Finite Group Databasebeta

← #11906323

Subgroups — #11906323

Order 1152.

3180 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#544C211yesmaximal, characteristic, complemented
2#10596200C212yesmaximal, complemented
3#10596198C212yesmaximal, complemented
4C3⋊D3×C4⋊Q8C212yesmaximal, complemented
5#10596193C212yesmaximal, complemented
6#10596161C212yesmaximal, complemented
7#10596160C212yesmaximal, complemented
8#10596159C212yesmaximal, complemented
9#10596156C212yesmaximal, complemented
10#10596107C214yesmaximal, complemented
11#10596103C214yesmaximal, complemented
12#10595994C211yesmaximal, characteristic
13#10595993C211yesmaximal, characteristic
14#10595990C211yesmaximal, characteristic, complemented
15#10595988C211yesmaximal, characteristic, complemented
16#10595975C211yesmaximal, characteristic
17C2×#64097C211yesmaximal, characteristic, complemented
18#86586—34nomaximal
19C2×Q8×C3⋊D3C2214yes—
20C2×#3828C2211yescharacteristic
21C22×#634C2212yes—
22C32×C4⋊Q8C2212yes—
23C32×C4⋊Q8C2212yes—
24C32×#125C2212yes—
25C32×#125C2212yes—
26C32×C22⋊Q8C2214yes—
27C32×#117C2211yescharacteristic
28C32×#117C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30#64155C2214yes—
31#64153C2214yes—
32#64153C2214yes—
33C4×#638C2214yes—
34#64135C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×#3750C2212yes—
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64106C2214yes—
39#64105C2214yes—
40#64105C2214yes—
41#64105C2214yes—
42#64105C2214yes—
43#64102C2211yescharacteristic
44#64102C2212yes—
45#64102C2211yescharacteristic
46#64101C2212yes—
47#64101C2212yes—
48C4⋊C4×C3⋊D3C2214yes—
49C4⋊C4×C3⋊D3C2212yes—
50C4⋊C4×C3⋊D3C2212yes—
51#64099C2212yes—
52#64099C2211yescharacteristic
53#64099C2211yescharacteristic
54#64098C2214yes—
55#64098C2214yes—
56#64097C2214yes—
57#64097C2214yes—
58#64097C2212yes—
59#64097C2211yescharacteristic
60#64097C2212yes—
61#64097C2212yes—
62#64097C2212yes—
63#64097C2212yes—
64#64097C2211yescharacteristic
65#64096C2214yes—
66#64096C2214yes—
67#64096C2211yescharacteristic
68#64096C2212yes—
69#64096C2211yescharacteristic
70#64090C2212yes—
71#64090C2214yes—
72#64090C2212yes—
73#64087C2212yes—
74#64087C2214yes—
75#64087C2212yes—
76C4×C4⋊(C3⋊D3)C2212yes—
77#64081C2212yes—
78C42×C3⋊D3C2212yes—
79#64079C2212yes—
80#64078C2212yes—
81C4×#634C2212yes—
82C4×#634C2212yes—
83C4×#634C2212yes—
84C3×#544D314yescomplemented
85#5729—38no—
86#5727—38no—
87D3×C4⋊Q8—38no—
88#5722—38no—
89#5690—38no—
90#5689—38no—
91#5688—38no—
92#5685—38no—
93#5636—316no—
94#5632—316no—
95#5523—34no—
96#5522—34no—
97#5519—34no—
98#5517—34no—
99#5504—34no—
100C2×#888—34no—
101C2×C32×Q8C2314yes—
102C22×C32×C4C2312yes—
103C22×C32×C4C2311yescharacteristic
104C2×#638C2312yes—
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2312yes—
108Q8×C3⋊D3—48no—
109#3828Q818yescomplemented
