Finite Group Databasebeta

← #16799514

Subgroups — #16799514

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131314C211yesmaximal, characteristic
2#13131273C211yesmaximal, characteristic
3#13130949C211yesmaximal, characteristic, complemented
4#13130949C211yesmaximal, characteristic, complemented
5#13130948C211yesmaximal, characteristic, complemented
6#13130947C211yesmaximal, characteristic, complemented
7#13130787C211yesmaximal, characteristic
8#13130787C211yesmaximal, characteristic
9#13130786C211yesmaximal, characteristic
10#13130785C211yesmaximal, characteristic
11#13130650C211yesmaximal, characteristic, complemented
12#13130650C211yesmaximal, characteristic, complemented
13C4×#88102C211yesmaximal, characteristic, complemented
14C4×#88101C211yesmaximal, characteristic, complemented
15D13×#433C211yesmaximal, characteristic
16C2×#88237C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18D13×#117C2211yescharacteristic
19#11719136C2211yescharacteristic
20#11719136C2211yescharacteristic
21C2×#88102C2211yescharacteristic
22C2×#88102C2211yescharacteristic
23C2×#88102C2211yescharacteristic
24C2×#88102C2211yescharacteristic
25C2×#88101C2211yescharacteristic
26C2×#88101C2211yescharacteristic
27C2×#88101C2211yescharacteristic
28C2×#88101C2211yescharacteristic
29#11719082—21no—
30#11719082—21no—
31C4⋊C4×#261—21no—
32C4⋊C4×#261—21no—
33#11719071—21no—
34#11719071—21no—
35C22⋊C4×#261—21no—
36C22⋊C4×#261—21no—
37#11719060C2211yescharacteristic
38#11719059C2211yescharacteristic
39C4×C4⋊#261C2211yescharacteristic
40C4×C4⋊#261C2211yescharacteristic
41C4×C4⋊#261C2211yescharacteristic
42C4×C4⋊#261C2211yescharacteristic
43C4×C4⋊#261C2211yescharacteristic
44C4×C4⋊#261C2211yescharacteristic
45C13×#433C411yescharacteristic, complemented
46#11718661C411yescharacteristic, complemented
47#11718501C411yescharacteristic, complemented
48#11718501C411yescharacteristic, complemented
49D13×C4⋊C8C2211yescharacteristic
50D13×C4⋊C8C2211yescharacteristic
51D13×C22⋊C8C2211yescharacteristic
52D13×C22⋊C8C2211yescharacteristic
53#11718381C411yescharacteristic, complemented
54#11718381C411yescharacteristic, complemented
55#11718370C411yescharacteristic, complemented
56D13×#97C2211yescharacteristic
57#11718351C411yescharacteristic, complemented
58C4×C8×D13C2211yescharacteristic
59#11718265C2211yescharacteristic
60#11718265C2211yescharacteristic
61#11718265C2211yescharacteristic
62#11718265C2211yescharacteristic
63#11718265C2211yescharacteristic
64#11718265C2211yescharacteristic
65#11718265C2211yescharacteristic
66#11718265C2211yescharacteristic
67C23×#261—21no—
68C22×C4×D13C2311yescharacteristic
69C2×C22⋊#261—21no—
70C2×C22⋊#261—21no—
71C2×C22⋊#261—21no—
72#88237—22no—
73#88237—22no—
74C2×C4⋊#261—21no—
75C2×C4⋊#261—22no—
76C2×C4⋊#261—22no—
77C2×C4⋊#261—21no—
78C2×C4⋊#261—21no—
79C2×C4⋊#261C2311yescharacteristic
80C2×C4⋊#261C2311yescharacteristic
81C2×C4⋊#261C2311yescharacteristic
82C2×C4⋊#261C2311yescharacteristic
83C2×C4⋊#261C2311yescharacteristic
84C2×C4⋊#261C2311yescharacteristic
85C2×C4⋊#261C2311yescharacteristic
