Finite Group Databasebeta

← #11906320

Subgroups — #11906320

Order 1152.

3180 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
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3#10596193C211yesmaximal, characteristic, complemented
4#10596160C212yesmaximal, complemented
5#10596156C212yesmaximal, complemented
6#10596106C212yesmaximal, complemented
7#10596103C214yesmaximal, complemented
8#10596094C214yesmaximal, complemented
9#10596093C212yesmaximal, complemented
10#10596049C211yesmaximal, characteristic, complemented
11Q8×#634C211yesmaximal, characteristic, complemented
12#10596017C212yesmaximal
13#10596014C211yesmaximal, characteristic, complemented
14D4×#634C212yesmaximal, complemented
15C4×#3830C211yesmaximal, characteristic
16#10595982C212yesmaximal, complemented
17C2×#64097C212yesmaximal, complemented
18#86926—34nomaximal
19C2×Q8×C3⋊D3C2212yes—
20C2×#3830C2211yescharacteristic
21C22×#634C2214yes—
22C32×C4⋊Q8C2211yescharacteristic
23C32×#125C2212yes—
24C32×C22⋊Q8C2214yes—
25C32×C22⋊Q8C2212yes—
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×C4×D4C2212yes—
29C2×C32×C4⋊C4C2212yes—
30#64155C2211yescharacteristic
31Q8×C3⋊Dic3C2212yes—
32#64153C2214yes—
33#64153C2212yes—
34#64153C2211yescharacteristic
35D4×C3⋊Dic3C2211yescharacteristic
36D4×C3⋊Dic3C2212yes—
37C4×#638C2214yes—
38C4×#638C2212yes—
39C2×C4⋊(C3⋊Dic3)C2212yes—
40#64133C2214yes—
41#64133C2212yes—
42C2×#3750C2214yes—
43C2×C4×C3⋊Dic3C2212yes—
44#64106C2214yes—
45#64106C2211yescharacteristic
46#64105C2212yes—
47#64105C2214yes—
48#64101C2211yescharacteristic
49C4⋊C4×C3⋊D3C2212yes—
50C4⋊C4×C3⋊D3C2212yes—
51#64099C2212yes—
52#64098C2214yes—
53#64098C2214yes—
54#64098C2214yes—
55#64098C2212yes—
56#64097C2214yes—
57#64097C2214yes—
58#64097C2212yes—
59#64097C2212yes—
60#64097C2212yes—
61#64097C2214yes—
62#64097C2212yes—
63#64097C2211yescharacteristic
64#64097C2212yes—
65#64096C2214yes—
66#64096C2211yescharacteristic
67#64096C2212yes—
68#64096C2212yes—
69#64090C2212yes—
70#64090C2214yes—
71#64087C2214yes—
72#64087C2214yes—
73#64087C2214yes—
74#64086C2212yes—
75#64086C2214yes—
76#64081C2212yes—
77C42×C3⋊D3C2211yescharacteristic
78#64078C2212yes—
79#64078C2211yescharacteristic
80C4×#634C2212yes—
81C4×#634C2212yes—
82C4×#634C2211yescharacteristic
83C4×#634C2211yescharacteristic
84C3×#554D314yescomplemented
85D3×C4⋊Q8—34no—
86#5722—34no—
87#5689—38no—
88#5685—38no—
89#5635—38no—
90#5632—316no—
91#5623—316no—
92#5622—38no—
93#5578—34no—
94Q8×Dic6—34no—
95#5546—38no—
96#5543—34no—
97D4×Dic6—38no—
98C4×#237—34no—
99#5511—38no—
