Finite Group Databasebeta

← C2×#10594189 #11902623

Subgroups — C2×#10594189 #11902623

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C212yesmaximal, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63978C212yesmaximal, complemented
7C2×C4×#627C211yesmaximal, characteristic, complemented
8C2×#63915C211yesmaximal, characteristic, complemented
9C2×#63865C211yesmaximal, characteristic, complemented
10C2×#63852C212yesmaximal, complemented
11C2×#63851C212yesmaximal, complemented
12#10594189C2116yesmaximal, direct product factor
13C2×#5552—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yes—
19C22×C3×C4×D3C2212yes—
20C22×#627—28no—
21C22×#627C2212yes—
22C22×#627C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#627C2218yescomplemented
25C22×#626C2212yes—
26C22×#625C2211yescharacteristic
27C2×#3798—28no—
28C2×#3798C2218yescomplemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64090C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2212yes—
37C3×#67⋊C4C22116yescomplemented
38#63980C2218yescomplemented
39#63978C22116yescomplemented
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2212yes—
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C4×#627C2218yescomplemented
46#63915C2218yescomplemented
47#63865C2218yescomplemented
48#63852C22116yescomplemented
49#63851C22116yescomplemented
50C22×#235—32no—
51C23×Dic6—32no—
52C2×C3×C4×D4—32no—
53C2×#939—32no—
54C2×#939—32no—
55C2×#930—32no—
56C2×#924—32no—
57#5552—332no—
58C2×#896—32no—
59C2×#896—32no—
60C2×#885—32no—
61C2×#885—32no—
62C2×#67⋊C4—32no—
63C2×#67⋊C4—61no—
64C2×#67⋊C4D312yescomplemented
65C2×#875—32no—
66C2×C4×Dic6—32no—
67C24×C32C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—24no—
73C2×#638C2314yes—
74C22×C3⋊Dic3—24no—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2314yes—
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3C2314yes—
81C2×C3×#67—28no—
82C2×C3×#67C2318yes—
83C22×C3×Dic3—28no—
84C22×C3×Dic3C2318yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C2×C3×C4×D3—28no—
89C2×C3×C4×D3C2318yes—
90C2×#627—24no—
91C2×#627—28no—
92C2×#627—232no—
93C2×#627D418yescomplemented
94C2×#627C2318yes—
95C2×#627C2314yes—
96C2×#627C2314yes—
97C2×#626—28no—
98C2×#626C2318yes—
99C2×#625—24no—
100C2×#625C2314yes—
101#3798—232no—
102C32×C22⋊C4C2314yes—
103#3752C2314yes—
104#3750C2314yes—
105C4×C3⋊Dic3C2314yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×C4×Dic3C2318yes—
109#3724C2314yes—
110Dic3⋊Dic3C2318yes—
111#3722C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#548—91noSylow
115C22×C3×D4—32no—
116C23×C3×C4—32no—
117C23×C3×C4—32no—
118C22×#67—32no—
119C22×#67—32no—
120C22×#67—32no—
121C22×#67—61no—
122C22×#67C2×D312yes—
123C23×Dic3—32no—
124C23×Dic3—61no—
125C23×Dic3C2×D312yes—
126C2×#235—316no—
127C2×#235—616no—
128C22×D12—32no—
129C22×C4×D3—32no—
130C22×C4×D3—61no—
131C22×C4×D3C2×D312yes—
132C22×Dic6—32no—
133C22×Dic6—32no—
134C22×Dic6—32no—
135C22×Dic6—32no—
136C22×Dic6—316no—
137C22×Dic6—616no—
138C3×C4×D4—316no—
139C2×C3×C4⋊C4—32no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4C2×D312yes—
143C2×C3×C42—32no—
144C2×#217—32no—
145C2×#217—32no—
146#939—316no—
147#939—316no—
148#930—316no—