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2314yes—
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2312yes—
116C2×#634—44no—
117C2×#634C2312yes—
118C2×#634C2312yes—
119C2×#634C2314yes—
120C2×#634C2314yes—
121C2×#634C2314yes—
122C2×#634C2311yescharacteristic
123C32×C4⋊C4C2312yes—
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2314yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2312yes—
129C32×C4⋊C4C2314yes—
130C32×C4⋊C4C2311yescharacteristic
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135C32×C42C2312yes—
136#3757C2312yes—
137#3752C2312yes—
138#3752C2312yes—
139#3752C2314yes—
140#3752C2314yes—
141C4⋊(C3⋊Dic3)C2312yes—
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145C4⋊(C3⋊Dic3)C2312yes—
146C4⋊(C3⋊Dic3)C2314yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750C2312yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2312yes—
152#3750C2314yes—
153#3750C2314yes—
154#3750C2314yes—
155#3750C2312yes—
156#3750C2312yes—
157#3750C2314yes—
158#3750C2314yes—
159#3750C2314yes—
160C4×C3⋊Dic3C2311yescharacteristic
161C4×C3⋊Dic3C2311yescharacteristic
162C4×C3⋊Dic3C2312yes—
163C4×C3⋊Dic3C2314yes—
164C4×C3⋊Dic3C2311yescharacteristic
165C4×C3⋊Dic3C2312yes—
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2311yescharacteristic
168C4×C3⋊Dic3C2314yes—
169#3503—91noSylow
170C2×D3×Q8—316no—
171C2×#235—34no—
172C22×Dic6—38no—
173C3×C4⋊Q8C2×D318yes—
174C3×C4⋊Q8C2×D318yes—
175C3×#125C2×D318yes—
176C3×#125C2×D318yes—
177C3×C22⋊Q8C2×D3116yes—
178C3×#117C2×D314yes—
179C3×#117C2×D314yes—
180C2×C3×C4⋊C4C2×D314yes—
181#946—316no—
182#944—316no—
183#944—316no—
184C4×#67—316no—
185#926—34no—
186C2×C4⋊Dic3—34no—
187C2×Dic3⋊C4—38no—
188C2×C4×Dic3—34no—
189#897—316no—
190#896—316no—
191#896—316no—
192#896—316no—
193#896—316no—
194#893—34no—
195#893—38no—
196#893—34no—
197#892—38no—
198#892—38no—
199D3×C4⋊C4—316no—
200D3×C4⋊C4—38no—
201D3×C4⋊C4—38no—
202#890—38no—
203#890—34no—
204#890—34no—
205#889—316no—
206#889—316no—
207#888—316no—
208#888—316no—
209#888—38no—
210#888—34no—
211#888—38no—
212#888—38no—
213#888—38no—
214#888—38no—
215#888—34no—
216#887—316no—
217#887—316no—
218#887—34no—
219#887—38no—
220#887—34no—
221#67⋊C4—38no—
222#67⋊C4—316no—
223#67⋊C4—38no—
224#878—38no—
225#878—316no—
226#878—38no—
227C4×D12—38no—
228#872—38no—
229C42×D3—38no—
230#870—38no—
231#869—38no—
232C4×Dic6—38no—
233C4×Dic6—38no—
234C4×Dic6—38no—
235C23×C32C2411yescharacteristic
236C22×C3⋊D3C2412yes—
237C32×Q8—44no—
238C2×C32×C4—42no—
239C2×C32×C4C2×Q814yescomplemented
240C2×C32×C4C2412yes—
241C2×C32×C4C2412yes—
242C2×C32×C4C2412yes—
243C2×C32×C4C2414yes—
244C2×C32×C4C2412yes—
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638C2×Q818yescomplemented
248C2×C3⋊Dic3—22no—
249C2×C3⋊Dic3—22no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2412yes—
