Finite Group Databasebeta

← C2×#10595199 #11903836

Subgroups — C2×#10595199 #11903836

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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C212yesmaximal, complemented
5C2×#63969C212yesmaximal, complemented
6C2×#63962C212yesmaximal, complemented
7C2×#63959C212yesmaximal, complemented
8#10595199C2116yesmaximal, direct product factor
9C2×C4×#627C211yesmaximal, characteristic, complemented
10C2×Dic3×D12C211yesmaximal, characteristic, complemented
11C2×#63863C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5713—31nomaximal
14C2×#5681—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×D3×Dic3C2212yes—
23C2×#3757C2212yes—
24D4×C3⋊Dic3C2218yescomplemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×#940C2218yes—
30C3×#936C2218yescomplemented
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#67⋊Dic3C22116yescomplemented
34#63969C22116yescomplemented
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39#63962C22116yescomplemented
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43#63959C22116yescomplemented
44C2×Dic32C2212yes—
45C4×#627C2218yescomplemented
46Dic3×D12C2218yescomplemented
47#63863C2218yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×#127—31no—
50C2×C3×#124—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#940D311yescharacteristic
54C2×#936—31no—
55C2×#936—32no—
56C2×#936D311yescharacteristic, complemented
57C2×#935—32no—
58C2×#935—32no—
59C2×D4×Dic3—31no—
60C2×D4×Dic3—31no—
61C2×D4×Dic3—32no—
62C2×D4×Dic3—31no—
63C2×D4×Dic3—61no—
64#5713—316no—
65#5681—316no—
66C2×#886—32no—
67C2×#885—32no—
68C2×#883—32no—
69C2×#67⋊C4—32no—
70C2×C4×D12—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C23×C3×D3C2312yes—
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3—44no—
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2318yes—
84C2×C3×#67—28no—
85C2×C3×#67—44no—
86C2×C3×#67C2318yes—
87C2×C3×#67C2318yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×D12—24no—
94C2×C3×D12C2314yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6C2314yes—
97C2×#627—24no—
98C2×#627C2314yes—
99C2×D3×Dic3—44no—
100C2×D3×Dic3C2318yes—
101#3757C2318yes—
102C4⋊(C3⋊Dic3)C2314yes—
103C4×C3⋊Dic3C2314yes—
104C3×#217C2318yes—
105C3×#217C2318yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2314yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2314yes—
111Dic3⋊Dic3C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114(C2×D3)⋊Dic3C2318yes—
115Dic32C2318yes—
116C2×#559—91noSylow
117C22×C3×Q8—31no—
118C22×C3×D4—21no—
119C22×C3×D4—32no—
120C22×C3×D4—32no—
121C22×C3×D4—31no—
122C22×C3×D4C2×D311yescharacteristic
123C22×C3×D4C2×D311yescharacteristic
124C22×#67C2×D312yes—
125C22×#67C2×D312yes—
126C23×Dic3—32no—
127C23×Dic3—32no—
128C23×Dic3—32no—
129C23×Dic3—62no—
130C22×D12C2×D311yescharacteristic
131C22×C4×D3—32no—
132C22×Dic6—31no—
133C22×Dic6—31no—
134C22×Dic6C2×D311yescharacteristic
135C3×#127—38no—
136C3×#124—38no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—32no—
146C2×#217—62no—
147C2×#217C2×D312yes—
148C2×#217C2×D312yes—
149#947—38no—
150Q8×Dic3—38no—
151#940C2×D318yes—
152#936—38no—
153#936—316no—
154#936C2×D318yescomplemented
155#935—316no—
156#935—316no—
157D4×Dic3—38no—
158D4×Dic3—38no—
159D4×Dic3—316no—
