Finite Group Databasebeta

← #16791591

Subgroups — #16791591

Order 3328.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719071C211yesmaximal, characteristic
2C2×C22⋊C4×#261C211yesmaximal, characteristic
3#13130017C211yesmaximal, characteristic
4#13130017C211yesmaximal, characteristic
5#13130016C211yesmaximal, characteristic, complemented
6#13130015C211yesmaximal, characteristic, complemented
7#13130013C211yesmaximal, characteristic, complemented
8#13130012C211yesmaximal, characteristic, complemented
9#13130011C211yesmaximal, characteristic, complemented
10#13130011C211yesmaximal, characteristic, complemented
11#13130009C211yesmaximal, characteristic
12#13130009C211yesmaximal, characteristic
13C4×(C2×#261)⋊C4C211yesmaximal, characteristic, complemented
14#95×#261C211yesmaximal, characteristic, complemented
15D13×#388C211yesmaximal, characteristic
16C24×#261C2211yescharacteristic
17C22×C22⋊#261C2211yescharacteristic
18C22×C22⋊#261C2211yescharacteristic
19C22×C22⋊#261C2211yescharacteristic
20C22×C4⋊#261C2211yescharacteristic
21C22×C4×#261C2211yescharacteristic
22C22×C4×#261C2211yescharacteristic
23C22×C4×#261C2211yescharacteristic
24C22×C4×#261C2211yescharacteristic
25C22×C4×#261C2211yescharacteristic
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C22⋊C4×D13C2211yescharacteristic
28C2×C22⋊C4×D13C2211yescharacteristic
29C2×C22⋊C4×D13C2211yescharacteristic
30C2×C42×D13C2211yescharacteristic
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
47C2×(C2×#261)⋊C4C2211yescharacteristic
48C2×(C2×#261)⋊C4C2211yescharacteristic
49#11719071C418yescomplemented
50C22⋊C4×#261C418yescomplemented
51C13×#388C411yescharacteristic, complemented
52#11718651C411yescharacteristic, complemented
53#11718612C411yescharacteristic, complemented
54#11718606C411yescharacteristic, complemented
55#11718605C411yescharacteristic, complemented
56#11718601C411yescharacteristic, complemented
57#11718331C411yescharacteristic, complemented
58#11718330C411yescharacteristic, complemented
59D13×#95C2211yescharacteristic
60D13×#95C2211yescharacteristic
61C24×D13C2311yescharacteristic
62C23×#261—22no—
63C23×#261—22no—
64C23×#261—41no—
65C23×#261—41no—
66C23×#261—41no—
67C23×#261—41no—
68C23×#261C2×C414yes—
69C23×#261C2311yescharacteristic
70C23×#261C2311yescharacteristic
71C23×#261C2311yescharacteristic
72C23×#261C2311yescharacteristic
73C23×#261C2311yescharacteristic
74C23×#261C2311yescharacteristic
75C23×#261C2311yescharacteristic
76C23×#261C2311yescharacteristic
77C22×C4×D13C2311yescharacteristic
78C22×C4×D13C2311yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C22×C4×D13C2311yescharacteristic
81C22×C4×D13C2311yescharacteristic
82C22×C4×D13C2311yescharacteristic
83C2×C22⋊#261—22no—
84C2×C22⋊#261—22no—
85C2×C22⋊#261—41no—
86C2×C22⋊#261—41no—
87C2×C22⋊#261—41no—
88C2×C22⋊#261—41no—
89C2×C22⋊#261C2×C414yes—
90C2×C22⋊#261C2×C414yes—
91C2×C22⋊#261C2×C414yes—
92C2×C4⋊#261—41no—
93C2×C4⋊#261—41no—
94C2×C4⋊#261C2×C414yescomplemented
95C2×C4×#261—22no—
96C2×C4×#261—22no—
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×#261—41no—
104C2×C4×#261—41no—
105C2×C4×#261—41no—
106C2×C4×#261—41no—
107C2×C4×#261C2×C414yes—
108C2×C4×#261C2×C414yes—
109C2×C4×#261C2×C414yescomplemented
110C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
111C2×C13×C22⋊C4C2×C411yescharacteristic
112C2×C13×C22⋊C4C2×C411yescharacteristic
113C2×C13×C22⋊C4C2×C411yescharacteristic
114C2×C42×C13C2×C411yescharacteristic, complemented
115C2×C22⋊Dic13C2×C411yescharacteristic
116C2×C22⋊Dic13C2×C411yescharacteristic
117C2×C22⋊Dic13C2×C411yescharacteristic
118C2×#6103C2×C411yescharacteristic
119C2×#6103C2×C411yescharacteristic
120C2×#6103C2×C411yescharacteristic
