Finite Group Databasebeta

← #16791589

Subgroups — #16791589

Order 3328.

1406 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719082C211yesmaximal, characteristic
2C2×C4⋊C4×#261C211yesmaximal, characteristic
3#13130016C211yesmaximal, characteristic
4#13130016C211yesmaximal, characteristic
5#13130016C211yesmaximal, characteristic
6#13130015C211yesmaximal, characteristic
7#13130013C211yesmaximal, characteristic
8#13130012C211yesmaximal, characteristic
9#13130011C211yesmaximal, characteristic
10#13130011C211yesmaximal, characteristic
11#13130011C211yesmaximal, characteristic
12#13130011C211yesmaximal, characteristic
13C4×(C2×#261)⋊C4C211yesmaximal, 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
24C2×C4⋊C4×D13C2211yescharacteristic
25C2×C4⋊C4×D13C2211yescharacteristic
26C2×C42×D13C2211yescharacteristic
27C2×(C2×#261)⋊C4C2211yescharacteristic
28C2×(C2×#261)⋊C4C2211yescharacteristic
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#11719082C418yescomplemented
48C4⋊C4×#261C418yescomplemented
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—22no—
77C2×C4⋊#261—22no—
78C2×C4⋊#261—41no—
79C2×C4⋊#261—41no—
80C2×C4⋊#261C2×C414yes—
81C2×C4⋊#261C2×C414yes—
82C2×C4×#261—22no—
83C2×C4×#261—22no—
84C2×C4×#261—22no—
85C2×C4×#261—22no—
86C2×C4×#261—41no—
87C2×C4×#261—41no—
88C2×C4×#261—41no—
89C2×C4×#261—41no—
90C2×C4×#261—41no—
91C2×C4×#261—41no—
92C2×C4×#261—41no—
93C2×C4×#261—41no—
94C2×C4×#261—41no—
95C2×C4×#261—41no—
96C2×C4×#261C2×C414yes—
97C2×C4×#261C2×C414yes—
98C2×C4×#261C2×C414yes—
99C2×C4×#261C2×C414yes—
100C2×C13×C4⋊C4C2×C411yescharacteristic
101C2×C13×C4⋊C4C2×C411yescharacteristic
102C2×C42×C13C2×C411yescharacteristic
103C2×C4⋊Dic13C2×C411yescharacteristic
104C2×C4⋊Dic13C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×#6101C2×C411yescharacteristic
108C2×#6101C2×C411yescharacteristic
109C2×C4×Dic13C2×C411yescharacteristic
110C2×C4×Dic13C2×C411yescharacteristic
111C2×C4×Dic13C2×C411yescharacteristic
112C4⋊C4×D13—41no—
113C4⋊C4×D13—41no—
114C4⋊C4×D13C2×C414yes—
115C4⋊C4×D13C2×C414yes—
116C42×D13—41no—
117C42×D13—41no—
118(C2×#261)⋊C4—22no—
119(C2×#261)⋊C4—22no—
120(C2×#261)⋊C4—22no—
121(C2×#261)⋊C4—22no—
122(C2×#261)⋊C4—22no—
123(C2×#261)⋊C4—22no—
124(C2×#261)⋊C4—41no—
125(C2×#261)⋊C4—41no—
126(C2×#261)⋊C4—41no—
127(C2×#261)⋊C4—41no—
128(C2×#261)⋊C4—41no—
129(C2×#261)⋊C4—41no—
130(C2×#261)⋊C4—41no—
131(C2×#261)⋊C4—41no—
132(C2×#261)⋊C4C2×C414yes—
133(C2×#261)⋊C4C2×C414yes—
134(C2×#261)⋊C4C2×C414yes—
135(C2×#261)⋊C4C2×C414yes—
136(C2×#261)⋊C4C2×C414yes—
137(C2×#261)⋊C4C2×C414yes—
138C13×#95C2×C411yescharacteristic
139C13×#95C2×C411yescharacteristic
140C13×#95C2×C411yescharacteristic
141C13×#95C2×C411yescharacteristic
142#88071C2×C411yescharacteristic
143#88071C2×C411yescharacteristic
144#88071C2×C411yescharacteristic
145#88071C2×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#13787—131nomaximal, Sylow
155C23×D13C2411yescharacteristic
156C22×#261—21no—
157C22×#261—21no—
158C22×#261—21no—
159C22×#261—21no—
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×#261C22×C412yes—
201C22×#261C22×C412yes—
202C22×#261C22×C412yes—
203C22×#261C22×C412yes—
204C22×#261C22×C412yes—
205C22×#261C22×C412yes—
206C22×#261C22×C412yes—
207C22×#261C22×C412yes—
208C22×#261#4112yes—
209C22×#261#4112yes—
210C22×#261#4112yes—
211C22×#261#4112yes—
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C22×C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C22×C411yescharacteristic
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C22×C411yescharacteristic
218C22×C4×C13C22×C411yescharacteristic
