Finite Group Databasebeta

← #11909864

Subgroups — #11909864

Order 1152.

2976 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic
2#10596172C214yesmaximal, complemented
3#10596156C212yesmaximal, complemented
4#10596142C212yesmaximal, complemented
5#10596121C214yesmaximal, complemented
6#10596093C212yesmaximal, complemented
7#10596071C212yesmaximal
8#10596041C211yesmaximal, characteristic, complemented
9#10596038C211yesmaximal, characteristic, complemented
10#10596013C211yesmaximal, characteristic, complemented
11#10596012C212yesmaximal, complemented
12D4×#634C211yesmaximal, characteristic, complemented
13D4×#634C212yesmaximal, complemented
14#10595989C212yesmaximal, complemented
15#10595987C212yesmaximal, complemented
16#10595941C211yesmaximal, characteristic, complemented
17C2×C4×#634C211yesmaximal, characteristic, complemented
18#86129—34nomaximal
19C22×#634C2211yescharacteristic
20C22×#634C2212yes—
21C32×#126C2212yes—
22C32×#125C2211yescharacteristic
23C32×#124C2211yescharacteristic
24C32×#123C2212yes—
25C32×C22⋊Q8C2211yescharacteristic
26C32×#121C2211yescharacteristic
27C32×C4×Q8C2211yescharacteristic
28C32×C4×D4C2212yes—
29C32×C4×D4C2211yescharacteristic
30C32×#117C2212yes—
31C2×C32×C42C2211yescharacteristic
32Q8×C3⋊Dic3C2212yes—
33#64153C2212yes—
34#64145C2212yes—
35#64144C2214yes—
36D4×C3⋊Dic3C2214yes—
37D4×C3⋊Dic3C2212yes—
38#64135C2212yes—
39#64135C2212yes—
40C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
41#64133C2212yes—
42#64133C2212yes—
43#64133C2212yes—
44#64133C2212yes—
45C2×#3750C2212yes—
46C2×C4×C3⋊Dic3C2212yes—
47#64099C2214yes—
48#64099C2212yes—
49#64098C2214yes—
50#64098C2214yes—
51#64098C2214yes—
52#64098C2214yes—
53#64097C2214yes—
54#64097C2212yes—
55#64096C2214yes—
56#64096C2212yes—
57#64096C2212yes—
58#64096C2214yes—
59#64088C2214yes—
60#64088C2214yes—
61#64088C2214yes—
62#64088C2214yes—
63#64087C2214yes—
64#64087C2214yes—
65#64087C2214yes—
66#64086C2214yes—
67#64086C2214yes—
68#64086C2214yes—
69#64079C2212yes—
70#64079C2212yes—
71#64078C2211yescharacteristic
72#64078C2211yescharacteristic
73#64078C2212yes—
74C4×#634C2212yes—
75C4×#634C2212yes—
76C4×#634C2212yes—
77C4×#634C2211yescharacteristic
78C4×#634C2211yescharacteristic
79C4×#634C2211yescharacteristic
80C4×#634C2211yescharacteristic
81C4×#634C2212yes—
82C4×#634C2212yes—
83C4×#634C2212yes—
84C3×#529D314yes—
85#5701—316no—
86#5685—38no—
87#5671—38no—
88#5650—316no—
89#5622—38no—
90#5600—38no—
91#5570—34no—
92#5567—34no—
93#5542—34no—
94#5541—38no—
95D4×Dic6—34no—
96D4×Dic6—38no—
97#5518—38no—
98#5516—38no—
99#5470—34no—
100C2×C4×Dic6—34no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2312yes—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2314yes—
