Finite Group Databasebeta

← C2×#10594566 #11903837

Subgroups — C2×#10594566 #11903837

Order 1152.

2693 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×#63911C211yesmaximal, characteristic
6C2×C4×#626C212yesmaximal, complemented
7C2×#63864C211yesmaximal, characteristic, complemented
8C2×#63863C211yesmaximal, characteristic, complemented
9C2×#63853C212yesmaximal, complemented
10C2×#63852C212yesmaximal, complemented
11C2×#63850C212yesmaximal, complemented
12#10594566C2116yesmaximal, direct product factor
13C2×#5585—31nomaximal
14C2×#5559—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2212yes—
22C22×#626C2212yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×#3752C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64102C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#893C2218yescomplemented
33C3×#887C2218yescomplemented
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2212yes—
38C2×#3722C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C4×#627C2218yescomplemented
42#63911C2218yes—
43C4×#626C22116yescomplemented
44#63864C2218yescomplemented
45#63863C2218yescomplemented
46#63853C22116yescomplemented
47#63852C22116yescomplemented
48#63850C22116yescomplemented
49C2×C3×C4×Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#947—31no—
52C2×#947—31no—
53C2×#940—31no—
54C2×#936—31no—
55C2×#929—32no—
56C2×C4×#67—32no—
57#5585—316no—
58#5559—316no—
59C2×#894—32no—
60C2×#894—32no—
61C2×#893—31no—
62C2×#893—31no—
63C2×#893—61no—
64C2×#893D311yescharacteristic, complemented
65C2×#887D311yescharacteristic, complemented
66C2×#885—32no—
67C2×#883—32no—
68C2×#875—31no—
69C2×#875—32no—
70C2×#874—31no—
71C2×C4×D12—32no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2312yes—
75C23×C3×D3C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4⋊(C3⋊D3)—24no—
81C2×C4⋊(C3⋊D3)C2314yes—
82C2×C4×C3⋊D3—44no—
83C2×C4×C3⋊D3C2318yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×C3×C4×D3—44no—
92C2×C3×C4×D3C2318yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#627—24no—
96C2×#627C2314yes—
97C2×#626—28no—
98C2×#626—44no—
99C2×#626C2318yes—
100C2×#626C2318yes—
101C32×C4⋊C4C2314yes—
102#3752C2318yes—
103C4×C3⋊Dic3C2314yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2318yes—
107C3×C4×Dic3C2314yes—
108C3×C4×Dic3C2314yes—
109#3724C2314yes—
110Dic3⋊Dic3C2314yes—
111Dic3⋊Dic3C2314yes—
112#3722C2318yes—
113#3722C2318yes—
114(C2×D3)⋊Dic3C2318yes—
115(C2×D3)⋊Dic3C2318yes—
116C2×#559—91noSylow
117C22×C3×Q8—31no—
118C22×C3×D4—31no—
119C23×C3×C4—32no—
120C22×#67—32no—
121C22×#67—32no—
122C22×D12—32no—
123C22×D12—31no—
124C22×D12—31no—
125C22×D12—32no—
126C22×D12—61no—
127C22×D12C2×D311yescharacteristic
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—62no—
131C22×C4×D3C2×D312yes—
132C22×Dic6—31no—
133C22×Dic6—31no—
134C22×Dic6C2×D311yescharacteristic
135C3×C4×Q8—38no—
136C3×C4×D4—38no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4—32no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—32no—
145C2×#217—32no—
146C2×#217—32no—
147#947—38no—
148#947—38no—
149#940—38no—
150#936—38no—
151#929—316no—
152C4×#67—316no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—62no—
