Finite Group Databasebeta

← C2×#10593953 #11910269

Subgroups — C2×#10593953 #11910269

Order 1152.

2469 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63910C212yesmaximal, complemented
5C2×#63896C212yesmaximal, complemented
6C2×#63890C212yesmaximal, complemented
7C2×#63888C212yesmaximal, complemented
8C2×#63886C212yesmaximal, complemented
9C2×#63854C212yesmaximal, complemented
10#10593953C2116yesmaximal, direct product factor
11C2×#5700—31nomaximal
12C2×#5684—31nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×#626C2212yes—
18C22×#626C2212yes—
19C22×#624C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2212yes—
23C2×#3752C2212yes—
24#64084C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C3×#875C2218yescomplemented
32C3×#870C2218yescomplemented
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37#63910C22116yescomplemented
38#63896C22116yescomplemented
39#63890C22116yescomplemented
40#63888C22116yescomplemented
41#63886C22116yescomplemented
42#63854C22116yescomplemented
43C2×C3×#125—31no—
44C2×C3×#124—31no—
45C2×#946—32no—
46C2×#939—32no—
47#5700—316no—
48#5684—316no—
49C2×#896—32no—
50C2×#896—32no—
51C2×#895—32no—
52C2×#895—32no—
53C2×#894—32no—
54C2×#894—32no—
55C2×#886—32no—
56C2×#884—32no—
57C2×#883—32no—
58C2×#878—32no—
59C2×#875—31no—
60C2×#875—31no—
61C2×#875—61no—
62C2×#875D311yescharacteristic, complemented
63C2×#870D311yescharacteristic, complemented
64C23×C3⋊D3C2312yes—
65C23×C3×D3C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C2×C4⋊(C3⋊D3)—42no—
71C2×C4⋊(C3⋊D3)C2314yes—
72C2×#634—42no—
73C2×#634C2314yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×D12—42no—
78C2×C3×D12C2314yes—
79C2×C3×Dic6—42no—
80C2×C3×Dic6C2314yes—
81C2×#626—44no—
82C2×#626—44no—
83C2×#626C2318yes—
84C2×#626C2318yes—
85C2×#624—44no—
86C2×#624C2318yes—
87C2×D3×Dic3—44no—
88C2×D3×Dic3C2318yes—
89C32×C42C2314yes—
90#3752C2318yes—
91#3752C2318yes—
92C3×(C2×D3)⋊C4C2318yes—
93C3×(C2×D3)⋊C4C2318yes—
94C3×C4⋊Dic3C2314yes—
95C3×C4⋊Dic3C2314yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98#3724C2318yes—
99Dic3⋊Dic3C2318yes—
100#3722C2318yes—
101(C2×D3)⋊Dic3C2318yes—
102C2×#562—91noSylow
103C22×C3×Q8—31no—
104C22×C3×D4—31no—
105C22×#67—32no—
106C22×#67—32no—
107C23×Dic3—32no—
108C22×D12—32no—
109C22×D12—32no—
110C22×D12—31no—
111C22×D12—31no—
112C22×D12—61no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—32no—
115C22×C4×D3—32no—
116C22×C4×D3—32no—
117C22×Dic6—31no—
118C22×Dic6—31no—
119C22×Dic6—61no—
120C22×Dic6C2×D311yescharacteristic
121C3×#125—38no—
122C3×#124—38no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—21no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132C2×#217—32no—
133#946—316no—
134#939—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—32no—
142C2×(C2×D3)⋊C4—62no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4C2×D312yes—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4C2×D312yes—
153C2×Dic3⋊C4C2×D312yes—
154#896—316no—
155#896—316no—
156#895—316no—
157#895—316no—
158#894—316no—
159#894—316no—
160#886—316no—
161#884—316no—
162#883—316no—
163#878—316no—
164#875—38no—
165#875—38no—
166#875—68no—
167#875C2×D318yescomplemented
168#870C2×D318yescomplemented
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—24no—
171C22×C3⋊D3—24no—
172C22×C3⋊D3—24no—
173C22×C3⋊D3C2414yes—
174C22×C3×D3—24no—
175C22×C3×D3—24no—
176C22×C3×D3—24no—
177C22×C3×D3C2414yes—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4C2412yes—
182C2×C32×C4C2412yes—
183C2×C32×C4C2412yes—
184C2×C3⋊Dic3—24no—
185C2×C3⋊Dic3C2414yes—
186C4⋊(C3⋊D3)—44no—
187#634—44no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C3×D12—44no—
195C3×Dic6—44no—
196#626—48no—
197#626—48no—
198#624—48no—
199D3×Dic3—48no—
200#562—916no—
