Finite Group Databasebeta

← #16807753

Subgroups — #16807753

Order 3328.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719627C211yesmaximal, characteristic, complemented
2C22×Q8×#261C211yesmaximal, characteristic, complemented
3#13131365C213yesmaximal, complemented
4#13131362C213yesmaximal, complemented
5#13131360C213yesmaximal, complemented
6#13131352C213yesmaximal
7#13131351C211yesmaximal, characteristic, complemented
8Q8×C22⋊#261C211yesmaximal, characteristic, complemented
9Q8×C22⋊#261C211yesmaximal, characteristic, complemented
10#13131327C213yesmaximal, complemented
11#13131323C213yesmaximal, complemented
12C22⋊Q8×#261C213yesmaximal, complemented
13#13131290C213yesmaximal
14#13131276C211yesmaximal, characteristic, complemented
15D4×Q8×D13C211yesmaximal, characteristic
16C22×Q8×D13C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18#11719627—28no—
19C2×Q8×#261—28no—
20C2×Q8×#261C2211yescharacteristic
21C2×Q8×#261C2213yes—
22C2×Q8×#261C2211yescharacteristic
23C2×Q8×#261C2213yes—
24C2×Q8×#261C2213yes—
25C2×Q8×#261C2211yescharacteristic
26C2×Q8×#261C2213yes—
27C2×Q8×#261C2211yescharacteristic
28C2×#88237C2213yes—
29C2×#88237C2213yes—
30C22×C4⋊#261C2213yes—
31C22×C4×#261C2213yes—
32D4×Q8×C13C411yescharacteristic, complemented
33Q8×C22⋊D13C411yescharacteristic, complemented
34Q8×C22⋊D13C411yescharacteristic, complemented
35#11719432C413yescomplemented
36D13×C4⋊Q8C2213yes—
37#11719337C413yescomplemented
38#11719337C413yescomplemented
39D13×C22⋊Q8C2213yes—
40D13×C22⋊Q8C2213yes—
41Q8×D52C411yescharacteristic, complemented
42C4×Q8×D13C2211yescharacteristic
43C4×D4×D13C2213yes—
44D4×Dic26C413yescomplemented
45(C2×#261)⋊Q8C2213yes—
46(C2×#261)⋊Q8C2213yes—
47(C2×#261)⋊Q8C2213yes—
48(C2×#261)⋊Q8C2213yes—
49#11719150C2211yescharacteristic
50#11719150C2213yes—
51#11719136C2213yes—
52#11719136C2213yes—
53C4×C22⋊#261C2213yes—
54C4×C22⋊#261C2213yes—
55#11719083C2213yes—
56#11719083C2213yes—
57#11719083C2216yes—
58#11719082C2213yes—
59#11719082C2213yes—
60#11719082C2216yes—
61#11719082C2216yes—
62#11719082C2216yes—
63C4⋊C4×#261C2213yes—
64C4⋊C4×#261C2213yes—
65C4⋊C4×#261C2216yes—
66#11719071C2213yes—
67#11719071C2213yes—
68#11719071C2216yes—
69#11719070C2213yes—
70#11719070C2213yes—
71C22⋊C4×#261C2216yes—
72#11719060C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75#11719057C2213yes—
76C23×#261C2311yescharacteristic
77C23×#261C2313yes—
78C22×Q8×C13C2×C411yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic, complemented
80C2×Q8×D13—24no—
81C2×Q8×D13—24no—
82C2×Q8×D13—24no—
83C2×Q8×D13—24no—
84C2×Q8×D13C2×C413yes—
85C2×Q8×D13C2×C411yescharacteristic
86C2×Q8×D13C2×C413yescomplemented
87C2×Q8×D13C2×C411yescharacteristic, complemented
88C2×Q8×D13C2313yes—
89C2×Q8×D13C2313yes—
90C2×Q8×D13C2311yescharacteristic
