Finite Group Databasebeta

← C2×#10594814 #11901681

Subgroups — C2×#10594814 #11901681

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63975C212yesmaximal, complemented
5C2×#63953C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63895C212yesmaximal, complemented
8C2×#63894C211yesmaximal, characteristic, complemented
9C2×#63864C211yesmaximal, characteristic, complemented
10C2×#63848C212yesmaximal, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12#10594814C2116yesmaximal, direct product factor
13C2×#5643—31nomaximal
14C2×#5534—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2212yes—
20C22×#624C2212yes—
21#64139C2218yes—
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C3×#926C2218yescomplemented
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2218yescomplemented
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35#63975C22116yescomplemented
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×#3722C2212yes—
39C2×#3722C2212yes—
40C2×#3722C2212yes—
41C2×Dic32C2212yes—
42#63953C22116yescomplemented
43#63918C2218yescomplemented
44#63895C22116yescomplemented
45#63894C2218yescomplemented
46#63864C2218yescomplemented
47#63848C22116yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×#117—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#930—31no—
54C2×#930—31no—
55C2×#930—61no—
56C2×#926D311yescharacteristic, complemented
57C2×#924D311yescharacteristic, complemented
58#5643—316no—
59#5534—316no—
60C2×#898—32no—
61C2×#898—32no—
62C2×#897—32no—
63C2×#896—32no—
64C2×#893—31no—
65C2×#888—31no—
66C2×#885—32no—
67C2×#885—32no—
68C2×#883—32no—
69C2×#883—32no—
70C2×#875—31no—
71C2×C4×D12—31no—
72C2×#869—31no—
73C2×C4×Dic6—31no—
74C24×C32C2311yescharacteristic
75C23×C3⋊D3C2312yes—
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C2×#638—44no—
81C2×#638C2318yes—
82C22×C3⋊Dic3C2312yes—
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)C2314yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#627—44no—
94C2×#627C2318yes—
95C2×#624—44no—
96C2×#624C2318yes—
97#3752C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C3×#217C2318yes—
100C3×#217C2314yes—
101C3×#217C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110#3722C2318yes—
111#3722C2318yes—
112#3722C2318yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C23×C3×C4—21no—
117C23×C3×C4C2×D311yescharacteristic
118C23×C3×C4C2×D311yescharacteristic
119C22×#67—32no—
120C22×#67—32no—
121C22×#67—62no—
122C22×D12—31no—
123C22×D12—31no—
124C22×D12—61no—
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×Dic6—32no—
128C22×Dic6—32no—
129C22×Dic6C2×D311yescharacteristic
130C3×C22⋊Q8—38no—
131C3×#117—38no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×#217C2×D311yescharacteristic
142C2×#217C2×D312yes—
143C2×#217C2×D311yescharacteristic
144#947—38no—
145Q8×Dic3—38no—
146#930—38no—
147#930—38no—
148#930—68no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—62no—
158#926C2×D318yescomplemented
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—32no—
162C2×C4⋊Dic3—32no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3C2×D311yescharacteristic
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×C4⋊Dic3C2×D311yescharacteristic
167#924C2×D318yescomplemented
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4C2×D312yes—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175#898—316no—
176#898—316no—
177#897—316no—
178#896—316no—
179#893—38no—
180#888—38no—
181#885—316no—
182#885—316no—
183#883—316no—
184#883—316no—
185#875—38no—
186C4×D12—38no—
187#869—38no—
188C4×Dic6—38no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32C2412yes—
193C23×C32C2411yescharacteristic
194C22×C3⋊D3—24no—
195C22×C3⋊D3—24no—
196C22×C3⋊D3—24no—
197C22×C3⋊D3C2414yes—
198C2×C32×C4—22no—
199C2×C32×C4—28no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2412yes—
202C2×C32×C4C2412yes—
203#638—48no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3C2414yes—
206C4⋊(C3⋊D3)—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
