Finite Group Databasebeta

← C2×#10594592 #11901686

Subgroups — C2×#10594592 #11901686

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×#63913C212yesmaximal, complemented
5C2×#63908C211yesmaximal, characteristic
6C2×#63905C212yesmaximal, complemented
7C2×#63863C211yesmaximal, characteristic, complemented
8C2×#63858C212yesmaximal, complemented
9C2×#63857C212yesmaximal, complemented
10C2×#63855C211yesmaximal, characteristic, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12#10594592C2116yesmaximal, direct product factor
13C2×#5643—31nomaximal
14C2×#5561—31nomaximal
15C22×#634C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×#625C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64097C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#897C2218yescomplemented
31C3×#893C2218yescomplemented
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41#63913C22116yescomplemented
42#63908C2218yes—
43#63905C22116yescomplemented
44#63863C2218yescomplemented
45#63858C22116yescomplemented
46#63857C22116yescomplemented
47#63855C2218yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#938—31no—
54C2×#936—31no—
55C2×#930—31no—
56C2×#929—32no—
57C2×#926—31no—
58C2×#924—32no—
59#5643—316no—
60#5561—316no—
61C2×#898—32no—
62C2×#897—32no—
63C2×#897D311yescharacteristic, complemented
64C2×#893D311yescharacteristic, complemented
65C2×#888—31no—
66C2×#888—31no—
67C2×#888—61no—
68C2×#885—32no—
69C2×#885—32no—
70C2×#883—32no—
71C2×#879—32no—
72C2×#872—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×#634—44no—
82C2×#634C2318yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—44no—
91C2×C3×C4×D3C2314yes—
92C2×C3×C4×D3C2318yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#625—44no—
96C2×#625C2318yes—
97C32×C4⋊C4C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105Dic3⋊Dic3C2318yes—
106Dic3⋊Dic3C2314yes—
107Dic3⋊Dic3C2314yes—
108(C2×D3)⋊Dic3C2314yes—
109(C2×D3)⋊Dic3C2314yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—32no—
119C22×#67—32no—
120C22×#67—32no—
121C22×D12C2×D311yescharacteristic
122C22×C4×D3C2×D311yescharacteristic
123C22×C4×D3C2×D312yes—
124C22×Dic6—32no—
125C22×Dic6—32no—
126C22×Dic6—62no—
127C22×Dic6C2×D311yescharacteristic
128C3×C22⋊Q8—38no—
129C3×C4×D4—38no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—31no—
137C2×#217—32no—
138C2×#217—32no—
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—32no—
142#947—38no—
143Q8×Dic3—38no—
144#938—38no—
145#936—38no—
146#930—38no—
147#929—316no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4C2×D312yes—
154C2×(C2×D3)⋊C4C2×D312yes—
155#926—38no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—61no—
162C2×C4⋊Dic3C2×D312yes—
163#924—316no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—62no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3C2×D311yescharacteristic
176#898—316no—
177#897—316no—
178#897C2×D318yescomplemented
179#893C2×D318yescomplemented
180#888—38no—
181#888—38no—
182#888—68no—
183#885—316no—
184#885—316no—
185#883—316no—
186#879—316no—
187#872—38no—
188C4×Dic6—38no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—24no—
192C22×C3×D3—22no—
193C22×C3×D3—24no—
194C22×C3×D3—22no—
195C22×C3×D3—24no—
196C22×C3×D3C2414yes—
197C22×C3×D3C2412yes—
198C2×C32×C4—24no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2414yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3C2414yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208#634—48no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C3×D12—28no—
218C3×C4×D3—28no—
219C3×C4×D3—48no—
220C3×Dic6—28no—
221#625—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—92no—
226C2×#124—91no—
227C2×#123—92no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—92no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×#117—91no—
234C24×C3—32no—
235C24×C3—31no—
236C23×D3C22×D312yes—
237C23×D3C22×D311yescharacteristic
238C2×C3×Q8—34no—
239C2×C3×Q8—64no—