91C2×D4×D13C2311yescharacteristic
92C22×C4×D13C2313yes—
93C22×C4×D13C2313yes—
94C22×Dic26C2×C413yes—
95C22×Dic26C2×C413yescomplemented
96C2×C22⋊#261C2313yes—
97C2×C22⋊#261C2311yescharacteristic
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2311yescharacteristic
100C2×C22⋊#261C2311yescharacteristic
101C2×C22⋊#261C2313yes—
102Q8×#261—24no—
103Q8×#261—24no—
104Q8×#261—24no—
105Q8×#261—212no—
106Q8×#261—212no—
107Q8×#261—212no—
108Q8×#261—212no—
109Q8×#261D418yescomplemented
110#88237—212no—
111#88237—212no—
112C2×C4⋊#261—212no—
113C2×C4⋊#261C2313yes—
114C2×C4⋊#261C2313yes—
115C2×C4⋊#261C2313yes—
116C2×C4⋊#261C2313yes—
117C2×C4⋊#261C2313yes—
118C2×C4⋊#261C2313yes—
119C2×C4⋊#261C2316yes—
120C2×C4⋊#261C2313yes—
121C2×C4⋊#261C2313yes—
122C2×C4×#261—212no—
123C2×C4×#261C2313yes—
124C2×C4×#261C2313yes—
125C2×C4×#261C2313yes—
126C2×C4×#261C2316yes—
127C2×C4×#261C2313yes—
128C2×C4×#261C2313yes—
129C2×C4×#261C2316yes—
130C2×C4×#261C2313yes—
131C13×C4⋊Q8C2×C413yescomplemented
132C13×C22⋊Q8C2×C413yes—
133C13×C22⋊Q8C2×C413yescomplemented
134C4×Q8×C13C2×C411yescharacteristic, complemented
135C4×D4×C13C2×C413yes—
136#88200C2×C413yes—
137#88200C2×C413yescomplemented
138Q8×Dic13C2×C411yescharacteristic, complemented
139#88198C2×C413yescomplemented
140#88198C2×C413yescomplemented
141D4×Dic13C2×C413yes—
142C4×C22⋊D13C2×C413yes—
143C4×C22⋊D13C2×C413yes—
144#88178C2×C413yes—
145#88178C2×C413yescomplemented
146#88151C2×C413yes—
147#88151C2×C413yescomplemented
148#88150C2×C416yes—
149#88150C2×C416yescomplemented
150#88147C2×C413yes—
151C4⋊C4×D13C2313yes—
152C4⋊C4×D13C2316yes—
153C4⋊C4×D13C2313yes—
154#88142C2×C416yescomplemented
155#88142C2×C416yescomplemented
156#88141C2×C413yescomplemented
157#88135C2×C413yes—
158#88135C2×C413yes—
159C22⋊C4×D13C2313yes—
160C22⋊C4×D13C2313yes—
161#88132C2×C416yes—
162#88132C2×C416yescomplemented
163C4×D52C2×C413yes—
164C42×D13C2313yes—
165#88123C2×C413yescomplemented
166C4×Dic26C2×C413yescomplemented
167(C2×#261)⋊C4C2311yescharacteristic
168(C2×#261)⋊C4C2313yes—
169(C2×#261)⋊C4C2313yes—
170(C2×#261)⋊C4C2313yes—
171(C2×#261)⋊C4C2311yescharacteristic
172(C2×#261)⋊C4C2313yes—
173(C2×#261)⋊C4C2316yes—
174(C2×#261)⋊C4C2316yes—
175(C2×#261)⋊C4C2313yes—
176(C2×#261)⋊C4C2313yes—
177(C2×#261)⋊C4C2316yes—
178(C2×#261)⋊C4C2313yes—
179(C2×#261)⋊C4C2313yes—
180#34291—131nomaximal, Sylow
181C23×D13C2411yescharacteristic
182C23×D13C2411yescharacteristic
183C22×#261—22no—
184C22×#261—22no—
185C22×#261—22no—
186C22×#261—26no—
187C22×#261—26no—
188C22×#261—43no—
189C22×#261C2411yescharacteristic
190C22×#261C2413yes—
191C22×#261C2413yes—
192C22×#261C2413yes—
193C22×#261C2411yescharacteristic
194C22×#261C2411yescharacteristic
195C22×#261C2413yes—
196C22×#261C2411yescharacteristic
197C2×Q8×C13—24no—
198C2×Q8×C13—24no—