109C22×C3⋊Dic3C2312yes—
110C22×C3⋊Dic3C2312yes—
111C2×#634—24no—
112C2×#634—28no—
113C2×#634C2311yescharacteristic
114C2×#634C2312yes—
115C2×#634C2312yes—
116C2×#634C2312yes—
117C2×#634C2314yes—
118C2×#634C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2312yes—
121C32×C4⋊C4C2312yes—
122C32×C4⋊C4C2311yescharacteristic
123C32×C4⋊C4C2312yes—
124C32×C4⋊C4C2312yes—
125C32×C22⋊C4C2312yes—
126C32×C22⋊C4C2312yes—
127C32×C22⋊C4C2312yes—
128C32×C22⋊C4C2312yes—
129C32×C22⋊C4C2312yes—
130C32×C42C2311yescharacteristic
131C32×C42C2311yescharacteristic
132C32×C42C2311yescharacteristic
133C32×C42C2312yes—
134C32×C42C2311yescharacteristic
135#3757C2314yes—
136#3757C2314yes—
137#3757C2314yes—
138#3757C2314yes—
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2312yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2312yes—
146C4⋊(C3⋊Dic3)C2314yes—
147C4⋊(C3⋊Dic3)C2314yes—
148#3750C2312yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2312yes—
152#3750C2314yes—
153#3750C2314yes—
154#3750C2314yes—
155#3750C2314yes—
156#3750C2314yes—
157#3750C2314yes—
158#3750C2314yes—
159#3750C2314yes—
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2314yes—
162C4×C3⋊Dic3C2312yes—
163C4×C3⋊Dic3C2312yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2314yes—
166C4×C3⋊Dic3C2314yes—
167C4×C3⋊Dic3C2314yes—
168#3523—91noSylow
169C22×Dic6—34no—
170C22×Dic6—38no—
171C3×#126C2×D318yes—
172C3×#125C2×D314yes—
173C3×#124C2×D314yes—
174C3×#123C2×D318yes—
175C3×C22⋊Q8C2×D314yes—
176C3×#121C2×D314yes—
177C3×C4×Q8C2×D314yes—
178C3×C4×D4C2×D318yes—
179C3×C4×D4C2×D314yes—
180C3×#117C2×D318yes—
181C2×C3×C42C2×D314yes—
182Q8×Dic3—38no—
183#944—38no—
184#936—38no—
185#935—316no—
186D4×Dic3—316no—
187D4×Dic3—38no—
188#926—38no—
189#926—38no—
190C2×C4⋊Dic3—34no—
191#924—38no—
192#924—38no—
193#924—38no—
194#924—38no—
195C2×Dic3⋊C4—38no—
196C2×C4×Dic3—38no—
197#890—316no—
198#890—38no—
199#889—316no—
200#889—316no—
201#889—316no—
202#889—316no—
203#888—316no—
204#888—38no—
205#887—316no—
206#887—38no—
207#887—38no—
208#887—316no—
209#879—316no—
210#879—316no—
211#879—316no—
212#879—316no—
213#878—316no—
214#878—316no—
215#878—316no—
216#877—316no—
217#877—316no—
218#877—316no—
219#870—38no—
220#870—38no—
221#869—34no—
222#869—34no—
223#869—38no—
224C4×Dic6—38no—
225C4×Dic6—38no—
226C4×Dic6—38no—
227C4×Dic6—34no—
228C4×Dic6—34no—
229C4×Dic6—34no—
230C4×Dic6—34no—
231C4×Dic6—38no—
232C4×Dic6—38no—
233C4×Dic6—38no—
234C23×C32C2412yes—
235C23×C32C2411yescharacteristic
236C32×Q8—22no—
237C32×D4—24no—
238C32×D4—22no—
239C2×C32×C4—22no—
240C2×C32×C4—22no—
241C2×C32×C4—24no—
242C2×C32×C4—22no—