86C2×C4⋊#261C2311yescharacteristic
87C2×C4×#261—21no—
88C2×C4×#261—21no—
89C2×C4×#261—21no—
90C2×C4×#261—21no—
91C2×C4×#261—21no—
92C2×C4×#261—21no—
93C2×C4×#261—21no—
94C13×#117C2×C411yescharacteristic
95#88180C2×C411yescharacteristic
96C2×C8×D13C2311yescharacteristic
97C2×C8×D13C2311yescharacteristic
98C2×C8×D13C2311yescharacteristic
99C2×C8×D13C2311yescharacteristic
100#88146Q811yescharacteristic
101#88146Q811yescharacteristic
102C4⋊C4×D13D411yescharacteristic
103C4⋊C4×D13D411yescharacteristic
104C22⋊C4×D13D411yescharacteristic
105C22⋊C4×D13D411yescharacteristic
106#88131Q811yescharacteristic
107#88131Q811yescharacteristic
108#88126C2×C411yescharacteristic
109#88126C2×C411yescharacteristic
110C42×D13C2311yescharacteristic
111C42×D13C2311yescharacteristic
112(C2×#261)⋊C4—21no—
113(C2×#261)⋊C4—21no—
114(C2×#261)⋊C4—21no—
115(C2×#261)⋊C4—21no—
116(C2×#261)⋊C4—21no—
117(C2×#261)⋊C4—21no—
118(C2×#261)⋊C4—21no—
119(C2×#261)⋊C4—21no—
120(C2×#261)⋊C4—21no—
121(C2×#261)⋊C4—21no—
122#88102—22no—
123#88102—22no—
124#88102—22no—
125#88102—22no—
126#88101—22no—
127#88101—22no—
128#88101—22no—
129#88101—22no—
130C13×C4⋊C8C2×C411yescharacteristic, complemented
131C13×C4⋊C8C2×C411yescharacteristic, complemented
132C13×C22⋊C8C2×C411yescharacteristic
133C13×C22⋊C8C2×C411yescharacteristic
134C13×#97C2×C411yescharacteristic, complemented
135C4×C8×C13C2×C411yescharacteristic, complemented
136C22⋊#1055C2×C411yescharacteristic
137C22⋊#1055C2×C411yescharacteristic
138#88060C2×C411yescharacteristic
139#88060C2×C411yescharacteristic
140#88060C2×C411yescharacteristic
141#88060C2×C411yescharacteristic
142#88055C2×C411yescharacteristic, complemented
143#88055C2×C411yescharacteristic, complemented
144#88054C2×C411yescharacteristic, complemented
145#88054C2×C411yescharacteristic, complemented
146#88054C2×C411yescharacteristic, complemented
147#88054C2×C411yescharacteristic, complemented
148C8×Dic13C2×C411yescharacteristic, complemented
149C8×Dic13C2×C411yescharacteristic, complemented
150C4⋊#1055C2×C411yescharacteristic, complemented
151C4⋊#1055C2×C411yescharacteristic, complemented
152#88043C2×C411yescharacteristic, complemented
153C4×#1055C2×C411yescharacteristic, complemented
154#21367—131nomaximal, Sylow
155C23×D13C2×D411yescharacteristic
156C22×#261—21no—
157C22×#261—21no—
158C22×#261—21no—
159C22×#261—21no—
160C22×#261—24no—
161C22×#261—21no—
162C22×#261—21no—
163C22×#261—21no—
164C22×#261—21no—
165C22×#261—81no—
166C22×#261—81no—
167C22×C4×C13C22×C411yescharacteristic
168C22×Dic13C2×Q811yescharacteristic
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13C22×C411yescharacteristic
174C2×C4×D13C2×D411yescharacteristic
175C2×C4×D13C2×D411yescharacteristic
176C2×C4×D13C2×D411yescharacteristic
177C2×C4×D13C2×D411yescharacteristic
178C2×C4×D13C2×D411yescharacteristic
179C2×C4×D13C2×Q811yescharacteristic
180C2×C4×D13C2411yescharacteristic
181C22⋊#261—24no—
182C22⋊#261—81no—
183C22⋊#261—81no—
184C4⋊#261—24no—
185C4⋊#261—21no—
186C4⋊#261—21no—
187C4⋊#261—21no—
188C4⋊#261—21no—
189C4⋊#261—21no—
190C4⋊#261—21no—
