Finite Group Databasebeta

← #16791601

Subgroups — #16791601

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719083C211yesmaximal, characteristic
2C2×#11719082C211yesmaximal, characteristic
3#13130016C211yesmaximal, characteristic
4#13130016C211yesmaximal, characteristic
5#13130016C211yesmaximal, characteristic
6#13130016C211yesmaximal, characteristic
7#13130016C211yesmaximal, characteristic
8#13130015C211yesmaximal, characteristic
9#13130014C211yesmaximal, characteristic
10#13130013C211yesmaximal, characteristic
11#13130011C211yesmaximal, characteristic
12C4×(C2×#261)⋊C4C211yesmaximal, characteristic
13#95×#261C211yesmaximal, characteristic
14#95×#261C211yesmaximal, characteristic
15D13×#387C211yesmaximal, characteristic
16C22×C4⋊#261C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18C22×C4⋊#261C2211yescharacteristic
19C22×C4⋊#261C2211yescharacteristic
20C22×C4×#261C2211yescharacteristic
21C22×C4×#261C2211yescharacteristic
22C22×C4×#261C2211yescharacteristic
23C22×C4×#261C2211yescharacteristic
24C22×C4×#261C2211yescharacteristic
25C22×C4×#261C2211yescharacteristic
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×(C2×#261)⋊C4C2211yescharacteristic
30C2×(C2×#261)⋊C4C2211yescharacteristic
31C2×(C2×#261)⋊C4C2211yescharacteristic
32C2×(C2×#261)⋊C4C2211yescharacteristic
33C2×(C2×#261)⋊C4C2211yescharacteristic
34C2×(C2×#261)⋊C4C2211yescharacteristic
35C2×(C2×#261)⋊C4C2211yescharacteristic
36C2×(C2×#261)⋊C4C2211yescharacteristic
37C2×(C2×#261)⋊C4C2211yescharacteristic
38C2×(C2×#261)⋊C4C2211yescharacteristic
39C2×(C2×#261)⋊C4C2211yescharacteristic
40C2×(C2×#261)⋊C4C2211yescharacteristic
41C2×(C2×#261)⋊C4C2211yescharacteristic
42C2×(C2×#261)⋊C4C2211yescharacteristic
43C2×(C2×#261)⋊C4C2211yescharacteristic
44C2×(C2×#261)⋊C4C2211yescharacteristic
45C2×(C2×#261)⋊C4C2211yescharacteristic
46C2×(C2×#261)⋊C4C2211yescharacteristic
47#11719083C418yescomplemented
48#11719082C418yescomplemented
49C13×#387C411yescharacteristic, complemented
50#11718642C411yescharacteristic, complemented
51#11718639C411yescharacteristic, complemented
52#11718594C411yescharacteristic, complemented
53D13×#95C2211yescharacteristic
54D13×#95C2211yescharacteristic
55D13×#95C2211yescharacteristic
56D13×#95C2211yescharacteristic
57#11718316C411yescharacteristic, complemented
58#11718315C411yescharacteristic, complemented
59#11718314C411yescharacteristic, complemented
60#11718313C411yescharacteristic, complemented
61C23×#261C2311yescharacteristic
62C23×#261C2311yescharacteristic
63C23×#261C2311yescharacteristic
64C23×#261C2311yescharacteristic
65C23×#261C2311yescharacteristic
66C23×#261C2311yescharacteristic
67C23×#261C2311yescharacteristic
68C23×#261C2311yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×C4×D13C2311yescharacteristic
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×C4×D13C2311yescharacteristic
76C2×C4⋊#261—41no—
77C2×C4⋊#261—41no—
78C2×C4⋊#261—41no—
79C2×C4⋊#261—41no—
80C2×C4⋊#261—41no—
81C2×C4⋊#261—41no—
82C2×C4⋊#261—41no—
83C2×C4⋊#261—41no—
84C2×C4⋊#261C2×C414yes—
85C2×C4⋊#261C2×C414yes—
86C2×C4⋊#261C2×C414yes—
87C2×C4⋊#261C2×C414yes—
