Finite Group Databasebeta

← C2×#10594190 #11902728

Subgroups — C2×#10594190 #11902728

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic, complemented
4C2×C3×#884C212yesmaximal, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63979C212yesmaximal, complemented
7C2×#63914C211yesmaximal, characteristic, complemented
8C2×#63912C211yesmaximal, characteristic, complemented
9C2×#63886C212yesmaximal, complemented
10C2×#63879C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594190C2116yesmaximal, direct product factor
13C2×#5599—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×D12C2212yes—
20C22×C3×C4×D3C2212yes—
21C22×#627C2211yescharacteristic
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#625C2211yescharacteristic
25C22×#625C2212yes—
26C22×#625C2211yescharacteristic
27C2×#3805—28no—
28C2×#3805C2218yescomplemented
29C22×D3×Dic3C2212yes—
30C2×#3798—28no—
31C2×#3798C2218yescomplemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36#64090C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C3×#884C22116yescomplemented
40#63980C2218yescomplemented
41#63979C22116yescomplemented
42C2×#3724C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×Dic32C2212yes—
45#63914C2218yescomplemented
46#63912C2218yescomplemented
47#63886C22116yescomplemented
48#63879C22116yescomplemented
49#63838C2218yescomplemented
50C22×#237—32no—
51C22×#235—32no—
52C2×C3×#121—32no—
53C2×#940—32no—
54C2×#940—32no—
55C2×#940—32no—
56C2×#939—32no—
57C2×#939—32no—
58C2×C4×#67—32no—
59#5599—332no—
60C2×#895—32no—
61C2×#887—32no—
62C2×#884—32no—
63C2×#884D312yescomplemented
64C2×#67⋊C4—32no—
65C2×#67⋊C4—32no—
66C2×#67⋊C4—61no—
67C24×C32C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C23×C3×D3C2312yes—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C2×#638—24no—
74C2×#638C2314yes—
75C22×C3⋊Dic3—24no—
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2314yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3C2314yes—
82C2×C3×#67—28no—
83C2×C3×#67—44no—
84C2×C3×#67C2318yes—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C2×C3×D12—44no—
89C2×C3×D12C2318yes—
90C2×C3×C4×D3—28no—
91C2×C3×C4×D3C2318yes—
92C2×#627D418yescomplemented
93C2×#627C2314yes—
94C2×#626—28no—
95C2×#626—44no—
96C2×#626C2318yes—
97C2×#626C2318yes—
98C2×#625—24no—
99C2×#625—24no—
100C2×#625—28no—
101C2×#625C2314yes—
102C2×#625C2314yes—
103C2×#625C2318yes—
104#3805—232no—
105C2×D3×Dic3—28no—
106C2×D3×Dic3C2318yes—
107#3798—232no—
108C32×C22⋊C4C2314yes—
109#3752C2314yes—
110#3750C2314yes—
111C4×C3⋊Dic3C2314yes—
112C3×(C2×D3)⋊C4C2318yes—
113C3×Dic3⋊C4C2318yes—
114#3724C2314yes—
115(C2×D3)⋊Dic3C2318yes—
116Dic32C2318yes—
117C2×#550—91noSylow
118C22×C3×D4—32no—
119C22×C3×D4—32no—
120C22×C3×D4—32no—
121C23×C3×C4—32no—
122C22×#67—32no—
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—32no—
127C22×#67—32no—
128C22×#67—32no—
129C22×#67—61no—
130C22×#67C2×D312yes—
131C22×#67C2×D312yes—
132C23×Dic3—32no—
133C23×Dic3—32no—
134C23×Dic3—61no—
135C2×#237—316no—
136C2×#237—616no—
137C2×#235—316no—
138C2×#235—616no—
139C22×D12—32no—
140C22×D12—32no—
141C22×D12C2×D312yes—
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3—61no—
145C22×C4×D3C2×D312yes—
146C22×Dic6—32no—
147C3×#121—316no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4C2×D312yes—
152C2×#217—32no—
153#940—316no—
154#940—316no—
155#940—316no—
156#939—316no—