100C2×#888—38no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2312yes—
105C22×C32×C4C2314yes—
106C2×#638C2312yes—
107C22×C3⋊Dic3C2312yes—
108C22×C3⋊Dic3C2314yes—
109C22×C3⋊Dic3C2312yes—
110Q8×C3⋊D3—44no—
111#3830Q818yescomplemented
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×#634—48no—
117C2×#634C2311yescharacteristic
118C2×#634C2312yes—
119C2×#634C2314yes—
120C2×#634C2312yes—
121C2×#634C2314yes—
122C2×#634C2314yes—
123C2×#634C2311yescharacteristic
124C32×C4⋊C4C2312yes—
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C4⋊C4C2314yes—
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)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2312yes—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2314yes—
145C4⋊(C3⋊Dic3)C2312yes—
146C4⋊(C3⋊Dic3)C2314yes—
147#3750C2312yes—
148#3750C2312yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2314yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2314yes—
156#3750C2314yes—
157#3750C2314yes—
158#3750C2314yes—
159#3750C2314yes—
160C4×C3⋊Dic3C2311yescharacteristic
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2314yes—
163C4×C3⋊Dic3C2312yes—
164C4×C3⋊Dic3C2311yescharacteristic
165C4×C3⋊Dic3C2311yescharacteristic
166C4×C3⋊Dic3C2314yes—
167C4×C3⋊Dic3C2312yes—
168C4×C3⋊Dic3C2312yes—
169#3503—91noSylow
170C2×D3×Q8—38no—
171C2×#237—34no—
172C22×Dic6—316no—
173C3×C4⋊Q8C2×D314yes—
174C3×#125C2×D318yes—
175C3×C22⋊Q8C2×D3116yes—
176C3×C22⋊Q8C2×D318yes—
177C3×C4×Q8C2×D314yes—
178C3×C4×D4C2×D314yes—
179C3×C4×D4C2×D318yes—
180C2×C3×C4⋊C4C2×D318yes—
181#946—34no—
182Q8×Dic3—38no—
183#944—316no—
184#944—38no—
185#944—34no—
186D4×Dic3—34no—
187D4×Dic3—38no—
188C4×#67—316no—
189C4×#67—38no—
190C2×C4⋊Dic3—38no—
191#924—316no—
192#924—38no—
193C2×Dic3⋊C4—316no—
194C2×C4×Dic3—38no—
195#897—316no—
196#897—34no—
197#896—38no—
198#896—316no—
199#892—34no—
200D3×C4⋊C4—38no—
201D3×C4⋊C4—38no—
202#890—38no—
203#889—316no—
204#889—316no—
205#889—316no—
206#889—38no—
207#888—316no—
208#888—316no—
209#888—38no—
210#888—38no—
211#888—38no—
212#888—316no—
213#888—38no—
214#888—34no—
215#888—38no—
216#887—316no—
217#887—34no—
218#887—38no—
219#887—38no—
220#67⋊C4—38no—
221#67⋊C4—316no—
222#878—316no—
223#878—316no—
224#878—316no—
225#877—38no—
226#877—316no—
227#872—38no—
228C42×D3—34no—
229#869—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×C4C2412yes—
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2414yes—
246C2×C32×C4C2412yes—
247C2×C32×C4C2411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638C2×Q818yescomplemented
250C2×C3⋊Dic3—24no—
251C2×C3⋊Dic3—44no—
252C2×C3⋊Dic3C2×Q818yescomplemented