252C2×C3⋊Dic3C2411yescharacteristic
253C2×C3⋊Dic3C2411yescharacteristic
254C2×C3⋊Dic3C2414yes—
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2412yes—
257C2×C3⋊Dic3C2411yescharacteristic
258C2×C3⋊Dic3C2411yescharacteristic
259C4⋊(C3⋊D3)C2×Q814yescomplemented
260C4×C3⋊D3—24no—
261C4×C3⋊D3—24no—
262C4×C3⋊D3—44no—
263C4×C3⋊D3—44no—
264C4×C3⋊D3C2×Q818yescomplemented
265#634—28no—
266#634—24no—
267#634—24no—
268#634—44no—
269#634—44no—
270#634C2×Q814yescomplemented
271Q82—92no—
272#557—92no—
273#554—92no—
274#554—94no—
275D4×Q8—92no—
276D4×Q8—94no—
277#544—92no—
278#544—92no—
279#544—91no—
280#544C3⋊D311yescharacteristic, complemented
281#533—92no—
282#533—91no—
283C2×C4⋊Q8—92no—
284C2×C4⋊Q8—91no—
285#520—91no—
286#520—91no—
287C4×#41—91no—
288C2×C3×Q8C22×D3116yes—
289C22×C3×C4C22×D318yes—
290C22×C3×C4C22×D314yes—
291C2×#67—38no—
292C22×Dic3—34no—
293C22×Dic3—34no—
294C22×Dic3—38no—
295D3×Q8—1232no—
296#235—332no—
297C2×D12—34no—
298C2×C4×D3—38no—
299C2×C4×D3—38no—
300C2×C4×D3—38no—
301C2×C4×D3—316no—
302C2×C4×D3—316no—
303C2×Dic6—34no—
304C2×Dic6—38no—
305C2×Dic6—38no—
306C2×Dic6—316no—
307C2×Dic6—316no—
308C2×Dic6—316no—
309C2×Dic6—1216no—
310C3×C4⋊C4C22×D318yes—
311C3×C4⋊C4C22×D314yes—
312C3×C4⋊C4C22×D3116yes—
313C3×C4⋊C4C22×D3116yes—
314C3×C4⋊C4C22×D314yes—
315C3×C4⋊C4C22×D318yes—
316C3×C4⋊C4C22×D3116yes—
317C3×C4⋊C4C22×D314yes—
318C3×C4⋊C4C22×D314yes—
319C3×C22⋊C4C22×D318yes—
320C3×C22⋊C4C22×D318yes—
321C3×C42C22×D318yes—
322C3×C42C22×D318yes—
323#217—38no—
324(C2×D3)⋊C4—38no—
325(C2×D3)⋊C4—38no—
326(C2×D3)⋊C4—316no—
327(C2×D3)⋊C4—316no—
328C4⋊Dic3—38no—
329C4⋊Dic3—38no—
330C4⋊Dic3—38no—
331C4⋊Dic3—34no—
332C4⋊Dic3—38no—
333C4⋊Dic3—316no—
334C4⋊Dic3—34no—
335Dic3⋊C4—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4—38no—
338Dic3⋊C4—38no—
339Dic3⋊C4—316no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342Dic3⋊C4—38no—
343Dic3⋊C4—38no—
344Dic3⋊C4—316no—
345Dic3⋊C4—316no—
346Dic3⋊C4—316no—
347C4×Dic3—34no—
348C4×Dic3—34no—
349C4×Dic3—38no—
350C4×Dic3—316no—
351C4×Dic3—34no—
352C4×Dic3—38no—
353C4×Dic3—38no—
354C4×Dic3—34no—
355C4×Dic3—316no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32C22×Q812yes—
359C22×C32C2511yescharacteristic
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3C22×Q814yes—
363C32×C4—24no—
364C32×C4—22no—
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—22no—
368C32×C4C22×Q812yes—
369C32×C4C22×Q812yes—
370C3⋊Dic3—22no—
371C3⋊Dic3—24no—
372C3⋊Dic3—21no—
373C3⋊Dic3—22no—
374C3⋊Dic3—21no—
375C3⋊Dic3C22×Q814yes—
376C3⋊Dic3H(5,𝔽2)12yes—
377C3⋊Dic32−1+412yes—
378C2×#41—91no—
379C22×Q8—94no—
380C22×Q8—92no—
381C4⋊Q8—94no—
382C4⋊Q8—94no—
383C4⋊Q8—91no—
384C4⋊Q8—92no—
385C4⋊Q8—92no—
386C4⋊Q8—94no—
387C4⋊Q8—92no—
388C4⋊Q8—92no—
389C4⋊Q8—91no—
390C4⋊Q8—94no—
391C4⋊Q8—92no—
392C4⋊Q8—92no—
393C4⋊Q8C2×C3⋊D312yes—