157#939—316no—
158C4×#67—316no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4C2×D312yes—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—61no—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—61no—
171#895—316no—
172#887—316no—
173#884—316no—
174#884C2×D3116yescomplemented
175#67⋊C4—316no—
176#67⋊C4—316no—
177#67⋊C4—68no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32C2412yes—
182C23×C32C2411yescharacteristic
183C22×C3⋊D3—22no—
184C22×C3⋊D3—22no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3C2412yes—
187C22×C3×D3—24no—
188C22×C3×D3—24no—
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3C2414yes—
194C22×C3×D3C2414yes—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199#638—28no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—28no—
202C2×C3⋊Dic3C2×D414yes—
203C2×C3⋊Dic3#4114yescomplemented
204C2×C3⋊Dic3C2412yes—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2412yes—
207C4×C3⋊D3—28no—
208C3×#67—216no—
209C3×#67—48no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3C2×D418yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C3×D12—48no—
215C3×C4×D3—216no—
216#627C2×D4116yescomplemented
217#626—216no—
218#626—48no—
219#625—28no—
220#625—28no—
221#625—216no—
222D3×Dic3—216no—
223C22×#41—91no—
224C22×#41—91no—
225#550—916no—
226C2×#127—92no—
227C2×#127—91no—
228C2×#121—32no—
229C2×#121—91no—
230C2×#121—92no—
231C2×#121—91no—
232C2×C4×Q8—91no—
233C2×C4×D4—92no—
234C2×C4×D4—91no—
235C24×C3—21no—
236C24×C3—32no—
237C24×C3—32no—
238C24×C3C22×D312yes—
239C23×D3—32no—
240C23×D3—61no—
241C23×D3C22×D312yes—
242C23×D3C22×D312yes—
243C2×C3×D4—38no—
244C2×C3×D4—38no—
245C2×C3×D4—38no—
246C2×C3×D4—68no—
247C2×C3×D4—124no—
248C2×C3×D4—124no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—32no—
252C22×C3×C4—32no—
253C22×C3×C4—38no—
254C22×C3×C4—68no—
255C22×C3×C4C22×D312yes—
256C22×C3×C4C22×D312yes—
257C2×#67—28no—
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—38no—
263C2×#67—38no—
264C2×#67—38no—
265C2×#67—44no—
266C2×#67—64no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—68no—
270C2×#67—68no—
271C2×#67—68no—
272C2×#67—68no—
273C2×#67—68no—
274C2×#67—124no—
275C2×#67C22×D318yes—
276C2×#67C22×D318yes—
277C22×Dic3—32no—
278C22×Dic3—32no—
279C22×Dic3—38no—
280C22×Dic3—32no—
281C22×Dic3—38no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—64no—
285C22×Dic3—61no—
286C22×Dic3—68no—
287C22×Dic3—68no—
288C22×Dic3—124no—
289C22×Dic3C22×D312yes—
290C22×Dic3C22×D312yes—
291#237—664no—
292#235—664no—
293C2×D12—38no—
294C2×D12—38no—
295C2×D12—44no—
296C2×D12—68no—
297C2×D12—124no—
298C2×D12C22×D318yes—
299C2×C4×D3—28no—
300C2×C4×D3—38no—
301C2×C4×D3—38no—
302C2×C4×D3—64no—
303C2×C4×D3—68no—
304C2×C4×D3—68no—
305C2×C4×D3—124no—
306C2×C4×D3C22×D318yes—
307C2×Dic6—316no—
308C2×Dic6—38no—
309C3×C4⋊C4—38no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—38no—
312C3×C22⋊C4C22×D318yes—
313#217—38no—
314(C2×D3)⋊C4—38no—
315(C2×D3)⋊C4—38no—
316(C2×D3)⋊C4—64no—
317(C2×D3)⋊C4C22×D318yes—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4—64no—
321Dic3⋊C4C22×D318yes—
322C4×Dic3—38no—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3—64no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—44no—
330C22×C32C22×D412yes—
331C22×C32C2×#4112yes—
332C22×C32H(5,𝔽2)12yes—