88C2×C4×#261—22no—
89C2×C4×#261—22no—
90C2×C4×#261—22no—
91C2×C4×#261—41no—
92C2×C4×#261—41no—
93C2×C4×#261—41no—
94C2×C4×#261—41no—
95C2×C4×#261—41no—
96C2×C4×#261—41no—
97C2×C4×#261—41no—
98C2×C4×#261—41no—
99C2×C4×#261—41no—
100C2×C4×#261—41no—
101C2×C4×#261—41no—
102C2×C4×#261—41no—
103C2×C4×#261C2×C414yes—
104C2×C4×#261C2×C414yes—
105C2×C4×#261Q814yes—
106C2×C13×C4⋊C4C2×C411yescharacteristic
107C2×C13×C4⋊C4C2×C411yescharacteristic
108C2×C42×C13C2×C411yescharacteristic
109C2×C4⋊Dic13C2×C411yescharacteristic
110C2×C4⋊Dic13C2×C411yescharacteristic
111C2×#6101C2×C411yescharacteristic
112C2×#6101C2×C411yescharacteristic
113C2×#6101C2×C411yescharacteristic
114C2×#6101C2×C411yescharacteristic
115C2×C4×Dic13C2×C411yescharacteristic
116C2×C4×Dic13C2×C411yescharacteristic
117C2×C4×Dic13C2×C411yescharacteristic
118C4⋊C4×D13—41no—
119C4⋊C4×D13—41no—
120C4⋊C4×D13C2×C414yes—
121C4⋊C4×D13C2×C414yes—
122C42×D13—41no—
123C42×D13—41no—
124(C2×#261)⋊C4—22no—
125(C2×#261)⋊C4—22no—
126(C2×#261)⋊C4—22no—
127(C2×#261)⋊C4—22no—
128(C2×#261)⋊C4—22no—
129(C2×#261)⋊C4—22no—
130(C2×#261)⋊C4—41no—
131(C2×#261)⋊C4—41no—
132(C2×#261)⋊C4—41no—
133(C2×#261)⋊C4—41no—
134(C2×#261)⋊C4—41no—
135(C2×#261)⋊C4—41no—
136(C2×#261)⋊C4C2×C414yes—
137(C2×#261)⋊C4C2×C414yes—
138(C2×#261)⋊C4C2×C414yes—
139(C2×#261)⋊C4C2×C414yes—
140(C2×#261)⋊C4C2×C414yes—
141(C2×#261)⋊C4C2×C414yes—
142C13×#95C2×C411yescharacteristic
143C13×#95C2×C411yescharacteristic
144C13×#95C2×C411yescharacteristic
145C13×#95C2×C411yescharacteristic
146#88071C2×C411yescharacteristic
147#88071C2×C411yescharacteristic
148#88071C2×C411yescharacteristic
149#88071C2×C411yescharacteristic
150#88071C2×C411yescharacteristic
151#88071C2×C411yescharacteristic
152#88071C2×C411yescharacteristic
153#88071C2×C411yescharacteristic
154#88071C2×C411yescharacteristic
155#88071C2×C411yescharacteristic
156#88071C2×C411yescharacteristic
157#88071C2×C411yescharacteristic
158#13792—131nomaximal, Sylow
159C23×D13C2411yescharacteristic
160C22×#261—21no—
161C22×#261—21no—
162C22×#261—21no—
163C22×#261—21no—
164C22×#261—21no—
165C22×#261—21no—
166C22×#261—21no—
167C22×#261—21no—
168C22×#261—21no—
169C22×#261—21no—
170C22×#261—21no—
171C22×#261—21no—
172C22×#261—21no—
173C22×#261—21no—
174C22×#261—21no—
175C22×#261—21no—
176C22×#261—21no—
177C22×#261—21no—
178C22×#261—21no—
179C22×#261—21no—
180C22×#261—21no—
181C22×#261—21no—
182C22×#261—21no—
183C22×#261—21no—
184C22×#261—21no—
185C22×#261—21no—
186C22×#261—21no—
187C22×#261—21no—
188C22×#261—21no—
189C22×#261—21no—
190C22×#261—21no—
191C22×#261—21no—
192C22×#261—21no—
193C22×#261—21no—
194C22×#261—21no—
195C22×#261—21no—
196C22×#261—21no—
197C22×#261—21no—
198C22×#261—21no—
199C22×#261—21no—
200C22×#261—21no—
201C22×#261—21no—
202C22×#261—21no—
203C22×#261—21no—
204C22×#261C22×C412yes—
205C22×#261C22×C412yes—
206C22×#261C22×C412yes—
207C22×#261C22×C412yes—
208C22×#261C22×C412yes—
209C22×#261C22×C412yes—
210C22×#261C22×C412yes—
211C22×#261C22×C412yes—
212C22×#261C2×Q812yes—
213C22×#261C2×Q812yes—
214C22×#261#4112yes—
215C22×#261#4112yes—
