Finite Group Databasebeta

← C2×#10595210 #11903835

Subgroups — C2×#10595210 #11903835

Order 1152.

2729 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63975C212yesmaximal, complemented
5C2×#63966C212yesmaximal, complemented
6C2×#63953C212yesmaximal, complemented
7C2×#63952C212yesmaximal, complemented
8#10595210C2116yesmaximal, direct product factor
9C2×C4×#627C211yesmaximal, characteristic, complemented
10C2×#63894C211yesmaximal, characteristic, complemented
11C2×#63864C211yesmaximal, characteristic, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5681—31nomaximal
14C2×#5559—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C22×#638C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#624C2212yes—
23#64149C2218yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C3×#936C2218yescomplemented
29C3×D4×Dic3C2218yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#63975C22116yescomplemented
34C2×#3724C2211yescharacteristic
35#63966C22116yescomplemented
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2212yes—
40C2×#3722C2212yes—
41C2×#3722C2212yes—
42C2×Dic32C2212yes—
43#63953C22116yescomplemented
44#63952C22116yescomplemented
45C4×#627C2218yescomplemented
46#63894C2218yescomplemented
47#63864C2218yescomplemented
48#63843C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×D4—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#940—31no—
54C2×#940—31no—
55C2×#940—61no—
56C2×#936D311yescharacteristic, complemented
57C2×D4×Dic3D311yescharacteristic, complemented
58C2×#929—32no—
59C2×C4×#67—32no—
60#5681—316no—
61#5559—316no—
62C2×#893—31no—
63C2×#887—31no—
64C2×#886—32no—
65C2×#885—32no—
66C2×#885—32no—
67C2×#883—32no—
68C2×#883—32no—
69C2×#67⋊C4—32no—
70C2×#875—31no—
71C2×C4×D12—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C23×C3⋊D3C2312yes—
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C2×#638—28no—
80C2×#638—44no—
81C2×#638C2318yes—
82C2×#638C2318yes—
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C2×C4⋊(C3⋊D3)—24no—
86C2×C4⋊(C3⋊D3)C2314yes—
87C22×C3×Dic3—44no—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2318yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6C2314yes—
97C2×#627—24no—
98C2×#627C2314yes—
99C2×#624—44no—
100C2×#624C2318yes—
101C4×C3⋊Dic3C2314yes—
102C3×#217C2318yes—
103C3×#217C2318yes—
104C3×#217C2318yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2314yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2314yes—
111Dic3⋊Dic3C2314yes—
112#3722C2318yes—
113#3722C2318yes—
114#3722C2318yes—
115Dic32C2318yes—
116C2×#559—91noSylow
117C22×C3×Q8—31no—
118C22×C3×D4—21no—
119C22×C3×D4C2×D311yescharacteristic
120C22×C3×D4C2×D311yescharacteristic
121C23×C3×C4—32no—
122C22×#67—32no—
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—62no—
127C22×#67—62no—
128C23×Dic3C2×D312yes—
129C22×D12—31no—
130C22×D12—31no—
131C22×D12—61no—
132C22×C4×D3—32no—
133C22×C4×D3—32no—
134C22×Dic6—31no—
135C22×Dic6—31no—
136C22×Dic6C2×D311yescharacteristic
137C3×#124—38no—
138C3×C4×D4—38no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×#217C2×D312yes—
146C2×#217C2×D312yes—
147C2×#217C2×D312yes—
148#947—38no—
149Q8×Dic3—38no—
150#940—38no—
151#940—38no—
152#940—68no—