333C22×C32C2511yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—44no—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—48no—
345C2×C3×D3—48no—
346C32×C4—22no—
347C32×C4—22no—
348C3⋊Dic3—22no—
349C3⋊Dic3C22×D414yes—
350C3⋊Dic3C2×#4114yescomplemented
351C3×Dic3—24no—
352C3×Dic3C22×D418yes—
353C2×#41—98no—
354C2×#41—98no—
355C2×#41—188no—
356C2×#41—188no—
357C22×Q8—91no—
358C22×D4—32no—
359C22×D4—32no—
360C22×D4—32no—
361C22×D4—92no—
362C22×D4—92no—
363C22×D4—92no—
364C22×D4—91no—
365C22×D4—91no—
366C22×D4—91no—
367C23×C4—32no—
368C23×C4—92no—
369C23×C4—91no—
370C23×C4—91no—
371#127—916no—
372#127—98no—
373#121—316no—
374#121—98no—
375#121—916no—
376#121—98no—
377C4×Q8—98no—
378C4×D4—916no—
379C4×D4—98no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4D3211yescharacteristic
387C2×C42—92no—
388C2×C42—91no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—34no—
396C23×C3—34no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—64no—
400C23×C3—64no—
401C23×C3—64no—
402C23×C3—64no—
403C23×C3—64no—
404C23×C3—64no—
405C23×C3C23×D314yes—
406C23×C3C23×D312yes—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—34no—
414C22×D3—62no—
415C22×D3—64no—
416C22×D3—64no—
417C22×D3—64no—
418C22×D3—64no—
419C22×D3—122no—
420C22×D3—122no—
421C22×D3C23×D314yes—
422C22×D3C23×D314yes—
423C3×D4—616no—
424C3×D4—128no—
425C3×D4—128no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—38no—
431C2×C3×C4—34no—
432C2×C3×C4—34no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—616no—
436C2×C3×C4—64no—
437C2×C3×C4C23×D314yes—
438C2×C3×C4C23×D314yes—
439#67—216no—
440#67—48no—
441#67—616no—
442#67—616no—
443#67—616no—
444#67—616no—
445#67—616no—
446#67—616no—
447#67—616no—
448#67—128no—
449C2×Dic3—24no—
450C2×Dic3—38no—
451C2×Dic3—38no—
452C2×Dic3—34no—
453C2×Dic3—34no—
454C2×Dic3—34no—
455C2×Dic3—64no—
456C2×Dic3—64no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—616no—
461C2×Dic3—64no—
462C2×Dic3—616no—
463C2×Dic3—128no—
464C2×Dic3—122no—
465C2×Dic3D3×D418yes—
466C2×Dic3C23×D314yes—
467C2×Dic3C23×D314yes—
468D12—48no—
469D12—616no—
470D12—128no—
471C4×D3—216no—
472C4×D3—616no—
473C4×D3—616no—
474C4×D3—128no—
475Dic6—332no—
476C2×C32—42no—
477C2×C32#55014yescomplemented
478C2×C32C23×D411yescharacteristic
479C2×C32C22×#4111yescharacteristic
480C2×C32C2×H(5,𝔽2)11yescharacteristic
481C3⋊D3—42no—
482C3×D3—44no—
483C3×D3—44no—
484C24—32no—
485C24—32no—
486C24—91no—
487C24C2×D3211yescharacteristic
488#41—1832no—
489#41—1832no—
490C2×Q8—94no—
491C2×Q8—98no—
492C2×D4—38no—
493C2×D4—38no—
494C2×D4—38no—
495C2×D4—68no—
496C2×D4—98no—
497C2×D4—98no—
498C2×D4—98no—
499C2×D4—94no—
500C2×D4—94no—
501C2×D4—94no—
502C2×D4—124no—
503C2×D4—124no—
504C2×D4—188no—
505C2×D4—184no—
506C2×D4—184no—
507C2×D4—184no—
508C2×D4—188no—
509C2×D4—364no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—38no—
513C22×C4—68no—
514C22×C4—98no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—94no—
518C22×C4—91no—
519C22×C4—94no—
520C22×C4—184no—
521C22×C4—188no—
522C22×C4—184no—
523C22×C4C2×D3211yescharacteristic
524C22×C4C2×D3211yescharacteristic
525C4⋊C4—38no—
526C4⋊C4—94no—
527C4⋊C4—94no—
528C22⋊C4—38no—
529C22⋊C4—98no—
530C22⋊C4—94no—
531C22⋊C4C2×D3214yes—
532C42—98no—
533C42—94no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—21no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—48no—
545C22×C3—48no—
546C22×C3—64no—
547C22×C3—64no—
548C22×C3—64no—
