Finite Group Databasebeta

← #11903739

Subgroups — #11903739

Order 1152.

3204 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2#10596199C211yesmaximal, characteristic, complemented
3#10596193C211yesmaximal, characteristic, complemented
4#10596159C212yesmaximal, complemented
5#10596156C212yesmaximal, complemented
6#10596107C214yesmaximal, complemented
7#10596103C212yesmaximal, complemented
8#10596093C214yesmaximal, complemented
9#10596093C212yesmaximal, complemented
10C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
11#10596038C211yesmaximal, characteristic, complemented
12#10596010C212yesmaximal, complemented
13D4×#634C211yesmaximal, characteristic, complemented
14C4×#3830C212yesmaximal
15C4×#3830C211yesmaximal, characteristic
16#10595982C212yesmaximal, complemented
17C2×#64096C212yesmaximal, complemented
18#86923—34nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3830C2211yescharacteristic
21C22×#634C2212yes—
22C32×C4⋊Q8C2211yescharacteristic
23C32×#125C2212yes—
24C32×C22⋊Q8C2212yes—
25C32×C22⋊Q8C2214yes—
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×C4×D4C2212yes—
29C2×C32×C4⋊C4C2212yes—
30#64155C2212yes—
31Q8×C3⋊Dic3C2212yes—
32Q8×C3⋊Dic3C2211yescharacteristic
33#64153C2212yes—
34#64153C2214yes—
35D4×C3⋊Dic3C2212yes—
36D4×C3⋊Dic3C2211yescharacteristic
37C4×#638C2212yes—
38C4×#638C2214yes—
39#64133C2212yes—
40#64133C2214yes—
41C2×#3750C2214yes—
42C2×C4×C3⋊Dic3C2212yes—
43C2×C4×C3⋊Dic3C2214yes—
44#64106C2212yes—
45#64105C2214yes—
46#64105C2214yes—
47#64101C2211yescharacteristic
48#64101C2212yes—
49C4⋊C4×C3⋊D3C2212yes—
50C4⋊C4×C3⋊D3C2211yescharacteristic
51#64099C2212yes—
52#64098C2214yes—
53#64098C2214yes—
54#64098C2214yes—
55#64097C2214yes—
56#64097C2212yes—
57#64097C2212yes—
58#64097C2212yes—
59#64096C2212yes—
60#64096C2214yes—
61#64096C2211yescharacteristic
62#64096C2212yes—
63#64096C2214yes—
64#64096C2214yes—
65#64096C2212yes—
66#64096C2211yescharacteristic
67#64096C2212yes—
68#64096C2212yes—
69#64090C2214yes—
70#64090C2212yes—
71#64087C2214yes—
72#64087C2214yes—
73#64087C2214yes—
74#64086C2214yes—
75#64086C2212yes—
76C42×C3⋊D3C2212yes—
77C42×C3⋊D3C2211yescharacteristic
78#64079C2212yes—
79#64078C2211yescharacteristic
80C4×#634C2212yes—
81C4×#634C2212yes—
82C4×#634C2211yescharacteristic
83C4×#634C2211yescharacteristic
84C3×#554D314yescomplemented
85#5728—34no—
86#5722—34no—
87#5688—38no—
88#5685—38no—
89#5636—316no—
90#5632—38no—
91#5622—316no—
92#5622—38no—
93C4×D3×Q8—34no—
94#5567—34no—
95#5539—38no—
96D4×Dic6—34no—
97C4×#237—38no—
98C4×#237—34no—
99#5511—38no—
100C2×#887—38no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2312yes—
105C22×C32×C4C2314yes—
106C2×#638C2312yes—
107C22×C3⋊Dic3C2314yes—
108C22×C3⋊Dic3C2312yes—
109C22×C3⋊Dic3C2312yes—
110Q8×C3⋊D3—24no—
111#3830Q818yescomplemented