201C2×#125—31no—
202C2×#124—31no—
203C2×#124—91no—
204C2×#123—92no—
205C2×#123—92no—
206C2×C22⋊Q8—92no—
207C2×C22⋊Q8—92no—
208C2×#121—92no—
209C2×#121—92no—
210C24×C3—32no—
211C23×D3—32no—
212C23×D3—32no—
213C23×D3—62no—
214C23×D3C22×D312yes—
215C2×C3×Q8—34no—
216C2×C3×Q8—122no—
217C2×C3×D4—34no—
218C2×C3×D4—122no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—124no—
234C2×#67—124no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—38no—
238C22×Dic3—62no—
239C22×Dic3—124no—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C2×D12—38no—
244C2×D12—38no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—42no—
248C2×D12—64no—
249C2×D12—122no—
250C2×D12—122no—
251C2×D12—124no—
252C2×D12—124no—
253C2×D12—124no—
254C2×D12C22×D314yes—
255C2×C4×D3—38no—
256C2×C4×D3—38no—
257C2×C4×D3—38no—
258C2×C4×D3—124no—
259C2×C4×D3—124no—
260C2×C4×D3—124no—
261C2×Dic6—34no—
262C2×Dic6—34no—
263C2×Dic6—42no—
264C2×Dic6—64no—
265C2×Dic6—122no—
266C2×Dic6—122no—
267C2×Dic6—124no—
268C2×Dic6C22×D314yes—
269C3×C4⋊C4—34no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—38no—
272C3×C4⋊C4—38no—
273C3×C22⋊C4—38no—
274C3×C22⋊C4—38no—
275C3×C42—24no—
276C3×C42C22×D314yes—
277C3×C42C22×D314yes—
278#217—38no—
279(C2×D3)⋊C4—38no—
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4—38no—
283(C2×D3)⋊C4—38no—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—68no—
287(C2×D3)⋊C4—68no—
288(C2×D3)⋊C4C22×D318yes—
289(C2×D3)⋊C4C22×D318yes—
290C4⋊Dic3—38no—
291C4⋊Dic3C22×D314yes—
292C4⋊Dic3C22×D314yes—
293Dic3⋊C4—38no—
294Dic3⋊C4—38no—
295Dic3⋊C4—38no—
296Dic3⋊C4C22×D318yes—
297Dic3⋊C4C22×D318yes—
298C22×C32H(5,𝔽2)12yes—
299C22×C32H(5,𝔽2)12yes—
300C22×C322−1+412yes—
301C22×C32C2511yescharacteristic
302C2×C3⋊D3—24no—
303C2×C3⋊D3—24no—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—48no—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C32×C4—22no—
311C32×C4—22no—
312C32×C4—22no—
313C3⋊Dic3—24no—
314C3×Dic3—24no—
315C3×Dic3—24no—
316C3×Dic3—24no—
317C22×Q8—31no—
318C22×Q8—91no—
319C22×D4—31no—
320C22×D4—92no—
321C22×D4—92no—
322C22×D4—91no—
323C23×C4—92no—
324C23×C4—92no—
325#125—38no—
326#124—38no—
327#124—98no—
328#123—916no—
329#123—916no—
330C22⋊Q8—916no—
331C22⋊Q8—916no—
332#121—916no—
333#121—916no—
334C2×C4⋊C4—32no—
335C2×C4⋊C4—32no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—92no—
339C2×C4⋊C4—92no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C22⋊C4—92no—
346C2×C42D3211yescharacteristic
347C23×C3—21no—
348C23×C3—34no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3C23×D311yescharacteristic
353C23×C3C23×D311yescharacteristic
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—124no—
367C22×D3—124no—
368C22×D3—124no—
369C22×D3C23×D314yes—
370C3×Q8—124no—
371C3×D4—124no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—34no—
383C2×C3×C4—34no—
384C2×C3×C4—34no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4—64no—
390C2×C3×C4C23×D312yes—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D312yes—
393C2×C3×C4C23×D312yes—
394C2×C3×C4C23×D312yes—
395C2×C3×C4C23×D312yes—
396#67—128no—
397#67—128no—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—24no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—124no—
407C2×Dic3—128no—
408C2×Dic3C23×D314yes—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D314yes—
411D12—44no—
412D12—124no—
413D12—124no—
414D12—128no—
415D12—128no—
416D12—128no—
417C4×D3—128no—
418C4×D3—128no—
419C4×D3—128no—
420Dic6—44no—
421Dic6—124no—
422Dic6—124no—
423Dic6—128no—
424C2×C32#56214yescomplemented
425C2×C32C2×H(5,𝔽2)11yescharacteristic
426C2×C32C2×H(5,𝔽2)11yescharacteristic
427C2×C32C2×2−1+411yescharacteristic
428C3⋊D3—44no—
429C3×D3—44no—
430C24—32no—
431C24—92no—
432C2×Q8—34no—
433C2×Q8—94no—
