Finite Group Databasebeta

← #11906218

Subgroups — #11906218

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2C3×D3×C22⋊Q8C212yesmaximal, complemented
3#10595407C211yesmaximal, characteristic, complemented
4Q8×#625C211yesmaximal, characteristic, complemented
5#10595400C212yesmaximal, complemented
6C2×C4×#625C211yesmaximal, characteristic
7D3×#924C212yesmaximal, complemented
8#10594810C211yesmaximal, characteristic, complemented
9#10594534C212yesmaximal, complemented
10#10594533C214yesmaximal, complemented
11#10594532C212yesmaximal, complemented
12#10594531C211yesmaximal, characteristic, complemented
13#10594531C212yesmaximal, complemented
14#10594526C211yesmaximal, characteristic, complemented
15#10594181C212yesmaximal
16#10594170C214yesmaximal, complemented
17#10594033C212yesmaximal, complemented
18#85986—32nomaximal
19C2×C3×D3×Q8C2212yescomplemented
20C22×C3×C4×D3C2212yes—
21C22×#625C2211yescharacteristic
22C2×D3×Dic6C2212yescomplemented
23C32×C22⋊Q8C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25#64153C2211yescharacteristic, complemented
26#64133C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28#64098C2212yescomplemented
29#64097C2211yescharacteristic, complemented
30#64096C2211yescharacteristic, complemented
31#64096C2212yescomplemented
32#64087C2212yes—
33#64086C2212yes—
34C3×#946C2212yescomplemented
35C3×#924C2212yes—
36C3×#897C2212yescomplemented
37C3×#896C2214yescomplemented
38C3×D3×C4⋊C4C2212yescomplemented
39C3×D3×C4⋊C4C2214yescomplemented
40C3×D3×C22⋊C4C2214yes—
41C3×#878C2214yes—
42#63982C2212yes—
43D3×#217C2214yes—
44C2×#3724C2211yescharacteristic
45#63964C2214yes—
46C2×(C2×D3)⋊Dic3C2212yes—
47#63957C2212yes—
48#63919C2211yescharacteristic, complemented
49#63919C2212yescomplemented
50#63902C2212yes—
51#63902C2212yes—
52C4×#625C2212yes—
53C4×#625C2212yes—
54C4×#625C2211yescharacteristic
55C4×#625C2211yescharacteristic
56C4×#625C2212yes—
57C4×#625C2211yescharacteristic
58C4×#625C2212yes—
59C4×#625C2211yescharacteristic
60#63899C2214yescomplemented
61#63896C2214yescomplemented
62#63893C2214yescomplemented
63D3×C4⋊Dic3C2212yescomplemented
64#63887C2214yescomplemented
65#63879C2214yes—
66#63879C2214yes—
67D3×Dic3⋊C4C2214yescomplemented
68#63873C2211yescharacteristic, complemented
69#63873C2212yescomplemented
70#63870C2212yescomplemented
71#63870C2212yescomplemented
72#63870C2212yescomplemented
73#63857C2212yescomplemented
74#63857C2214yescomplemented
75#63856C2212yescomplemented
76#63856C2214yescomplemented
77#63851C2214yescomplemented
78#63851C2214yescomplemented
79#63851C2214yescomplemented
80#63847C2214yescomplemented
81#63843C2212yescomplemented
82#63839C2214yescomplemented
83#63838C2212yescomplemented
84C2×C3×C22⋊Q8—32no—
85Q8×#67—32no—
86Q8×#67—32no—
87C2×C4×#67—32no—
88C2×#924—32no—
89#5636—34no—
90#5636—34no—
91#5635—32no—
92#5635—32no—
93#5634—34no—
94#5632—32no—
95#5632—32no—
96D3×C22⋊Q8—32no—
97D3×C22⋊Q8D312yescomplemented
98#5623—34no—
99#5622—32no—
100#5622—32no—
101#5622—61no—