199C2×Q8×C13C22×C413yes—
200C2×Q8×C13C22×C413yes—
201C2×Q8×C13C22×C411yescharacteristic
202C2×D4×C13C22×C411yescharacteristic
203C22×C4×C13C22×C413yes—
204C22×C4×C13C22×C413yes—
205C2×C22⋊D13C22×C411yescharacteristic
206C2×C22⋊D13C22×C411yescharacteristic
207C22×Dic13C22×C413yes—
208C22×Dic13C22×C413yes—
209Q8×D13—24no—
210Q8×D13—24no—
211Q8×D13—26no—
212Q8×D13—26no—
213Q8×D13—26no—
214Q8×D13—26no—
215Q8×D13—212no—
216Q8×D13—212no—
217Q8×D13C2×D414yes—
218Q8×D13#4114yes—
219D4×D13—22no—
220D4×D13—22no—
221C2×D52C22×C411yescharacteristic
222C2×C4×D13—26no—
223C2×C4×D13—26no—
224C2×C4×D13—26no—
225C2×C4×D13—26no—
226C2×C4×D13C22×C413yes—
227C2×C4×D13C22×C413yes—
228C2×C4×D13C22×C413yes—
229C2×C4×D13C22×C413yes—
230C2×C4×D13C2411yescharacteristic
231C2×C4×D13C2413yes—
232C2×C4×D13C2413yes—
233C2×C4×D13C2413yes—
234C2×C4×D13C2413yes—
235C2×Dic26—212no—
236C2×Dic26—212no—
237C2×Dic26C22×C413yes—
238C2×Dic26C22×C413yes—
239C2×Dic26C22×C416yes—
240C2×Dic26C22×C416yes—
241C2×Dic26C22×C413yes—
242C22⋊#261—26no—
243C22⋊#261—22no—
244C22⋊#261—22no—
245C22⋊#261—26no—
246C22⋊#261—22no—
247C22⋊#261—43no—
248C4⋊#261—212no—
249C4⋊#261—26no—
250C4⋊#261—26no—
251C4⋊#261—26no—
252C4⋊#261—26no—
253C4⋊#261—26no—
254C4⋊#261—26no—
255C4⋊#261—43no—
256C4⋊#261C2×D4112yes—
257C4×#261—26no—
258C4×#261—26no—
259C4×#261—212no—
260C4×#261—26no—
261C4×#261—26no—
262C4×#261—26no—
263C4×#261—46no—
264C4×#261C2×D4112yes—
265C13×C4⋊C4C22×C413yes—
266C13×C4⋊C4C22×C413yes—
267C13×C4⋊C4C22×C416yes—
268C13×C22⋊C4C22×C413yes—
269C13×C22⋊C4C22×C413yes—
270C42×C13C22×C413yes—
271C22⋊Dic13C22×C413yes—
272C22⋊Dic13C22×C413yes—
273#6103C22×C413yes—
274#6103C22×C413yes—
275#6103C22×C413yes—
276#6103C22×C413yes—
277C4⋊Dic13C22×C413yes—
278C4⋊Dic13C22×C413yes—
279C4⋊Dic13C22×C416yes—
280#6101C22×C416yes—
281#6101C22×C416yes—
282#6101C22×C416yes—
283#6101C22×C413yes—
284#6101C22×C413yes—
285C4×Dic13C22×C413yes—
286C4×Dic13C22×C413yes—
287C4×Dic13C22×C413yes—
288C2×D4×Q8—131no—
289C2×#519—131no—
290C22×C4×Q8—131no—
291#2365—133no—
292#2362—133no—
293#2360—133no—
294#2352—133no—
295#2351—131no—
296Q8×C22⋊C4—131no—
297Q8×C22⋊C4—131no—
298#2327—133no—
299#2323—133no—
300C4×C22⋊Q8—133no—
301#2290—133no—
302#2276—131no—
303C23×C13C23×C411yescharacteristic
304C23×C13C23×C411yescharacteristic
305C22×D13—21no—
306C22×D13—21no—
307C22×D13—21no—
308C22×D13—21no—
309C22×D13—21no—
310C22×D13—21no—
311C22×D13—21no—
312C22×D13—21no—
313C22×D13—21no—
314C22×D13—21no—
315C22×D13C23×C411yescharacteristic
316C22×D13C23×C411yescharacteristic
317C22×D132−1+412yes—
318C22×D132−1+412yes—
319C22×D13C2511yescharacteristic
320C2×#261—28no—
321C2×#261—21no—
322C2×#261—21no—
323C2×#261—21no—
324C2×#261—21no—
325C2×#261—23no—
326C2×#261—23no—
327C2×#261—23no—
328C2×#261—21no—
329C2×#261—23no—
330C2×#261—21no—