162C2×(C2×D3)⋊C4C2×D312yes—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D312yes—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D312yes—
176#894—316no—
177#894—316no—
178#893—38no—
179#893—38no—
180#893—68no—
181#893C2×D318yescomplemented
182#887C2×D318yescomplemented
183#885—316no—
184#883—316no—
185#875—38no—
186#875—316no—
187#874—38no—
188C4×D12—316no—
189C4×Dic6—38no—
190C4×Dic6—38no—
191C23×C32C2411yescharacteristic
192C22×C3⋊D3—24no—
193C22×C3⋊D3—24no—
194C22×C3⋊D3—24no—
195C22×C3⋊D3C2414yes—
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3—24no—
199C22×C3×D3C2414yes—
200C2×C32×C4—24no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2414yes—
203C2×C32×C4C2412yes—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C4⋊(C3⋊D3)—28no—
209C4×C3⋊D3—48no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3#4114yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2412yes—
220C3×D12—28no—
221C3×C4×D3—48no—
222C3×Dic6—28no—
223#627—28no—
224#626—216no—
225#626—48no—
226#559—916no—
227C2×#127—91no—
228C2×#124—92no—
229C2×#124—91no—
230C2×#124—91no—
231C2×#123—92no—
232C2×#123—92no—
233C2×C4×Q8—31no—
234C2×C4×Q8—91no—
235C2×C4×D4—31no—
236C2×C4×D4—92no—
237C2×C4×D4—91no—
238C24×C3—32no—
239C23×D3—32no—
240C23×D3—32no—
241C23×D3—62no—
242C23×D3C22×D312yes—
243C2×C3×Q8—34no—
244C2×C3×Q8—64no—
245C2×C3×D4—34no—
246C2×C3×D4—64no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—38no—
255C22×C3×C4—124no—
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D312yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—68no—
263C2×#67—124no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—61no—
269C22×Dic3—61no—
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D311yescharacteristic
275C2×D12—24no—
276C2×D12—38no—
277C2×D12—34no—
278C2×D12—34no—
279C2×D12—38no—
280C2×D12—64no—
281C2×D12—68no—
282C2×D12—68no—
283C2×D12—64no—
284C2×D12—64no—
285C2×D12—124no—
286C2×D12C22×D314yes—
287C2×C4×D3—38no—
288C2×C4×D3—38no—
289C2×C4×D3—44no—
290C2×C4×D3—68no—
291C2×C4×D3—124no—
292C2×C4×D3—124no—
293C2×C4×D3—128no—
294C2×C4×D3C22×D318yes—
295C2×Dic6—24no—
296C2×Dic6—34no—
297C2×Dic6—34no—
298C2×Dic6—64no—
299C2×Dic6—64no—
300C2×Dic6C22×D314yes—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—38no—
303C3×C4⋊C4C22×D314yes—
304C3×C4⋊C4C22×D314yes—
305C3×C22⋊C4—38no—
306C3×C42—34no—
307C3×C42—34no—
308C3×C42—38no—
309#217—38no—
310#217—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—38no—
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4—38no—
315(C2×D3)⋊C4—38no—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—38no—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4—68no—
320(C2×D3)⋊C4C22×D318yes—
321C4⋊Dic3—34no—
322C4⋊Dic3—34no—
323Dic3⋊C4—34no—
324Dic3⋊C4—34no—
325Dic3⋊C4—34no—
326Dic3⋊C4—34no—
327Dic3⋊C4C22×D318yes—
328C4×Dic3—34no—
329C4×Dic3—34no—
330C4×Dic3—64no—
331C4×Dic3C22×D314yes—
332C4×Dic3C22×D314yes—
333C4×Dic3C22×D318yes—
334C22×C32C2×#4112yes—
335C22×C32C2×#4112yes—
336C22×C32H(5,𝔽2)12yes—
337C22×C32C2511yescharacteristic
338C2×C3⋊D3—24no—
339C2×C3⋊D3—24no—
340C2×C3⋊D3—24no—
341C2×C3⋊D3—48no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—48no—
346C32×C4—24no—
347C32×C4C2×#4114yes—
348C3⋊Dic3—22no—
349C3⋊Dic3—22no—
350C3×Dic3—22no—