191C4⋊#261—21no—
192C4⋊#261—21no—
193C4⋊#261—21no—
194C4⋊#261—21no—
195C4⋊#261—21no—
196C4⋊#261—21no—
197C4⋊#261—81no—
198C4⋊#261—81no—
199C4⋊#261#4112yes—
200C4⋊#261#4112yes—
201C4⋊#261#4112yes—
202C4⋊#261#4112yes—
203C4×#261—24no—
204C4×#261—81no—
205C4×#261—81no—
206C4×#261—81no—
207C4×#261—81no—
208C4×#261—81no—
209C4×#261—81no—
210C2×C8×C13C22×C411yescharacteristic
211C2×C8×C13C22×C411yescharacteristic
212C2×C8×C13C22×C411yescharacteristic
213C2×C8×C13C22×C411yescharacteristic
214C13×C4⋊C4C4⋊C411yescharacteristic
215C13×C4⋊C4C4⋊C411yescharacteristic
216C13×C22⋊C4C4⋊C411yescharacteristic
217C13×C22⋊C4C4⋊C411yescharacteristic
218C42×C13C22×C411yescharacteristic
219C42×C13C22×C411yescharacteristic
220C22⋊Dic13C4⋊C411yescharacteristic
221C22⋊Dic13C4⋊C411yescharacteristic
222#6103C4⋊C411yescharacteristic
223#6103C4⋊C411yescharacteristic
224#6103C4⋊C411yescharacteristic
225#6103C4⋊C411yescharacteristic
226C4⋊Dic13C4⋊C411yescharacteristic
227C4⋊Dic13C4⋊C411yescharacteristic
228#6101C4⋊C411yescharacteristic
229#6101C4⋊C411yescharacteristic
230#6101C4⋊C411yescharacteristic
231#6101C4⋊C411yescharacteristic
232C4×Dic13C22×C411yescharacteristic
233C4×Dic13C22×C411yescharacteristic
234C4×Dic13C2×Q811yescharacteristic
235C4×Dic13C2×Q811yescharacteristic
236C4×Dic13C2×Q811yescharacteristic
237C4×Dic13C2×Q811yescharacteristic
238C2×#1055C22×C411yescharacteristic
239C2×#1055C22×C411yescharacteristic
240C2×#1055C22×C411yescharacteristic
241C2×#1055C22×C411yescharacteristic
242C8×D13—21no—
243C8×D13—21no—
244C8×D13—21no—
245C8×D13—21no—
246C8×D13—21no—
247C8×D13—21no—
248C8×D13—21no—
249C8×D13—21no—
250C2×#433—131no—
251#2314—131no—
252#2274—131no—
253#1949—131no—
254#1949—131no—
255#1948—131no—
256#1947—131no—
257#1854—131no—
258#1854—131no—
259#1853—131no—
260#1852—131no—
261#1776—131no—
262#1776—131no—
263C4×#107—131no—
264C4×#106—131no—
265C23×C13C2×C4⋊C411yescharacteristic
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—21no—
272C22×D13C2×C4⋊C411yescharacteristic
273C22×D13C22×D411yescharacteristic
274C2×#261—22no—
275C2×#261—22no—
276C2×#261—22no—
277C2×#261—22no—
278C2×#261—41no—
279C2×#261—41no—
280C2×#261—41no—
281C2×#261—41no—
282C2×#261—41no—
283C2×#261—41no—
284C2×#261—41no—
285C2×#261—41no—
286C2×#261—41no—
287C2×#261—41no—
288C2×#261—41no—
289C2×#261—41no—
290C2×#261—41no—
291C2×#261—41no—
292C2×#261—41no—
293C2×#261—41no—
294C2×#261—41no—
295C2×#261—41no—
296C2×#261—41no—
297C2×#261—41no—
298C2×#261—84no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13C2×C4⋊C411yescharacteristic
302C2×C4×C13C2×C4⋊C411yescharacteristic
303C2×C4×C13C2×C4⋊C411yescharacteristic
304C2×C4×C13C2×C4⋊C411yescharacteristic
305C2×C4×C13C2×C4⋊C411yescharacteristic
306C2×C4×C13C23×C411yescharacteristic
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13C2×C4⋊C411yescharacteristic
310C2×Dic13C2×C4⋊C411yescharacteristic
311C2×Dic13C2×C4⋊C411yescharacteristic
312C2×Dic13C2×C4⋊C411yescharacteristic
313C2×Dic13C2×C4⋊C411yescharacteristic
314C2×Dic13C22×Q811yescharacteristic
315C4×D13—21no—
316C4×D13—21no—
317C4×D13—21no—