394C4⋊Q8C2×C3⋊D312yes—
395#125—91no—
396#125—91no—
397#125—94no—
398#125—94no—
399#125—92no—
400#125—92no—
401#125C2×C3⋊D312yes—
402#125C2×C3⋊D312yes—
403C22⋊Q8—94no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8—94no—
407C22⋊Q8—94no—
408C22⋊Q8—94no—
409C22⋊Q8—92no—
410C22⋊Q8—92no—
411C22⋊Q8—94no—
412C22⋊Q8C2×C3⋊D314yes—
413C4×Q8—91no—
414C4×Q8—91no—
415C4×Q8—92no—
416C4×Q8—94no—
417C4×Q8—94no—
418C4×Q8—92no—
419C4×Q8—92no—
420C4×Q8—92no—
421C4×D4—94no—
422C4×D4—91no—
423C4×D4—91no—
424C4×D4—92no—
425C4×D4—92no—
426C4×D4—92no—
427C4×D4—94no—
428C4×D4—92no—
429#117—91no—
430#117—92no—
431#117—92no—
432#117—92no—
433#117C2×C3⋊D311yescharacteristic
434#117C2×C3⋊D311yescharacteristic
435C2×C4⋊C4—91no—
436C2×C4⋊C4—92no—
437C2×C4⋊C4—92no—
438C2×C4⋊C4—92no—
439C2×C4⋊C4—94no—
440C2×C4⋊C4C2×C3⋊D311yescharacteristic
441C2×C42—91no—
442C2×C42—92no—
443C23×C3C23×D314yes—
444C22×D3—38no—
445C3×Q8—416no—
446C2×C3×C4—48no—
447C2×C3×C4D3×Q8116yescomplemented
448C2×C3×C4C23×D318yes—
449C2×C3×C4C23×D318yes—
450C2×C3×C4C23×D318yes—
451C2×C3×C4C23×D3116yes—
452C2×C3×C4C23×D318yes—
453C2×C3×C4C23×D314yes—
454C2×C3×C4C23×D314yes—
455#67—332no—
456C2×Dic3—38no—
457C2×Dic3—34no—
458C2×Dic3—34no—
459C2×Dic3—38no—
460C2×Dic3—34no—
461C2×Dic3—34no—
462C2×Dic3—316no—
463C2×Dic3—38no—
464C2×Dic3—68no—
465C2×Dic3—68no—
466C2×Dic3—128no—
467D12—316no—
468C4×D3—332no—
469C4×D3—616no—
470C4×D3—616no—
471C4×D3—1216no—
472C4×D3—1216no—
473Dic6—316no—
474Dic6—616no—
475Dic6—632no—
476Dic6—616no—
477Dic6—1216no—
478Dic6—1216no—
479C2×C32—22no—
480C2×C32C23×Q811yescharacteristic
481C2×C32C2×H(5,𝔽2)11yescharacteristic
482C2×C32C2×2−1+411yescharacteristic
483C3⋊D3—24no—
484#41—98no—
485C2×Q8—91no—
486C2×Q8—92no—
487C2×Q8—94no—
488C2×Q8—92no—
489C2×Q8—94no—
490C2×Q8—94no—
491C2×Q8—364no—
492C2×Q8—368no—
493C2×Q8C22×C3⋊D314yes—
494C2×D4—92no—
495C2×D4—91no—
496C22×C4—92no—
497C22×C4—91no—
498C22×C4—91no—
499C22×C4—92no—
500C22×C4—92no—
501C22×C4—92no—
502C22×C4—94no—
503C22×C4—94no—
504C22×C4C22×C3⋊D312yes—
505C22×C4C22×C3⋊D311yescharacteristic
506C4⋊C4—92no—
507C4⋊C4—91no—
508C4⋊C4—94no—
509C4⋊C4—92no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4—92no—
513C4⋊C4—94no—
514C4⋊C4—94no—
515C4⋊C4—91no—
516C4⋊C4—92no—
517C4⋊C4—92no—
518C4⋊C4—92no—
519C4⋊C4—94no—
520C4⋊C4—92no—
521C4⋊C4—92no—
522C4⋊C4—92no—
523C4⋊C4—94no—
524C4⋊C4—92no—
525C4⋊C4C22×C3⋊D311yescharacteristic
526C4⋊C4C22×C3⋊D312yes—
527C4⋊C4C22×C3⋊D314yes—
528C4⋊C4C22×C3⋊D312yes—
529C4⋊C4C22×C3⋊D311yescharacteristic
530C4⋊C4C22×C3⋊D311yescharacteristic
531C4⋊C4C22×C3⋊D311yescharacteristic
532C4⋊C4C22×C3⋊D314yes—
533C4⋊C4C22×C3⋊D314yes—
534C22⋊C4—92no—
535C22⋊C4—94no—
536C22⋊C4—92no—
537C22⋊C4—92no—
538C22⋊C4—94no—
539C22⋊C4C22×C3⋊D312yes—
540C22⋊C4C22×C3⋊D312yes—
541C42—91no—
542C42—91no—
543C42—92no—
544C42—92no—
545C42—91no—