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×#634—28no—
118C2×#634C2312yes—
119C2×#634C2312yes—
120C2×#634C2314yes—
121C2×#634C2314yes—
122C2×#634C2311yescharacteristic
123C2×#634C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2314yes—
129C32×C4⋊C4C2312yes—
130C32×C4⋊C4C2312yes—
131C32×C22⋊C4C2314yes—
132C32×C22⋊C4C2312yes—
133C32×C42C2311yescharacteristic
134C32×C42C2312yes—
135#3757C2312yes—
136#3757C2314yes—
137#3752C2312yes—
138#3752C2314yes—
139C4⋊(C3⋊Dic3)C2312yes—
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2312yes—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2314yes—
145#3750C2314yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2312yes—
149#3750C2312yes—
150#3750C2314yes—
151#3750C2314yes—
152#3750C2312yes—
153#3750C2314yes—
154#3750C2314yes—
155#3750C2314yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2312yes—
160C4×C3⋊Dic3C2314yes—
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2311yescharacteristic
163C4×C3⋊Dic3C2312yes—
164C4×C3⋊Dic3C2311yescharacteristic
165C4×C3⋊Dic3C2312yes—
166C4×C3⋊Dic3C2314yes—
167C4×C3⋊Dic3C2314yes—
168C4×C3⋊Dic3C2312yes—
169Q8×#41—91noSylow
170C2×D3×Q8—34no—
171C2×#237—34no—
172C22×Dic6—38no—
173C3×C4⋊Q8C2×D314yes—
174C3×#125C2×D318yes—
175C3×C22⋊Q8C2×D318yes—
176C3×C22⋊Q8C2×D3116yes—
177C3×C4×Q8C2×D314yes—
178C3×C4×D4C2×D314yes—
179C3×C4×D4C2×D318yes—
180C2×C3×C4⋊C4C2×D318yes—
181#946—38no—
182Q8×Dic3—38no—
183Q8×Dic3—34no—
184#944—38no—
185#944—316no—
186D4×Dic3—38no—
187D4×Dic3—34no—
188C4×#67—38no—
189C4×#67—316no—
190#924—38no—
191#924—316no—
192C2×Dic3⋊C4—316no—
193C2×C4×Dic3—38no—
194C2×C4×Dic3—316no—
195#897—38no—
196#896—316no—
197#896—316no—
198#892—34no—
199#892—38no—
200D3×C4⋊C4—38no—
201D3×C4⋊C4—34no—
202#890—38no—
203#889—316no—
204#889—316no—
205#889—316no—
206#888—316no—
207#888—38no—
208#888—38no—
209#888—38no—
210#887—38no—
211#887—316no—
212#887—34no—
213#887—38no—
214#887—316no—
215#887—316no—
216#887—38no—
217#887—34no—
218#887—38no—
219#887—38no—
220#67⋊C4—316no—
221#67⋊C4—38no—
222#878—316no—
223#878—316no—
224#878—316no—
225#877—316no—
226#877—38no—
227C42×D3—38no—
228C42×D3—34no—
229#870—38no—
230#869—34no—
231C4×Dic6—38no—
232C4×Dic6—38no—
233C4×Dic6—34no—
234C4×Dic6—34no—
235C23×C32C2412yes—
236C22×C3⋊D3C2411yescharacteristic
237C32×Q8—22no—
238C32×Q8—42no—
239C32×D4C2×Q814yescomplemented
240C2×C32×C4—24no—
241C2×C32×C4—44no—
242C2×C32×C4C2412yes—
243C2×C32×C4C2414yes—
244C2×C32×C4C2412yes—
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2412yes—
247C2×C32×C4C2411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638C2×Q818yescomplemented
250C2×C3⋊Dic3—28no—
251C2×C3⋊Dic3—42no—
252C2×C3⋊Dic3C2×Q818yescomplemented
253C2×C3⋊Dic3C2411yescharacteristic
254C2×C3⋊Dic3C2412yes—