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—61no—
155C2×(C2×D3)⋊C4C2×D312yes—
156C2×C4⋊Dic3—32no—
157#924—316no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4C2×D312yes—
163C2×C4×Dic3—32no—
164C2×C4×Dic3—61no—
165C2×C4×Dic3C2×D312yes—
166#896—316no—
167#896—316no—
168#885—316no—
169#885—316no—
170#67⋊C4—316no—
171#67⋊C4—68no—
172#67⋊C4C2×D3116yescomplemented
173#875—316no—
174C4×Dic6—316no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32#4114yescomplemented
178C23×C32C2412yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3C2412yes—
184C22×C3×D3—24no—
185C22×C3×D3—24no—
186C22×C3×D3—24no—
187C22×C3×D3C2414yes—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4C2412yes—
191C2×C32×C4C2412yes—
192#638—28no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—28no—
196C2×C3⋊Dic3C2×D414yes—
197C2×C3⋊Dic3C2412yes—
198C2×C3⋊Dic3C2412yes—
199C2×C3⋊Dic3C2412yes—
200C4×C3⋊D3—28no—
201C3×#67—216no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—216no—
205C2×C3×Dic3C2×D418yes—
206C2×C3×Dic3C2414yes—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2414yes—
209C3×C4×D3—216no—
210#627—28no—
211#627—216no—
212#627C2×D4116yescomplemented
213#626—216no—
214#625—28no—
215C22×#41—91no—
216C23×Q8—91no—
217#548—916no—
218C2×#124—92no—
219C2×#124—91no—
220C2×C22⋊Q8—91no—
221C2×C22⋊Q8—92no—
222C2×#121—92no—
223C2×#121—91no—
224C2×C4×Q8—91no—
225C2×C4×D4—32no—
226C2×C4×D4—91no—
227C24×C3—21no—
228C24×C3—32no—
229C24×C3C22×D312yes—
230C23×D3—32no—
231C23×D3—61no—
232C23×D3C22×D312yes—
233C2×C3×D4—38no—
234C2×C3×D4—68no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—32no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—38no—
241C22×C3×C4—38no—
242C22×C3×C4—68no—
243C22×C3×C4—68no—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D312yes—
246C2×#67—28no—
247C2×#67—38no—
248C2×#67—38no—
249C2×#67—38no—
250C2×#67—64no—
251C2×#67—68no—
252C2×#67—68no—
253C2×#67—68no—
254C2×#67—68no—
255C2×#67C22×D318yes—
256C22×Dic3—28no—
257C22×Dic3—32no—
258C22×Dic3—38no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—61no—
262C22×Dic3—61no—
263C22×Dic3—64no—
264C22×Dic3—61no—
265C22×Dic3—68no—
266C22×Dic3—124no—
267C22×Dic3C22×D318yes—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D312yes—
271#235—664no—
272C2×D12—38no—
273C2×D12—68no—
274C2×C4×D3—28no—
275C2×C4×D3—38no—
276C2×C4×D3—64no—
277C2×C4×D3—68no—
278C2×C4×D3—124no—
279C2×C4×D3C22×D318yes—
280C2×Dic6—316no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—38no—
284C2×Dic6—38no—
285C2×Dic6—664no—
286C2×Dic6—68no—
287C2×Dic6—68no—
288C2×Dic6—68no—
289C3×C4⋊C4—38no—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—38no—
292C3×C22⋊C4C22×D318yes—
293C3×C42—38no—
294#217—38no—
295#217—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4C22×D318yes—
303C4⋊Dic3—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—64no—
308Dic3⋊C4C22×D318yes—
309C4×Dic3—38no—
310C4×Dic3—64no—
311C4×Dic3C22×D318yes—
312C22×C32—28no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32C22×D412yes—
316C22×C32C2×#4112yes—
317C22×C32C2×#4114yescomplemented
318C22×C322−1+412yes—
319C22×C32C2511yescharacteristic
320C2×C3⋊D3—22no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—44no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—24no—