219C22×Dic13C22×C411yescharacteristic
220C22×Dic13C22×C411yescharacteristic
221C22×Dic13C22×C411yescharacteristic
222C22×Dic13C22×C411yescharacteristic
223C22×Dic13C22×C411yescharacteristic
224C22×Dic13C22×C411yescharacteristic
225C22×Dic13C22×C411yescharacteristic
226C2×C4×D13—21no—
227C2×C4×D13—21no—
228C2×C4×D13—21no—
229C2×C4×D13—21no—
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×D13C22×C412yes—
263C2×C4×D13C22×C412yes—
264C2×C4×D13C22×C412yes—
265C2×C4×D13C22×C412yes—
266C2×C4×D13C22×C412yes—
267C2×C4×D13C22×C412yes—
268C4⋊#261—28no—
269C4⋊#261—44no—
270C4×#261—28no—
271C4×#261—44no—
272C4×#261—44no—
273C4×#261—44no—
274C4×#261—44no—
275C4×#261—44no—
276C13×C4⋊C4—41no—
277C13×C4⋊C4C4214yescomplemented
278C42×C13—41no—
279C4⋊Dic13—41no—
280C4⋊Dic13C4214yescomplemented
281#6101—41no—
282#6101—41no—
283#6101C4214yescomplemented
284#6101C4214yescomplemented
285C4×Dic13—41no—
286C4×Dic13—41no—
287C4×Dic13—41no—
288C2×#387—131no—
289C2×#387—131no—
290C2×C4×C4⋊C4—131no—
291#1436—131no—
292#1436—131no—
293#1436—131no—
294#1436—131no—
295C4⋊#95—131no—
296#1434—131no—
297#1434—131no—
298#1434—131no—
299#1434—131no—
300#1434—131no—
301C4×#95—131no—
302C4×#95—131no—
303C23×C13C23×C411yescharacteristic
304C22×D13C23×C411yescharacteristic
305C22×D13C23×C411yescharacteristic
306C22×D13C2×#4111yescharacteristic
307C22×D13C2×#4111yescharacteristic
308C22×D13C2×#4111yescharacteristic
309C22×D13C2×#4111yescharacteristic
310C22×D13H(5,𝔽2)11yescharacteristic
311C22×D13H(5,𝔽2)11yescharacteristic
312C22×D13H(5,𝔽2)11yescharacteristic
313C22×D13H(5,𝔽2)11yescharacteristic
314C22×D132−1+411yescharacteristic
315C22×D132−1+411yescharacteristic
316C22×D132−1+411yescharacteristic
317C22×D132−1+411yescharacteristic
318C2×#261—22no—
319C2×#261—22no—
320C2×#261—22no—
321C2×#261—22no—
322C2×#261—22no—
323C2×#261—22no—
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—41no—
349C2×#261—41no—
350C2×#261—41no—
351C2×#261—41no—
352C2×#261—41no—
353C2×#261—41no—
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#11714yes—
373C2×#261#11714yes—
374C2×C4×C13—21no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—21no—
379C2×C4×C13—21no—
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×C13C2×C4212yes—
393C2×C4×C13C2×C4212yes—
394C2×C4×C13C2×C4212yes—
395C2×Dic13—21no—
396C2×Dic13—21no—
397C2×Dic13—21no—
398C2×Dic13—21no—
399C2×Dic13—21no—
400C2×Dic13—21no—
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×Dic13C2×C4212yes—
414C2×Dic13C2×C4212yes—
415C2×Dic13C2×C4212yes—
416C4×D13—22no—
417C4×D13—22no—
418C4×D13—22no—
419C4×D13—22no—
420C4×D13—22no—
421C4×D13—22no—
422C4×D13—22no—
423C4×D13—22no—
424C4×D13—22no—
425C4×D13—22no—
426C4×D13—22no—
427C4×D13—22no—
428C4×D13—41no—
429C4×D13—41no—
430C4×D13—41no—
431C4×D13—41no—
432C4×D13—41no—
433C4×D13—41no—
434C4×D13—41no—
435C4×D13—41no—
436C4×D13—41no—
437C4×D13—41no—
438C4×D13—41no—
439C4×D13—41no—
440C4×D13—41no—
441C4×D13—41no—
442C4×D13—41no—
443C4×D13—41no—
444C22×C4⋊C4—131no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C42—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42—131no—
452C22×C42—131no—
453C22×C42—131no—
454C22×C42—131no—
455#387—138no—
456#387—131no—
457#387—131no—
458#387—131no—
459#387—131no—
460#387—131no—
461#387—131no—
462#387—131no—
463#387#26111yescharacteristic, complemented
464C4×C4⋊C4—138no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
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—
489C22×C13C22×C4211yescharacteristic
490C22×C13C4×#4111yescharacteristic
491C22×C13C4×#4111yescharacteristic
492C22×C13#51811yescharacteristic