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2414yes—
257C2×C3⋊Dic3C2411yescharacteristic
258C2×C3⋊Dic3C2411yescharacteristic
259C2×C3⋊Dic3C2412yes—
260C2×C3⋊Dic3C2412yes—
261C4×C3⋊D3—22no—
262C4×C3⋊D3—24no—
263C4×C3⋊D3—42no—
264C4×C3⋊D3—41no—
265C4×C3⋊D3C2×Q814yescomplemented
266#634—24no—
267#634—28no—
268#634—24no—
269#634—44no—
270#634C2×Q814yescomplemented
271#634#4114yescomplemented
272Q82—91no—
273#557—92no—
274#557—91no—
275#554—94no—
276#554—92no—
277#554—92no—
278#554C3⋊D311yescharacteristic, complemented
279D4×Q8—92no—
280D4×Q8—91no—
281#533—91no—
282#533—92no—
283#533—92no—
284#533—94no—
285C4×#41—92no—
286C4×#41—91no—
287C2×C4×Q8—91no—
288C2×C4×Q8—92no—
289C2×C3×Q8C22×D314yes—
290C2×C3×Q8C22×D318yes—
291C2×C3×D4C22×D314yes—
292C22×C3×C4C22×D318yes—
293C22×C3×C4C22×D3116yes—
294C2×#67—38no—
295C22×Dic3—38no—
296C22×Dic3—316no—
297C22×Dic3—38no—
298D3×Q8—616no—
299#237—332no—
300C2×C4×D3—34no—
301C2×C4×D3—38no—
302C2×C4×D3—34no—
303C2×C4×D3—34no—
304C2×C4×D3—38no—
305C2×Dic6—34no—
306C2×Dic6—34no—
307C2×Dic6—38no—
308C2×Dic6—38no—
309C2×Dic6—316no—
310C2×Dic6—316no—
311C2×Dic6—632no—
312C3×C4⋊C4C22×D314yes—
313C3×C4⋊C4C22×D318yes—
314C3×C4⋊C4C22×D3116yes—
315C3×C4⋊C4C22×D314yes—
316C3×C4⋊C4C22×D3116yes—
317C3×C4⋊C4C22×D318yes—
318C3×C4⋊C4C22×D318yes—
319C3×C22⋊C4C22×D3116yes—
320C3×C22⋊C4C22×D318yes—
321C3×C42C22×D314yes—
322C3×C42C22×D318yes—
323#217—38no—
324#217—316no—
325(C2×D3)⋊C4—38no—
326(C2×D3)⋊C4—316no—
327C4⋊Dic3—38no—
328C4⋊Dic3—34no—
329C4⋊Dic3—38no—
330C4⋊Dic3—34no—
331C4⋊Dic3—38no—
332C4⋊Dic3—316no—
333Dic3⋊C4—316no—
334Dic3⋊C4—38no—
335Dic3⋊C4—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4—38no—
338Dic3⋊C4—316no—
339Dic3⋊C4—316no—
340Dic3⋊C4—38no—
341Dic3⋊C4—316no—
342Dic3⋊C4—316no—
343Dic3⋊C4—316no—
344Dic3⋊C4—316no—
345C4×Dic3—38no—
346C4×Dic3—34no—
347C4×Dic3—38no—
348C4×Dic3—316no—
349C4×Dic3—38no—
350C4×Dic3—34no—
351C4×Dic3—38no—
352C4×Dic3—34no—
353C4×Dic3—38no—
354C4×Dic3—316no—
355C4×Dic3—316no—
356C4×Dic3—38no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32C22×Q814yes—
360C22×C32C2511yescharacteristic
361C2×C3⋊D3—21no—
362C2×C3⋊D3—21no—
363C2×C3⋊D3C22×Q812yes—
364C32×C4—22no—
365C32×C4—22no—
366C32×C4—24no—
367C32×C4—22no—
368C32×C4—21no—
369C32×C4C22×Q812yes—
370C32×C4C2×#4112yes—
371C3⋊Dic3—21no—
372C3⋊Dic3—24no—
373C3⋊Dic3—22no—
374C3⋊Dic3—22no—
375C3⋊Dic3—21no—
376C3⋊Dic3C22×Q814yes—
377C3⋊Dic3C22×Q812yes—
378C3⋊Dic3C2×#4114yes—
379C2×#41—91no—
380C22×Q8—91no—
381C22×Q8—92no—
382C4⋊Q8—92no—
383C4⋊Q8—94no—
384C4⋊Q8—94no—
385C4⋊Q8—92no—
386C4⋊Q8—92no—
387C4⋊Q8—92no—
388C4⋊Q8—91no—
389C4⋊Q8C2×C3⋊D311yescharacteristic
390#125—94no—
391#125—94no—
392#125—94no—
393#125—92no—
394#125—92no—
395#125C2×C3⋊D312yes—
396C22⋊Q8—92no—
397C22⋊Q8—92no—
398C22⋊Q8—94no—
399C22⋊Q8—94no—
400C22⋊Q8—92no—