318C4×D13—21no—
319C4×D13—21no—
320C4×D13—21no—
321C4×D13—21no—
322C4×D13—21no—
323C4×D13—21no—
324C4×D13—21no—
325C4×D13—21no—
326C4×D13—21no—
327C4×D13—21no—
328C4×D13—21no—
329C4×D13C2×#4111yescharacteristic
330C4×D13C2×#4111yescharacteristic
331C4×D13C2×#4111yescharacteristic
332C4×D13C2×#4111yescharacteristic
333C8×C13—21no—
334C8×C13—21no—
335C8×C13—21no—
336C8×C13—21no—
337#1055—21no—
338#1055—21no—
339#1055—21no—
340#1055—21no—
341C2×#117—131no—
342C2×#117—131no—
343C22×C4⋊C4—131no—
344#433—131no—
345#433—131no—
346#433—131no—
347#433—131no—
348#433—131no—
349#433—131no—
350#433—131no—
351#433#26111yescharacteristic, complemented
352C2×#107—131no—
353C2×#107—131no—
354C2×#107—131no—
355C2×#107—131no—
356C2×#106—131no—
357C2×#106—131no—
358C2×#106—131no—
359C2×#106—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8—131no—
364C2×#97—131no—
365C2×C4×C8—131no—
366#388—261no—
367#388—261no—
368#387—261no—
369#387—261no—
370#384—131no—
371#382—131no—
372#380—131no—
373#380—131no—
374C4×C4⋊C4—131no—
375C4×C4⋊C4—131no—
376C4×C4⋊C4—131no—
377C4×C4⋊C4—131no—
378C4×C4⋊C4—131no—
379C4×C4⋊C4—131no—
380C4×C4⋊C4—261no—
381C4×C4⋊C4—261no—
382C4×C22⋊C4—261no—
383C4×C22⋊C4—261no—
384#340—131no—
385#340—131no—
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#340—131no—
391#340—131no—
392C22×C13—21no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13C22×C4⋊C411yescharacteristic
396C2×D13—21no—
397C2×D13—21no—
398C2×D13—21no—
399C2×D13—41no—
400C2×D13—41no—
401C2×D13—41no—
402C2×D13—41no—
403C2×D13#52511yescharacteristic
404C2×D13#52511yescharacteristic
405C2×D13#57611yescharacteristic
406C2×D13#57711yescharacteristic
407C2×D13#57711yescharacteristic
408C2×D13#57811yescharacteristic
409#261—42no—
410#261—42no—
411#261—42no—
412#261—42no—
413#261—81no—
414#261—81no—
415#261—81no—
416#261—81no—
417C4×C13—21no—
418C4×C13—21no—
419C4×C13—21no—
420C4×C13—21no—
421C4×C13—21no—
422C4×C13C4×#4111yescharacteristic
423C4×C13C4×#4111yescharacteristic
424Dic13—21no—
425Dic13—21no—
426Dic13—21no—
427Dic13—21no—
428Dic13—21no—
429Dic13#53311yescharacteristic
430Dic13#53311yescharacteristic
431C23×C4—131no—
432C23×C4—261no—
433C22×C8—131no—
434C22×C8—131no—
435C22×C8—131no—
436C22×C8—131no—
437#117—131no—
438#117—131no—
439#117—131no—
440#117—131no—
441#117—131no—
442#117—131no—
443#117—131no—
444#117—262no—
445#117—262no—
446#117C2×#26111yescharacteristic
447C2×C4⋊C4—131no—
448C2×C4⋊C4—131no—
449C2×C4⋊C4—131no—
450C2×C4⋊C4—131no—
451C2×C4⋊C4—131no—
452C2×C4⋊C4—131no—
453C2×C4⋊C4—131no—
454C2×C4⋊C4—131no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—261no—
460C2×C4⋊C4—261no—
461C2×C4⋊C4—261no—
462C2×C22⋊C4—131no—
463C2×C22⋊C4—131no—
464C2×C22⋊C4—261no—
465C2×C22⋊C4—261no—
466C2×C22⋊C4—261no—
467C2×C42—131no—
468C2×C42—131no—
469C2×C42—261no—
470C2×C42—261no—
471C2×C42—261no—
472C2×C42—261no—
473C2×C42—261no—
474C2×C42—261no—
475C2×C42—261no—
476#107—262no—
477#107—262no—
478#107—262no—
479#107—262no—
480#106—262no—
481#106—262no—
482#106—262no—
483#106—262no—
484C4⋊C8—131no—
485C4⋊C8—131no—
