Finite Group Databasebeta

← #16797516

Subgroups — #16797516

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719147C211yesmaximal, characteristic
2C2×#11719146C211yesmaximal, characteristic
3#13130578C211yesmaximal, characteristic, complemented
4#13130578C211yesmaximal, characteristic, complemented
5#13130577C211yesmaximal, characteristic, complemented
6#13130577C211yesmaximal, characteristic, complemented
7#13130574C211yesmaximal, characteristic, complemented
8#13130573C211yesmaximal, characteristic, complemented
9#13130570C211yesmaximal, characteristic, complemented
10C22⋊C4×#1057C211yesmaximal, characteristic, complemented
11#13130566C211yesmaximal, characteristic, complemented
12#13130566C211yesmaximal, characteristic, complemented
13#13130562C211yesmaximal, characteristic, complemented
14C4×C22⋊#1057C211yesmaximal, characteristic, complemented
15#13117321C211yesmaximal, characteristic
16C22×#6129C2211yescharacteristic
17C22×#6122C2211yescharacteristic
18C23×#1057C2211yescharacteristic
19C22×#6118C2211yescharacteristic
20C22×D13⋊C8C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C2×#88131C2211yescharacteristic
23C2×C22⋊#1057C2211yescharacteristic
24C2×C22⋊#1057C2211yescharacteristic
25C2×C22⋊#1057C2211yescharacteristic
26C2×C22⋊#1057C2211yescharacteristic
27C2×C22⋊#1057C2211yescharacteristic
28C2×C22⋊#1057C2211yescharacteristic
29#11719147C418yescomplemented
30#11719146C418yescomplemented
31C2×#88111C2211yescharacteristic
32C2×#88111C2211yescharacteristic
33C2×#88110C2211yescharacteristic
34C2×#88110C2211yescharacteristic
35C2×#88110C2211yescharacteristic
36C2×#88110C2211yescharacteristic
37C2×C4×#1057C2211yescharacteristic
38C2×C4×#1057C2211yescharacteristic
39C2×C4×#1057C2211yescharacteristic
40C2×C4×#1057C2211yescharacteristic
41C13×#386C411yescharacteristic
42#11718881C411yescharacteristic
43#11718874C411yescharacteristic
44#11718619C411yescharacteristic
45#11718618C411yescharacteristic
46#11718618C411yescharacteristic
47C22⋊C4×Dic13C2211yescharacteristic
48C22⋊C4×Dic13C2211yescharacteristic
49#11718327C2211yescharacteristic
50#11718327C2211yescharacteristic
51#11718307C411yescharacteristic
52#11718307C411yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61C22×D4×C13C2×C411yescharacteristic
62C23×C4×C13C2×C411yescharacteristic
63C22×C22⋊D13C2×C411yescharacteristic
64C22×C22⋊D13C2×C411yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C2×#6129—41no—
69C2×#6129—41no—
70C2×#6129—41no—
71C2×#6129—41no—
72C2×#6129C2×C414yes—
73C2×#6129C2×C414yes—
74C22×C4×D13C2311yescharacteristic
75C22×Dic26C2×C411yescharacteristic
76C2×#6122—41no—
77C2×#6122—41no—
78C2×#6122C2×C414yescomplemented
79C22×#1057—41no—
80C22×#1057—41no—
81C22×#1057C2×C414yescomplemented
82C22×#1057C2311yescharacteristic
83C22×#1057C2311yescharacteristic
84C22×#1057C2311yescharacteristic
85C22×#1057C2311yescharacteristic
86C22×#1057C2311yescharacteristic
87C22×#1057C2311yescharacteristic
88C22×#1057C2311yescharacteristic
89C22×#1057C2311yescharacteristic
90C2×#6118—41no—
91C2×#6118—41no—
92C2×#6118C2×C414yescomplemented
93C2×D13⋊C8—41no—
94C2×D13⋊C8—41no—
95C2×D13⋊C8C2×C414yescomplemented
96C2×C13×C22⋊C4C2×C411yescharacteristic
97C2×C13×C22⋊C4C2×C411yescharacteristic
98C2×C13×C22⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic13C2×C411yescharacteristic
100C2×C22⋊Dic13C2×C411yescharacteristic
101C2×C22⋊Dic13C2×C411yescharacteristic
102C2×#6103C2×C411yescharacteristic
103C2×#6103C2×C411yescharacteristic
104C2×#6103C2×C411yescharacteristic
105C2×#6103C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×#6101C2×C411yescharacteristic
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13C2×C411yescharacteristic
111C2×C4×Dic13C2×C411yescharacteristic