331C2×#261—23no—
332C2×#261—23no—
333C2×#261—23no—
334C2×#261—21no—
335C2×#261—23no—
336C2×#261—21no—
337C2×#261—21no—
338C2×#261—23no—
339C2×#261—23no—
340C2×#261—21no—
341C2×#261—23no—
342C2×#261—412no—
343C2×#261C22×D412yes—
344C2×#261C22×D416yes—
345C2×#2612−1+412yes—
346Q8×C13—26no—
347Q8×C13—26no—
348Q8×C13C4×D414yes—
349D4×C13—22no—
350C2×C4×C13—26no—
351C2×C4×C13—26no—
352C2×C4×C13C23×C411yescharacteristic
353C2×C4×C13C23×C413yes—
354C2×C4×C13C23×C413yes—
355C2×C4×C13C23×C413yes—
356C2×C4×C13C23×C413yes—
357C22⋊D13—22no—
358C22⋊D13—22no—
359C2×Dic13—26no—
360C2×Dic13—26no—
361C2×Dic13C23×C411yescharacteristic
362C2×Dic13C23×C413yes—
363C2×Dic13C23×C413yes—
364C2×Dic13C23×C413yes—
365C2×Dic13C23×C413yes—
366D52—22no—
367C4×D13—23no—
368C4×D13—23no—
369C4×D13—23no—
370C4×D13—23no—
371C4×D13—23no—
372C4×D13—21no—
373C4×D13—21no—
374C4×D13—23no—
375C4×D13—26no—
376C4×D13—26no—
377C4×D13—26no—
378C4×D13—26no—
379C4×D13C22×D416yes—
380C4×D13C2×#4116yes—
381Dic26—26no—
382Dic26—26no—
383Dic26—212no—
384Dic26—212no—
385Dic26C4×D4112yes—
386C23×Q8—131no—
387C23×Q8—131no—
388D4×Q8—131no—
389D4×Q8—131no—
390D4×Q8—133no—
391D4×Q8—133no—
392D4×Q8—133no—
393D4×Q8—131no—
394D4×Q8—133no—
395D4×Q8#26111yescharacteristic, complemented
396C2×C4⋊Q8—133no—
397C2×C22⋊Q8—133no—
398C2×C22⋊Q8—133no—
399#519—268no—
400C2×C4×Q8—131no—
401C2×C4×Q8—131no—
402C2×C4×Q8—133no—
403C2×C4×Q8—133no—
404C2×C4×Q8—131no—
405C2×C4×Q8—131no—
406C2×C4×Q8—131no—
407C2×C4×Q8—133no—
408C2×C4×Q8—133no—
409C2×C4×Q8—268no—
410C2×C4×D4—133no—
411C2×#117—133no—
412C2×#117—133no—
413C22×C4⋊C4—133no—
414C22×C42—133no—
415#391—133no—
416#391—133no—
417#391—133no—
418#391—133no—
419#389—133no—
420#389—136no—
421#389—133no—
422#388—133no—
423#388—136no—
424#388—133no—
425#387—136no—
426#387—133no—
427#387—136no—
428#387—136no—
429#387—133no—
430#386—133no—
431#386—131no—
432#385—133no—
433#385—133no—
434#382—133no—
435#380—133no—
436#380—133no—
437C4×C4⋊C4—133no—
438C4×C4⋊C4—133no—
439C4×C4⋊C4—133no—
440C4×C4⋊C4—133no—
441C4×C4⋊C4—136no—
442C4×C22⋊C4—133no—
443C4×C22⋊C4—133no—
444C4×C22⋊C4—136no—
445#376—133no—
446C22×C13—21no—
447C22×C13—21no—
448C22×C13—21no—
449C22×C13—21no—
450C22×C13—21no—
451C22×C13#51912yescomplemented
452C22×C13C24×C411yescharacteristic
453C2×D13—21no—
454C2×D13—21no—
455C2×D13—22no—
456C2×D13—22no—
457C2×D13—22no—
458C2×D13—22no—
459C2×D13—21no—
460C2×D13—21no—
461C2×D13—21no—
462C2×D13—41no—
463C2×D13—41no—
464C2×D13—41no—
465C2×D13—41no—
466C2×D13#51912yescomplemented
467C2×D13C23×D411yescharacteristic
468C2×D13C22×#4111yescharacteristic
469C2×D13C2×2−1+411yescharacteristic
470C2×D13C2×2−1+411yescharacteristic
471C2×D13C2×2−1+411yescharacteristic
472C2×D13#58511yescharacteristic
473#261—22no—
474#261—22no—
475#261—26no—
476#261—43no—