401C22⋊Q8—94no—
402C22⋊Q8—94no—
403C22⋊Q8—94no—
404C22⋊Q8—94no—
405C22⋊Q8C2×C3⋊D312yes—
406C22⋊Q8C2×C3⋊D314yes—
407C4×Q8—91no—
408C4×Q8—92no—
409C4×Q8—91no—
410C4×Q8—92no—
411C4×Q8—92no—
412C4×Q8—94no—
413C4×Q8—92no—
414C4×Q8—94no—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—94no—
419C4×Q8—91no—
420C4×Q8—92no—
421C4×Q8—92no—
422C4×Q8—91no—
423C4×Q8C2×C3⋊D311yescharacteristic
424C4×D4—92no—
425C4×D4—91no—
426C4×D4—92no—
427C4×D4—94no—
428C4×D4—94no—
429C4×D4—92no—
430C4×D4C2×C3⋊D311yescharacteristic
431C4×D4C2×C3⋊D312yes—
432#117—92no—
433#117—91no—
434#117—94no—
435#117—92no—
436C2×C4⋊C4—94no—
437C2×C4⋊C4—92no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4C2×C3⋊D312yes—
440C2×C42—94no—
441C2×C42—92no—
442C2×C42—91no—
443C2×C42—92no—
444C23×C3C23×D318yes—
445C22×D3—34no—
446C3×Q8—28no—
447C3×Q8—48no—
448C3×D4D3×Q8116yescomplemented
449C2×C3×C4—216no—
450C2×C3×C4—416no—
451C2×C3×C4C23×D318yes—
452C2×C3×C4C23×D3116yes—
453C2×C3×C4C23×D318yes—
454C2×C3×C4C23×D314yes—
455C2×C3×C4C23×D318yes—
456C2×C3×C4C23×D314yes—
457C2×C3×C4C23×D314yes—
458#67—332no—
459C2×Dic3—332no—
460C2×Dic3—34no—
461C2×Dic3—38no—
462C2×Dic3—38no—
463C2×Dic3—34no—
464C2×Dic3—38no—
465C2×Dic3—38no—
466C2×Dic3—316no—
467C2×Dic3—34no—
468C2×Dic3—632no—
469C2×Dic3—128no—
470C4×D3—316no—
471C4×D3—616no—
472C4×D3—68no—
473C4×D3—128no—
474C4×D3—124no—
475Dic6—316no—
476Dic6—316no—
477Dic6—632no—
478Dic6—616no—
479Dic6—616no—
480Dic6—1216no—
481C2×C32—24no—
482C2×C32C23×Q811yescharacteristic
483C2×C32C22×#4111yescharacteristic
484C2×C32#58511yescharacteristic
485C3⋊D3—22no—
486#41—98no—
487C2×Q8—91no—
488C2×Q8—91no—
489C2×Q8—94no—
490C2×Q8—92no—
491C2×Q8—92no—
492C2×Q8—94no—
493C2×Q8—188no—
494C2×Q8—184no—
495C2×Q8C22×C3⋊D311yescharacteristic
496C2×Q8C22×C3⋊D312yes—
497C2×D4—92no—
498C2×D4C22×C3⋊D311yescharacteristic
499C22×C4—92no—
500C22×C4—91no—
501C22×C4—94no—
502C22×C4—92no—
503C22×C4—92no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—92no—
507C22×C4C22×C3⋊D312yes—
508C22×C4C22×C3⋊D314yes—
509C4⋊C4—92no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4—92no—
513C4⋊C4—92no—
514C4⋊C4—94no—
515C4⋊C4—92no—
516C4⋊C4—91no—
517C4⋊C4—94no—
518C4⋊C4—92no—
519C4⋊C4—92no—
520C4⋊C4—94no—
521C4⋊C4—92no—
522C4⋊C4—91no—
523C4⋊C4—94no—
524C4⋊C4—94no—
525C4⋊C4—94no—
526C4⋊C4—92no—
527C4⋊C4C22×C3⋊D311yescharacteristic
528C4⋊C4C22×C3⋊D312yes—
529C4⋊C4C22×C3⋊D314yes—
530C4⋊C4C22×C3⋊D312yes—
531C4⋊C4C22×C3⋊D312yes—
532C4⋊C4C22×C3⋊D311yescharacteristic
533C4⋊C4C22×C3⋊D314yes—
534C22⋊C4—94no—
535C22⋊C4—92no—
536C22⋊C4—94no—
537C22⋊C4—92no—
538C22⋊C4C22×C3⋊D314yes—
539C22⋊C4C22×C3⋊D312yes—
540C42—92no—
541C42—91no—
542C42—94no—
543C42—92no—
544C42—91no—
545C42—92no—
546C42—92no—
547C42—94no—
548C42—91no—
549C42—94no—
550C42—92no—
551C42—92no—
552C42C22×C3⋊D312yes—