112C2×C4×Dic13C2311yescharacteristic
113C2×C4×Dic13C2311yescharacteristic
114C2×C4×Dic13C2311yescharacteristic
115C2×C4×Dic13C2311yescharacteristic
116#88131—41no—
117#88131—41no—
118C22⋊#1057C2×C414yes—
119C22⋊#1057C2×C414yes—
120C22⋊#1057C2×C414yes—
121C22⋊#1057C2×C414yes—
122C22⋊#1057C2×C414yescomplemented
123C22⋊#1057C2×C414yescomplemented
124#88111C2×C414yescomplemented
125#88111C2×C414yescomplemented
126#88110—41no—
127#88110—41no—
128#88110—41no—
129#88110—41no—
130C4×#1057—41no—
131C4×#1057—41no—
132C4×#1057—41no—
133C4×#1057—41no—
134C13×#95C2×C411yescharacteristic
135C13×#95C2×C411yescharacteristic
136#88071C2×C411yescharacteristic
137#88071C2×C411yescharacteristic
138#88071C2×C411yescharacteristic
139#88071C2×C411yescharacteristic
140#88071C2×C411yescharacteristic
141#88071C2×C411yescharacteristic
142#20531—131nomaximal, Sylow
143C24×C13C22×C411yescharacteristic
144C24×C13C22×C411yescharacteristic
145C23×D13C22×C411yescharacteristic
146C2×D4×C13—41no—
147C2×D4×C13—41no—
148C2×D4×C13C4214yes—
149C22×C4×C13—22no—
150C22×C4×C13—41no—
151C22×C4×C13—41no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C2×C22⋊D13—41no—
158C2×C22⋊D13—41no—
159C2×C22⋊D13—41no—
160C2×C22⋊D13—41no—
161C2×C22⋊D13C4214yes—
162C2×C22⋊D13C4214yes—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—22no—
172C22×Dic13—41no—
173C22×Dic13—41no—
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C412yes—
180C22×Dic13C22×C412yes—
181C22×Dic13C22×C412yes—
182C22×Dic13C22×C412yes—
183C22×Dic13C22×C411yescharacteristic
184C22×Dic13C2411yescharacteristic
185#6129—44no—
186#6129—44no—
187#6129—44no—
188#6129—44no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13C22×C412yes—
194C2×C4×D13C22×C412yes—
195C2×Dic26—41no—
196C2×Dic26—41no—
197C2×Dic26C4214yes—
198#6122—44no—
199C2×#1057—21no—
200C2×#1057—21no—
201C2×#1057—21no—
202C2×#1057—21no—
203C2×#1057—21no—
204C2×#1057—21no—
205C2×#1057—21no—
206C2×#1057—21no—
207C2×#1057—21no—
208C2×#1057—21no—
209C2×#1057—21no—
210C2×#1057—21no—
211C2×#1057—21no—
212C2×#1057—21no—
213C2×#1057—21no—
214C2×#1057—21no—
215C2×#1057—44no—
216C2×#1057C22×C412yes—
217C2×#1057C22×C412yes—
218C2×#1057C22×C412yes—
219C2×#1057C22×C412yes—
220C2×#1057C22×C412yes—
221C2×#1057C22×C412yes—
222C2×#1057C22×C412yes—
223C2×#1057C22×C412yes—
224#6118—44no—
225D13⋊C8—44no—
226C13×C22⋊C4—22no—
227C13×C22⋊C4—41no—
228C13×C22⋊C4—41no—
229C22⋊Dic13—22no—
230C22⋊Dic13—41no—
231C22⋊Dic13—41no—
232#6103—22no—
233#6103—22no—
234#6103—41no—
235#6103—41no—
236#6101—41no—
237#6101—41no—
238C4×Dic13—21no—
239C4×Dic13—21no—
240C4×Dic13—21no—
241C4×Dic13—21no—
242C4×Dic13—21no—
243C4×Dic13—21no—
244C4×Dic13—21no—
245C4×Dic13—21no—
246C4×Dic13—41no—
247C4×Dic13—41no—
248C2×#408—131no—
249C2×#408—131no—
250#2297—131no—
251#1753—131no—
252#1753—131no—
253#1753—131no—
254#1753—131no—
255#1752—131no—
256#1752—131no—
257C8×C22⋊C4—131no—
258C8×C22⋊C4—131no—
259#1750—131no—
260#1750—131no—
261#1749—131no—
262C4×C22⋊C8—131no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13C2×C4212yes—
276C23×C13C2×C4212yes—
277C23×C13C23×C411yescharacteristic
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13—21no—
284C22×D13C2×C4212yes—
285D4×C13—44no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—44no—
300C2×C4×C13C2×C4212yes—
301C2×C4×C13#13112yes—
302C22⋊D13—44no—
303C22⋊D13—44no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13—44no—
328C2×Dic13C2×C4212yes—
329C2×Dic13C2×C4212yes—
330C2×Dic13#13112yes—
331C2×Dic13C23×C411yescharacteristic
332C2×Dic13C23×C411yescharacteristic
333C2×Dic13H(5,𝔽2)11yescharacteristic
334C2×Dic13H(5,𝔽2)11yescharacteristic
335C2×Dic13H(5,𝔽2)11yescharacteristic
336C2×Dic13H(5,𝔽2)11yescharacteristic
337C4×D13—22no—
338C4×D13—22no—
339C4×D13—22no—