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C22×C411yescharacteristic
218C22×C4×C13C22×C411yescharacteristic
219C22×C4×C13C22×C411yescharacteristic
220C22×C4×C13C22×C411yescharacteristic
221C22×C4×C13C22×C411yescharacteristic
222C22×C4×C13C22×C411yescharacteristic
223C22×Dic13C22×C411yescharacteristic
224C22×Dic13C22×C411yescharacteristic
225C22×Dic13C22×C411yescharacteristic
226C22×Dic13C22×C411yescharacteristic
227C22×Dic13C22×C411yescharacteristic
228C22×Dic13C22×C411yescharacteristic
229C22×Dic13C22×C411yescharacteristic
230C2×C4×D13—21no—
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×C4×D13—21no—
234C2×C4×D13—21no—
235C2×C4×D13—21no—
236C2×C4×D13—21no—
237C2×C4×D13—21no—
238C2×C4×D13—21no—
239C2×C4×D13—21no—
240C2×C4×D13—21no—
241C2×C4×D13—21no—
242C2×C4×D13—21no—
243C2×C4×D13—21no—
244C2×C4×D13—21no—
245C2×C4×D13—21no—
246C2×C4×D13—21no—
247C2×C4×D13—21no—
248C2×C4×D13—21no—
249C2×C4×D13—21no—
250C2×C4×D13—21no—
251C2×C4×D13—21no—
252C2×C4×D13—21no—
253C2×C4×D13—21no—
254C2×C4×D13—21no—
255C2×C4×D13—21no—
256C2×C4×D13—21no—
257C2×C4×D13—21no—
258C2×C4×D13—21no—
259C2×C4×D13—21no—
260C2×C4×D13—21no—
261C2×C4×D13—21no—
262C2×C4×D13—21no—
263C2×C4×D13—21no—
264C2×C4×D13C22×C412yes—
265C2×C4×D13C22×C412yes—
266C2×C4×D13C22×C412yes—
267C2×C4×D13C22×C412yes—
268C2×C4×D13C22×C412yes—
269C2×C4×D13C22×C412yes—
270C2×C4×D13C2×Q812yes—
271C2×C4×D13#4112yes—
272C4⋊#261—44no—
273C4⋊#261—44no—
274C4⋊#261—44no—
275C4⋊#261—44no—
276C4×#261—44no—
277C4×#261—44no—
278C4×#261—44no—
279C4×#261—44no—
280C4×#261—44no—
281C4×#261—44no—
282C13×C4⋊C4—41no—
283C13×C4⋊C4C4214yescomplemented
284C42×C13—41no—
285C4⋊Dic13—41no—
286C4⋊Dic13C4214yescomplemented
287#6101—41no—
288#6101—41no—
289#6101C4214yescomplemented
290#6101C4214yescomplemented
291C4×Dic13—41no—
292C4×Dic13—41no—
293C4×Dic13—41no—
294C2×#389—131no—
295C2×#387—131no—
296C2×#387—131no—
297#1436—131no—
298#1436—131no—
299#1436—131no—
300#1436—131no—
301#1436—131no—
302#1436—131no—
303C4⋊#95—131no—
304C4⋊#95—131no—
305#1434—131no—
306C4×#95—131no—
307C4×#95—131no—
308C4×#95—131no—
309C23×C13C23×C411yescharacteristic
310C22×D13C23×C411yescharacteristic
311C22×D13C23×C411yescharacteristic
312C22×D13C22×Q811yescharacteristic
313C22×D13C2×#4111yescharacteristic
314C22×D13C2×#4111yescharacteristic
315C22×D13C2×#4111yescharacteristic
316C22×D13H(5,𝔽2)11yescharacteristic
317C22×D13H(5,𝔽2)11yescharacteristic
318C22×D13H(5,𝔽2)11yescharacteristic
319C22×D13H(5,𝔽2)11yescharacteristic
320C22×D13H(5,𝔽2)11yescharacteristic
321C22×D132−1+411yescharacteristic
322C22×D132−1+411yescharacteristic
323C22×D132−1+411yescharacteristic
324C2×#261—22no—
325C2×#261—22no—
326C2×#261—22no—
327C2×#261—22no—
328C2×#261—22no—
329C2×#261—22no—
330C2×#261—22no—
331C2×#261—22no—
332C2×#261—22no—
333C2×#261—22no—
334C2×#261—22no—
335C2×#261—22no—
336C2×#261—22no—
337C2×#261—22no—
338C2×#261—22no—
339C2×#261—22no—
340C2×#261—22no—
341C2×#261—22no—
342C2×#261—22no—
343C2×#261—22no—
344C2×#261—22no—
345C2×#261—22no—
346C2×#261—22no—
347C2×#261—22no—
348C2×#261—22no—
349C2×#261—22no—
350C2×#261—22no—
351C2×#261—22no—
352C2×#261—22no—