477#261—41no—
478#261—43no—
479#261—43no—
480#261—41no—
481C4×C13—23no—
482C4×C13—23no—
483C4×C13—21no—
484C4×C13—23no—
485C4×C13C2×C4×D416yes—
486Dic13—23no—
487Dic13—23no—
488Dic13—21no—
489Dic13—23no—
490Dic13C2×C4×D416yes—
491C22×Q8—131no—
492C22×Q8—133no—
493C22×Q8—133no—
494C22×Q8—133no—
495C22×Q8—131no—
496C22×Q8—133no—
497C22×Q8—131no—
498C22×Q8—133no—
499C22×Q8—133no—
500C22×Q8—264no—
501C22×Q8—264no—
502C22×Q8—264no—
503C22×Q8—264no—
504C22×Q8C2×#26111yescharacteristic
505C22×Q8C2×#26111yescharacteristic, complemented
506C22×D4—131no—
507C23×C4—133no—
508C23×C4—133no—
509C23×C4—131no—
510C23×C4—133no—
511C4⋊Q8—133no—
512C4⋊Q8—133no—
513C4⋊Q8—136no—
514C4⋊Q8—136no—
515C4⋊Q8—133no—
516C4⋊Q8C2×#26113yescomplemented
517C22⋊Q8—133no—
518C22⋊Q8—133no—
519C22⋊Q8—133no—
520C22⋊Q8—133no—
521C22⋊Q8—136no—
522C22⋊Q8—136no—
523C22⋊Q8—133no—
524C22⋊Q8—133no—
525C22⋊Q8—136no—
526C22⋊Q8—136no—
527C22⋊Q8C2×#26113yes—
528C22⋊Q8C2×#26113yescomplemented
529C4×Q8—138no—
530C4×Q8—131no—
531C4×Q8—133no—
532C4×Q8—133no—
533C4×Q8—2612no—
534C4×Q8—2612no—
535C4×Q8—2612no—
536C4×Q8—2612no—
537C4×Q8—264no—
538C4×Q8—264no—
539C4×Q8—264no—
540C4×Q8C2×#26111yescharacteristic, complemented
541C4×D4—133no—
542C4×D4—133no—
543C4×D4—133no—
544C4×D4—133no—
545C4×D4—133no—
546C4×D4—133no—
547C4×D4—133no—
548C4×D4C2×#26113yes—
549#117—2612no—
550#117—2612no—
551C2×C4⋊C4—133no—
552C2×C4⋊C4—133no—
553C2×C4⋊C4—133no—
554C2×C4⋊C4—136no—
555C2×C4⋊C4—133no—
556C2×C4⋊C4—136no—
557C2×C4⋊C4—133no—
558C2×C4⋊C4—133no—
559C2×C4⋊C4—133no—
560C2×C4⋊C4—133no—
561C2×C4⋊C4—133no—
562C2×C4⋊C4—133no—
563C2×C4⋊C4—2612no—
564C2×C22⋊C4—133no—
565C2×C22⋊C4—133no—
566C2×C22⋊C4—131no—
567C2×C22⋊C4—133no—
568C2×C22⋊C4—133no—
569C2×C22⋊C4—131no—
570C2×C22⋊C4—131no—
571C2×C22⋊C4—133no—
572C2×C42—133no—
573C2×C42—133no—
574C2×C42—136no—
575C2×C42—133no—
576C2×C42—133no—
577C2×C42—133no—
578C2×C42—133no—
579C2×C42—133no—
580C2×C42—136no—
581C2×C42—2612no—
582#95—131no—
583#95—133no—
584#95—133no—
585#95—133no—
586#95—133no—
587#95—136no—
588#95—136no—
589#95—133no—
590#95—133no—
591#95—133no—
592#95—131no—
593#95—136no—
594#95—133no—
595C2×C13—22no—
596C2×C13—41no—
597C2×C13C22×C4×D411yescharacteristic
598C2×C13C2×#51911yescharacteristic
599C2×C13C4×2−1+411yescharacteristic
600D13—22no—
601D13—41no—
602D13#348611yescharacteristic
603D13#348911yescharacteristic
604D13#351611yescharacteristic
605D13#352311yescharacteristic
606C24—131no—
607C24—131no—
608C2×Q8—24no—
609C2×Q8—24no—
610C2×Q8—134no—
611C2×Q8—134no—
612C2×Q8—133no—
613C2×Q8—136no—
614C2×Q8—136no—
615C2×Q8—133no—
616C2×Q8—133no—
617C2×Q8—2612no—
618C2×Q8—2612no—
619C2×Q8—266no—
620C2×Q8—266no—
621C2×Q8—266no—
622C2×Q8—266no—
623C2×Q8—2612no—
624C2×Q8—2612no—
625C2×Q8—264no—
626C2×Q8—264no—
627C2×Q8C22×#26113yes—