340C4×D13—22no—
341Dic26—44no—
342#1057—22no—
343#1057—22no—
344#1057—22no—
345#1057—22no—
346#1057—22no—
347#1057—22no—
348#1057—22no—
349#1057—22no—
350C22×#41—131no—
351C22×M16—131no—
352C22×M16—131no—
353C23×C8—131no—
354C23×C8—131no—
355C2×#117—131no—
356C22×C42—131no—
357#408—138no—
358#408—138no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8—131no—
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×C22⋊C8—131no—
367C2×#97—131no—
368C2×#97—131no—
369C2×#97—131no—
370C2×#97—131no—
371C2×C4×C8—131no—
372C2×C4×C8—131no—
373C2×C4×C8—131no—
374C2×C4×C8—131no—
375#391—131no—
376#391—131no—
377#390—131no—
378#390—131no—
379#386—131no—
380#386—131no—
381#386—131no—
382#386#26111yescharacteristic
383C4×C22⋊C4—131no—
384C4×C22⋊C4—131no—
385C4×C22⋊C4—131no—
386C4×C22⋊C4—131no—
387#336—131no—
388#336—131no—
389#336—131no—
390#336—131no—
391#336—131no—
392#336—131no—
393#336—131no—
394#336—131no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13C22×C4211yescharacteristic
410C22×C13#51811yescharacteristic
411C22×C13#51811yescharacteristic
412C22×C13C2×#13111yescharacteristic
413C22×C13C2×#13111yescharacteristic
414C22×C13#56811yescharacteristic
415C22×C13#56811yescharacteristic
416C2×D13—22no—
417C2×D13—22no—
418C2×D13—22no—
419C2×D13—41no—
420C2×D13—41no—
421C2×D13—41no—
422C2×D13—41no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13—41no—
428Dic13—22no—
429Dic13—22no—
430Dic13—22no—
431Dic13—41no—
432Dic13—41no—
433Dic13—41no—
434Dic13#51811yescharacteristic
435Dic13#51811yescharacteristic
436Dic13#51811yescharacteristic
437Dic13#51811yescharacteristic
438C2×#41—134no—
439C2×#41—134no—
440C2×#41—521no—
441C2×#41—521no—
442C2×#41—521no—
443C2×#41—521no—
444C22×Q8—131no—
445C22×D4—131no—
446C22×D4—131no—
447C22×D4C2×#26111yescharacteristic
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4C2×#26111yescharacteristic
453C2×M16—134no—
454C2×M16—134no—
455C2×M16—521no—
456C2×M16—521no—
457C2×M16—521no—
458C2×M16—521no—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8—131no—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—134no—
468C22×C8—134no—
469C22×C8—521no—
470C22×C8—521no—
471C22×C8—521no—
472C22×C8—521no—
473#117—521no—
474#117—521no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4C2×#26111yescharacteristic
485C2×C22⋊C4C2×#26111yescharacteristic
486C2×C22⋊C4C2×#26111yescharacteristic
487C2×C42—131no—
488C2×C42—131no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—131no—
493C2×C42—521no—
494C2×C42—521no—
495C22⋊C8—134no—
496C22⋊C8—134no—
497C22⋊C8—134no—
498C22⋊C8—134no—
499C22⋊C8—134no—
500C22⋊C8—134no—
501C22⋊C8—134no—
502C22⋊C8—134no—
503#97—521no—
504#97—521no—
505#97—521no—
506#97—521no—
507C4×C8—521no—
508C4×C8—521no—
509C4×C8—521no—
510C4×C8—521no—
511#95—131no—
512#95—131no—
513#95—131no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95C2×#26111yescharacteristic
518#95C2×#26111yescharacteristic
519C2×C13—42no—
520C2×C13—42no—
521C2×C13#227311yescharacteristic
522C2×C13C4×#13111yescharacteristic
523C2×C13#287511yescharacteristic
524C2×C13#297611yescharacteristic
525C2×C13#297611yescharacteristic
526C2×C13#298111yescharacteristic
527C2×C13#298111yescharacteristic
528D13—42no—
529C24—131no—
530C24C22×#26111yescharacteristic
531C24C22×#26111yescharacteristic
532#41—524no—
533#41—524no—
534#41—524no—
535#41—524no—
536C2×Q8—134no—
537C2×Q8—521no—
538C2×Q8—521no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—134no—
542C2×D4—134no—
543C2×D4—521no—
544C2×D4—521no—
545C2×D4—521no—
546C2×D4—521no—
547C2×D4C4×#26114yes—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—131no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—132no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—131no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—262no—