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—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2412yes—
219C3×Dic6—28no—
220#627—48no—
221#624—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—91no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—92no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—91no—
233C2×#117—31no—
234C24×C3—21no—
235C24×C3C22×D311yescharacteristic
236C24×C3C22×D311yescharacteristic
237C23×D3—32no—
238C23×D3—32no—
239C23×D3—62no—
240C2×C3×Q8—34no—
241C2×C3×Q8—64no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—31no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—44no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D314yes—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D314yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—68no—
263C2×#67—124no—
264C2×#67—124no—
265C2×#67—128no—
266C22×Dic3—32no—
267C22×Dic3—32no—
268C22×Dic3—62no—
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D312yes—
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D312yes—
275C2×D12—34no—
276C2×D12—34no—
277C2×D12—64no—
278C2×D12—64no—
279C2×D12—64no—
280C2×D12—124no—
281C2×C4×D3—38no—
282C2×C4×D3—38no—
283C2×C4×D3—124no—
284C2×C4×D3—124no—
285C2×Dic6—24no—
286C2×Dic6—38no—
287C2×Dic6—38no—
288C2×Dic6—124no—
289C2×Dic6—124no—
290C2×Dic6C22×D314yes—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4—34no—
295C3×C22⋊C4—34no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—34no—
298C3×C42—34no—
299C3×C42—34no—
300#217C22×D314yes—
301#217C22×D318yes—
302#217C22×D314yes—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—68no—
312C4⋊Dic3—34no—
313C4⋊Dic3—34no—
314C4⋊Dic3—38no—
315C4⋊Dic3—38no—
316C4⋊Dic3—64no—
317C4⋊Dic3C22×D314yes—
318C4⋊Dic3C22×D314yes—
319C4⋊Dic3C22×D314yes—
320Dic3⋊C4—38no—
321Dic3⋊C4—38no—
322Dic3⋊C4C22×D318yes—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3C22×D314yes—
326C4×Dic3C22×D314yes—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—44no—
331C22×C32C2×#4112yes—
332C22×C32H(5,𝔽2)12yes—
333C22×C322−1+412yes—
334C22×C32C2511yescharacteristic
335C2×C3⋊D3—24no—
336C2×C3⋊D3—24no—
337C2×C3⋊D3—24no—
338C2×C3⋊D3—48no—
339C32×C4—22no—
340C32×C4C2×#4114yes—
341C3⋊Dic3—24no—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C22×Q8—31no—
349C22×Q8—92no—
350C22×D4—92no—
351C22×D4—91no—
352C23×C4—92no—
353C23×C4D3211yescharacteristic
354C4⋊Q8—98no—
355#126—916no—
356#124—98no—
357#124—916no—
358#123—916no—
359C22⋊Q8—38no—
360C22⋊Q8—916no—
361#121—98no—
362C4×Q8—98no—
363C4×D4—98no—
364#117—38no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—91no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—92no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3C23×D312yes—
394C23×C3C23×D312yes—
395C23×C3C23×D311yescharacteristic
396C23×C3C23×D311yescharacteristic
397C22×D3—34no—
398C22×D3—34no—
399C22×D3—64no—
400C22×D3—64no—
401C22×D3—64no—
402C22×D3—64no—
403C22×D3—64no—
404C22×D3—64no—
405C22×D3—64no—
406C22×D3—124no—
407C22×D3—124no—
408C22×D3—124no—
409C3×Q8—68no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—28no—
413C2×C3×C4—28no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—32no—
418C2×C3×C4—34no—
419C2×C3×C4—32no—
420C2×C3×C4—34no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—48no—
424C2×C3×C4—42no—
425C2×C3×C4—64no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—64no—
430C2×C3×C4—62no—
431C2×C3×C4#23514yes—
432C2×C3×C4#23714yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D312yes—
437#67—128no—
438#67—128no—
439#67—1216no—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—34no—
447C2×Dic3—34no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3—124no—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D314yes—
454C2×Dic3C23×D312yes—
455C2×Dic3C23×D312yes—
456C2×Dic3C23×D312yes—
457C2×Dic3C23×D314yes—
458D12—68no—
459D12—68no—
460D12—128no—
461C4×D3—128no—
462C4×D3—128no—
463Dic6—28no—
464Dic6—128no—
465Dic6—128no—
466C2×C32—42no—
467C2×C32#54214yescomplemented
468C2×C32C22×#4111yescharacteristic
469C2×C32C2×H(5,𝔽2)11yescharacteristic