628C2×Q8C22×#26113yes—
629C2×Q8C22×#26111yescharacteristic
630C2×D4—131no—
631C2×D4—131no—
632C2×D4—131no—
633C2×D4—262no—
634C2×D4—262no—
635C2×D4C22×#26111yescharacteristic
636C22×C4—133no—
637C22×C4—131no—
638C22×C4—131no—
639C22×C4—133no—
640C22×C4—133no—
641C22×C4—133no—
642C22×C4—131no—
643C22×C4—133no—
644C22×C4—133no—
645C22×C4—133no—
646C22×C4—133no—
647C22×C4—133no—
648C22×C4—133no—
649C22×C4—133no—
650C22×C4—131no—
651C22×C4—133no—
652C22×C4—133no—
653C22×C4—133no—
654C22×C4—131no—
655C22×C4—266no—
656C22×C4—266no—
657C22×C4—266no—
658C22×C4—266no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—266no—
662C22×C4—262no—
663C22×C4—266no—
664C22×C4—523no—
665C22×C4C22×#26113yes—
666C22×C4C22×#26113yes—
667C4⋊C4—1312no—
668C4⋊C4—133no—
669C4⋊C4—133no—
670C4⋊C4—133no—
671C4⋊C4—136no—
672C4⋊C4—133no—
673C4⋊C4—136no—
674C4⋊C4—136no—
675C4⋊C4—136no—
676C4⋊C4—266no—
677C4⋊C4—2612no—
678C4⋊C4—266no—
679C4⋊C4—266no—
680C4⋊C4—266no—
681C4⋊C4—266no—
682C4⋊C4—266no—
683C4⋊C4—523no—
684C4⋊C4C22×#26113yes—
685C4⋊C4C22×#26113yes—
686C4⋊C4C22×#26116yes—
687C22⋊C4—133no—
688C22⋊C4—133no—
689C22⋊C4—133no—
690C22⋊C4—133no—
691C22⋊C4—133no—
692C22⋊C4—133no—
693C22⋊C4—262no—
694C22⋊C4—266no—
695C22⋊C4—262no—
696C22⋊C4—266no—
697C22⋊C4—262no—
698C22⋊C4—523no—
699C22⋊C4C22×#26113yes—
700C22⋊C4C22×#26113yes—
701C42—1312no—
702C42—133no—
703C42—133no—
704C42—133no—
705C42—266no—
706C42—266no—
707C42—266no—
708C42—266no—
709C42—2612no—
710C42—266no—
711C42—526no—
712C42C22×#26113yes—
713C13#3429111yescharacteristic, complemented, Sylow
714C23—131no—
715C23—132no—
716C23—132no—
717C23—131no—
718C23—131no—
719C23—261no—
720C23—261no—
721C23—261no—
722C23—261no—
723C23—261no—
724C23—261no—
725C23—261no—
726C23—261no—
727C23—261no—
728C23—261no—
729C23C23×#26111yescharacteristic
730C23C23×#26111yescharacteristic
731Q8—26no—
732Q8—26no—
733Q8—1312no—
734Q8—2612no—
735Q8—2612no—
736Q8—266no—
737Q8—266no—
738Q8D4×#26114yes—
739D4—22no—
740D4—262no—
741D4—262no—
742D4—262no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—133no—
746C2×C4—136no—
747C2×C4—136no—
748C2×C4—132no—
749C2×C4—136no—
750C2×C4—132no—
751C2×C4—131no—
752C2×C4—133no—
753C2×C4—133no—
754C2×C4—133no—
755C2×C4—266no—
756C2×C4—266no—
757C2×C4—263no—
758C2×C4—263no—
759C2×C4—263no—
760C2×C4—263no—
761C2×C4—263no—
762C2×C4—263no—
763C2×C4—261no—
764C2×C4—261no—
765C2×C4—266no—
766C2×C4—266no—
767C2×C4—261no—
768C2×C4—263no—
769C2×C4—261no—
770C2×C4—261no—
771C2×C4—261no—
772C2×C4—263no—
773C2×C4—268no—
774C2×C4—266no—
775C2×C4—266no—
776C2×C4—263no—
777C2×C4—261no—
778C2×C4—261no—
779C2×C4—263no—
780C2×C4—263no—
781C2×C4—263no—
782C2×C4—261no—
783C2×C4—263no—
784C2×C4—263no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—263no—
788C2×C4—263no—
789C2×C4—261no—