493C22×C13#51911yescharacteristic
494C22×C13#52011yescharacteristic
495C22×C13#52011yescharacteristic
496C2×D13C2×#11711yescharacteristic
497C2×D13C2×#11711yescharacteristic
498C2×D13C4×#4111yescharacteristic
499C2×D13C4×#4111yescharacteristic
500C2×D13#51811yescharacteristic
501C2×D13#51811yescharacteristic
502C2×D13#51911yescharacteristic
503C2×D13#51911yescharacteristic
504C2×D13#52011yescharacteristic
505C2×D13#52011yescharacteristic
506C2×D13#52011yescharacteristic
507C2×D13#52011yescharacteristic
508C2×D13#53811yescharacteristic
509C2×D13#53811yescharacteristic
510C2×D13#53911yescharacteristic
511C2×D13#53911yescharacteristic
512C2×D13#53911yescharacteristic
513C2×D13#53911yescharacteristic
514C2×D13#53911yescharacteristic
515C2×D13#53911yescharacteristic
516C2×D13#54011yescharacteristic
517C2×D13#54111yescharacteristic
518C2×D13#54111yescharacteristic
519C2×D13#54111yescharacteristic
520C2×D13#54211yescharacteristic
521C2×D13#54211yescharacteristic
522C2×D13#54211yescharacteristic
523C2×D13#54211yescharacteristic
524#261—24no—
525#261—24no—
526#261—42no—
527#261—42no—
528#261—42no—
529#261—42no—
530#261—42no—
531#261—42no—
532C4×C13—22no—
533C4×C13—22no—
534C4×C13—22no—
535C4×C13—41no—
536C4×C13—41no—
537C4×C13—41no—
538C4×C13—41no—
539Dic13—22no—
540Dic13—22no—
541Dic13—22no—
542Dic13—41no—
543Dic13—41no—
544Dic13—41no—
545Dic13—41no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
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—
561C2×C4⋊C4—131no—
562C2×C4⋊C4—131no—
563C2×C4⋊C4—131no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—131no—
569C2×C4⋊C4—131no—
570C2×C4⋊C4—131no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—521no—
574C2×C4⋊C4—521no—
575C2×C4⋊C4—521no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4C2×#26111yescharacteristic
578C2×C4⋊C4C2×#26111yescharacteristic
579C2×C42—134no—
580C2×C42—134no—
581C2×C42—134no—
582C2×C42—134no—
583C2×C42—131no—
584C2×C42—131no—
585C2×C42—131no—
586C2×C42—262no—
587C2×C42—262no—
588C2×C42—262no—
589C2×C42—262no—
590C2×C42—521no—
591C2×C42—521no—
592C2×C42—521no—
593C2×C42—521no—
594C2×C42—521no—
595C2×C42—521no—
596C2×C42—521no—
597C2×C42—521no—
598C2×C42—521no—
599C2×C42—521no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42C2×#26111yescharacteristic
603#95—134no—
604#95—134no—
605#95—134no—
606#95—134no—
607#95—134no—
608#95—134no—
609#95—131no—
610#95—131no—
611#95—131no—
612#95—131no—
613#95—131no—
614#95—131no—
615#95—131no—
616#95—131no—
617#95—131no—
618#95—131no—
619#95—131no—
620#95—131no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—521no—
628#95—521no—
629#95—521no—
630#95—521no—
631#95—521no—
632#95—521no—
633#95—521no—
634#95—521no—
635#95C2×#26111yescharacteristic
636#95C2×#26111yescharacteristic
637#95C2×#26111yescharacteristic
638#95C2×#26111yescharacteristic
639C2×C13C4×#11711yescharacteristic
640C2×C13#227511yescharacteristic
641C2×C13#227611yescharacteristic
642C2×C13#233211yescharacteristic
643C2×C13#233411yescharacteristic
644C2×C13#233511yescharacteristic
645C2×C13#233611yescharacteristic
646D13#231311yescharacteristic
647D13#231411yescharacteristic
648D13#231811yescharacteristic
649D13#232011yescharacteristic
650D13#233211yescharacteristic
651D13#233411yescharacteristic
652D13#233511yescharacteristic
653D13#233611yescharacteristic
654C24—131no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—131no—
662C22×C4—131no—
663C22×C4—131no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—131no—
677C22×C4—131no—
678C22×C4—131no—
679C22×C4—131no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