351C3×Dic3—24no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3C2×#4114yes—
355C22×Q8—31no—
356C22×Q8—91no—
357C22×D4—31no—
358C22×D4—92no—
359C22×D4—92no—
360C22×D4—91no—
361C23×C4—32no—
362C23×C4—92no—
363#127—98no—
364#124—916no—
365#124—98no—
366#124—98no—
367#123—916no—
368#123—916no—
369C4×Q8—38no—
370C4×Q8—98no—
371C4×D4—38no—
372C4×D4—916no—
373C4×D4—98no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4D3211yescharacteristic
379C2×C22⋊C4—32no—
380C2×C22⋊C4—92no—
381C2×C22⋊C4—92no—
382C2×C22⋊C4—92no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C42—31no—
386C2×C42—32no—
387C2×C42—31no—
388C2×C42—91no—
389C23×C3—21no—
390C23×C3—34no—
391C23×C3—64no—
392C23×C3—64no—
393C23×C3—64no—
394C23×C3C23×D311yescharacteristic
395C23×C3C23×D311yescharacteristic
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—34no—
400C22×D3—34no—
401C22×D3—64no—
402C22×D3—68no—
403C22×D3—64no—
404C22×D3—64no—
405C22×D3—64no—
406C22×D3—64no—
407C22×D3—64no—
408C22×D3—64no—
409C22×D3—124no—
410C22×D3—124no—
411C22×D3C23×D314yes—
412C3×Q8—68no—
413C3×D4—68no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—34no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—32no—
424C2×C3×C4—34no—
425C2×C3×C4—44no—
426C2×C3×C4—64no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—128no—
431C2×C3×C4#23514yes—
432C2×C3×C4#23514yes—
433C2×C3×C4C23×D314yes—
434C2×C3×C4C23×D314yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D312yes—
437#67—616no—
438#67—128no—
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—64no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—122no—
455C2×Dic3#23914yes—
456C2×Dic3C23×D312yes—
457C2×Dic3C23×D312yes—
458C2×Dic3C23×D312yes—
459C2×Dic3C23×D314yes—
460C2×Dic3C23×D312yes—
461D12—28no—
462D12—616no—
463D12—616no—
464D12—68no—
465D12—68no—
466D12—128no—
467C4×D3—48no—
468C4×D3—128no—
469C4×D3—128no—
470C4×D3—1216no—
471Dic6—28no—
472Dic6—68no—
473Dic6—68no—
474C2×C32#55914yescomplemented
475C2×C32C22×#4111yescharacteristic
476C2×C32C22×#4111yescharacteristic
477C2×C32C2×H(5,𝔽2)11yescharacteristic
478C3⋊D3—44no—
479C3×D3—44no—
480C24—32no—
481C24—92no—
482C2×Q8—34no—
483C2×Q8—64no—
484C2×Q8—94no—
485C2×Q8—184no—
486C2×D4—34no—
487C2×D4—64no—
488C2×D4—98no—
489C2×D4—98no—
490C2×D4—94no—
491C2×D4—188no—
492C2×D4—184no—
493C2×D4—364no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—32no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—38no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—98no—
503C22×C4—124no—
504C22×C4—364no—
505C22×C4C2×D3212yes—
506C22×C4C2×D3211yescharacteristic
507C4⋊C4—38no—
508C4⋊C4—94no—
509C4⋊C4—94no—
510C4⋊C4—94no—
511C4⋊C4C2×D3214yes—
512C22⋊C4—38no—
513C22⋊C4—98no—
514C22⋊C4—98no—
515C22⋊C4—98no—
516C22⋊C4—98no—
517C22⋊C4—98no—
518C42—34no—
519C42—38no—
520C42—34no—
521C42—94no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—128no—
530C22×C3C2×#23512yes—
531C22×C3C2×#23512yes—
532C22×C3#100412yes—
533C22×C3C2×#23912yes—
534C22×C3D3×#4112yes—
535C22×C3#100912yes—
536C22×C3C24×D311yescharacteristic
537C22×C3C24×D311yescharacteristic
538C2×D3—24no—
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—48no—
542C2×D3—68no—
543C2×D3—64no—
544C2×D3—64no—
545C2×D3—64no—
546C2×D3—64no—