434C2×Q8—122no—
435C2×Q8—362no—
436C2×D4—34no—
437C2×D4—98no—
438C2×D4—98no—
439C2×D4—94no—
440C2×D4—122no—
441C2×D4—362no—
442C2×D4—364no—
443C2×D4—364no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—98no—
448C22×C4—98no—
449C22×C4—92no—
450C22×C4—364no—
451C22×C4—364no—
452C22×C4C2×D3211yescharacteristic
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—38no—
456C4⋊C4—38no—
457C4⋊C4—34no—
458C4⋊C4—34no—
459C4⋊C4—98no—
460C4⋊C4—98no—
461C22⋊C4—38no—
462C22⋊C4—38no—
463C22⋊C4—98no—
464C22⋊C4—98no—
465C22⋊C4—98no—
466C22⋊C4—98no—
467C42C2×D3214yes—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—64no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—128no—
476C22×C3#100412yes—
477C22×C3#100712yes—
478C22×C3#100912yes—
479C22×C3#100912yes—
480C22×C3#100912yes—
481C22×C3#101012yes—
482C22×C3C24×D311yescharacteristic
483C22×C3C24×D311yescharacteristic
484C2×D3—24no—
485C2×D3—24no—
486C2×D3—24no—
487C2×D3—48no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—124no—
497C2×D3—128no—
498C2×D3—128no—
499C2×D3—248no—
500C3×C4—24no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—42no—
508C3×C4—42no—
509C3×C4—64no—
510C3×C4—64no—
511C3×C4—64no—
512Dic3—24no—
513Dic3—24no—
514Dic3—24no—
515Dic3—64no—
516Dic3—64no—
517Dic3—124no—
518C32C2×#56211yescharacteristic, complemented, Sylow
519C23—34no—
520C23—64no—
521C23—64no—
522C23—64no—
523C23—94no—
524C23—184no—
525C23—184no—
526C23—184no—
527C23C22×D3211yescharacteristic
528Q8—124no—
529Q8—364no—
530D4—124no—
531D4—364no—
532D4—368no—
533D4—368no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—34no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—64no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—94no—
544C2×C4—184no—
545C2×C4—368no—
546C2×C4—368no—
547C2×C4C22×D3212yes—
548C2×C4C22×D3212yes—
549C2×C4C22×D3212yes—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—24no—
554C2×C3—124no—
555C2×C3#568414yescomplemented
556C2×C3#570014yescomplemented
557C2×C3C2×#100411yescharacteristic
558C2×C3C2×#100711yescharacteristic
559C2×C3C2×#100911yescharacteristic
560C2×C3C2×#100911yescharacteristic
561C2×C3C2×#100911yescharacteristic
562C2×C3C2×#101011yescharacteristic
563D3—44no—
564D3—124no—
565D3—124no—
566D3—244no—
567C22—64no—
568C22—64no—
569C22—64no—
570C22—128no—
571C22—184no—
572C22—184no—
573C22—184no—
574C22—368no—
575C22#6429712yes—
576C22#6430712yes—
577C22#6430812yes—
578C22C23×D3211yescharacteristic
579C4—22no—
580C4—22no—
581C4—22no—
582C4—64no—
583C4—64no—
584C4—64no—
585C4—184no—
586C3—21no—
587C3C2×#568411yescharacteristic, complemented
588C3C2×#570011yescharacteristic, complemented
589C2—124no—
590C2—364no—
591C2#1059395314yesdirect product factor
592C2C2×#6429711yescharacteristic
593C2C2×#6430711yescharacteristic
594C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64084C2semidirect
2. C2×C3×#875C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63910C2semidirect
5. C2×#63896C2semidirect
6. C2×#63890C2semidirect
7. C2×#63888C2semidirect
8. C2×#63886C2semidirect
9. C2×#63854C2semidirect
10. #10593953C2direct (N × H)
24. #64084C22semidirect
31. C3×#875C22semidirect
32. C3×#870C22semidirect
37. #63910C22semidirect
38. #63896C22semidirect
39. #63890C22semidirect
40. #63888C22semidirect
41. #63886C22semidirect
42. #63854C22semidirect
62. C2×#875D3semidirect
63. C2×#870D3semidirect
167. #875C2×D3semidirect
168. #870C2×D3semidirect
424. C2×C32#562semidirect
518. C32C2×#562semidirect
555. C2×C3#5684semidirect
556. C2×C3#5700semidirect
587. C3C2×#5684semidirect
588. C3C2×#5700semidirect
591. C2#10593953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×#8752
C2×C3×#8702
C2×#639102
C2×#638962
C2×#638902
C2×#638882
C2×#638862
C2×#638542
#105939532
C2×#57003
C2×#56843