Finite Group Databasebeta

← #11906311

Subgroups — #11906311

Order 1152.

3180 conjugacy classes of subgroups.

The subgroup lattice has 651 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic, complemented
2Q8×#638C212yesmaximal, complemented
3C2×#64153C212yesmaximal, complemented
4#10596200C212yesmaximal, complemented
5C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
6#10596193C212yesmaximal, complemented
7#10596192C211yesmaximal, characteristic, complemented
8#10596107C214yesmaximal, complemented
9#10596103C212yesmaximal, complemented
10#10596094C214yesmaximal, complemented
11#10596093C212yesmaximal, complemented
12#10596049C211yesmaximal, characteristic, complemented
13#10596038C211yesmaximal, characteristic, complemented
14#10596017C212yesmaximal
15#10596010C212yesmaximal, complemented
16D4×#634C211yesmaximal, characteristic, complemented
17C4×#3830C211yesmaximal, characteristic
18#86747—34nomaximal
19C22×C32×Q8C2212yes—
20C2×Q8×C3⋊D3C2212yes—
21C2×#3830C2211yescharacteristic
22C22×#634C2212yes—
23C32×C4⋊Q8C2211yescharacteristic
24C32×C4⋊Q8C2212yes—
25C32×C22⋊Q8C2212yes—
26C32×C22⋊Q8C2214yes—
27C32×C4×Q8C2211yescharacteristic
28C32×C4×D4C2211yescharacteristic
29C32×C4×D4C2212yes—
30#64155C2214yes—
31#64155C2211yescharacteristic
32Q8×C3⋊Dic3C2212yes—
33#64153C2212yes—
34#64153C2214yes—
35#64153C2214yes—
36#64153C2212yes—
37#64153C2214yes—
38#64153C2211yescharacteristic
39#64153C2212yes—
40D4×C3⋊Dic3C2211yescharacteristic
41D4×C3⋊Dic3C2212yes—
42C4×#638C2212yes—
43C4×#638C2214yes—
44#64133C2212yes—
45#64133C2214yes—
46C2×#3750C2214yes—
47C2×#3750C2214yes—
48C2×C4×C3⋊Dic3C2212yes—
49#64106C2211yescharacteristic
50#64105C2214yes—
51#64105C2212yes—
52#64101C2211yescharacteristic
53C4⋊C4×C3⋊D3C2212yes—
54C4⋊C4×C3⋊D3C2212yes—
55#64099C2212yes—
56#64098C2214yes—
57#64098C2214yes—
58#64098C2214yes—
59#64098C2212yes—
60#64097C2214yes—
61#64097C2212yes—
62#64097C2212yes—
63#64097C2212yes—
64#64097C2211yescharacteristic
65#64096C2212yes—
66#64096C2214yes—
67#64096C2212yes—
68#64096C2211yescharacteristic
69#64090C2214yes—
70#64090C2212yes—
71#64087C2214yes—
72#64087C2214yes—
73#64087C2214yes—
74#64086C2212yes—
75#64086C2214yes—
76#64081C2212yes—
77C42×C3⋊D3C2211yescharacteristic
78#64079C2212yes—
79#64078C2211yescharacteristic
80C4×#634C2211yescharacteristic
81C4×#634C2211yescharacteristic
82C4×#634C2212yes—
83C4×#634C2212yes—
84C3×D4×Q8D314yescomplemented
85Q8×#67—38no—
86C2×#944—38no—
87#5729—38no—
88D3×C4⋊Q8—34no—
89#5722—38no—
90#5721—34no—
91#5636—316no—
92#5632—38no—
93#5623—316no—
94#5622—38no—
95#5578—34no—
96#5567—34no—
97#5546—38no—
98#5539—38no—
99D4×Dic6—34no—
100C4×#237—34no—
101C2×C32×Q8—44no—
102C2×C32×Q8C2312yes—
103C2×C32×Q8C2311yescharacteristic
104C2×C32×Q8C2314yes—
105C2×C32×D4C2311yescharacteristic
106C22×C32×C4C2312yes—
107C22×C32×C4C2314yes—