160D4×Dic3—38no—
161D4×Dic3—68no—
162C2×(C2×D3)⋊C4—32no—
163C2×(C2×D3)⋊C4—32no—
164C2×(C2×D3)⋊C4—32no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—32no—
170C2×C4⋊Dic3—61no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—32no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—32no—
179C2×C4×Dic3—32no—
180C2×C4×Dic3—61no—
181C2×C4×Dic3C2×D311yescharacteristic
182C2×C4×Dic3C2×D311yescharacteristic
183#886—316no—
184#885—316no—
185#883—316no—
186#67⋊C4—316no—
187C4×D12—38no—
188C4×Dic6—38no—
189C4×Dic6—38no—
190C4×Dic6—38no—
191C23×C32—24no—
192C23×C32—24no—
193C23×C32—24no—
194C23×C32C2414yes—
195C23×C32C2411yescharacteristic
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3—24no—
199C22×C3×D3C2414yes—
200C32×D4—28no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3—48no—
207C2×C3⋊Dic3C2414yes—
208C2×C3⋊Dic3C2412yes—
209C2×C3⋊Dic3C2412yes—
210C3×#67—216no—
211C3×#67—48no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3#4114yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2412yes—
220C2×C3×Dic3C2412yes—
221C2×C3×Dic3C2412yes—
222C3×D12—28no—
223C3×Dic6—28no—
224#627—28no—
225D3×Dic3—48no—
226#559—916no—
227C2×#127—31no—
228C2×#124—31no—
229C2×#124—92no—
230C2×#124—91no—
231C2×#123—92no—
232C2×#123—92no—
233C2×C4×Q8—91no—
234C2×C4×Q8—91no—
235C2×C4×D4—91no—
236C2×C4×D4—92no—
237C2×C4×D4—91no—
238C24×C3—22no—
239C24×C3—32no—
240C24×C3C22×D312yes—
241C24×C3C22×D312yes—
242C23×D3C22×D312yes—
243C2×C3×Q8—34no—
244C2×C3×Q8—64no—
245C2×C3×D4—28no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—24no—
249C2×C3×D4—38no—
250C2×C3×D4—38no—
251C2×C3×D4—34no—
252C2×C3×D4—68no—
253C2×C3×D4—64no—
254C2×C3×D4—124no—
255C2×C3×D4C22×D314yes—
256C2×C3×D4C22×D314yes—
257C22×C3×C4—21no—
258C22×C3×C4—31no—
259C22×C3×C4—32no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C2×#67—28no—
266C2×#67—44no—
267C2×#67C22×D318yes—
268C2×#67C22×D318yes—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—32no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—32no—
275C22×Dic3—38no—
276C22×Dic3—38no—
277C22×Dic3—38no—
278C22×Dic3—61no—
279C22×Dic3—61no—
280C22×Dic3—62no—
281C22×Dic3—68no—
282C22×Dic3—124no—
283C22×Dic3—124no—
284C22×Dic3—124no—
285C22×Dic3—128no—
286C22×Dic3C22×D312yes—
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291C2×D12—24no—
292C2×D12C22×D314yes—
293C2×C4×D3—38no—
294C2×C4×D3—124no—
295C2×Dic6—24no—
296C2×Dic6—34no—
297C2×Dic6—34no—
298C2×Dic6—64no—
299C2×Dic6—64no—
300C2×Dic6C22×D314yes—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—38no—
303C3×C42—34no—
304C3×C42—34no—
305#217—38no—
306#217—38no—
307#217—38no—
308#217—38no—
309#217—38no—
310#217—68no—
311#217C22×D318yes—
312#217C22×D318yes—
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4—38no—
315(C2×D3)⋊C4—38no—
316C4⋊Dic3—34no—
317C4⋊Dic3—34no—
318C4⋊Dic3—34no—
319C4⋊Dic3—34no—
320C4⋊Dic3—38no—
321C4⋊Dic3—64no—
322Dic3⋊C4—34no—
323Dic3⋊C4—34no—
324Dic3⋊C4—38no—
325Dic3⋊C4—34no—
326Dic3⋊C4—34no—
327C4×Dic3—34no—
328C4×Dic3—34no—
329C4×Dic3—38no—
330C4×Dic3—38no—
331C4×Dic3—64no—
332C4×Dic3C22×D314yes—
333C4×Dic3C22×D314yes—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32—24no—
337C22×C32—48no—
338C22×C32C2×#4112yes—
339C22×C32C2×#4112yes—
340C22×C32H(5,𝔽2)12yes—