243C2×C32×C4C2411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2412yes—
246C2×C32×C4C2412yes—
247C2×C32×C4C2412yes—
248C2×C32×C4C2411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—24no—
253C2×C3⋊Dic3—24no—
254C2×C3⋊Dic3—28no—
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2414yes—
257C2×C3⋊Dic3C2412yes—
258C2×C3⋊Dic3C2414yes—
259C2×C3⋊Dic3C2412yes—
260C2×C3⋊Dic3C2412yes—
261#634—22no—
262#634—24no—
263#634—24no—
264#634—24no—
265#634—28no—
266#634#4114yes—
267#557—92no—
268#557—91no—
269#557—91no—
270#556—92no—
271#556—91no—
272#552—94no—
273#552—92no—
274D4×Q8—92no—
275D4×Q8—91no—
276#541—94no—
277#541—92no—
278#533—92no—
279#533—91no—
280#529—92no—
281#529C3⋊D311yescharacteristic
282#519—92no—
283C2×C4×Q8—91no—
284C2×C3×Q8C22×D314yes—
285C2×C3×D4C22×D318yes—
286C2×C3×D4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D318yes—
291C22×Dic3—316no—
292C22×Dic3—38no—
293C22×Dic3—38no—
294C2×Dic6—34no—
295C2×Dic6—34no—
296C2×Dic6—38no—
297C2×Dic6—38no—
298C2×Dic6—38no—
299C2×Dic6—316no—
300C2×Dic6—616no—
301C2×Dic6—632no—
302C3×C4⋊C4C22×D314yes—
303C3×C4⋊C4C22×D318yes—
304C3×C4⋊C4C22×D318yes—
305C3×C4⋊C4C22×D314yes—
306C3×C4⋊C4C22×D318yes—
307C3×C4⋊C4C22×D318yes—
308C3×C22⋊C4C22×D318yes—
309C3×C22⋊C4C22×D318yes—
310C3×C22⋊C4C22×D318yes—
311C3×C22⋊C4C22×D318yes—
312C3×C22⋊C4C22×D318yes—
313C3×C42C22×D314yes—
314C3×C42C22×D314yes—
315C3×C42C22×D314yes—
316C3×C42C22×D318yes—
317C3×C42C22×D314yes—
318#217—316no—
319#217—316no—
320#217—316no—
321#217—316no—
322C4⋊Dic3—34no—
323C4⋊Dic3—38no—
324C4⋊Dic3—34no—
325C4⋊Dic3—38no—
326C4⋊Dic3—38no—
327C4⋊Dic3—38no—
328C4⋊Dic3—38no—
329C4⋊Dic3—316no—
330C4⋊Dic3—316no—
331Dic3⋊C4—38no—
332Dic3⋊C4—38no—
333Dic3⋊C4—38no—
334Dic3⋊C4—38no—
335Dic3⋊C4—316no—
336Dic3⋊C4—316no—
337Dic3⋊C4—316no—
338Dic3⋊C4—316no—
339Dic3⋊C4—316no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342Dic3⋊C4—316no—
343C4×Dic3—38no—
344C4×Dic3—316no—
345C4×Dic3—38no—
346C4×Dic3—38no—
347C4×Dic3—38no—
348C4×Dic3—316no—
349C4×Dic3—316no—
350C4×Dic3—316no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C32×C4—22no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—22no—
364C32×C4—22no—
365C32×C4C2×#4112yes—
366C32×C42−1+412yes—
367C3⋊Dic3—22no—
368C3⋊Dic3—24no—
369C3⋊Dic3—24no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3C2×#4114yes—
373C22×Q8—91no—
374C22×Q8—92no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—94no—
378C4⋊Q8—91no—
379C4⋊Q8—91no—
380C4⋊Q8—92no—
381#126—94no—
382#126—94no—
383#126—94no—
384#126—94no—
385#126C2×C3⋊D312yes—
386#125—92no—
387#125—94no—
388#125—94no—
389#125—94no—
390#125—94no—
391#125—94no—
392#125—92no—
393#125—92no—
394#125C2×C3⋊D311yescharacteristic
395#124—92no—