327C2×C3×D3—48no—
328C32×C4—22no—
329C32×C4—22no—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3⋊Dic3C22×D414yes—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3C22×D418yes—
336C2×#41—98no—
337C2×#41—188no—
338C22×Q8—91no—
339C22×Q8—92no—
340C22×Q8—91no—
341C22×Q8—98no—
342C22×Q8—188no—
343C22×D4—32no—
344C22×D4—92no—
345C22×D4—91no—
346C22×D4—91no—
347C23×C4—32no—
348C23×C4—32no—
349C23×C4—91no—
350C23×C4—91no—
351#124—916no—
352#124—98no—
353C22⋊Q8—98no—
354C22⋊Q8—916no—
355#121—916no—
356#121—98no—
357C4×Q8—98no—
358C4×D4—316no—
359C4×D4—98no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4D3211yescharacteristic
370C2×C42—32no—
371C2×C42—91no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—22no—
375C23×C3—21no—
376C23×C3—24no—
377C23×C3—34no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—64no—
381C23×C3—64no—
382C23×C3—64no—
383C23×C3#23518yescomplemented
384C23×C3C23×D314yes—
385C23×C3C23×D312yes—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—34no—
390C22×D3—62no—
391C22×D3—64no—
392C22×D3—64no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3C23×D314yes—
398C3×D4—616no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—38no—
404C2×C3×C4—34no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—616no—
410C2×C3×C4—616no—
411C2×C3×C4—64no—
412C2×C3×C4—64no—
413C2×C3×C4C23×D314yes—
414C2×C3×C4C23×D314yes—
415#67—216no—
416#67—616no—
417#67—616no—
418#67—616no—
419#67—616no—
420C2×Dic3—24no—
421C2×Dic3—24no—
422C2×Dic3—216no—
423C2×Dic3—38no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—616no—
432C2×Dic3—64no—
433C2×Dic3—64no—
434C2×Dic3—64no—
435C2×Dic3—128no—
436C2×Dic3—122no—
437C2×Dic3D3×D418yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D314yes—
440C2×Dic3C23×D314yes—
441D12—616no—
442C4×D3—216no—
443C4×D3—616no—
444C4×D3—128no—
445Dic6—332no—
446Dic6—616no—
447Dic6—616no—
448Dic6—616no—
449C2×C32—24no—
450C2×C32#54814yescomplemented
451C2×C32C23×D411yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C2×C32C2×2−1+411yescharacteristic
454C3⋊D3—42no—
455C3×D3—44no—
456C24—32no—
457C24—91no—
458C24C2×D3211yescharacteristic
459#41—1832no—
460C2×Q8—94no—
461C2×Q8—98no—
462C2×Q8—98no—
463C2×Q8—94no—
464C2×Q8—188no—
465C2×Q8—184no—
466C2×Q8—1832no—
467C2×D4—38no—
468C2×D4—68no—
469C2×D4—98no—
470C2×D4—94no—
471C2×D4—94no—
472C2×D4—188no—
473C2×D4—184no—
474C2×D4—184no—
475C22×C4—32no—
476C22×C4—38no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—38no—
480C22×C4—68no—
481C22×C4—68no—
482C22×C4—91no—
483C22×C4—94no—
484C22×C4—91no—
485C22×C4—91no—
486C22×C4—94no—
487C22×C4—184no—
488C22×C4—184no—
489C22×C4C2×D3211yescharacteristic
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—38no—
492C4⋊C4—94no—
493C4⋊C4—98no—
494C4⋊C4—94no—
495C22⋊C4—38no—
496C22⋊C4—98no—
497C22⋊C4—98no—
498C22⋊C4—98no—
499C22⋊C4—94no—
500C22⋊C4C2×D3214yes—
501C42—38no—
502C42—94no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—216no—
506C22×C3—22no—
507C22×C3—24no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—48no—
514C22×C3—64no—
515C22×C3—64no—
516C22×C3—64no—
517C22×C3—128no—
518C22×C3C2×#23514yes—
519C22×C3C2×#23518yescomplemented