108C2×#638C2312yes—
109C22×C3⋊Dic3C2312yes—
110C22×C3⋊Dic3C2314yes—
111C22×C3⋊Dic3C2312yes—
112Q8×C3⋊D3—44no—
113#3830Q818yescomplemented
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×C4×C3⋊D3C2314yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×#634—44no—
119C2×#634C2312yes—
120C2×#634C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2314yes—
123C2×#634C2314yes—
124C2×#634C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127C32×C4⋊C4C2314yes—
128C32×C4⋊C4C2312yes—
129C32×C4⋊C4C2312yes—
130C32×C4⋊C4C2312yes—
131C32×C22⋊C4C2314yes—
132C32×C22⋊C4C2312yes—
133C32×C42C2311yescharacteristic
134C32×C42C2312yes—
135#3757C2314yes—
136#3757C2312yes—
137#3752C2312yes—
138#3752C2312yes—
139#3752C2312yes—
140C4⋊(C3⋊Dic3)C2312yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2314yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2314yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2314yes—
152#3750C2314yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2312yes—
156#3750C2314yes—
157#3750C2314yes—
158#3750C2314yes—
159#3750C2314yes—
160#3750C2314yes—
161C4×C3⋊Dic3C2311yescharacteristic
162C4×C3⋊Dic3C2312yes—
163C4×C3⋊Dic3C2314yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2311yescharacteristic
166C4×C3⋊Dic3C2311yescharacteristic
167C4×C3⋊Dic3C2314yes—
168C4×C3⋊Dic3C2312yes—
169C4×C3⋊Dic3C2312yes—
170#3503—91noSylow
171C22×C3×Q8C2×D318yes—
172C2×D3×Q8—38no—
173C2×#237—34no—
174C22×Dic6—38no—
175C3×C4⋊Q8C2×D314yes—
176C3×C4⋊Q8C2×D318yes—
177C3×C22⋊Q8C2×D318yes—
178C3×C22⋊Q8C2×D3116yes—
179C3×C4×Q8C2×D314yes—
180C3×C4×D4C2×D314yes—
181C3×C4×D4C2×D318yes—
182#946—316no—
183#946—34no—
184Q8×Dic3—38no—
185#944—38no—
186#944—316no—
187#944—316no—
188#944—38no—
189#944—316no—
190#944—34no—
191#944—38no—
192D4×Dic3—34no—
193D4×Dic3—38no—
194C4×#67—38no—
195C4×#67—316no—
196#924—38no—
197#924—316no—
198C2×Dic3⋊C4—316no—
199C2×Dic3⋊C4—316no—
200C2×C4×Dic3—38no—
201#897—34no—
202#896—316no—
203#896—38no—
204#892—34no—
205D3×C4⋊C4—38no—
206D3×C4⋊C4—38no—
207#890—38no—
208#889—316no—
209#889—316no—
210#889—316no—
211#889—38no—
212#888—316no—
213#888—38no—
214#888—38no—
215#888—38no—
216#888—34no—
217#887—38no—
218#887—316no—
219#887—38no—
220#887—34no—
221#67⋊C4—316no—
222#67⋊C4—38no—
223#878—316no—
224#878—316no—
225#878—316no—
226#877—38no—
227#877—316no—
228#872—38no—
229C42×D3—34no—
230#870—38no—
231#869—34no—
232C4×Dic6—34no—
233C4×Dic6—34no—
234C4×Dic6—38no—
235C4×Dic6—38no—
236C23×C32C2412yes—
237C22×C3⋊D3C2411yescharacteristic
238C32×Q8—24no—
239C32×Q8—22no—
240C32×Q8—44no—
241C32×D4C2×Q814yescomplemented
242C2×C32×C4—24no—
243C2×C32×C4—44no—
244C2×C32×C4C2412yes—
245C2×C32×C4C2412yes—
246C2×C32×C4C2411yescharacteristic
247C2×C32×C4C2414yes—
248C2×C32×C4C2412yes—
249C2×C32×C4C2411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638C2×Q818yescomplemented