549C22×C3—64no—
550C22×C3—64no—
551C22×C3—64no—
552C22×C3—128no—
553C22×C3—128no—
554C22×C3C2×D3×D414yes—
555C22×C3#100414yes—
556C22×C3D3×#4114yes—
557C22×C3C24×D312yes—
558C2×D3—24no—
559C2×D3—24no—
560C2×D3—24no—
561C2×D3—24no—
562C2×D3—24no—
563C2×D3—24no—
564C2×D3—48no—
565C2×D3—48no—
566C2×D3—64no—
567C2×D3—64no—
568C2×D3—64no—
569C2×D3—64no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—128no—
573C2×D3—128no—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—38no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—64no—
580Dic3—24no—
581Dic3—38no—
582Dic3—38no—
583Dic3—64no—
584Dic3—64no—
585Dic3—64no—
586Dic3—122no—
587Dic3C2×D3×D418yes—
588C32C2×#55011yescharacteristic, complemented, Sylow
589C23—22no—
590C23—22no—
591C23—22no—
592C23—34no—
593C23—34no—
594C23—64no—
595C23—64no—
596C23—64no—
597C23—64no—
598C23—64no—
599C23—64no—
600C23—92no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23C22×D3212yes—
605C23C22×D3211yescharacteristic
606Q8—916no—
607D4—616no—
608D4—128no—
609D4—128no—
610D4—1816no—
611D4—188no—
612D4—188no—
613D4—188no—
614D4—1816no—
615D4—368no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—38no—
619C2×C4—34no—
620C2×C4—34no—
621C2×C4—616no—
622C2×C4—64no—
623C2×C4—94no—
624C2×C4—94no—
625C2×C4—92no—
626C2×C4—92no—
627C2×C4—92no—
628C2×C4—188no—
629C2×C4—1816no—
630C2×C4—188no—
631C2×C4—182no—
632C2×C4C22×D3212yes—
633C2×C4C22×D3212yes—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—24no—
638C2×C3—44no—
639C2×C3—44no—
640C2×C3—124no—
641C2×C3—124no—
642C2×C3#559918yescomplemented
643C2×C3C22×D3×D412yes—
644C2×C3C2×#100412yes—
645C2×C3C2×D3×#4112yes—
646D3—44no—
647D3—44no—
648D3—124no—
649D3—124no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—44no—
654C22—64no—
655C22—64no—
656C22—64no—
657C22—64no—
658C22—64no—
659C22—64no—
660C22—128no—
661C22—128no—
662C22—182no—
663C22—182no—
664C22—182no—
665C22—364no—
666C22#6430612yes—
667C22D32×D412yes—
668C22#6431312yes—
669C22C23×D3211yescharacteristic
670C4—22no—
671C4—22no—
672C4—38no—
673C4—64no—
674C4—94no—
675C4—94no—
676C4—182no—
677C3—21no—
678C3C2×#559912yescomplemented
679C2—42no—
680C2—124no—
681C2—124no—
682C2—362no—
683C2#1059419014yesdirect product factor
684C2C2×#6430611yescharacteristic
685C2C2×D32×D411yescharacteristic
686C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C22×#3798C2semidirect
3. C2×#64090C2semidirect
4. C2×C3×#884C2semidirect
5. C2×#63980C2semidirect
6. C2×#63979C2semidirect
7. C2×#63914C2semidirect
8. C2×#63912C2semidirect
9. C2×#63886C2semidirect
10. C2×#63879C2semidirect
11. C2×#63838C2semidirect
12. #10594190C2direct (N × H)
28. C2×#3805C22semidirect
31. C2×#3798C22semidirect
36. #64090C22semidirect
39. C3×#884C22semidirect
40. #63980C22semidirect
41. #63979C22semidirect
45. #63914C22semidirect
46. #63912C22semidirect
47. #63886C22semidirect
48. #63879C22semidirect
49. #63838C22semidirect
63. C2×#884D3semidirect
92. C2×#627D4semidirect
174. #884C2×D3semidirect
203. C2×C3⋊Dic3#41semidirect
216. #627C2×D4semidirect
350. C3⋊Dic3C2×#41semidirect
477. C2×C32#550semidirect
588. C32C2×#550semidirect
642. C2×C3#5599semidirect
678. C3C2×#5599semidirect
683. C2#10594190direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×#37982
C2×#640902
C2×C3×#8842
C2×#639802
C2×#639792
C2×#639142
C2×#639122
C2×#638862
C2×#638792
C2×#638382
#105941902
C2×#55993