102#5511—32no—
103#5511—34no—
104#5511—32no—
105#5511—34no—
106#5486—34no—
107#5483—34no—
108C23×C3×D3C2312yes—
109C2×C32×Q8C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×#634C2311yescharacteristic
114C2×#634C2312yes—
115C22×C3×Dic3C2312yes—
116C3×D3×Q8—44no—
117C2×C3×C4×D3—44no—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6C2312yes—
125C2×C3×Dic6C2314yes—
126C2×#627C2314yes—
127C2×#627C2312yes—
128C2×#625Q818yescomplemented
129C2×#625C2312yes—
130C2×#625C2311yescharacteristic
131C2×#625C2311yescharacteristic
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134D3×Dic6—44no—
135C32×C4⋊C4C2312yes—
136C32×C4⋊C4C2311yescharacteristic
137C32×C22⋊C4C2312yes—
138#3757C2312yes—
139C4⋊(C3⋊Dic3)C2312yes—
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141#3750C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144#3750C2312yes—
145#3750C2312yes—
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2311yescharacteristic
151C4×C3⋊Dic3C2311yescharacteristic
152C3×#217C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2314yes—
156C3×C4⋊Dic3C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160#3724C2312yes—
161#3724C2312yes—
162#3724C2314yes—
163#3724C2312yes—
164#3724C2311yescharacteristic
165#3724C2311yescharacteristic
166#3724C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2312yes—
172(C2×D3)⋊Dic3C2312yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175(C2×D3)⋊Dic3C2312yes—
176Dic32C2314yes—
177#3501—91noSylow
178C22×C3×Q8—32no—
179C23×C3×C4—32no—
180C22×#67—32no—
181C2×D3×Q8—32no—
182C2×D3×Q8C2×D312yescomplemented
183C22×C4×D3C2×D312yes—
184C22×Dic6—32no—
185C3×C22⋊Q8—21no—
186C3×C22⋊Q8—32no—
187C3×C22⋊Q8—32no—
188C3×C22⋊Q8—32no—
189C3×C22⋊Q8—34no—
190C3×C22⋊Q8—34no—
191C3×C22⋊Q8C2×D312yes—
192C2×C3×C4⋊C4—32no—
193C2×C3×C4⋊C4—34no—
194C2×C3×C22⋊C4—34no—
195C2×#217—32no—
196C2×#217—34no—
197#946—34no—
198#946—32no—
199#946—34no—
200#946C2×D312yescomplemented
201Q8×Dic3—32no—
202Q8×Dic3—32no—
203Q8×Dic3—61no—
204#944—32no—
205#944—32no—
206#944—34no—
207#944—34no—
208#944—61no—
209C4×#67—32no—
210C4×#67—32no—
211C4×#67—32no—
212C4×#67—32no—
213C4×#67—34no—
214C4×#67—34no—
215C4×#67—32no—
216C4×#67—32no—
217C4×#67—32no—
218C4×#67—32no—
219C4×#67—34no—
220C4×#67—34no—
221C2×(C2×D3)⋊C4—32no—
222C2×C4⋊Dic3—32no—
223#924—32no—
224#924—34no—
225#924—32no—
226#924—34no—
227#924—34no—
228#924—32no—
229#924—34no—
230#924—34no—
231#924—34no—
232#924—61no—
233#924C2×D312yes—
234C2×Dic3⋊C4—32no—
235C2×Dic3⋊C4—34no—
236C2×C4×Dic3—32no—
237C2×C4×Dic3—61no—
238#897—32no—
239#897—34no—
240#897—34no—
241#897C2×D312yescomplemented
242#896—34no—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896C2×D314yescomplemented
248D3×C4⋊C4—32no—
249D3×C4⋊C4—34no—
250D3×C4⋊C4C2×D312yescomplemented
251D3×C4⋊C4C2×D314yescomplemented
252#889—34no—
253#889—34no—
254#889—34no—
255#889—34no—
256#889—34no—
257#889—34no—
258#889—62no—
259#888—34no—
260#888—32no—
261#888—34no—
262#888—32no—
263#888—61no—
264#887—32no—
265#887—32no—
