
585C4—64no—
586C4—184no—
587C4—182no—
588C3—21no—
589C3C2×#562012yescomplemented
590C2—42no—
591C2—124no—
592C2—124no—
593C2—362no—
594C2#1059431014yesdirect product factor
595C2C2×#6430811yescharacteristic
596C2C2×#6431312yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#560
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×#64095C2semidirect
2. C2×C3×#884C2semidirect
3. C2×#63983C2semidirect
4. C2×#63980C2semidirect
5. C2×#63979C2semidirect
6. C2×#63922C2semidirect
7. C2×#63908C2semidirect
8. C2×#63861C2semidirect
9. C2×#63850C2semidirect
10. #10594310C2direct (N × H)
14. C23×C3⋊Dic3C22semidirect
16. C22×C3×#67C22semidirect
18. C22×C3×C4×D3C22semidirect
21. C22×#625C22semidirect
22. C2×C32×C22⋊C4C22semidirect
24. C2×C4⋊(C3⋊Dic3)C22semidirect
25. #64095C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. C3×#884C22semidirect
29. #63983C22semidirect
30. #63980C22semidirect
31. #63979C22semidirect
32. C2×#3724C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C2×Dic32C22semidirect
38. #63922C22semidirect
39. #63908C22semidirect
40. #63861C22semidirect
41. #63850C22semidirect
56. C2×#884D3semidirect
72. C22×C3⋊Dic3C23semidirect
76. C2×C3×#67C23semidirect
82. C2×C3×C4×D3C23semidirect
88. C2×#625C23semidirect
89. C32×C22⋊C4C23semidirect
91. C4⋊(C3⋊Dic3)C23semidirect
93. C3×Dic3⋊C4C23semidirect
94. #3724C23semidirect
98. (C2×D3)⋊Dic3C23semidirect
99. Dic32C23semidirect
113. C22×#67C2×D3semidirect
118. C22×C4×D3C2×D3semidirect
123. C2×C3×C22⋊C4C2×D3semidirect
148. C2×Dic3⋊C4C2×D3semidirect
154. #884C2×D3semidirect
244. C2×#67C22×D3semidirect
261. C2×C4×D3C22×D3semidirect
265. C3×C22⋊C4C22×D3semidirect
282. Dic3⋊C4C22×D3semidirect
335. C2×C22⋊C4D32semidirect
415. C2×C32#560semidirect
460. C22⋊C4C2×D32semidirect
512. C32C2×#560semidirect
557. C2×C3#5620semidirect
589. C3C2×#5620semidirect
594. C2#10594310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640952
C2×C3×#8842
C2×#639832
C2×#639802
C2×#639792
C2×#639222
C2×#639082
C2×#638612
C2×#638502
#105943102
C2×#56203