252C2×C3⋊Dic3—24no—
253C2×C3⋊Dic3—44no—
254C2×C3⋊Dic3C2×Q818yescomplemented
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2412yes—
257C2×C3⋊Dic3C2411yescharacteristic
258C2×C3⋊Dic3C2412yes—
259C2×C3⋊Dic3C2414yes—
260C2×C3⋊Dic3C2412yes—
261C2×C3⋊Dic3C2411yescharacteristic
262C2×C3⋊Dic3C2411yescharacteristic
263C4×C3⋊D3—22no—
264C4×C3⋊D3—22no—
265C4×C3⋊D3—44no—
266C4×C3⋊D3C2×Q814yescomplemented
267#634—22no—
268#634—24no—
269#634—24no—
270#634—44no—
271#634—44no—
272#634C2×Q814yescomplemented
273Q82—92no—
274#557—91no—
275#557—91no—
276#554—94no—
277#554—92no—
278D4×Q8—92no—
279D4×Q8—92no—
280D4×Q8—91no—
281D4×Q8C3⋊D311yescharacteristic, complemented
282#544—92no—
283#544—94no—
284#533—92no—
285#533—91no—
286C2×C4⋊Q8—92no—
287C2×C4⋊Q8—91no—
288#520—92no—
289C4×#41—91no—
290C2×C3×Q8—416no—
291C2×C3×Q8C22×D314yes—
292C2×C3×Q8C22×D318yes—
293C2×C3×Q8C22×D3116yes—
294C2×C3×D4C22×D314yes—
295C22×C3×C4C22×D318yes—
296C22×C3×C4C22×D3116yes—
297C2×#67—38no—
298C22×Dic3—38no—
299C22×Dic3—38no—
300C22×Dic3—316no—
301D3×Q8—1216no—
302#237—332no—
303C2×C4×D3—34no—
304C2×C4×D3—34no—
305C2×C4×D3—34no—
306C2×C4×D3—316no—
307C2×Dic6—34no—
308C2×Dic6—38no—
309C2×Dic6—34no—
310C2×Dic6—38no—
311C2×Dic6—316no—
312C2×Dic6—316no—
313C2×Dic6—1216no—
314C3×C4⋊C4C22×D314yes—
315C3×C4⋊C4C22×D314yes—
316C3×C4⋊C4C22×D3116yes—
317C3×C4⋊C4C22×D318yes—
318C3×C4⋊C4C22×D318yes—
319C3×C4⋊C4C22×D318yes—
320C3×C22⋊C4C22×D3116yes—
321C3×C22⋊C4C22×D318yes—
322C3×C42C22×D314yes—
323C3×C42C22×D318yes—
324#217—316no—
325#217—38no—
326(C2×D3)⋊C4—38no—
327(C2×D3)⋊C4—38no—
328(C2×D3)⋊C4—38no—
329C4⋊Dic3—38no—
330C4⋊Dic3—34no—
331C4⋊Dic3—38no—
332C4⋊Dic3—34no—
333C4⋊Dic3—38no—
334C4⋊Dic3—316no—
335Dic3⋊C4—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4—316no—
338Dic3⋊C4—38no—
339Dic3⋊C4—38no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342Dic3⋊C4—38no—
343Dic3⋊C4—38no—
344Dic3⋊C4—38no—
345Dic3⋊C4—316no—
346Dic3⋊C4—316no—
347Dic3⋊C4—316no—
348Dic3⋊C4—316no—
349Dic3⋊C4—316no—
350C4×Dic3—34no—
351C4×Dic3—38no—
352C4×Dic3—316no—
353C4×Dic3—38no—
354C4×Dic3—34no—
355C4×Dic3—34no—
356C4×Dic3—316no—
357C4×Dic3—38no—
358C4×Dic3—38no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32C22×Q814yes—
362C22×C32C2511yescharacteristic
363C2×C3⋊D3—21no—
364C2×C3⋊D3—21no—
365C2×C3⋊D3C22×Q812yes—
366C32×C4—22no—
367C32×C4—24no—
368C32×C4—22no—
369C32×C4—22no—
370C32×C4—21no—
371C32×C4C22×Q812yes—
372C32×C4H(5,𝔽2)12yes—
373C3⋊Dic3—24no—
374C3⋊Dic3—22no—
375C3⋊Dic3—21no—
376C3⋊Dic3—22no—
377C3⋊Dic3—22no—
378C3⋊Dic3C22×Q814yes—
379C3⋊Dic3C22×Q812yes—
380C3⋊Dic32−1+412yes—
381C2×#41—91no—
382C22×Q8—92no—
383C22×Q8—92no—
384C22×Q8C2×C3⋊D312yes—
385C4⋊Q8—92no—
386C4⋊Q8—91no—
387C4⋊Q8—94no—
388C4⋊Q8—92no—
389C4⋊Q8—92no—
390C4⋊Q8—94no—
391C4⋊Q8—94no—
392C4⋊Q8—92no—
393C4⋊Q8—92no—
394C4⋊Q8—91no—
395C4⋊Q8—94no—