341C22×C32C2511yescharacteristic
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—48no—
346C32×C4C2×#4114yes—
347C3⋊Dic3—22no—
348C3⋊Dic3—22no—
349C3⋊Dic3—24no—
350C3×Dic3—22no—
351C3×Dic3—24no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3C2×#4114yes—
355C22×Q8—31no—
356C22×Q8—91no—
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—31no—
360C22×D4D3211yescharacteristic
361C23×C4—92no—
362C23×C4—92no—
363#127—38no—
364#124—38no—
365#124—916no—
366#124—98no—
367#123—916no—
368#123—916no—
369C4×Q8—98no—
370C4×Q8—98no—
371C4×D4—98no—
372C4×D4—916no—
373C4×D4—98no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—92no—
378C2×C4⋊C4—91no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4—92no—
382C2×C22⋊C4—92no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C42—31no—
386C2×C42—31no—
387C2×C42—92no—
388C2×C42—91no—
389C23×C3—28no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—21no—
398C23×C3—34no—
399C23×C3—44no—
400C23×C3—44no—
401C23×C3—64no—
402C23×C3—64no—
403C23×C3—64no—
404C23×C3C23×D314yes—
405C23×C3C23×D314yes—
406C23×C3C23×D311yescharacteristic
407C23×C3C23×D311yescharacteristic
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3C23×D314yes—
412C3×Q8—68no—
413C3×D4—216no—
414C3×D4—28no—
415C3×D4—28no—
416C3×D4—616no—
417C3×D4—68no—
418C3×D4—128no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—34no—
422C2×C3×C4—32no—
423C2×C3×C4—34no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—62no—
428C2×C3×C4—64no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4#23714yes—
432C2×C3×C4#23714yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435#67—216no—
436#67—48no—
437C2×Dic3—24no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—34no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—34no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3—62no—
452C2×Dic3—64no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—64no—
457C2×Dic3—122no—
458C2×Dic3—124no—
459C2×Dic3—128no—
460C2×Dic3—128no—
461C2×Dic3—128no—
462C2×Dic3—1216no—
463C2×Dic3#23714yes—
464C2×Dic3C23×D314yes—
465C2×Dic3C23×D312yes—
466C2×Dic3C23×D312yes—
467C2×Dic3C23×D312yes—
468C2×Dic3C23×D312yes—
469D12—28no—
470C4×D3—128no—
471Dic6—28no—
472Dic6—68no—
473Dic6—68no—
474C2×C32—44no—
475C2×C32#55914yescomplemented
476C2×C32C22×#4111yescharacteristic
477C2×C32C22×#4111yescharacteristic
478C2×C32C2×H(5,𝔽2)11yescharacteristic
479C3×D3—44no—
480C24—32no—
481C24C2×D3212yes—
482C2×Q8—34no—
483C2×Q8—64no—
484C2×Q8—94no—
485C2×Q8—184no—
486C2×D4—24no—
487C2×D4—38no—
488C2×D4—38no—
489C2×D4—34no—
490C2×D4—68no—
491C2×D4—64no—
492C2×D4—124no—
493C2×D4C2×D3214yes—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—32no—
499C22×C4—98no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—92no—
503C22×C4—98no—
504C22×C4—364no—
505C22×C4—364no—
506C22×C4C2×D3211yescharacteristic
507C4⋊C4—94no—
508C4⋊C4—94no—
509C4⋊C4—94no—
510C4⋊C4—98no—
511C4⋊C4—94no—
512C22⋊C4—38no—
513C22⋊C4—38no—
514C22⋊C4—98no—
515C22⋊C4—98no—
516C22⋊C4—98no—
517C22⋊C4—98no—
518C42—34no—
519C42—34no—
520C42—98no—
521C42—94no—
522C22×C3—28no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—21no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—416no—
536C22×C3—48no—
537C22×C3—48no—
538C22×C3—64no—
539C22×C3—64no—