153#936C2×D318yescomplemented
154D4×Dic3C2×D318yescomplemented
155#929—316no—
156C4×#67—316no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—32no—
162C2×(C2×D3)⋊C4—32no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—32no—
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—32no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3—32no—
176C2×C4×Dic3—61no—
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179#893—38no—
180#887—38no—
181#886—316no—
182#885—316no—
183#885—316no—
184#883—316no—
185#883—316no—
186#67⋊C4—316no—
187#875—38no—
188C4×D12—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—
203#638—216no—
204#638—48no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3#4114yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2412yes—
209C4⋊(C3⋊D3)—28no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—48no—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2412yes—
220C2×C3×Dic3C2412yes—
221C2×C3×Dic3C2412yes—
222C2×C3×Dic3C2412yes—
223C3×Dic6—28no—
224#627—28no—
225#624—48no—
226#559—916no—
227C2×#127—91no—
228C2×#124—31no—
229C2×#124—91no—
230C2×#124—92no—
231C2×#123—92no—
232C2×#123—92no—
233C2×C4×Q8—91no—
234C2×C4×Q8—91no—
235C2×C4×D4—31no—
236C2×C4×D4—91no—
237C2×C4×D4—92no—
238C24×C3—22no—
239C24×C3C22×D312yes—
240C24×C3C22×D312yes—
241C23×D3—32no—
242C23×D3—32no—
243C23×D3—62no—
244C2×C3×Q8—34no—
245C2×C3×Q8—64no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—24no—
249C2×C3×D4—44no—
250C2×C3×D4C22×D314yes—
251C2×C3×D4C22×D314yes—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—38no—
260C22×C3×C4—124no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—38no—
264C2×#67—38no—
265C2×#67—38no—
266C2×#67—38no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—68no—
270C2×#67—68no—
271C2×#67—128no—
272C2×#67—124no—
273C2×#67—124no—
274C2×#67—128no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—44no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3C22×D312yes—
283C22×Dic3C22×D312yes—
284C22×Dic3C22×D311yescharacteristic
285C22×Dic3C22×D311yescharacteristic
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D318yes—
289C2×D12—34no—
290C2×D12—34no—
291C2×D12—64no—
292C2×D12—64no—
293C2×D12—64no—
294C2×D12—124no—
295C2×C4×D3—38no—
296C2×C4×D3—38no—
297C2×C4×D3—124no—
298C2×C4×D3—124no—
299C2×Dic6—24no—
300C2×Dic6—34no—
301C2×Dic6—34no—
302C2×Dic6—64no—
303C2×Dic6—64no—
304C2×Dic6C22×D314yes—
305C3×C4⋊C4—34no—
306C3×C22⋊C4—38no—
307C3×C22⋊C4—38no—
308C3×C22⋊C4—38no—
309C3×C42—34no—
310C3×C42—34no—
311#217C22×D318yes—
312#217C22×D318yes—
313#217C22×D318yes—
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—38no—
320C4⋊Dic3—34no—
321C4⋊Dic3—34no—
322C4⋊Dic3—38no—
323C4⋊Dic3C22×D314yes—
324Dic3⋊C4—34no—
325Dic3⋊C4—34no—
326Dic3⋊C4—34no—
327Dic3⋊C4—34no—
328Dic3⋊C4—38no—
329C4×Dic3—34no—
330C4×Dic3—34no—
331C4×Dic3—38no—
332C4×Dic3—38no—
333C4×Dic3—64no—
334C4×Dic3C22×D314yes—
335C4×Dic3C22×D314yes—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32—24no—
339C22×C32—48no—
340C22×C32C2×#4112yes—
341C22×C32C2×#4112yes—
342C22×C32H(5,𝔽2)12yes—
343C22×C32C2511yescharacteristic
344C2×C3⋊D3—24no—
345C2×C3⋊D3—24no—
346C2×C3⋊D3—24no—
347C2×C3⋊D3—48no—
348C32×C4C2×#4114yes—