396#124C2×C3⋊D311yescharacteristic
397#123—94no—
398#123C2×C3⋊D312yes—
399C22⋊Q8—92no—
400C22⋊Q8—92no—
401C22⋊Q8—92no—
402C22⋊Q8—92no—
403C22⋊Q8—94no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8C2×C3⋊D311yescharacteristic
407#121C2×C3⋊D311yescharacteristic
408C4×Q8—92no—
409C4×Q8—94no—
410C4×Q8—94no—
411C4×Q8—92no—
412C4×Q8—92no—
413C4×Q8—91no—
414C4×Q8—92no—
415C4×Q8—91no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—91no—
419C4×Q8—92no—
420C4×Q8—92no—
421C4×Q8—92no—
422C4×Q8—92no—
423C4×Q8C2×C3⋊D311yescharacteristic
424C4×D4—94no—
425C4×D4—92no—
426C4×D4C2×C3⋊D312yes—
427C4×D4C2×C3⋊D311yescharacteristic
428#117—92no—
429#117—92no—
430#117—94no—
431#117—94no—
432#117—94no—
433#117C2×C3⋊D312yes—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42C2×C3⋊D311yescharacteristic
438C23×C3C23×D318yes—
439C23×C3C23×D314yes—
440C3×Q8—28no—
441C3×D4—216no—
442C3×D4—28no—
443C2×C3×C4—28no—
444C2×C3×C4—28no—
445C2×C3×C4—216no—
446C2×C3×C4—28no—
447C2×C3×C4C23×D314yes—
448C2×C3×C4C23×D314yes—
449C2×C3×C4C23×D318yes—
450C2×C3×C4C23×D318yes—
451C2×C3×C4C23×D318yes—
452C2×C3×C4C23×D314yes—
453C2×C3×C4C23×D314yes—
454C2×C3×C4C23×D314yes—
455C2×C3×C4C23×D314yes—
456C2×Dic3—38no—
457C2×Dic3—38no—
458C2×Dic3—316no—
459C2×Dic3—38no—
460C2×Dic3—316no—
461C2×Dic3—38no—
462C2×Dic3—616no—
463C2×Dic3—632no—
464C2×Dic3—616no—
465Dic6—316no—
466Dic6—616no—
467Dic6—632no—
468Dic6—68no—
469Dic6—616no—
470Dic6—616no—
471C2×C32—22no—
472C2×C32—42no—
473C2×C32C22×#4111yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C2×C32C2×2−1+411yescharacteristic
476C2×Q8—91no—
477C2×Q8—92no—
478C2×Q8—94no—
479C2×Q8—92no—
480C2×Q8—91no—
481C2×Q8—92no—
482C2×Q8—184no—
483C2×Q8—188no—
484C2×Q8C22×C3⋊D311yescharacteristic
485C2×D4C22×C3⋊D312yes—
486C2×D4C22×C3⋊D311yescharacteristic
487C22×C4—92no—
488C22×C4—92no—
489C22×C4—94no—
490C22×C4C22×C3⋊D311yescharacteristic
491C22×C4C22×C3⋊D311yescharacteristic
492C22×C4C22×C3⋊D311yescharacteristic
493C22×C4C22×C3⋊D312yes—
494C4⋊C4—92no—
495C4⋊C4—91no—
496C4⋊C4—92no—
497C4⋊C4—91no—
498C4⋊C4—92no—
499C4⋊C4—92no—
500C4⋊C4—92no—
501C4⋊C4—94no—
502C4⋊C4—92no—
503C4⋊C4—94no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C4⋊C4—92no—
507C4⋊C4—94no—
508C4⋊C4—92no—
509C4⋊C4—92no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4—94no—
513C4⋊C4—94no—
514C4⋊C4—94no—
515C4⋊C4C22×C3⋊D312yes—
516C4⋊C4C22×C3⋊D312yes—
517C4⋊C4C22×C3⋊D311yescharacteristic
518C4⋊C4C22×C3⋊D312yes—
519C4⋊C4C22×C3⋊D311yescharacteristic
520C4⋊C4C22×C3⋊D312yes—
521C22⋊C4—94no—
522C22⋊C4—94no—
523C22⋊C4—94no—
524C22⋊C4—94no—
525C22⋊C4C22×C3⋊D312yes—
526C22⋊C4C22×C3⋊D312yes—
527C22⋊C4C22×C3⋊D312yes—
528C22⋊C4C22×C3⋊D312yes—