266#887—34no—
267#887—34no—
268#887—61no—
269#887—62no—
270#67⋊C4—34no—
271#67⋊C4—34no—
272#67⋊C4—34no—
273#67⋊C4—34no—
274D3×C22⋊C4—34no—
275D3×C22⋊C4C2×D314yes—
276#878—34no—
277#878—34no—
278#878—34no—
279#878—34no—
280#878—34no—
281#878—34no—
282#878—34no—
283#878—62no—
284#878C2×D314yes—
285#877—34no—
286#877—34no—
287#877—62no—
288C23×C32C2411yescharacteristic
289C22×C3×D3—42no—
290C22×C3×D3—42no—
291C22×C3×D3C2×Q818yescomplemented
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C32×Q8—22no—
295C2×C32×C4—22no—
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2412yes—
298C2×C32×C4C2412yes—
299C2×C32×C4C2411yescharacteristic
300C2×C3⋊Dic3—41no—
301C2×C3⋊Dic3C2×Q814yescomplemented
302C2×C3⋊Dic3C2411yescharacteristic
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308#634—22no—
309#634—42no—
310C2×C3×Dic3—42no—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2414yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C3×C4×D3—24no—
316C3×C4×D3—24no—
317C3×C4×D3—42no—
318C3×C4×D3—42no—
319C3×C4×D3—44no—
320C3×C4×D3—44no—
321C3×Dic6—24no—
322C3×Dic6—44no—
323#627—44no—
324#627—42no—
325#625C2×Q818yescomplemented
326#625C2×Q814yescomplemented
327#625C2×Q814yescomplemented
328D3×Dic3—44no—
329D3×Dic3—44no—
330#554—91no—
331#554—92no—
332#554—92no—
333#554—94no—
334#554—91no—
335#554—92no—
336D4×Q8—91no—
337D4×Q8—92no—
338D4×Q8—91no—
339#544—92no—
340#543—94no—
341#533—91no—
342#533—91no—
343C2×C22⋊Q8—32no—
344C2×C22⋊Q8—92no—
345#518—92no—
346C2×C4×D4—91no—
347C24×C3—32no—
348C23×D3C22×D312yes—
349C2×C3×Q8—21no—
350C2×C3×Q8—32no—
351C2×C3×Q8—34no—
352C2×C3×Q8—124no—
353C2×C3×Q8C22×D312yes—
354C22×C3×C4—21no—
355C22×C3×C4—32no—
356C22×C3×C4—32no—
357C22×C3×C4—32no—
358C22×C3×C4—32no—
359C22×C3×C4—34no—
360C22×C3×C4—34no—
361C22×C3×C4—32no—
362C22×C3×C4—124no—
363C22×C3×C4C22×D312yes—
364C2×#67—316no—
365C2×#67—32no—
366C2×#67—32no—
367C2×#67—32no—
368C2×#67—32no—
369C22×Dic3—32no—
370C22×Dic3—32no—
371C22×Dic3—34no—
372C22×Dic3—34no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3C22×D312yes—
376D3×Q8—44no—
377D3×Q8—124no—
378C2×C4×D3—34no—
379C2×C4×D3—34no—
380C2×C4×D3—44no—
381C2×C4×D3C22×D312yes—
382C2×C4×D3C22×D312yes—
383C2×C4×D3C22×D314yes—
384C2×C4×D3C22×D314yes—
385C2×C4×D3C22×D312yes—
386C2×C4×D3C22×D312yes—
387C2×Dic6—32no—
388C2×Dic6—34no—
389C2×Dic6—34no—
390C2×Dic6—34no—
391C2×Dic6—34no—
392C2×Dic6—62no—
393C2×Dic6—61no—
394C2×Dic6—124no—
395C2×Dic6C22×D312yes—
396C2×Dic6C22×D314yes—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—22no—
399C3×C4⋊C4—32no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—34no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4C22×D312yes—
405C3×C4⋊C4C22×D314yes—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4C22×D314yes—
411#217—34no—
412#217—32no—
413#217—32no—
414#217—32no—
415#217—32no—
416#217—34no—
417#217—34no—
418#217—62no—
419#217C22×D314yes—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—32no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—32no—