353C2×#261—22no—
354C2×#261—41no—
355C2×#261—41no—
356C2×#261—41no—
357C2×#261—41no—
358C2×#261—41no—
359C2×#261—41no—
360C2×#261—41no—
361C2×#261—41no—
362C2×#261—41no—
363C2×#261—41no—
364C2×#261—41no—
365C2×#261—41no—
366C2×#261—41no—
367C2×#261—41no—
368C2×#261—41no—
369C2×#261—41no—
370C2×#261—41no—
371C2×#261—41no—
372C2×#261—41no—
373C2×#261—41no—
374C2×#261—41no—
375C2×#261—41no—
376C2×#261—41no—
377C2×#261—41no—
378C2×#261C4×Q814yes—
379C2×#261C4×Q814yes—
380C2×C4×C13—21no—
381C2×C4×C13—21no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13—21no—
390C2×C4×C13—21no—
391C2×C4×C13—21no—
392C2×C4×C13—21no—
393C2×C4×C13—21no—
394C2×C4×C13—21no—
395C2×C4×C13—21no—
396C2×C4×C13—21no—
397C2×C4×C13C2×C4212yes—
398C2×C4×C13C2×C4212yes—
399C2×C4×C13C2×C4212yes—
400C2×C4×C13C4×Q812yes—
401C2×Dic13—21no—
402C2×Dic13—21no—
403C2×Dic13—21no—
404C2×Dic13—21no—
405C2×Dic13—21no—
406C2×Dic13—21no—
407C2×Dic13—21no—
408C2×Dic13—21no—
409C2×Dic13—21no—
410C2×Dic13—21no—
411C2×Dic13—21no—
412C2×Dic13—21no—
413C2×Dic13—21no—
414C2×Dic13—21no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—21no—
418C2×Dic13C2×C4212yes—
419C2×Dic13C2×C4212yes—
420C2×Dic13C2×C4212yes—
421C2×Dic13C4×Q812yes—
422C4×D13—22no—
423C4×D13—22no—
424C4×D13—22no—
425C4×D13—22no—
426C4×D13—22no—
427C4×D13—22no—
428C4×D13—22no—
429C4×D13—22no—
430C4×D13—22no—
431C4×D13—22no—
432C4×D13—22no—
433C4×D13—22no—
434C4×D13—22no—
435C4×D13—22no—
436C4×D13—22no—
437C4×D13—22no—
438C4×D13—41no—
439C4×D13—41no—
440C4×D13—41no—
441C4×D13—41no—
442C4×D13—41no—
443C4×D13—41no—
444C4×D13—41no—
445C4×D13—41no—
446C4×D13—41no—
447C4×D13—41no—
448C4×D13—41no—
449C4×D13—41no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4—131no—
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463#389—138no—
464#387—138no—
465#387—131no—
466#387—131no—
467#387—131no—
468#387—131no—
469#387—131no—
470#387—131no—
471#387—131no—
472#387#26111yescharacteristic, complemented
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C22×C13C22×C4211yescharacteristic
496C22×C13C2×C4×Q811yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13#51811yescharacteristic
499C22×C13#52011yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C2×D13C2×C4×Q811yescharacteristic
503C2×D13C2×C4×Q811yescharacteristic
504C2×D13C4×#4111yescharacteristic
505C2×D13C4×#4111yescharacteristic
506C2×D13#51811yescharacteristic
507C2×D13#51811yescharacteristic
508C2×D13#51811yescharacteristic
509C2×D13#51911yescharacteristic
510C2×D13#52011yescharacteristic
511C2×D13#52011yescharacteristic
512C2×D13#52011yescharacteristic
513C2×D13#52011yescharacteristic
514C2×D13#53811yescharacteristic
515C2×D13#53811yescharacteristic
516C2×D13#53811yescharacteristic
517C2×D13#53911yescharacteristic
518C2×D13#53911yescharacteristic
519C2×D13#53911yescharacteristic
520C2×D13#54011yescharacteristic
521C2×D13#54011yescharacteristic
522C2×D13#54111yescharacteristic
523C2×D13#54111yescharacteristic
524C2×D13#54211yescharacteristic
525C2×D13#54211yescharacteristic
526C2×D13#54311yescharacteristic
527C2×D13#54411yescharacteristic
528C2×D13#54411yescharacteristic