470C2×C32C2×2−1+411yescharacteristic
471C3⋊D3—44no—
472C24—92no—
473C24C2×D3211yescharacteristic
474C2×Q8—34no—
475C2×Q8—64no—
476C2×Q8—98no—
477C2×Q8—364no—
478C2×D4—98no—
479C2×D4—94no—
480C2×D4—184no—
481C2×D4—364no—
482C22×C4—24no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—98no—
490C22×C4—92no—
491C22×C4—364no—
492C22×C4C2×D3214yes—
493C22×C4C2×D3211yescharacteristic
494C22×C4C2×D3211yescharacteristic
495C4⋊C4—34no—
496C4⋊C4—34no—
497C4⋊C4—34no—
498C4⋊C4—38no—
499C4⋊C4—98no—
500C4⋊C4—98no—
501C4⋊C4—94no—
502C22⋊C4—34no—
503C22⋊C4—34no—
504C22⋊C4—38no—
505C22⋊C4—98no—
506C22⋊C4—98no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C42—34no—
510C42—34no—
511C42—98no—
512C22×C3—24no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—48no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3C2×#23512yes—
529C22×C3C2×#23712yes—
530C22×C3#100712yes—
531C22×C3#100912yes—
532C22×C3#100912yes—
533C22×C3#101012yes—
534C22×C3C24×D311yescharacteristic
535C22×C3C24×D311yescharacteristic
536C2×D3—64no—
537C2×D3—64no—
538C2×D3—64no—
539C2×D3—64no—
540C2×D3—64no—
541C2×D3—64no—
542C2×D3—124no—
543C2×D3—124no—
544C2×D3—124no—
545C2×D3—128no—
546C2×D3—128no—
547C2×D3—248no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—24no—
551C3×C4—42no—
552C3×C4—64no—
553C3×C4—62no—
554C3×C4—62no—
555C3×C4—62no—
556C3×C4—64no—
557C3×C4—62no—
558C3×C4C2×#23514yes—
559C3×C4C2×#23714yes—
560Dic3—24no—
561Dic3—22no—
562Dic3—24no—
563Dic3—22no—
564Dic3—22no—
565Dic3—22no—
566Dic3—64no—
567Dic3—64no—
568Dic3—124no—
569C32C2×#54211yescharacteristic, complemented, Sylow
570C23—22no—
571C23—22no—
572C23—22no—
573C23—94no—
574C23—184no—
575C23—184no—
576C23—184no—
577C23C22×D3212yes—
578C23C22×D3211yescharacteristic
579Q8—68no—
580Q8—368no—
581D4—188no—
582D4—368no—
583C2×C4—22no—
584C2×C4—28no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—62no—
596C2×C4—64no—
597C2×C4—94no—
598C2×C4—184no—
599C2×C4—368no—
600C2×C4#380414yes—
601C2×C4C22×D3212yes—
602C2×C4C22×D3212yes—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—24no—
607C2×C3—44no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3#553414yescomplemented
611C2×C3#564314yescomplemented
612C2×C3C22×#23511yescharacteristic
613C2×C3C22×#23711yescharacteristic
614C2×C3C2×#100711yescharacteristic
615C2×C3C2×#100911yescharacteristic
616C2×C3C2×#100911yescharacteristic
617C2×C3C2×#101011yescharacteristic
618D3—124no—
619D3—124no—
620D3—244no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—44no—
625C22—184no—
626C22—184no—
627C22—184no—
628C22—368no—
629C22#6429712yes—
630C22#6430812yes—
631C22C2×#380412yes—
632C22C23×D3211yescharacteristic
633C4—22no—
634C4—62no—
635C4—62no—
636C4—62no—
637C4—64no—
638C4—62no—
639C4—64no—
640C4—184no—
641C4C2×#380414yes—
642C3—21no—
643C3C2×#553411yescharacteristic, complemented
644C3C2×#564311yescharacteristic, complemented
645C2—42no—
646C2—364no—
647C2#1059481414yesdirect product factor
648C2C2×#6429711yescharacteristic
649C2C2×#6430811yescharacteristic
650C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×C3×#924C2semidirect
4. C2×#63975C2semidirect
5. C2×#63953C2semidirect
6. C2×#63918C2semidirect
7. C2×#63895C2semidirect
8. C2×#63894C2semidirect
9. C2×#63864C2semidirect
10. C2×#63848C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. #10594814C2direct (N × H)
27. C3×#926C22semidirect
31. C3×#924C22semidirect
35. #63975C22semidirect
42. #63953C22semidirect
43. #63918C22semidirect
44. #63895C22semidirect
45. #63894C22semidirect
46. #63864C22semidirect
47. #63848C22semidirect
48. Dic3×Dic6C22semidirect
56. C2×#926D3semidirect
57. C2×#924D3semidirect
158. #926C2×D3semidirect
167. #924C2×D3semidirect
467. C2×C32#542semidirect
569. C32C2×#542semidirect
610. C2×C3#5534semidirect
611. C2×C3#5643semidirect
643. C3C2×#5534semidirect
644. C3C2×#5643semidirect
647. C2#10594814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9262
C2×C3×#9242
C2×#639752
C2×#639532
C2×#639182
C2×#638952
C2×#638942
C2×#638642
C2×#638482
C2×Dic3×Dic62
#105948142
C2×#56433
C2×#55343