253C2×C3⋊Dic3C2412yes—
254C2×C3⋊Dic3C2411yescharacteristic
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2412yes—
257C2×C3⋊Dic3C2414yes—
258C2×C3⋊Dic3C2412yes—
259C2×C3⋊Dic3C2411yescharacteristic
260C2×C3⋊Dic3C2411yescharacteristic
261C4×C3⋊D3—22no—
262C4×C3⋊D3—22no—
263C4×C3⋊D3—44no—
264C4×C3⋊D3C2×Q814yescomplemented
265#634—22no—
266#634—24no—
267#634—28no—
268#634—44no—
269#634—44no—
270#634—42no—
271#634C2×Q814yescomplemented
272Q82—91no—
273Q82—91no—
274#557—92no—
275#554—92no—
276#554—91no—
277#554—92no—
278#554C3⋊D311yescharacteristic, complemented
279D4×Q8—94no—
280D4×Q8—92no—
281#544—92no—
282#544—94no—
283#533—92no—
284#533—91no—
285C2×C4⋊Q8—91no—
286C2×C4⋊Q8—92no—
287#520—92no—
288C4×#41—91no—
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—38no—
297C22×Dic3—316no—
298D3×Q8—1216no—
299#237—332no—
300C2×C4×D3—34no—
301C2×C4×D3—34no—
302C2×C4×D3—34no—
303C2×C4×D3—316no—
304C2×Dic6—34no—
305C2×Dic6—34no—
306C2×Dic6—38no—
307C2×Dic6—316no—
308C2×Dic6—38no—
309C2×Dic6—316no—
310C2×Dic6—316no—
311C2×Dic6—1232no—
312C3×C4⋊C4C22×D318yes—
313C3×C4⋊C4C22×D318yes—
314C3×C4⋊C4C22×D3116yes—
315C3×C4⋊C4C22×D314yes—
316C3×C4⋊C4C22×D314yes—
317C3×C4⋊C4C22×D3116yes—
318C3×C4⋊C4C22×D318yes—
319C3×C22⋊C4C22×D3116yes—
320C3×C22⋊C4C22×D318yes—
321C3×C42C22×D314yes—
322C3×C42C22×D318yes—
323#217—316no—
324#217—38no—
325(C2×D3)⋊C4—38no—
326(C2×D3)⋊C4—38no—
327(C2×D3)⋊C4—38no—
328C4⋊Dic3—34no—
329C4⋊Dic3—38no—
330C4⋊Dic3—34no—
331C4⋊Dic3—38no—
332C4⋊Dic3—316no—
333C4⋊Dic3—38no—
334C4⋊Dic3—316no—
335Dic3⋊C4—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4—38no—
338Dic3⋊C4—38no—
339Dic3⋊C4—316no—
340Dic3⋊C4—38no—
341Dic3⋊C4—38no—
342Dic3⋊C4—38no—
343Dic3⋊C4—316no—
344Dic3⋊C4—316no—
345Dic3⋊C4—316no—
346Dic3⋊C4—316no—
347Dic3⋊C4—316no—
348C4×Dic3—34no—
349C4×Dic3—38no—
350C4×Dic3—316no—
351C4×Dic3—38no—
352C4×Dic3—34no—
353C4×Dic3—34no—
354C4×Dic3—316no—
355C4×Dic3—38no—
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—24no—
366C32×C4—21no—
367C32×C4—22no—
368C32×C4—22no—
369C32×C4C22×Q812yes—
370C32×C42−1+412yes—
371C3⋊Dic3—24no—
372C3⋊Dic3—22no—
373C3⋊Dic3—22no—
374C3⋊Dic3—22no—
375C3⋊Dic3—21no—
376C3⋊Dic3C22×Q814yes—
377C3⋊Dic3C22×Q812yes—
378C3⋊Dic3H(5,𝔽2)12yes—
379C2×#41—91no—
380C22×Q8—92no—
381C22×Q8—94no—
382C4⋊Q8—92no—
383C4⋊Q8—91no—
384C4⋊Q8—94no—
385C4⋊Q8—92no—
386C4⋊Q8—91no—
387C4⋊Q8—94no—
388C4⋊Q8—94no—
389C4⋊Q8—92no—
390C4⋊Q8—92no—
391C4⋊Q8—92no—
392C4⋊Q8—94no—
393C4⋊Q8—92no—
394C4⋊Q8—91no—
395C4⋊Q8—92no—
396C4⋊Q8C2×C3⋊D311yescharacteristic
397#125—92no—
398#125—94no—
399#125—94no—