486C4⋊C8—131no—
487C4⋊C8—131no—
488C4⋊C8—131no—
489C4⋊C8—131no—
490C4⋊C8C2×#26111yescharacteristic, complemented
491C4⋊C8C2×#26111yescharacteristic, complemented
492C22⋊C8—131no—
493C22⋊C8—131no—
494C22⋊C8—131no—
495C22⋊C8—131no—
496C22⋊C8—131no—
497C22⋊C8—131no—
498C22⋊C8C2×#26111yescharacteristic
499C22⋊C8C2×#26111yescharacteristic
500#97—131no—
501#97—131no—
502#97—131no—
503#97C2×#26111yescharacteristic, complemented
504C4×C8—131no—
505C4×C8—131no—
506C4×C8—131no—
507C4×C8C2×#26111yescharacteristic, complemented
508#95—261no—
509#95—261no—
510#95—261no—
511#95—261no—
512#95—261no—
513#95—261no—
514#95—261no—
515#95—261no—
516#95—261no—
517#95—261no—
518C2×C13—41no—
519C2×C13#229611yescharacteristic
520C2×C13#291211yescharacteristic
521C2×C13#291311yescharacteristic
522D13—41no—
523D13#311811yescharacteristic
524D13#311911yescharacteristic
525D13#312011yescharacteristic
526D13#312111yescharacteristic
527C24—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—261no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—261no—
542C22×C4—261no—
543C22×C4—261no—
544C22×C4—261no—
545C22×C4—264no—
546C22×C4—261no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—1041no—
551C22×C4—1041no—
552C22×C4C22×#26111yescharacteristic
553C2×C8—131no—
554C2×C8—131no—
555C2×C8—131no—
556C2×C8—131no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—261no—
561C2×C8—261no—
562C2×C8—261no—
563C2×C8—261no—
564C2×C8—261no—
565C2×C8C22×#26111yescharacteristic
566C2×C8C22×#26111yescharacteristic
567C2×C8C22×#26111yescharacteristic
568C2×C8C22×#26111yescharacteristic
569C4⋊C4—131no—
570C4⋊C4—131no—
571C4⋊C4—131no—
572C4⋊C4—131no—
573C4⋊C4—131no—
574C4⋊C4—131no—
575C4⋊C4—132no—
576C4⋊C4—132no—
577C4⋊C4—132no—
578C4⋊C4—132no—
579C4⋊C4—261no—
580C4⋊C4—261no—
581C4⋊C4—261no—
582C4⋊C4—261no—
583C4⋊C4—261no—
584C4⋊C4—261no—
585C4⋊C4—261no—
586C4⋊C4—261no—
587C4⋊C4—261no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—264no—
592C4⋊C4—1041no—
593C4⋊C4—1041no—
594C4⋊C4C4⋊#26111yescharacteristic
595C4⋊C4C4⋊#26111yescharacteristic
596C22⋊C4—131no—
597C22⋊C4—131no—
598C22⋊C4—131no—
599C22⋊C4—131no—
600C22⋊C4—131no—
601C22⋊C4—131no—
602C22⋊C4—264no—
603C22⋊C4—1041no—
604C22⋊C4—1041no—
605C22⋊C4C4⋊#26111yescharacteristic
606C22⋊C4C4⋊#26111yescharacteristic
607C42—131no—
608C42—131no—
609C42—131no—
610C42—131no—
611C42—131no—
612C42—131no—
613C42—264no—
614C42—1041no—
615C42—1041no—
616C42—1041no—
617C42—1041no—
618C42—1041no—
619C42—1041no—
620C42C22×#26111yescharacteristic
621C42C22×#26111yescharacteristic
622C13#2136711yescharacteristic, complemented, Sylow
623C23—131no—
624C23—131no—
625C23—261no—
626C23—261no—
627C23—261no—
628C23—261no—
629C23—261no—
630C23—261no—
631C23C2×C4⋊#26111yescharacteristic
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—131no—
635C2×C4—131no—
636C2×C4—131no—
637C2×C4—131no—
638C2×C4—131no—
639C2×C4—131no—
640C2×C4—131no—
641C2×C4—131no—
642C2×C4—131no—
643C2×C4—131no—
644C2×C4—261no—
645C2×C4—261no—
646C2×C4—261no—
647C2×C4—261no—
648C2×C4—261no—
649C2×C4—261no—
650C2×C4—261no—