529C2×D13#54411yescharacteristic
530#261—24no—
531#261—24no—
532#261—42no—
533#261—42no—
534#261—42no—
535#261—42no—
536#261—42no—
537#261—42no—
538C4×C13—22no—
539C4×C13—22no—
540C4×C13—22no—
541C4×C13—22no—
542C4×C13—41no—
543C4×C13—41no—
544C4×C13—41no—
545Dic13—22no—
546Dic13—22no—
547Dic13—22no—
548Dic13—22no—
549Dic13—41no—
550Dic13—41no—
551Dic13—41no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C2×C4⋊C4—131no—
568C2×C4⋊C4—131no—
569C2×C4⋊C4—131no—
570C2×C4⋊C4—134no—
571C2×C4⋊C4—134no—
572C2×C4⋊C4—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—131no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—521no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4—521no—
584C2×C4⋊C4—521no—
585C2×C4⋊C4—521no—
586C2×C4⋊C4—521no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4C2×#26111yescharacteristic
590C2×C4⋊C4C2×#26111yescharacteristic
591C2×C42—134no—
592C2×C42—134no—
593C2×C42—134no—
594C2×C42—131no—
595C2×C42—131no—
596C2×C42—131no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604C2×C42—521no—
605C2×C42—521no—
606C2×C42—521no—
607C2×C42—521no—
608C2×C42—521no—
609C2×C42—521no—
610C2×C42—521no—
611C2×C42—521no—
612C2×C42—521no—
613C2×C42—521no—
614C2×C42C2×#26111yescharacteristic
615#95—134no—
616#95—134no—
617#95—134no—
618#95—134no—
619#95—134no—
620#95—134no—
621#95—131no—
622#95—131no—
623#95—131no—
624#95—131no—
625#95—131no—
626#95—131no—
627#95—131no—
628#95—131no—
629#95—131no—
630#95—131no—
631#95—131no—
632#95—131no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—262no—
637#95—262no—
638#95—262no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95—521no—
643#95—521no—
644#95—521no—
645#95C2×#26111yescharacteristic
646#95C2×#26111yescharacteristic
647#95C2×#26111yescharacteristic
648#95C2×#26111yescharacteristic
649C2×C13C42×Q811yescharacteristic
650C2×C13#227411yescharacteristic
651C2×C13#227511yescharacteristic
652C2×C13#232911yescharacteristic
653C2×C13#233011yescharacteristic
654C2×C13#233411yescharacteristic
655C2×C13#233511yescharacteristic
656D13#232911yescharacteristic
657D13#232911yescharacteristic
658D13#233011yescharacteristic
659D13#233111yescharacteristic
660D13#233311yescharacteristic
661D13#233411yescharacteristic
662D13#233511yescharacteristic
663D13#233611yescharacteristic
664C24—131no—
665C22×C4—132no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—131no—
672C22×C4—131no—
673C22×C4—131no—
674C22×C4—131no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—131no—
690C22×C4—131no—
691C22×C4—131no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4C22×#26111yescharacteristic
771C22×C4C22×#26111yescharacteristic
772C22×C4C22×#26111yescharacteristic
773C22×C4C22×#26111yescharacteristic
774C22×C4C22×#26111yescharacteristic
775C22×C4C22×#26111yescharacteristic
776C22×C4C22×#26111yescharacteristic
777C4⋊C4—41no—
778C4⋊C4—134no—
779C4⋊C4—134no—
780C4⋊C4—134no—
781C4⋊C4—521no—
782C4⋊C4—521no—
783C4⋊C4—521no—
784C4⋊C4—524no—
785C4⋊C4—524no—
786C4⋊C4—524no—
787C4⋊C4—524no—
788C4⋊C4C4×#26114yescomplemented
789C42—41no—
790C42—521no—
791C42—521no—
792C42—521no—