529C22⋊C4C22×C3⋊D312yes—
530C42—92no—
531C42—92no—
532C42—92no—
533C42—92no—
534C42—94no—
535C42—94no—
536C42—94no—
537C42—94no—
538C42C22×C3⋊D311yescharacteristic
539C42C22×C3⋊D311yescharacteristic
540C42C22×C3⋊D311yescharacteristic
541C42C22×C3⋊D311yescharacteristic
542C42C22×C3⋊D312yes—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—28no—
546C22×C3—28no—
547C22×C3—28no—
548C22×C3#101018yes—
549C22×C3C24×D314yes—
550C3×C4—28no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—24no—
555C3×C4—28no—
556C3×C4—28no—
557C3×C4D3×#4118yes—
558C3×C4#101018yes—
559Dic3—316no—
560Dic3—68no—
561Dic3—616no—
562Dic3—616no—
563Dic3—68no—
564Dic3—68no—
565C32#352311yescharacteristic, complemented, Sylow
566C23C23×C3⋊D312yes—
567C23C23×C3⋊D311yescharacteristic
568Q8—22no—
569Q8—94no—
570Q8—188no—
571Q8—184no—
572Q8—182no—
573Q8—184no—
574Q8—184no—
575D4—24no—
576D4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—94no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—94no—
587C2×C4—184no—
588C2×C4—188no—
589C2×C4—184no—
590C2×C4C23×C3⋊D311yescharacteristic
591C2×C4C23×C3⋊D311yescharacteristic
592C2×C4C23×C3⋊D312yes—
593C2×C4C23×C3⋊D312yes—
594C2×C4C23×C3⋊D312yes—
595C2×C4C23×C3⋊D311yescharacteristic
596C2×C4C23×C3⋊D311yescharacteristic
597C2×C4C23×C3⋊D311yescharacteristic
598C2×C4C23×C3⋊D311yescharacteristic
599C2×C3—28no—
600C2×C3—48no—
601C2×C3C2×D3×#4114yes—
602C2×C3C2×#101014yes—
603C2×C3C2×#101014yes—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22#6436712yes—
610C22C24×C3⋊D311yescharacteristic
611C4—22no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—22no—
617C4—22no—
618C4—94no—
619C4—182no—
620C4—184no—
621C4—182no—
622C4—182no—
623C4—184no—
624C4#41×C3⋊D312yes—
625C4#6436712yes—
626C3#8612914yescomplemented
627C2—22no—
628C2—42no—
629C2C2×#41×C3⋊D311yescharacteristic
630C2C2×#6436711yescharacteristic
631C2C2×#6436711yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#529C2
prime radicalC32×#121C22
hypercenter#529C3⋊D3
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #10596172C2semidirect
3. #10596156C2semidirect
4. #10596142C2semidirect
5. #10596121C2semidirect
6. #10596093C2semidirect
8. #10596041C2semidirect
9. #10596038C2semidirect
10. #10596013C2semidirect
11. #10596012C2semidirect
12. D4×#634C2semidirect
13. D4×#634C2semidirect
14. #10595989C2semidirect
15. #10595987C2semidirect
16. #10595941C2semidirect
17. C2×C4×#634C2semidirect
565. C32#3523semidirect
626. C3#86129semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
#105961722
#105961562
#105961422
#105961212
#105960932
#105960712
#105960412
#105960382
#105960132
#105960122
D4×#6342
#105959892
#105959872
#105959412
C2×C4×#6342
#861293