520C22×C3C2×D3×D414yes—
521C22×C3#101014yes—
522C22×C3C24×D312yes—
523C2×D3—24no—
524C2×D3—24no—
525C2×D3—24no—
526C2×D3—48no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—128no—
534C2×D3—128no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—38no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—64no—
541C3×C4—64no—
542Dic3—24no—
543Dic3—24no—
544Dic3—38no—
545Dic3—64no—
546Dic3—64no—
547Dic3—64no—
548Dic3—64no—
549Dic3—122no—
550Dic3C2×D3×D418yes—
551C32C2×#54811yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—34no—
555C23—64no—
556C23—64no—
557C23—64no—
558C23—92no—
559C23—182no—
560C23—182no—
561C23—182no—
562C23#379814yescomplemented
563C23C22×D3212yes—
564C23C22×D3211yescharacteristic
565Q8—916no—
566Q8—1816no—
567Q8—188no—
568D4—616no—
569D4—1816no—
570D4—188no—
571D4—188no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—38no—
575C2×C4—34no—
576C2×C4—34no—
577C2×C4—34no—
578C2×C4—616no—
579C2×C4—616no—
580C2×C4—64no—
581C2×C4—64no—
582C2×C4—94no—
583C2×C4—92no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—188no—
587C2×C4—188no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4C22×D3212yes—
591C2×C4C22×D3212yes—
592C2×C3—28no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—24no—
597C2×C3—44no—
598C2×C3—124no—
599C2×C3#555218yescomplemented
600C2×C3C22×#23512yes—
601C2×C3C22×D3×D412yes—
602C2×C3C2×#101012yes—
603D3—44no—
604D3—124no—
605D3—124no—
606C22—22no—
607C22—22no—
608C22—28no—
609C22—64no—
610C22—64no—
611C22—64no—
612C22—128no—
613C22—182no—
614C22—182no—
615C22—182no—
616C22—364no—
617C22C2×#379812yes—
618C22C2×#379814yescomplemented
619C22#6430912yes—
620C22D32×D412yes—
621C22C23×D3211yescharacteristic
622C4—22no—
623C4—22no—
624C4—38no—
625C4—64no—
626C4—64no—
627C4—94no—
628C4—182no—
629C4—182no—
630C3—21no—
631C3C2×#555212yescomplemented
632C2—24no—
633C2—124no—
634C2—362no—
635C2#1059418914yesdirect product factor
636C2C22×#379811yescharacteristic
637C2C2×#6430911yescharacteristic
638C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
2. C22×#3798C2semidirect
3. C2×#64090C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C2×#63980C2semidirect
6. C2×#63978C2semidirect
7. C2×C4×#627C2semidirect
8. C2×#63915C2semidirect
9. C2×#63865C2semidirect
10. C2×#63852C2semidirect
11. C2×#63851C2semidirect
12. #10594189C2direct (N × H)
24. C22×#627C22semidirect
28. C2×#3798C22semidirect
33. #64090C22semidirect
37. C3×#67⋊C4C22semidirect
38. #63980C22semidirect
39. #63978C22semidirect
45. C4×#627C22semidirect
46. #63915C22semidirect
47. #63865C22semidirect
48. #63852C22semidirect
49. #63851C22semidirect
64. C2×#67⋊C4D3semidirect
93. C2×#627D4semidirect
172. #67⋊C4C2×D3semidirect
177. C23×C32#41semidirect
212. #627C2×D4semidirect
317. C22×C32C2×#41semidirect
383. C23×C3#235semidirect
450. C2×C32#548semidirect
519. C22×C3C2×#235semidirect
551. C32C2×#548semidirect
562. C23#3798semidirect
599. C2×C3#5552semidirect
618. C22C2×#3798semidirect
631. C3C2×#5552semidirect
635. C2#10594189direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37982
C2×#640902
C2×C3×#67⋊C42
C2×#639802
C2×#639782
C2×C4×#6272
C2×#639152
C2×#638652
C2×#638522
C2×#638512
#105941892
C2×#55523