400#125—94no—
401#125—92no—
402#125C2×C3⋊D312yes—
403C22⋊Q8—91no—
404C22⋊Q8—92no—
405C22⋊Q8—94no—
406C22⋊Q8—92no—
407C22⋊Q8—91no—
408C22⋊Q8—94no—
409C22⋊Q8—94no—
410C22⋊Q8—94no—
411C22⋊Q8—94no—
412C22⋊Q8—94no—
413C22⋊Q8C2×C3⋊D312yes—
414C22⋊Q8C2×C3⋊D314yes—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—94no—
419C4×Q8—92no—
420C4×Q8—91no—
421C4×Q8—92no—
422C4×Q8—92no—
423C4×Q8—91no—
424C4×Q8C2×C3⋊D311yescharacteristic
425C4×D4—91no—
426C4×D4—92no—
427C4×D4—92no—
428C4×D4—94no—
429C4×D4—92no—
430C4×D4—94no—
431C4×D4C2×C3⋊D311yescharacteristic
432C4×D4C2×C3⋊D312yes—
433#117—91no—
434#117—92no—
435#117—94no—
436#117—92no—
437C2×C4⋊C4—94no—
438C2×C4⋊C4—92no—
439C2×C4⋊C4—92no—
440C2×C4⋊C4—92no—
441C2×C4⋊C4C2×C3⋊D312yes—
442C2×C42—92no—
443C2×C42—91no—
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×D318yes—
453C2×C3×C4C23×D314yes—
454C2×C3×C4C23×D3116yes—
455C2×C3×C4C23×D318yes—
456C2×C3×C4C23×D314yes—
457C2×C3×C4C23×D314yes—
458#67—332no—
459C2×Dic3—332no—
460C2×Dic3—38no—
461C2×Dic3—34no—
462C2×Dic3—34no—
463C2×Dic3—38no—
464C2×Dic3—34no—
465C2×Dic3—38no—
466C2×Dic3—38no—
467C2×Dic3—316no—
468C2×Dic3—616no—
469C2×Dic3—1216no—
470C4×D3—316no—
471C4×D3—68no—
472C4×D3—68no—
473C4×D3—1216no—
474Dic6—316no—
475Dic6—616no—
476Dic6—632no—
477Dic6—68no—
478Dic6—1216no—
479Dic6—1216no—
480Dic6—128no—
481C2×C32—24no—
482C2×C32C23×Q811yescharacteristic
483C2×C32C2×H(5,𝔽2)11yescharacteristic
484C2×C32C2×2−1+411yescharacteristic
485C3⋊D3—22no—
486#41—98no—
487C2×Q8—91no—
488C2×Q8—91no—
489C2×Q8—94no—
490C2×Q8—92no—
491C2×Q8—94no—
492C2×Q8—94no—
493C2×Q8—92no—
494C2×Q8—368no—
495C2×Q8—364no—
496C2×Q8C22×C3⋊D311yescharacteristic
497C2×Q8C22×C3⋊D312yes—
498C2×D4—92no—
499C2×D4C22×C3⋊D311yescharacteristic
500C22×C4—92no—
501C22×C4—91no—
502C22×C4—92no—
503C22×C4—94no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—94no—
507C22×C4C22×C3⋊D312yes—
508C22×C4C22×C3⋊D314yes—
509C4⋊C4—94no—
510C4⋊C4—92no—
511C4⋊C4—91no—
512C4⋊C4—92no—
513C4⋊C4—94no—
514C4⋊C4—94no—
515C4⋊C4—92no—
516C4⋊C4—94no—
517C4⋊C4—94no—
518C4⋊C4—92no—
519C4⋊C4—92no—
520C4⋊C4—92no—
521C4⋊C4—91no—
522C4⋊C4—92no—
523C4⋊C4—94no—
524C4⋊C4—92no—
525C4⋊C4—92no—
526C4⋊C4—94no—
527C4⋊C4—92no—
528C4⋊C4—94no—
529C4⋊C4C22×C3⋊D312yes—
530C4⋊C4C22×C3⋊D312yes—
531C4⋊C4C22×C3⋊D311yescharacteristic
532C4⋊C4C22×C3⋊D314yes—
533C4⋊C4C22×C3⋊D311yescharacteristic
534C4⋊C4C22×C3⋊D314yes—
535C4⋊C4C22×C3⋊D312yes—
536C22⋊C4—94no—
537C22⋊C4—92no—
538C22⋊C4—92no—
539C22⋊C4—92no—
540C22⋊C4—92no—
541C22⋊C4C22×C3⋊D314yes—
542C22⋊C4C22×C3⋊D312yes—
543C42—91no—
544C42—91no—