651C2×C4—261no—
652C2×C4—261no—
653C2×C4—261no—
654C2×C4—261no—
655C2×C4—261no—
656C2×C4—261no—
657C2×C4—261no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—262no—
661C2×C4—262no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—521no—
665C2×C4—521no—
666C2×C4—521no—
667C2×C4—521no—
668C2×C4—521no—
669C2×C4—521no—
670C2×C4—521no—
671C2×C4—521no—
672C2×C4—521no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—521no—
676C2×C4—521no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—1044no—
685C2×C4C2×C4⋊#26111yescharacteristic
686C2×C4C2×C4⋊#26111yescharacteristic
687C2×C4C2×C4⋊#26111yescharacteristic
688C2×C4C2×C4⋊#26111yescharacteristic
689C2×C4C2×C4⋊#26111yescharacteristic
690C2×C4C23×#26111yescharacteristic
691C8—21no—
692C8—21no—
693C8—21no—
694C8—21no—
695C8—261no—
696C8—261no—
697C8—261no—
698C8—261no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—131no—
703C22—131no—
704C22—131no—
705C22—131no—
706C22—131no—
707C22—131no—
708C22—261no—
709C22—261no—
710C22—261no—
711C22—521no—
712C22—521no—
713C22—521no—
714C22—521no—
715C22C22×C4⋊#26111yescharacteristic
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—131no—
722C4—131no—
723C4—261no—
724C4—261no—
725C4—261no—
726C4—261no—
727C4—261no—
728C4—522no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—1041no—
733C4—1041no—
734C4—1041no—
735C4—1041no—
736C4#41×#26111yescharacteristic
737C4#41×#26111yescharacteristic
738C2—41no—
739C2—131no—
740C2—131no—
741C2—131no—
742C2—131no—
743C2—521no—
744C2#1313129611yescharacteristic
745C2#1313149011yescharacteristic
746C2#1313149111yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#433C4
socleC22×C13C22×C4⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenter#433#261
hypocenterC13#21367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #13130949C2semidirect
4. #13130949C2semidirect
5. #13130948C2semidirect
6. #13130947C2semidirect
11. #13130650C2semidirect
12. #13130650C2semidirect
13. C4×#88102C2semidirect
14. C4×#88101C2semidirect
45. C13×#433C4semidirect
46. #11718661C4semidirect
47. #11718501C4semidirect
48. #11718501C4semidirect
53. #11718381C4semidirect
54. #11718381C4semidirect
55. #11718370C4semidirect
57. #11718351C4semidirect
130. C13×C4⋊C8C2×C4semidirect
131. C13×C4⋊C8C2×C4semidirect
134. C13×#97C2×C4semidirect
135. C4×C8×C13C2×C4semidirect
142. #88055C2×C4semidirect
143. #88055C2×C4semidirect
144. #88054C2×C4semidirect
145. #88054C2×C4semidirect
146. #88054C2×C4semidirect
147. #88054C2×C4semidirect
148. C8×Dic13C2×C4semidirect
149. C8×Dic13C2×C4semidirect
150. C4⋊#1055C2×C4semidirect
151. C4⋊#1055C2×C4semidirect
152. #88043C2×C4semidirect
153. C4×#1055C2×C4semidirect
351. #433#261semidirect
490. C4⋊C8C2×#261semidirect
491. C4⋊C8C2×#261semidirect
503. #97C2×#261semidirect
507. C4×C8C2×#261semidirect
622. C13#21367semidirect

Maximal subgroups

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

subgroupindex
#131313142
#131312732
#131309492
#131309482
#131309472
#131307872
#131307862
#131307852
#131306502
C4×#881022
C4×#881012
D13×#4332
#2136713