577C22×C4—521no—
578C22×C4—521no—
579C22×C4C22×#26111yescharacteristic
580C22×C4C22×#26111yescharacteristic
581C22×C4C22×#26111yescharacteristic
582C22×C4C22×#26111yescharacteristic
583C22×C4C22×#26111yescharacteristic
584M16—524no—
585M16—524no—
586C2×C8—132no—
587C2×C8—132no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—132no—
591C2×C8—132no—
592C2×C8—132no—
593C2×C8—132no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C2×C8—261no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—524no—
611C2×C8—524no—
612C4⋊C4—521no—
613C4⋊C4—521no—
614C22⋊C4—22no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—262no—
620C22⋊C4—521no—
621C22⋊C4—521no—
622C22⋊C4—521no—
623C22⋊C4—521no—
624C42—261no—
625C42—261no—
626C42—261no—
627C42—261no—
628C42—261no—
629C42—261no—
630C42—261no—
631C42—261no—
632C42—521no—
633C42—521no—
634C13#2053111yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—132no—
648C23—261no—
649C23—261no—
650C23—261no—
651C23—261no—
652C23—261no—
653C23—261no—
654C23C2×C4×#26112yes—
655C23C2×C4×#26112yes—
656C23C23×#26111yescharacteristic
657Q8—524no—
658D4—44no—
659D4—524no—
660D4—524no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—44no—
675C2×C4—131no—
676C2×C4—131no—
677C2×C4—131no—
678C2×C4—131no—
679C2×C4—131no—
680C2×C4—131no—
681C2×C4—132no—
682C2×C4—132no—
683C2×C4—132no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—261no—
697C2×C4—261no—
698C2×C4—261no—
699C2×C4—261no—
700C2×C4—261no—
701C2×C4—261no—
702C2×C4—261no—
703C2×C4—261no—
704C2×C4—261no—
705C2×C4—261no—
706C2×C4—261no—
707C2×C4—261no—
708C2×C4—261no—
709C2×C4—261no—
710C2×C4—261no—
711C2×C4—524no—
712C2×C4C2×C4×#26112yes—
713C2×C4#8823812yes—
714C8—262no—
715C8—262no—
716C8—262no—
717C8—262no—
718C8—262no—
719C8—262no—
720C8—262no—
721C8—262no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—262no—
737C22—262no—
738C22—262no—
739C22—521no—
740C22—521no—
741C22—521no—
742C22—521no—
743C22C22×C4×#26111yescharacteristic
744C22C2×#8823811yescharacteristic
745C22#1171962111yescharacteristic
746C22#1171962311yescharacteristic
747C22#1171962311yescharacteristic
748C22D13⋊#13111yescharacteristic
749C22#1171962911yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—131no—
756C4—131no—
757C4—131no—
758C4—131no—
759C4—262no—
760C4—262no—
761C4—262no—
762C4—521no—
763C4—521no—
764C4—521no—
765C2—42no—
766C2—42no—
767C2—522no—
768C2#1313127211yescharacteristic
769C2C4×#8823811yescharacteristic
770C2#1313140711yescharacteristic
771C2#1313170211yescharacteristic
772C2#1313170411yescharacteristic
773C2#1313172411yescharacteristic
774C2#1313172611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#386C4
socleC23×C13C23×C4
prime radicalC22×#6129C22
cosocleC22×Dic13C24
hypercenter#386#261
hypocenterC13#20531
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #13130578C2semidirect
4. #13130578C2semidirect
5. #13130577C2semidirect
6. #13130577C2semidirect
7. #13130574C2semidirect
8. #13130573C2semidirect
9. #13130570C2semidirect
10. C22⋊C4×#1057C2semidirect
11. #13130566C2semidirect
12. #13130566C2semidirect
13. #13130562C2semidirect
14. C4×C22⋊#1057C2semidirect
29. #11719147C4semidirect
30. #11719146C4semidirect
78. C2×#6122C2×C4semidirect
81. C22×#1057C2×C4semidirect
92. C2×#6118C2×C4semidirect
95. C2×D13⋊C8C2×C4semidirect
122. C22⋊#1057C2×C4semidirect
123. C22⋊#1057C2×C4semidirect
124. #88111C2×C4semidirect
125. #88111C2×C4semidirect
634. C13#20531semidirect

Maximal subgroups

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

subgroupindex
C2×#117191472
C2×#117191462
#131305782
#131305772
#131305742
#131305732
#131305702
C22⋊C4×#10572
#131305662
#131305622
C4×C22⋊#10572
#131173212
#2053113