240C2×C3×D4—34no—
241C2×C3×D4—64no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—34no—
249C22×C3×C4—38no—
250C22×C3×C4—64no—
251C22×C3×C4—124no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—38no—
257C2×#67—38no—
258C2×#67—124no—
259C2×#67—124no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—61no—
267C22×Dic3—61no—
268C22×Dic3—62no—
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D312yes—
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C2×D12—24no—
274C2×D12C22×D314yes—
275C2×C4×D3—24no—
276C2×C4×D3—44no—
277C2×C4×D3C22×D314yes—
278C2×C4×D3C22×D318yes—
279C2×Dic6—24no—
280C2×Dic6—38no—
281C2×Dic6—38no—
282C2×Dic6—68no—
283C2×Dic6—124no—
284C2×Dic6—124no—
285C2×Dic6—128no—
286C2×Dic6C22×D314yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4C22×D314yes—
290C3×C4⋊C4C22×D314yes—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C42—34no—
294#217—38no—
295#217—38no—
296#217—34no—
297#217—34no—
298#217—38no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—34no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4C22×D318yes—
305(C2×D3)⋊C4C22×D318yes—
306C4⋊Dic3—34no—
307C4⋊Dic3—34no—
308C4⋊Dic3—38no—
309C4⋊Dic3—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—64no—
312C4⋊Dic3C22×D318yes—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—34no—
317Dic3⋊C4—34no—
318Dic3⋊C4—68no—
319C4×Dic3—34no—
320C4×Dic3—34no—
321C4×Dic3—38no—
322C4×Dic3—38no—
323C4×Dic3—64no—
324C4×Dic3C22×D314yes—
325C22×C32C2×#4112yes—
326C22×C32H(5,𝔽2)12yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—22no—
332C2×C3×D3—24no—
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—44no—
336C2×C3×D3—48no—
337C32×C4—24no—
338C32×C4C2×#4114yes—
339C3⋊Dic3—22no—
340C3⋊Dic3—22no—
341C3⋊Dic3—24no—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C22×Q8—31no—
347C22×Q8—92no—
348C22×D4—31no—
349C22×D4—92no—
350C23×C4—31no—
351C23×C4—32no—
352C4⋊Q8—98no—
353#126—916no—
354#124—916no—
355#124—98no—
356#123—916no—
357C22⋊Q8—38no—
358C22⋊Q8—916no—
359#121—98no—
360C4×Q8—98no—
361C4×D4—38no—
362#117—98no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4D3211yescharacteristic
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—91no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—92no—
379C2×C42—91no—
380C23×C3—21no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—62no—
384C23×C3—64no—
385C23×C3—62no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—62no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—24no—
392C22×D3—22no—
393C22×D3—24no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3C23×D314yes—
398C22×D3C23×D312yes—
399C3×Q8—68no—
400C3×D4—68no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—32no—
407C2×C3×C4—34no—
408C2×C3×C4—32no—
409C2×C3×C4—32no—
410C2×C3×C4—44no—
411C2×C3×C4—62no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—68no—
416C2×C3×C4—128no—
417C2×C3×C4#23514yes—
418C2×C3×C4#23714yes—
419C2×C3×C4C23×D314yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D312yes—
422C2×C3×C4C23×D312yes—
423#67—128no—
424#67—128no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—32no—
430C2×Dic3—32no—
431C2×Dic3—34no—
432C2×Dic3—34no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—64no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—62no—
446C2×Dic3—124no—
447C2×Dic3C23×D312yes—
448C2×Dic3C23×D314yes—
449C2×Dic3C23×D312yes—
450C2×Dic3C23×D312yes—
451D12—28no—
452C4×D3—28no—
453C4×D3—48no—
454Dic6—28no—
455Dic6—128no—
456Dic6—128no—
457Dic6—1216no—
458C2×C32#54214yescomplemented
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×H(5,𝔽2)11yescharacteristic
461C2×C32C2×2−1+411yescharacteristic
462C3×D3—44no—
463C3×D3—42no—
464C24—31no—
465C24—32no—
466C2×Q8—34no—
467C2×Q8—64no—
468C2×Q8—98no—
469C2×Q8—364no—
470C2×D4—34no—
471C2×D4—64no—
472C2×D4—98no—
473C2×D4—364no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—32no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—38no—