793C42—524no—
794C42—524no—
795C42—524no—
796C42—524no—
797C42—524no—
798C42—524no—
799C13#1379211yescharacteristic, complemented, Sylow
800C23—131no—
801C23—131no—
802C23—131no—
803C23—131no—
804C23—131no—
805C23—131no—
806C23—131no—
807C23—131no—
808C23—131no—
809C23—131no—
810C23—131no—
811C23—131no—
812C23—131no—
813C23—131no—
814C23C23×#26111yescharacteristic
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—134no—
833C2×C4—134no—
834C2×C4—132no—
835C2×C4—132no—
836C2×C4—132no—
837C2×C4—132no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—261no—
867C2×C4—261no—
868C2×C4—261no—
869C2×C4—261no—
870C2×C4—261no—
871C2×C4—261no—
872C2×C4—261no—
873C2×C4—261no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—261no—
893C2×C4—261no—
894C2×C4—261no—
895C2×C4—261no—
896C2×C4—261no—
897C2×C4—261no—
898C2×C4—261no—
899C2×C4—261no—
900C2×C4—261no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4C2×C4×#26112yes—
938C2×C4C2×C4×#26112yes—
939C2×C4C2×C4×#26112yes—
940C2×C4Q8×#26112yes—
941C22—131no—
942C22—131no—
943C22—131no—
944C22—131no—
945C22—131no—
946C22—131no—
947C22—131no—
948C22—131no—
949C22—131no—
950C22—131no—
951C22—131no—
952C22—131no—
953C22—131no—
954C22—131no—
955C22—131no—
956C22—131no—
957C22—131no—
958C22—131no—
959C22—131no—
960C22—131no—
961C22—131no—
962C22—131no—
963C22—131no—
964C22—131no—
965C22—131no—
966C22—131no—
967C22—131no—
968C22—131no—
969C22C22×C4×#26111yescharacteristic
970C22#1171962311yescharacteristic
971C22C2×Q8×#26111yescharacteristic
972C22#41×#26111yescharacteristic
973C22#1171963111yescharacteristic
974C22#1171963111yescharacteristic
975C22#1171963111yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—264no—
984C4—264no—
985C4—262no—
986C4—262no—
987C4—262no—
988C4—262no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4—522no—
993C4—522no—
994C4—522no—
995C4—521no—
996C4—521no—
997C4—521no—
998C2—131no—
999C2—131no—
1000C2—131no—
1001C2—131no—
1002C2—131no—
1003C2—131no—
1004C2—131no—
1005C2—131no—
1006C2C4×Q8×#26111yescharacteristic
1007C2#1313127311yescharacteristic
1008C2#1313127511yescharacteristic
1009C2#1313132911yescharacteristic
1010C2#1313133011yescharacteristic
1011C2#1313133411yescharacteristic
1012C2#1313133511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#387C4
socleC23×C13C23×C4
prime radical, cosocleC23×D13C24
hypercenter#387#261
hypocenterC13#13792
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
47. #11719083C4semidirect
48. #11719082C4semidirect
49. C13×#387C4semidirect
50. #11718642C4semidirect
51. #11718639C4semidirect
52. #11718594C4semidirect
57. #11718316C4semidirect
58. #11718315C4semidirect
59. #11718314C4semidirect
60. #11718313C4semidirect
283. C13×C4⋊C4C42semidirect
286. C4⋊Dic13C42semidirect
289. #6101C42semidirect
290. #6101C42semidirect
472. #387#261semidirect
788. C4⋊C4C4×#261semidirect
799. C13#13792semidirect

Maximal subgroups

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

subgroupindex
C2×#117190832
C2×#117190822
#131300162
#131300152
#131300142
#131300132
#131300112
C4×(C2×#261)⋊C42
#95×#2612
D13×#3872
#1379213