396C4⋊Q8—92no—
397C4⋊Q8—91no—
398C4⋊Q8C2×C3⋊D311yescharacteristic
399C4⋊Q8C2×C3⋊D312yes—
400#125—94no—
401#125—92no—
402#125—94no—
403#125—94no—
404#125—92no—
405#125—92no—
406C22⋊Q8—91no—
407C22⋊Q8—94no—
408C22⋊Q8—92no—
409C22⋊Q8—94no—
410C22⋊Q8—91no—
411C22⋊Q8—92no—
412C22⋊Q8—94no—
413C22⋊Q8—94no—
414C22⋊Q8—94no—
415C22⋊Q8—94no—
416C22⋊Q8C2×C3⋊D312yes—
417C22⋊Q8C2×C3⋊D314yes—
418C4×Q8—92no—
419C4×Q8—91no—
420C4×Q8—92no—
421C4×Q8—92no—
422C4×Q8—94no—
423C4×Q8—91no—
424C4×Q8—92no—
425C4×Q8—91no—
426C4×Q8—92no—
427C4×Q8C2×C3⋊D311yescharacteristic
428C4×D4—91no—
429C4×D4—92no—
430C4×D4—92no—
431C4×D4—94no—
432C4×D4—92no—
433C4×D4—94no—
434C4×D4C2×C3⋊D311yescharacteristic
435C4×D4C2×C3⋊D312yes—
436#117—91no—
437#117—92no—
438#117—94no—
439#117—92no—
440C2×C4⋊C4—94no—
441C2×C4⋊C4—94no—
442C2×C4⋊C4—92no—
443C2×C4⋊C4—92no—
444C2×C42—92no—
445C2×C42—91no—
446C23×C3C23×D318yes—
447C22×D3—34no—
448C3×Q8—216no—
449C3×Q8—28no—
450C3×Q8—416no—
451C3×D4D3×Q8116yescomplemented
452C2×C3×C4—216no—
453C2×C3×C4—416no—
454C2×C3×C4C23×D318yes—
455C2×C3×C4C23×D318yes—
456C2×C3×C4C23×D314yes—
457C2×C3×C4C23×D3116yes—
458C2×C3×C4C23×D318yes—
459C2×C3×C4C23×D314yes—
460C2×C3×C4C23×D314yes—
461#67—332no—
462C2×Dic3—332no—
463C2×Dic3—38no—
464C2×Dic3—34no—
465C2×Dic3—34no—
466C2×Dic3—38no—
467C2×Dic3—38no—
468C2×Dic3—34no—
469C2×Dic3—38no—
470C2×Dic3—316no—
471C2×Dic3—616no—
472C2×Dic3—1216no—
473C4×D3—316no—
474C4×D3—68no—
475C4×D3—68no—
476C4×D3—1216no—
477Dic6—316no—
478Dic6—616no—
479Dic6—68no—
480Dic6—616no—
481Dic6—1216no—
482Dic6—1216no—
483C2×C32—24no—
484C2×C32C23×Q811yescharacteristic
485C2×C32C2×H(5,𝔽2)11yescharacteristic
486C2×C32C2×2−1+411yescharacteristic
487C3⋊D3—22no—
488#41—98no—
489C2×Q8—44no—
490C2×Q8—91no—
491C2×Q8—92no—
492C2×Q8—92no—
493C2×Q8—91no—
494C2×Q8—94no—
495C2×Q8—94no—
496C2×Q8—364no—
497C2×Q8—364no—
498C2×Q8C22×C3⋊D312yes—
499C2×Q8C22×C3⋊D311yescharacteristic
500C2×Q8C22×C3⋊D314yes—
501C2×D4—92no—
502C2×D4C22×C3⋊D311yescharacteristic
503C22×C4—92no—
504C22×C4—91no—
505C22×C4—92no—
506C22×C4—94no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—94no—
510C22×C4C22×C3⋊D312yes—
511C22×C4C22×C3⋊D314yes—
512C4⋊C4—94no—
513C4⋊C4—92no—
514C4⋊C4—94no—
515C4⋊C4—92no—
516C4⋊C4—94no—
517C4⋊C4—94no—
518C4⋊C4—92no—
519C4⋊C4—94no—
520C4⋊C4—94no—
521C4⋊C4—92no—
522C4⋊C4—92no—
523C4⋊C4—92no—
524C4⋊C4—91no—
525C4⋊C4—92no—
526C4⋊C4—91no—
527C4⋊C4—92no—
528C4⋊C4—94no—
529C4⋊C4—94no—
530C4⋊C4—92no—
531C4⋊C4—94no—
532C4⋊C4—92no—
533C4⋊C4C22×C3⋊D312yes—
534C4⋊C4C22×C3⋊D312yes—
535C4⋊C4C22×C3⋊D311yescharacteristic
536C4⋊C4C22×C3⋊D311yescharacteristic
537C4⋊C4C22×C3⋊D314yes—
538C4⋊C4C22×C3⋊D312yes—
539C22⋊C4—94no—
540C22⋊C4—92no—
541C22⋊C4—92no—
542C22⋊C4—92no—
543C22⋊C4—92no—
544C22⋊C4C22×C3⋊D314yes—
545C22⋊C4C22×C3⋊D312yes—
546C42—91no—
547C42—92no—
548C42—91no—
549C42—92no—