790C2×C4—263no—
791C2×C4—5212no—
792C2×C4C23×#26111yescharacteristic
793C2×C4C23×#26113yes—
794C2×C4C23×#26113yes—
795C2×C4C23×#26113yes—
796C2×C4C23×#26113yes—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—131no—
803C22—131no—
804C22—131no—
805C22—131no—
806C22—131no—
807C22—131no—
808C22—132no—
809C22—262no—
810C22—262no—
811C22—262no—
812C22—262no—
813C22—261no—
814C22—261no—
815C22—261no—
816C22—261no—
817C22—261no—
818C22—521no—
819C22—521no—
820C22—521no—
821C22—521no—
822C22#1171962712yescomplemented
823C22C24×#26111yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—136no—
829C4—262no—
830C4—262no—
831C4—266no—
832C4—263no—
833C4—263no—
834C4—261no—
835C4—263no—
836C4—521no—
837C4—523no—
838C4—523no—
839C4—521no—
840C4—523no—
841C4C2×D4×#26116yes—
842C2—22no—
843C2—41no—
844C2—131no—
845C2—131no—
846C2—131no—
847C2—131no—
848C2—262no—
849C2—521no—
850C2C22×D4×#26111yescharacteristic
851C2C2×#1171962711yescharacteristic
852C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingD4×Q8×C13C4
prime radicalC2×D4×D13C23
cosocleC22×D13C25
hypercenterD4×Q8#261
hypocenterC13#34291
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11719627C2semidirect
2. C22×Q8×#261C2semidirect
3. #13131365C2semidirect
4. #13131362C2semidirect
5. #13131360C2semidirect
7. #13131351C2semidirect
8. Q8×C22⋊#261C2semidirect
9. Q8×C22⋊#261C2semidirect
10. #13131327C2semidirect
11. #13131323C2semidirect
12. C22⋊Q8×#261C2semidirect
14. #13131276C2semidirect
32. D4×Q8×C13C4semidirect
33. Q8×C22⋊D13C4semidirect
34. Q8×C22⋊D13C4semidirect
35. #11719432C4semidirect
37. #11719337C4semidirect
38. #11719337C4semidirect
41. Q8×D52C4semidirect
44. D4×Dic26C4semidirect
79. C22×Q8×C13C2×C4semidirect
86. C2×Q8×D13C2×C4semidirect
87. C2×Q8×D13C2×C4semidirect
95. C22×Dic26C2×C4semidirect
109. Q8×#261D4semidirect
131. C13×C4⋊Q8C2×C4semidirect
133. C13×C22⋊Q8C2×C4semidirect
134. C4×Q8×C13C2×C4semidirect
137. #88200C2×C4semidirect
138. Q8×Dic13C2×C4semidirect
139. #88198C2×C4semidirect
140. #88198C2×C4semidirect
145. #88178C2×C4semidirect
147. #88151C2×C4semidirect
149. #88150C2×C4semidirect
154. #88142C2×C4semidirect
155. #88142C2×C4semidirect
156. #88141C2×C4semidirect
162. #88132C2×C4semidirect
165. #88123C2×C4semidirect
166. C4×Dic26C2×C4semidirect
395. D4×Q8#261semidirect
451. C22×C13#519semidirect
466. C2×D13#519semidirect
505. C22×Q8C2×#261semidirect
516. C4⋊Q8C2×#261semidirect
528. C22⋊Q8C2×#261semidirect
540. C4×Q8C2×#261semidirect
713. C13#34291semidirect
822. C22#11719627semidirect

Maximal subgroups

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

subgroupindex
C2×#117196272
C22×Q8×#2612
#131313652
#131313622
#131313602
#131313522
#131313512
Q8×C22⋊#2612
#131313272
#131313232
C22⋊Q8×#2612
#131312902
#131312762
D4×Q8×D132
#3429113