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×C4C22×#26111yescharacteristic
761C22×C4C22×#26111yescharacteristic
762C22×C4C22×#26111yescharacteristic
763C22×C4C22×#26111yescharacteristic
764C22×C4C22×#26111yescharacteristic
765C22×C4C22×#26111yescharacteristic
766C22×C4C22×#26111yescharacteristic
767C4⋊C4—41no—
768C4⋊C4—134no—
769C4⋊C4—134no—
770C4⋊C4—134no—
771C4⋊C4—268no—
772C4⋊C4—521no—
773C4⋊C4—521no—
774C4⋊C4—521no—
775C4⋊C4—524no—
776C4⋊C4C4×#26114yescomplemented
777C42—41no—
778C42—268no—
779C42—521no—
780C42—521no—
781C42—521no—
782C42—524no—
783C42—524no—
784C42—524no—
785C42—524no—
786C42—524no—
787C13#1378711yescharacteristic, complemented, Sylow
788C23—131no—
789C23—131no—
790C23—131no—
791C23—131no—
792C23—131no—
793C23—131no—
794C23—131no—
795C23—131no—
796C23—131no—
797C23—131no—
798C23—131no—
799C23—131no—
800C23—131no—
801C23—131no—
802C23C23×#26111yescharacteristic
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—134no—
822C2×C4—134no—
823C2×C4—132no—
824C2×C4—132no—
825C2×C4—132no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
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—261no—
851C2×C4—261no—
852C2×C4—261no—
853C2×C4—261no—
854C2×C4—261no—
855C2×C4—261no—
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—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—261no—
875C2×C4—261no—
876C2×C4—261no—
877C2×C4—261no—
878C2×C4—261no—
879C2×C4—261no—
880C2×C4—261no—
881C2×C4—261no—
882C2×C4—261no—
883C2×C4—261no—
884C2×C4—261no—
885C2×C4—261no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
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×C4C2×C4×#26112yes—
927C2×C4C2×C4×#26112yes—
928C2×C4C2×C4×#26112yes—
929C22—131no—
930C22—131no—
931C22—131no—
932C22—131no—
933C22—131no—
934C22—131no—
935C22—131no—
936C22—131no—
937C22—131no—
938C22—131no—
939C22—131no—
940C22—131no—
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—
957C22C22×C4×#26111yescharacteristic
958C22#1171962311yescharacteristic
959C22#1171962711yescharacteristic
960C22#41×#26111yescharacteristic
961C22#41×#26111yescharacteristic
962C22#1171963111yescharacteristic
963C22#1171963111yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—41no—
971C4—264no—
972C4—264no—
973C4—262no—
974C4—262no—
975C4—262no—
976C4—522no—
977C4—522no—
978C4—522no—
979C4—522no—
980C4—522no—
981C4—522no—
982C4—521no—
983C4—521no—
984C4—521no—
985C4—521no—
986C2—131no—
987C2—131no—
988C2—131no—
989C2—131no—
990C2—131no—
991C2—131no—
992C2—131no—
993C2—131no—
994C2#117×#26111yescharacteristic
995C2#1313127511yescharacteristic
996C2#1313127611yescharacteristic
997C2#1313133211yescharacteristic
998C2#1313133411yescharacteristic
999C2#1313133511yescharacteristic
1000C2#1313133611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#387C4
socleC23×C13C23×C4
prime radical, cosocleC23×D13C24
hypercenter#387#261
hypocenterC13#13787
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
47. #11719082C4semidirect
48. C4⋊C4×#261C4semidirect
49. C13×#387C4semidirect
50. #11718642C4semidirect
51. #11718639C4semidirect
52. #11718594C4semidirect
57. #11718316C4semidirect
58. #11718315C4semidirect
59. #11718314C4semidirect
60. #11718313C4semidirect
277. C13×C4⋊C4C42semidirect
280. C4⋊Dic13C42semidirect
283. #6101C42semidirect
284. #6101C42semidirect
463. #387#261semidirect
776. C4⋊C4C4×#261semidirect
787. C13#13787semidirect

Maximal subgroups

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

subgroupindex
C2×#117190822
C2×C4⋊C4×#2612
#131300162
#131300152
#131300132
#131300122
#131300112
C4×(C2×#261)⋊C42
#95×#2612
D13×#3872
#1378713