546C42—91no—
547C42—94no—
548C42—94no—
549C42—92no—
550C42C22×C3⋊D312yes—
551C42C22×C3⋊D312yes—
552C22×C3—24no—
553C22×C3—24no—
554C22×C3C2×D3×Q818yes—
555C22×C3C24×D314yes—
556C2×D3—316no—
557C2×D3—68no—
558C2×D3—68no—
559C3×C4—216no—
560C3×C4—28no—
561C3×C4—28no—
562C3×C4—28no—
563C3×C4—28no—
564C3×C4C2×D3×Q818yes—
565C3×C4C2×D3×Q818yes—
566Dic3—316no—
567Dic3—38no—
568Dic3—38no—
569Dic3—68no—
570Dic3—616no—
571Dic3—64no—
572Dic3—68no—
573Dic3—64no—
574C32#350311yescharacteristic, complemented, Sylow
575C23—92no—
576C23C23×C3⋊D311yescharacteristic
577Q8—44no—
578Q8—94no—
579Q8—188no—
580Q8—184no—
581Q8—184no—
582Q8—364no—
583Q8—364no—
584D4—98no—
585D4—94no—
586C2×C4—42no—
587C2×C4—92no—
588C2×C4—91no—
589C2×C4—91no—
590C2×C4—98no—
591C2×C4—92no—
592C2×C4—91no—
593C2×C4—91no—
594C2×C4—92no—
595C2×C4—94no—
596C2×C4—184no—
597C2×C4—184no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—364no—
601C2×C4—364no—
602C2×C4—362no—
603C2×C4Q8×C3⋊D314yescomplemented
604C2×C4C23×C3⋊D312yes—
605C2×C4C23×C3⋊D312yes—
606C2×C4C23×C3⋊D312yes—
607C2×C4C23×C3⋊D314yes—
608C2×C4C23×C3⋊D312yes—
609C2×C4C23×C3⋊D311yescharacteristic
610C2×C4C23×C3⋊D311yescharacteristic
611C2×C3—28no—
612C2×C3C22×D3×Q814yes—
613C2×C3D3×H(5,𝔽2)14yes—
614C2×C3D3×2−1+414yes—
615D3—616no—
616C22—21no—
617C22—21no—
618C22—94no—
619C22—182no—
620C22—182no—
621C22C2×Q8×C3⋊D312yes—
622C22C24×C3⋊D311yescharacteristic
623C4—24no—
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—94no—
629C4—92no—
630C4—92no—
631C4—181no—
632C4—182no—
633C4—184no—
634C4—181no—
635C4—182no—
636C4C2×Q8×C3⋊D312yes—
637C4C2×Q8×C3⋊D312yes—
638C3#8658614yescomplemented
639C2—22no—
640C2—184no—
641C2C22×Q8×C3⋊D311yescharacteristic
642C2C3⋊D3×H(5,𝔽2)11yescharacteristic
643C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#544C2
prime radicalC2×#3828C22
hypercenter#544C3⋊D3
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C32×#544C2semidirect
2. #10596200C2semidirect
3. #10596198C2semidirect
4. C3⋊D3×C4⋊Q8C2semidirect
5. #10596193C2semidirect
6. #10596161C2semidirect
7. #10596160C2semidirect
8. #10596159C2semidirect
9. #10596156C2semidirect
10. #10596107C2semidirect
11. #10596103C2semidirect
14. #10595990C2semidirect
15. #10595988C2semidirect
17. C2×#64097C2semidirect
84. C3×#544D3semidirect
109. #3828Q8semidirect
239. C2×C32×C4C2×Q8semidirect
247. #638C2×Q8semidirect
259. C4⋊(C3⋊D3)C2×Q8semidirect
264. C4×C3⋊D3C2×Q8semidirect
270. #634C2×Q8semidirect
280. #544C3⋊D3semidirect
447. C2×C3×C4D3×Q8semidirect
574. C32#3503semidirect
603. C2×C4Q8×C3⋊D3semidirect
638. C3#86586semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
#105962002
#105961982
C3⋊D3×C4⋊Q82
#105961932
#105961612
#105961602
#105961592
#105961562
#105961072
#105961032
#105959942
#105959932
#105959902
#105959882
#105959752
C2×#640972
#865863