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4C22×D314yes—
427(C2×D3)⋊C4C22×D314yes—
428C4⋊Dic3—34no—
429C4⋊Dic3—32no—
430C4⋊Dic3—34no—
431C4⋊Dic3—34no—
432C4⋊Dic3—34no—
433C4⋊Dic3—62no—
434C4⋊Dic3—61no—
435C4⋊Dic3C22×D314yes—
436C4⋊Dic3C22×D312yes—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—32no—
449Dic3⋊C4—32no—
450Dic3⋊C4—32no—
451Dic3⋊C4—32no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—32no—
465C4×Dic3—32no—
466C4×Dic3—32no—
467C4×Dic3—32no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—62no—
471C4×Dic3—62no—
472C4×Dic3—61no—
473C4×Dic3—61no—
474C4×Dic3—61no—
475C4×Dic3—61no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32C22×Q812yes—
479C22×C32C2511yescharacteristic
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—48no—
485C2×C3×D3C22×Q814yes—
486C2×C3×D3C22×Q814yes—
487C32×C4—22no—
488C32×C4—21no—
489C32×C4—22no—
490C32×C4H(5,𝔽2)12yes—
491C3⋊Dic3—21no—
492C3⋊Dic3—22no—
493C3⋊Dic3—22no—
494C3⋊Dic3—21no—
495C3⋊Dic3C22×Q812yes—
496C3⋊Dic3C22×Q812yes—
497C3×Dic3—24no—
498C3×Dic3—22no—
499C3×Dic3—22no—
500C3×Dic3—24no—
501C22×Q8—32no—
502C22×Q8—92no—
503C22×D4—91no—
504C23×C4—32no—
505C4⋊Q8—91no—
506C4⋊Q8—92no—
507C4⋊Q8—94no—
508C4⋊Q8—91no—
509C4⋊Q8—92no—
510C4⋊Q8—91no—
511C4⋊Q8—91no—
512#125—92no—
513#125—94no—
514#125—92no—
515#125—92no—
516#125—92no—
517C22⋊Q8—32no—
518C22⋊Q8—32no—
519C22⋊Q8—32no—
520C22⋊Q8—34no—
521C22⋊Q8—34no—
522C22⋊Q8—92no—
523C22⋊Q8—94no—
524C22⋊Q8—94no—
525C22⋊Q8—94no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528C22⋊Q8—92no—
529C22⋊Q8—94no—
530C22⋊Q8—94no—
531C22⋊Q8—94no—
532C22⋊Q8—94no—
533C22⋊Q8—92no—
534C22⋊Q8—94no—
535C22⋊Q8—91no—
536C22⋊Q8—92no—
537C22⋊Q8D3211yescharacteristic
538C4×Q8—92no—
539C4×Q8—92no—
540C4×Q8—91no—
541C4×Q8—91no—
542C4×Q8—92no—
543C4×D4—92no—
544C4×D4—92no—
545C4×D4—94no—
546C4×D4—94no—
547C4×D4—91no—
548C4×D4—92no—
549C4×D4—91no—
550C4×D4—91no—
551C4×D4—92no—
552C4×D4—91no—
553C4×D4—92no—
554C4×D4—92no—
555#117—92no—
556#117—92no—
557C2×C4⋊C4—34no—
558C2×C4⋊C4—32no—
559C2×C4⋊C4—94no—
560C2×C4⋊C4—92no—
561C2×C4⋊C4—91no—
562C2×C22⋊C4—34no—
563C2×C22⋊C4—94no—
564C2×C22⋊C4—92no—
565C2×C42—91no—
566C23×C3—21no—
567C23×C3—32no—
568C23×C3—32no—
569C23×C3—38no—
570C23×C3—122no—
571C23×C3—122no—
572C23×C3C23×D312yes—
573C22×D3—42no—
574C22×D3—42no—
575C22×D3D3×Q818yescomplemented
576C22×D3C23×D312yes—
577C22×D3C23×D312yes—
578C3×Q8—24no—
579C3×Q8—42no—
580C3×Q8—64no—
581C3×Q8—124no—
582C2×C3×C4—24no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—34no—
588C2×C3×C4—34no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—42no—
592C2×C3×C4—64no—
593C2×C3×C4—64no—
594C2×C3×C4—124no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4—124no—
598C2×C3×C4—122no—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D314yes—
601C2×C3×C4C23×D314yes—
602C2×C3×C4C23×D312yes—
603#67—38no—
604#67—38no—
605#67—38no—
606#67—38no—
607C2×Dic3—38no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—42no—