545C42—92no—
546C42—92no—
547C42—92no—
548C42—91no—
549C42—94no—
550C42—94no—
551C42—92no—
552C42C22×C3⋊D311yescharacteristic
553C42C22×C3⋊D312yes—
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—28no—
564C3×C4—216no—
565C3×C4—24no—
566C3×C4C2×D3×Q818yes—
567C3×C4#101018yes—
568Dic3—316no—
569Dic3—38no—
570Dic3—38no—
571Dic3—68no—
572Dic3—64no—
573Dic3—616no—
574Dic3—68no—
575Dic3—68no—
576C32#350311yescharacteristic, complemented, Sylow
577C23—91no—
578C23C23×C3⋊D312yes—
579Q8—22no—
580Q8—42no—
581Q8—94no—
582Q8—184no—
583Q8—188no—
584Q8—182no—
585Q8—364no—
586Q8—364no—
587Q8—362no—
588D4—98no—
589D4Q8×C3⋊D314yescomplemented
590C2×C4—24no—
591C2×C4—44no—
592C2×C4—98no—
593C2×C4—92no—
594C2×C4—91no—
595C2×C4—91no—
596C2×C4—94no—
597C2×C4—92no—
598C2×C4—91no—
599C2×C4—92no—
600C2×C4—94no—
601C2×C4—92no—
602C2×C4—182no—
603C2×C4—184no—
604C2×C4—182no—
605C2×C4—364no—
606C2×C4—364no—
607C2×C4C23×C3⋊D312yes—
608C2×C4C23×C3⋊D312yes—
609C2×C4C23×C3⋊D311yescharacteristic
610C2×C4C23×C3⋊D314yes—
611C2×C4C23×C3⋊D312yes—
612C2×C4C23×C3⋊D311yescharacteristic
613C2×C4C23×C3⋊D311yescharacteristic
614C2×C3—216no—
615C2×C3C22×D3×Q814yes—
616C2×C3C2×#101014yes—
617C2×C3D3×H(5,𝔽2)14yes—
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—92no—
634C4—181no—
635C4—182no—
636C4—182no—
637C4—184no—
638C4—182no—
639C4C2×Q8×C3⋊D312yes—
640C4#6436712yes—
641C3#8692614yescomplemented
642C2—24no—
643C2—182no—
644C2C22×Q8×C3⋊D311yescharacteristic
645C2C2×#6436711yescharacteristic
646C2C3⋊D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#554C2
prime radicalC2×#3830C22
hypercenter#554C3⋊D3
hypocenterC32#3503
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. C3⋊D3×C4⋊Q8C2semidirect
3. #10596193C2semidirect
4. #10596160C2semidirect
5. #10596156C2semidirect
6. #10596106C2semidirect
7. #10596103C2semidirect
8. #10596094C2semidirect
9. #10596093C2semidirect
10. #10596049C2semidirect
11. Q8×#634C2semidirect
13. #10596014C2semidirect
14. D4×#634C2semidirect
16. #10595982C2semidirect
17. C2×#64097C2semidirect
84. C3×#554D3semidirect
111. #3830Q8semidirect
239. C32×D4C2×Q8semidirect
249. #638C2×Q8semidirect
252. C2×C3⋊Dic3C2×Q8semidirect
264. C4×C3⋊D3C2×Q8semidirect
271. #634C2×Q8semidirect
278. #554C3⋊D3semidirect
448. C3×D4D3×Q8semidirect
576. C32#3503semidirect
589. D4Q8×C3⋊D3semidirect
641. C3#86926semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
C3⋊D3×C4⋊Q82
#105961932
#105961602
#105961562
#105961062
#105961032
#105960942
#105960932
#105960492
Q8×#6342
#105960172
#105960142
D4×#6342
C4×#38302
#105959822
C2×#640972
#869263