349C3⋊Dic3—22no—
350C3⋊Dic3C2×#4114yes—
351C3×Dic3—22no—
352C3×Dic3—22no—
353C3×Dic3—24no—
354C3×Dic3—22no—
355C3×Dic3—24no—
356C3×Dic3—22no—
357C22×Q8—31no—
358C22×Q8—91no—
359C22×D4—92no—
360C22×D4—92no—
361C22×D4—91no—
362C22×D4D3211yescharacteristic
363C23×C4—32no—
364C23×C4—92no—
365#127—98no—
366#124—38no—
367#124—98no—
368#124—916no—
369#123—916no—
370#123—916no—
371C4×Q8—98no—
372C4×Q8—98no—
373C4×D4—38no—
374C4×D4—98no—
375C4×D4—916no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—92no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—92no—
386C2×C22⋊C4—92no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—92no—
390C2×C42—91no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—21no—
399C23×C3—44no—
400C23×C3—44no—
401C23×C3—44no—
402C23×C3C23×D314yes—
403C23×C3C23×D314yes—
404C23×C3C23×D311yescharacteristic
405C23×C3C23×D311yescharacteristic
406C22×D3—34no—
407C22×D3—34no—
408C22×D3—64no—
409C22×D3—64no—
410C22×D3—64no—
411C22×D3—64no—
412C22×D3—64no—
413C22×D3—64no—
414C22×D3—64no—
415C22×D3—124no—
416C22×D3—124no—
417C22×D3—124no—
418C3×Q8—68no—
419C3×D4—28no—
420C3×D4—28no—
421C3×D4—48no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—34no—
425C2×C3×C4—34no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—64no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—64no—
435C2×C3×C4—62no—
436C2×C3×C4—128no—
437C2×C3×C4#23514yes—
438C2×C3×C4#23714yes—
439C2×C3×C4C23×D312yes—
440C2×C3×C4C23×D312yes—
441#67—616no—
442#67—616no—
443#67—1216no—
444#67—128no—
445#67—128no—
446#67—1216no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—34no—
454C2×Dic3—34no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—32no—
459C2×Dic3—48no—
460C2×Dic3—64no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—64no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3C23×D314yes—
467C2×Dic3C23×D314yes—
468C2×Dic3C23×D312yes—
469C2×Dic3C23×D312yes—
470C2×Dic3C23×D312yes—
471C2×Dic3C23×D312yes—
472D12—68no—
473D12—68no—
474D12—128no—
475C4×D3—128no—
476C4×D3—128no—
477Dic6—28no—
478Dic6—68no—
479Dic6—68no—
480C2×C32—44no—
481C2×C32#55914yescomplemented
482C2×C32C22×#4111yescharacteristic
483C2×C32C22×#4111yescharacteristic
484C2×C32C2×H(5,𝔽2)11yescharacteristic
485C3⋊D3—44no—
486C24—92no—
487C24C2×D3212yes—
488C2×Q8—34no—
489C2×Q8—64no—
490C2×Q8—94no—
491C2×Q8—184no—
492C2×D4—24no—
493C2×D4—98no—
494C2×D4—98no—
495C2×D4—94no—
496C2×D4—188no—
497C2×D4—184no—
498C2×D4—364no—
499C2×D4C2×D3214yes—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—38no—
507C22×C4—98no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—124no—
511C22×C4—364no—
512C22×C4C2×D3211yescharacteristic
513C4⋊C4—34no—
514C4⋊C4—94no—
515C4⋊C4—94no—
516C4⋊C4—94no—
517C4⋊C4—98no—
518C22⋊C4—38no—
519C22⋊C4—38no—
520C22⋊C4—38no—
521C22⋊C4—98no—
522C22⋊C4—98no—
523C22⋊C4—98no—
524C42—34no—
525C42—34no—
526C42—98no—
527C42—94no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—48no—
542C22×C3—48no—
543C22×C3—88no—
544C22×C3C2×#23512yes—
545C22×C3C2×#23712yes—
546C22×C3#100412yes—
547C22×C3D3×#4112yes—
548C22×C3D3×#4112yes—
549C22×C3#100912yes—
550C22×C3C24×D311yescharacteristic
551C22×C3C24×D311yescharacteristic