540C22×C3—64no—
541C22×C3—128no—
542C22×C3C2×#23712yes—
543C22×C3C2×#23712yes—
544C22×C3C2×#23712yes—
545C22×C3#100412yes—
546C22×C3D3×#4112yes—
547C22×C3#100912yes—
548C22×C3C24×D311yescharacteristic
549C22×C3C24×D311yescharacteristic
550C2×D3—24no—
551C2×D3—24no—
552C2×D3—24no—
553C2×D3—48no—
554C3×C4—24no—
555C3×C4—34no—
556C3×C4—62no—
557C3×C4—64no—
558C3×C4—62no—
559C3×C4—62no—
560C3×C4C2×#23714yes—
561C3×C4C2×#23714yes—
562Dic3—24no—
563Dic3—22no—
564Dic3—22no—
565Dic3—22no—
566Dic3—64no—
567Dic3—62no—
568Dic3—64no—
569Dic3—62no—
570Dic3—62no—
571Dic3—62no—
572Dic3—64no—
573Dic3—124no—
574Dic3—122no—
575Dic3C2×#23714yes—
576C32C2×#55911yescharacteristic, complemented, Sylow
577C23—24no—
578C23—24no—
579C23—24no—
580C23—34no—
581C23—64no—
582C23—64no—
583C23—64no—
584C23C22×D3214yes—
585C23C22×D3211yescharacteristic
586Q8—68no—
587Q8—188no—
588D4—28no—
589D4—616no—
590D4—68no—
591D4—128no—
592C2×C4—34no—
593C2×C4—32no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—34no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—64no—
602C2×C4—92no—
603C2×C4—92no—
604C2×C4—94no—
605C2×C4—182no—
606C2×C4—182no—
607C2×C4—184no—
608C2×C4—368no—
609C2×C4—368no—
610C2×C4#380514yes—
611C2×C4C22×D3212yes—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—24no—
616C2×C3—48no—
617C2×C3—44no—
618C2×C3—44no—
619C2×C3—124no—
620C2×C3#568114yescomplemented
621C2×C3#571314yescomplemented
622C2×C3C22×#23711yescharacteristic
623C2×C3C22×#23711yescharacteristic
624C2×C3C22×#23711yescharacteristic
625C2×C3C2×#100411yescharacteristic
626C2×C3C2×D3×#4111yescharacteristic
627C2×C3C2×#100911yescharacteristic
628D3—44no—
629C22—24no—
630C22—24no—
631C22—24no—
632C22—48no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—128no—
637C22D3×#23712yes—
638C22#6431412yes—
639C22C2×#380512yes—
640C22C23×D3211yescharacteristic
641C4—34no—
642C4—62no—
643C4—62no—
644C4—62no—
645C4—64no—
646C4—182no—
647C4—182no—
648C4—184no—
649C4C2×#380514yes—
650C3—21no—
651C3C2×#568111yescharacteristic, complemented
652C3C2×#571311yescharacteristic, complemented
653C2—44no—
654C2—124no—
655C2#1059519914yesdirect product factor
656C2C2×D3×#23711yescharacteristic
657C2C2×#6431411yescharacteristic
658C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#559
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×C3×#936C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C2×#63969C2semidirect
6. C2×#63962C2semidirect
7. C2×#63959C2semidirect
8. #10595199C2direct (N × H)
9. C2×C4×#627C2semidirect
10. C2×Dic3×D12C2semidirect
11. C2×#63863C2semidirect
12. C2×Dic3×Dic6C2semidirect
24. D4×C3⋊Dic3C22semidirect
30. C3×#936C22semidirect
33. #67⋊Dic3C22semidirect
34. #63969C22semidirect
39. #63962C22semidirect
43. #63959C22semidirect
45. C4×#627C22semidirect
46. Dic3×D12C22semidirect
47. #63863C22semidirect
48. Dic3×Dic6C22semidirect
56. C2×#936D3semidirect
154. #936C2×D3semidirect
475. C2×C32#559semidirect
576. C32C2×#559semidirect
620. C2×C3#5681semidirect
621. C2×C3#5713semidirect
651. C3C2×#5681semidirect
652. C3C2×#5713semidirect
655. C2#10595199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9402
C2×C3×#9362
C2×#67⋊Dic32
C2×#639692
C2×#639622
C2×#639592
#105951992
C2×C4×#6272
C2×Dic3×D122
C2×#638632
C2×Dic3×Dic62
C2×#57133
C2×#56813