553C42C22×C3⋊D311yescharacteristic
554C22×C3—28no—
555C22×C3—28no—
556C22×C3C2×D3×Q8116yes—
557C22×C3C24×D314yes—
558C2×D3—38no—
559C2×D3—64no—
560C2×D3—64no—
561C3×C4—28no—
562C3×C4—28no—
563C3×C4—216no—
564C3×C4—28no—
565C3×C4—24no—
566C3×C4C2×D3×Q818yes—
567C3×C4D3×#4118yes—
568Dic3—316no—
569Dic3—38no—
570Dic3—316no—
571Dic3—64no—
572Dic3—616no—
573Dic3—68no—
574Dic3—68no—
575Dic3—64no—
576C32Q8×#4111yescharacteristic, complemented, Sylow
577C23—91no—
578C23C23×C3⋊D312yes—
579Q8—22no—
580Q8—42no—
581Q8—94no—
582Q8—94no—
583Q8—188no—
584Q8—184no—
585Q8—184no—
586Q8—364no—
587D4—98no—
588D4Q8×C3⋊D314yescomplemented
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—98no—
592C2×C4—91no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—94no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—94no—
599C2×C4—92no—
600C2×C4—92no—
601C2×C4—184no—
602C2×C4—188no—
603C2×C4—182no—
604C2×C4—362no—
605C2×C4—361no—
606C2×C4—362no—
607C2×C4C23×C3⋊D312yes—
608C2×C4C23×C3⋊D314yes—
609C2×C4C23×C3⋊D312yes—
610C2×C4C23×C3⋊D311yescharacteristic
611C2×C4C23×C3⋊D312yes—
612C2×C4C23×C3⋊D311yescharacteristic
613C2×C4C23×C3⋊D311yescharacteristic
614C2×C3—216no—
615C2×C3C22×D3×Q814yes—
616C2×C3C2×D3×#4114yes—
617C2×C3#596614yes—
618D3—68no—
619C22—22no—
620C22—22no—
621C22—92no—
622C22—181no—
623C22—181no—
624C22C2×Q8×C3⋊D314yes—
625C22C24×C3⋊D311yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—24no—
630C4—21no—
631C4—92no—
632C4—94no—
633C4—94no—
634C4—184no—
635C4—181no—
636C4—181no—
637C4—182no—
638C4—182no—
639C4C2×Q8×C3⋊D312yes—
640C4#41×C3⋊D312yes—
641C3#8692314yescomplemented
642C2—24no—
643C2—182no—
644C2C22×Q8×C3⋊D311yescharacteristic
645C2C2×#41×C3⋊D311yescharacteristic
646C2#1059675811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#554C2
prime radicalC2×#3830C22
hypercenter#554C3⋊D3
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. #10596199C2semidirect
3. #10596193C2semidirect
4. #10596159C2semidirect
5. #10596156C2semidirect
6. #10596107C2semidirect
7. #10596103C2semidirect
8. #10596093C2semidirect
9. #10596093C2semidirect
10. C4×Q8×C3⋊D3C2semidirect
11. #10596038C2semidirect
12. #10596010C2semidirect
13. D4×#634C2semidirect
16. #10595982C2semidirect
17. C2×#64096C2semidirect
84. C3×#554D3semidirect
111. #3830Q8semidirect
239. C32×D4C2×Q8semidirect
249. #638C2×Q8semidirect
252. C2×C3⋊Dic3C2×Q8semidirect
265. C4×C3⋊D3C2×Q8semidirect
270. #634C2×Q8semidirect
271. #634#41semidirect
278. #554C3⋊D3semidirect
448. C3×D4D3×Q8semidirect
576. C32Q8×#41semidirect
588. D4Q8×C3⋊D3semidirect
641. C3#86923semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
#105961992
#105961932
#105961592
#105961562
#105961072
#105961032
#105960932
C4×Q8×C3⋊D32
#105960382
#105960102
D4×#6342
C4×#38302
#105959822
C2×#640962
#869233