552C2×D3—64no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—64no—
557C2×D3—64no—
558C2×D3—124no—
559C2×D3—124no—
560C2×D3—124no—
561C2×D3—128no—
562C2×D3—128no—
563C2×D3—248no—
564C3×C4—24no—
565C3×C4—64no—
566C3×C4—62no—
567C3×C4—62no—
568C3×C4—62no—
569C3×C4—64no—
570C3×C4—62no—
571C3×C4C2×#23514yes—
572C3×C4C2×#23714yes—
573Dic3—24no—
574Dic3—24no—
575Dic3—22no—
576Dic3—22no—
577Dic3—22no—
578Dic3—22no—
579Dic3—34no—
580Dic3—34no—
581Dic3—64no—
582Dic3—64no—
583Dic3—62no—
584Dic3—62no—
585C32C2×#55911yescharacteristic, complemented, Sylow
586C23—24no—
587C23—24no—
588C23—24no—
589C23—94no—
590C23—184no—
591C23—184no—
592C23—184no—
593C23C22×D3214yes—
594C23C22×D3211yescharacteristic
595Q8—68no—
596Q8—188no—
597D4—28no—
598D4—1816no—
599D4—188no—
600D4—368no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—34no—
606C2×C4—34no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—64no—
611C2×C4—62no—
612C2×C4—64no—
613C2×C4—94no—
614C2×C4—92no—
615C2×C4—92no—
616C2×C4—128no—
617C2×C4—182no—
618C2×C4—368no—
619C2×C4#380414yes—
620C2×C4C22×D3212yes—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—24no—
625C2×C3—44no—
626C2×C3—44no—
627C2×C3—84no—
628C2×C3#555914yescomplemented
629C2×C3#568114yescomplemented
630C2×C3C22×#23511yescharacteristic
631C2×C3C22×#23711yescharacteristic
632C2×C3C2×#100411yescharacteristic
633C2×C3C2×D3×#4111yescharacteristic
634C2×C3C2×D3×#4111yescharacteristic
635C2×C3C2×#100911yescharacteristic
636D3—124no—
637D3—124no—
638D3—244no—
639C22—24no—
640C22—24no—
641C22—24no—
642C22—48no—
643C22—184no—
644C22—184no—
645C22—184no—
646C22—368no—
647C22#6431212yes—
648C22#6431412yes—
649C22C2×#380412yes—
650C22C23×D3211yescharacteristic
651C4—62no—
652C4—62no—
653C4—62no—
654C4—64no—
655C4—62no—
656C4—64no—
657C4—94no—
658C4—182no—
659C4C2×#380414yes—
660C3—21no—
661C3C2×#555911yescharacteristic, complemented
662C3C2×#568111yescharacteristic, complemented
663C2—44no—
664C2—364no—
665C2#1059521014yesdirect product factor
666C2C2×#6431211yescharacteristic
667C2C2×#6431411yescharacteristic
668C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64149C2
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
2. C2×C3×#936C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63975C2semidirect
5. C2×#63966C2semidirect
6. C2×#63953C2semidirect
7. C2×#63952C2semidirect
8. #10595210C2direct (N × H)
9. C2×C4×#627C2semidirect
10. C2×#63894C2semidirect
11. C2×#63864C2semidirect
12. C2×#63843C2semidirect
28. C3×#936C22semidirect
29. C3×D4×Dic3C22semidirect
33. #63975C22semidirect
35. #63966C22semidirect
43. #63953C22semidirect
44. #63952C22semidirect
45. C4×#627C22semidirect
46. #63894C22semidirect
47. #63864C22semidirect
48. #63843C22semidirect
56. C2×#936D3semidirect
57. C2×D4×Dic3D3semidirect
153. #936C2×D3semidirect
154. D4×Dic3C2×D3semidirect
481. C2×C32#559semidirect
585. C32C2×#559semidirect
628. C2×C3#5559semidirect
629. C2×C3#5681semidirect
661. C3C2×#5559semidirect
662. C3C2×#5681semidirect
665. C2#10595210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×#9362
C2×C3×D4×Dic32
C2×#639752
C2×#639662
C2×#639532
C2×#639522
#105952102
C2×C4×#6272
C2×#638942
C2×#638642
C2×#638432
C2×#56813
C2×#55593