480C22×C4—64no—
481C22×C4—91no—
482C22×C4—91no—
483C22×C4—92no—
484C22×C4—124no—
485C22×C4C2×D3212yes—
486C22×C4C2×D3211yescharacteristic
487C4⋊C4—38no—
488C4⋊C4—94no—
489C4⋊C4—94no—
490C4⋊C4—98no—
491C4⋊C4—94no—
492C4⋊C4—98no—
493C4⋊C4C2×D3214yes—
494C22⋊C4—38no—
495C22⋊C4—38no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C22⋊C4—98no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C42—34no—
502C42—98no—
503C42—94no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—62no—
509C22×C3—64no—
510C22×C3—62no—
511C22×C3—64no—
512C22×C3—64no—
513C22×C3—62no—
514C22×C3—128no—
515C22×C3—124no—
516C22×C3C2×#23512yes—
517C22×C3C2×#23712yes—
518C22×C3#100412yes—
519C22×C3#100712yes—
520C22×C3#100912yes—
521C22×C3#101012yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—24no—
525C2×D3—22no—
526C2×D3—24no—
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—24no—
530C2×D3—44no—
531C2×D3—48no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—44no—
536C3×C4—62no—
537C3×C4—64no—
538C3×C4—62no—
539C3×C4—62no—
540C3×C4C2×#23514yes—
541C3×C4C2×#23714yes—
542Dic3—24no—
543Dic3—22no—
544Dic3—22no—
545Dic3—22no—
546Dic3—64no—
547Dic3—64no—
548Dic3—62no—
549Dic3—64no—
550Dic3—62no—
551Dic3—62no—
552Dic3—64no—
553Dic3—62no—
554Dic3—124no—
555C32C2×#54211yescharacteristic, complemented, Sylow
556C23—32no—
557C23—34no—
558C23—62no—
559C23—64no—
560C23—64no—
561C23—62no—
562C23—62no—
563C23—64no—
564C23C22×D3211yescharacteristic
565Q8—68no—
566Q8—368no—
567D4—68no—
568D4—368no—
569C2×C4—24no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—68no—
579C2×C4—92no—
580C2×C4—92no—
581C2×C4—94no—
582C2×C4—128no—
583C2×C4—184no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4#379514yes—
587C2×C4C22×D3214yes—
588C2×C4C22×D3212yes—
589C2×C3—24no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—122no—
594C2×C3—124no—
595C2×C3#556114yescomplemented
596C2×C3#564314yescomplemented
597C2×C3C22×#23511yescharacteristic
598C2×C3C22×#23711yescharacteristic
599C2×C3C2×#100411yescharacteristic
600C2×C3C2×#100711yescharacteristic
601C2×C3C2×#100911yescharacteristic
602C2×C3C2×#101011yescharacteristic
603D3—44no—
604D3—42no—
605C22—62no—
606C22—64no—
607C22—64no—
608C22—62no—
609C22—62no—
610C22—64no—
611C22—124no—
612C22—128no—
613C22C2×#379512yes—
614C22#6431412yes—
615C22#6431512yes—
616C22C23×D3211yescharacteristic
617C4—24no—
618C4—62no—
619C4—64no—
620C4—62no—
621C4—62no—
622C4—184no—
623C4—182no—
624C4—182no—
625C4C2×#379514yes—
626C3—21no—
627C3C2×#556111yescharacteristic, complemented
628C3C2×#564311yescharacteristic, complemented
629C2—122no—
630C2—124no—
631C2#1059459214yesdirect product factor
632C2C22×#379511yescharacteristic
633C2C2×#6431411yescharacteristic
634C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63908C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64097C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#893C2semidirect
4. C2×#63913C2semidirect
6. C2×#63905C2semidirect
7. C2×#63863C2semidirect
8. C2×#63858C2semidirect
9. C2×#63857C2semidirect
10. C2×#63855C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. #10594592C2direct (N × H)
25. #64097C22semidirect
30. C3×#897C22semidirect
31. C3×#893C22semidirect
41. #63913C22semidirect
43. #63905C22semidirect
44. #63863C22semidirect
45. #63858C22semidirect
46. #63857C22semidirect
47. #63855C22semidirect
48. Dic3×Dic6C22semidirect
63. C2×#897D3semidirect
64. C2×#893D3semidirect
178. #897C2×D3semidirect
179. #893C2×D3semidirect
458. C2×C32#542semidirect
555. C32C2×#542semidirect
595. C2×C3#5561semidirect
596. C2×C3#5643semidirect
627. C3C2×#5561semidirect
628. C3C2×#5643semidirect
631. C2#10594592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×C3×#8972
C2×C3×#8932
C2×#639132
C2×#639082
C2×#639052
C2×#638632
C2×#638582
C2×#638572
C2×#638552
C2×Dic3×Dic62
#105945922
C2×#56433
C2×#55613