615C2×Dic3—64no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—124no—
623C2×Dic3—124no—
624C2×Dic3—122no—
625C2×Dic3—122no—
626C2×Dic3C23×D314yes—
627C2×Dic3C23×D314yes—
628C2×Dic3C23×D312yes—
629C2×Dic3C23×D312yes—
630C4×D3—24no—
631C4×D3—24no—
632C4×D3—42no—
633C4×D3—42no—
634C4×D3—44no—
635C4×D3—44no—
636C4×D3—124no—
637C4×D3—124no—
638Dic6—24no—
639Dic6—44no—
640Dic6—64no—
641Dic6—122no—
642Dic6—124no—
643Dic6—124no—
644Dic6—124no—
645Dic6—124no—
646Dic6—124no—
647C2×C32—22no—
648C2×C32C23×Q811yescharacteristic
649C2×C32C2×H(5,𝔽2)11yescharacteristic
650C2×C32#58511yescharacteristic
651C3×D3—24no—
652C3×D3—24no—
653C24—32no—
654C2×Q8—32no—
655C2×Q8—34no—
656C2×Q8—92no—
657C2×Q8—94no—
658C2×Q8—91no—
659C2×Q8—92no—
660C2×Q8—124no—
661C2×Q8—364no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—91no—
664C2×D4—92no—
665C2×D4—91no—
666C2×D4—98no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—34no—
671C22×C4—34no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—94no—
675C22×C4—94no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—124no—
679C22×C4C2×D3211yescharacteristic
680C4⋊C4—34no—
681C4⋊C4—32no—
682C4⋊C4—34no—
683C4⋊C4—34no—
684C4⋊C4—34no—
685C4⋊C4—91no—
686C4⋊C4—92no—
687C4⋊C4—91no—
688C4⋊C4—94no—
689C4⋊C4—94no—
690C4⋊C4—94no—
691C4⋊C4—92no—
692C4⋊C4—92no—
693C4⋊C4—94no—
694C4⋊C4—92no—
695C4⋊C4—92no—
696C4⋊C4—91no—
697C4⋊C4—92no—
698C4⋊C4—92no—
699C4⋊C4—92no—
700C4⋊C4—92no—
701C4⋊C4—92no—
702C4⋊C4C2×D3212yes—
703C4⋊C4C2×D3211yescharacteristic
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22⋊C4—92no—
712C22⋊C4—92no—
713C22⋊C4—92no—
714C22⋊C4C2×D3212yes—
715C42—94no—
716C42—91no—
717C42—91no—
718C42—91no—
719C42—91no—
720C42—92no—
721C42—92no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—34no—
727C22×C3—34no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—128no—
735C22×C3C2×D3×Q814yes—
736C22×C3C24×D312yes—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—48no—
742C2×D3C2×D3×Q814yes—
743C2×D3C2×D3×Q814yes—
744C3×C4—24no—
745C3×C4—22no—
746C3×C4—24no—
747C3×C4—22no—
748C3×C4—42no—
749C3×C4—41no—
750C3×C4—42no—
751C3×C4—62no—
752C3×C4—64no—
753C3×C4—62no—
754C3×C4—64no—
755C3×C4#100414yes—
756Dic3—24no—
757Dic3—22no—
758Dic3—22no—
759Dic3—24no—
760Dic3—34no—
761Dic3—34no—
762Dic3—62no—
763Dic3—62no—
764Dic3—62no—
765Dic3—64no—
766Dic3—62no—
767Dic3—62no—
768Dic3—64no—
769Dic3—122no—
770Dic3—122no—
771Dic3—121no—
772C32#350111yescharacteristic, complemented, Sylow
773C23—32no—
774C23—32no—
775C23—38no—
776C23—122no—
777C23—122no—
778C23C22×D3211yescharacteristic
779Q8—22no—
780Q8—64no—
781Q8—124no—
782Q8—182no—
783Q8—362no—
784Q8—364no—
785Q8—362no—
786D4—94no—
787D4—98no—
788D4—94no—
789C2×C4—22no—
790C2×C4—34no—
791C2×C4—34no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—64no—
795C2×C4—64no—
796C2×C4—94no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—91no—
800C2×C4—91no—
801C2×C4—92no—
802C2×C4—92no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—124no—
806C2×C4—124no—
807C2×C4—122no—