547C2×D3—64no—
548C2×D3—64no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—1216no—
552C2×D3—128no—
553C2×D3—128no—
554C3×C4—24no—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—34no—
558C3×C4—44no—
559C3×C4—64no—
560C3×C4—62no—
561C3×C4—62no—
562C3×C4—62no—
563C3×C4C2×#23514yes—
564C3×C4C2×#23514yes—
565Dic3—24no—
566Dic3—22no—
567Dic3—22no—
568Dic3—22no—
569Dic3—64no—
570Dic3—62no—
571Dic3—62no—
572Dic3—62no—
573Dic3—62no—
574Dic3—122no—
575Dic3C2×#23914yes—
576C32C2×#55911yescharacteristic, complemented, Sylow
577C23—34no—
578C23—64no—
579C23—64no—
580C23—64no—
581C23—94no—
582C23—184no—
583C23—184no—
584C23—184no—
585C23C22×D3211yescharacteristic
586Q8—68no—
587Q8—188no—
588D4—68no—
589D4—1816no—
590D4—188no—
591D4—368no—
592C2×C4—24no—
593C2×C4—34no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—34no—
597C2×C4—32no—
598C2×C4—32no—
599C2×C4—64no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—92no—
604C2×C4—92no—
605C2×C4—128no—
606C2×C4—182no—
607C2×C4—182no—
608C2×C4—368no—
609C2×C4#379814yes—
610C2×C4C22×D3214yes—
611C2×C4C22×D3212yes—
612C2×C3—24no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—124no—
617C2×C3#555914yescomplemented
618C2×C3#558514yescomplemented
619C2×C3C22×#23511yescharacteristic
620C2×C3C22×#23511yescharacteristic
621C2×C3C2×#100411yescharacteristic
622C2×C3C22×#23911yescharacteristic
623C2×C3C2×D3×#4111yescharacteristic
624C2×C3C2×#100911yescharacteristic
625D3—44no—
626D3—128no—
627D3—124no—
628D3—124no—
629C22—64no—
630C22—64no—
631C22—64no—
632C22—128no—
633C22—184no—
634C22—184no—
635C22—184no—
636C22—368no—
637C22C2×#379812yes—
638C22#6431412yes—
639C22D3×#23912yes—
640C22C23×D3211yescharacteristic
641C4—24no—
642C4—34no—
643C4—64no—
644C4—62no—
645C4—62no—
646C4—62no—
647C4—182no—
648C4—182no—
649C4C2×#379814yes—
650C3—21no—
651C3C2×#555911yescharacteristic, complemented
652C3C2×#558511yescharacteristic, complemented
653C2—124no—
654C2—364no—
655C2#1059456614yesdirect product factor
656C2C22×#379811yescharacteristic
657C2C2×#6431411yescharacteristic
658C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63911C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#559
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×#64102C2semidirect
2. C2×C3×#893C2semidirect
3. C2×C3×#887C2semidirect
4. C2×C4×#627C2semidirect
6. C2×C4×#626C2semidirect
7. C2×#63864C2semidirect
8. C2×#63863C2semidirect
9. C2×#63853C2semidirect
10. C2×#63852C2semidirect
11. C2×#63850C2semidirect
12. #10594566C2direct (N × H)
26. #64102C22semidirect
32. C3×#893C22semidirect
33. C3×#887C22semidirect
41. C4×#627C22semidirect
43. C4×#626C22semidirect
44. #63864C22semidirect
45. #63863C22semidirect
46. #63853C22semidirect
47. #63852C22semidirect
48. #63850C22semidirect
64. C2×#893D3semidirect
65. C2×#887D3semidirect
181. #893C2×D3semidirect
182. #887C2×D3semidirect
474. C2×C32#559semidirect
576. C32C2×#559semidirect
617. C2×C3#5559semidirect
618. C2×C3#5585semidirect
651. C3C2×#5559semidirect
652. C3C2×#5585semidirect
655. C2#10594566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8932
C2×C3×#8872
C2×C4×#6272
C2×#639112
C2×C4×#6262
C2×#638642
C2×#638632
C2×#638532
C2×#638522
C2×#638502
#105945662
C2×#55853
C2×#55593