550C42—92no—
551C42—91no—
552C42—94no—
553C42—94no—
554C42—92no—
555C42C22×C3⋊D311yescharacteristic
556C42C22×C3⋊D312yes—
557C22×C3—28no—
558C22×C3—28no—
559C22×C3C2×D3×Q8116yes—
560C22×C3C24×D314yes—
561C2×D3—38no—
562C2×D3—64no—
563C2×D3—64no—
564C3×C4—28no—
565C3×C4—216no—
566C3×C4—28no—
567C3×C4—28no—
568C3×C4—24no—
569C3×C4#100418yes—
570C3×C4C2×D3×Q818yes—
571Dic3—316no—
572Dic3—38no—
573Dic3—38no—
574Dic3—616no—
575Dic3—68no—
576Dic3—64no—
577Dic3—68no—
578Dic3—68no—
579C32#350311yescharacteristic, complemented, Sylow
580C23—91no—
581C23C23×C3⋊D312yes—
582Q8—22no—
583Q8—24no—
584Q8—44no—
585Q8—94no—
586Q8—184no—
587Q8—182no—
588Q8—184no—
589Q8—364no—
590Q8—364no—
591D4—98no—
592D4Q8×C3⋊D314yescomplemented
593C2×C4—24no—
594C2×C4—44no—
595C2×C4—98no—
596C2×C4—92no—
597C2×C4—91no—
598C2×C4—91no—
599C2×C4—94no—
600C2×C4—92no—
601C2×C4—92no—
602C2×C4—91no—
603C2×C4—94no—
604C2×C4—92no—
605C2×C4—182no—
606C2×C4—184no—
607C2×C4—182no—
608C2×C4—364no—
609C2×C4—364no—
610C2×C4C23×C3⋊D312yes—
611C2×C4C23×C3⋊D312yes—
612C2×C4C23×C3⋊D311yescharacteristic
613C2×C4C23×C3⋊D314yes—
614C2×C4C23×C3⋊D312yes—
615C2×C4C23×C3⋊D311yescharacteristic
616C2×C4C23×C3⋊D311yescharacteristic
617C2×C3—216no—
618C2×C3C2×#100414yes—
619C2×C3C22×D3×Q814yes—
620C2×C3D3×2−1+414yes—
621D3—68no—
622C22—22no—
623C22—22no—
624C22—92no—
625C22—181no—
626C22—181no—
627C22C2×Q8×C3⋊D314yes—
628C22C24×C3⋊D311yescharacteristic
629C4—22no—
630C4—22no—
631C4—24no—
632C4—21no—
633C4—22no—
634C4—92no—
635C4—94no—
636C4—92no—
637C4—181no—
638C4—184no—
639C4—182no—
640C4—182no—
641C4—182no—
642C4#6436112yes—
643C4C2×Q8×C3⋊D312yes—
644C3#8674714yescomplemented
645C2—24no—
646C2—182no—
647C2C2×#6436111yescharacteristic
648C2C22×Q8×C3⋊D311yescharacteristic
649C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×D4×Q8C2
prime radicalC2×#3830C22
hypercenterD4×Q8C3⋊D3
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C32×D4×Q8C2semidirect
2. Q8×#638C2semidirect
3. C2×#64153C2semidirect
4. #10596200C2semidirect
5. C3⋊D3×C4⋊Q8C2semidirect
6. #10596193C2semidirect
7. #10596192C2semidirect
8. #10596107C2semidirect
9. #10596103C2semidirect
10. #10596094C2semidirect
11. #10596093C2semidirect
12. #10596049C2semidirect
13. #10596038C2semidirect
15. #10596010C2semidirect
16. D4×#634C2semidirect
84. C3×D4×Q8D3semidirect
113. #3830Q8semidirect
241. C32×D4C2×Q8semidirect
251. #638C2×Q8semidirect
254. C2×C3⋊Dic3C2×Q8semidirect
266. C4×C3⋊D3C2×Q8semidirect
272. #634C2×Q8semidirect
281. D4×Q8C3⋊D3semidirect
451. C3×D4D3×Q8semidirect
579. C32#3503semidirect
592. D4Q8×C3⋊D3semidirect
644. C3#86747semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
Q8×#6382
C2×#641532
#105962002
C3⋊D3×C4⋊Q82
#105961932
#105961922
#105961072
#105961032
#105960942
#105960932
#105960492
#105960382
#105960172
#105960102
D4×#6342
C4×#38302
#867473