808C2×C4—364no—
809C2×C4—364no—
810C2×C4—361no—
811C2×C4C22×D3211yescharacteristic
812C2×C4C22×D3212yes—
813C2×C4C22×D3212yes—
814C2×C4C22×D3211yescharacteristic
815C2×C3—24no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—42no—
820C2×C3—64no—
821C2×C3—64no—
822C2×C3C2×#100412yes—
823C2×C3C22×D3×Q812yes—
824C2×C3#596412yes—
825D3—24no—
826D3—24no—
827C22—21no—
828C22—21no—
829C22—34no—
830C22—34no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—128no—
836C22D32×Q812yes—
837C22C23×D3211yescharacteristic
838C4—21no—
839C4—22no—
840C4—22no—
841C4—62no—
842C4—62no—
843C4—64no—
844C4—64no—
845C4—92no—
846C4—92no—
847C4—182no—
848C4—182no—
849C4—181no—
850C4—181no—
851C4#6431312yes—
852C3—21no—
853C3#8598612yescomplemented
854C2—22no—
855C2—64no—
856C2—64no—
857C2C2×#6431311yescharacteristic
858C2C2×D32×Q811yescharacteristic
859C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC22×#625C22
hypercenterC22⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
2. C3×D3×C22⋊Q8C2semidirect
3. #10595407C2semidirect
4. Q8×#625C2semidirect
5. #10595400C2semidirect
7. D3×#924C2semidirect
8. #10594810C2semidirect
9. #10594534C2semidirect
10. #10594533C2semidirect
11. #10594532C2semidirect
12. #10594531C2semidirect
13. #10594531C2semidirect
14. #10594526C2semidirect
16. #10594170C2semidirect
17. #10594033C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C2×D3×Dic6C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. #64153C22semidirect
28. #64098C22semidirect
29. #64097C22semidirect
30. #64096C22semidirect
31. #64096C22semidirect
34. C3×#946C22semidirect
36. C3×#897C22semidirect
37. C3×#896C22semidirect
38. C3×D3×C4⋊C4C22semidirect
39. C3×D3×C4⋊C4C22semidirect
48. #63919C22semidirect
49. #63919C22semidirect
60. #63899C22semidirect
61. #63896C22semidirect
62. #63893C22semidirect
63. D3×C4⋊Dic3C22semidirect
64. #63887C22semidirect
67. D3×Dic3⋊C4C22semidirect
68. #63873C22semidirect
69. #63873C22semidirect
70. #63870C22semidirect
71. #63870C22semidirect
72. #63870C22semidirect
73. #63857C22semidirect
74. #63857C22semidirect
75. #63856C22semidirect
76. #63856C22semidirect
77. #63851C22semidirect
78. #63851C22semidirect
79. #63851C22semidirect
80. #63847C22semidirect
81. #63843C22semidirect
82. #63839C22semidirect
83. #63838C22semidirect
97. D3×C22⋊Q8D3semidirect
128. C2×#625Q8semidirect
182. C2×D3×Q8C2×D3semidirect
200. #946C2×D3semidirect
241. #897C2×D3semidirect
247. #896C2×D3semidirect
250. D3×C4⋊C4C2×D3semidirect
251. D3×C4⋊C4C2×D3semidirect
291. C22×C3×D3C2×Q8semidirect
301. C2×C3⋊Dic3C2×Q8semidirect
325. #625C2×Q8semidirect
326. #625C2×Q8semidirect
327. #625C2×Q8semidirect
575. C22×D3D3×Q8semidirect
772. C32#3501semidirect
853. C3#85986semidirect

Maximal subgroups

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

subgroupindex
#105960932
C3×D3×C22⋊Q82
#105954072
Q8×#6252
#105954002
C2×C4×#6252
D3×#9242
#105948102
#105945342
#105945332
#105945322
#105945312
#105945262
#105941812
#105941702
#105940332
#859863