121C2×#6103C2×C411yescharacteristic
122C2×#6103C2×C411yescharacteristic
123C2×#6103C2×C411yescharacteristic
124C2×C4⋊Dic13C2×C411yescharacteristic, complemented
125C2×#6101C2×C411yescharacteristic, complemented
126C2×#6101C2×C411yescharacteristic, complemented
127C2×C4×Dic13C2×C411yescharacteristic, complemented
128C2×C4×Dic13C2×C411yescharacteristic, complemented
129C2×C4×Dic13C2×C411yescharacteristic, complemented
130C4⋊C4×D13—41no—
131C4⋊C4×D13—41no—
132C22⋊C4×D13—41no—
133C22⋊C4×D13—41no—
134C22⋊C4×D13—41no—
135C22⋊C4×D13—41no—
136C22⋊C4×D13C2×C414yes—
137C22⋊C4×D13C2×C414yes—
138C42×D13—41no—
139C42×D13—41no—
140(C2×#261)⋊C4—22no—
141(C2×#261)⋊C4—22no—
142(C2×#261)⋊C4—22no—
143(C2×#261)⋊C4—22no—
144(C2×#261)⋊C4—22no—
145(C2×#261)⋊C4—22no—
146(C2×#261)⋊C4—41no—
147(C2×#261)⋊C4—41no—
148(C2×#261)⋊C4—41no—
149(C2×#261)⋊C4—41no—
150(C2×#261)⋊C4—41no—
151(C2×#261)⋊C4—41no—
152(C2×#261)⋊C4—41no—
153(C2×#261)⋊C4—41no—
154(C2×#261)⋊C4C2×C414yes—
155(C2×#261)⋊C4C2×C414yes—
156(C2×#261)⋊C4C2×C414yescomplemented
157(C2×#261)⋊C4C2×C414yescomplemented
158C13×#95C2×C411yescharacteristic, complemented
159C13×#95C2×C411yescharacteristic, complemented
160#88071C2×C411yescharacteristic, complemented
161#88071C2×C411yescharacteristic, complemented
162#88071C2×C411yescharacteristic, complemented
163#88071C2×C411yescharacteristic, complemented
164#88071C2×C411yescharacteristic, complemented
165#88071C2×C411yescharacteristic, complemented
166#13788—131nomaximal, Sylow
167C24×C13C22×C411yescharacteristic
168C23×D13—21no—
169C23×D13—21no—
170C23×D13—21no—
171C23×D13—21no—
172C23×D13—21no—
173C23×D13—21no—
174C23×D13—21no—
175C23×D13—21no—
176C23×D13—21no—
177C23×D13—21no—
178C23×D13—21no—
179C23×D13—21no—
180C23×D13C22×C411yescharacteristic
181C23×D13C22×C412yes—
182C23×D13C22×C412yes—
183C23×D13C2411yescharacteristic
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×#261—21no—
205C22×#261—21no—
206C22×#261—21no—
207C22×#261—21no—
208C22×#261—21no—
209C22×#261—21no—
210C22×#261—21no—
211C22×#261—21no—
212C22×#261—21no—
213C22×#261—21no—
214C22×#261—21no—
215C22×#261—21no—
216C22×#261—21no—
217C22×#261—21no—
218C22×#261—21no—
219C22×#261—21no—
220C22×#261—21no—
221C22×#261—21no—
222C22×#261—21no—
223C22×#261—21no—
224C22×#261—21no—
225C22×#261—21no—
226C22×#261—21no—
227C22×#261—21no—
228C22×#261—28no—
229C22×#261—44no—
230C22×#261—44no—
231C22×#261—44no—
232C22×#261—44no—
233C22×#261—44no—
234C22×#261—44no—
235C22×#261C22×C412yes—
236C22×#261C22×C412yes—
237C22×#261C22×C412yes—
238C22×#261C22×C412yes—
239C22×#261C22×C412yes—
240C22×#261C22×C412yes—
241C22×#261C22×C412yes—
242C22×#261C22×C412yes—
243C22×#261#4112yes—
244C22×#261#4112yes—
245C22×#261#4112yes—
246C22×#261#4112yes—
247C22×C4×C13C22×C411yescharacteristic
248C22×C4×C13C22×C411yescharacteristic
249C22×C4×C13C22×C411yescharacteristic
250C22×C4×C13C22×C411yescharacteristic
251C22×C4×C13C22×C411yescharacteristic
252C22×C4×C13C22×C411yescharacteristic
253C22×Dic13C22×C411yescharacteristic
254C22×Dic13C22×C411yescharacteristic
255C22×Dic13C22×C411yescharacteristic
256C22×Dic13C22×C411yescharacteristic
257C22×Dic13C22×C411yescharacteristic
258C22×Dic13C22×C411yescharacteristic
259C2×C4×D13—21no—
260C2×C4×D13—21no—
261C2×C4×D13—21no—
262C2×C4×D13—21no—
263C2×C4×D13—21no—
264C2×C4×D13—21no—
265C2×C4×D13—21no—
266C2×C4×D13—21no—
267C2×C4×D13—21no—
268C2×C4×D13—21no—
269C2×C4×D13—21no—
270C2×C4×D13—21no—
271C2×C4×D13—21no—
272C2×C4×D13—21no—
273C2×C4×D13—21no—
274C2×C4×D13—21no—
275C2×C4×D13—21no—
276C2×C4×D13—21no—
277C2×C4×D13—21no—
278C2×C4×D13—21no—
279C2×C4×D13—21no—
280C2×C4×D13—21no—
281C2×C4×D13—21no—
282C2×C4×D13—21no—
283C2×C4×D13—21no—
284C2×C4×D13—21no—
285C2×C4×D13—21no—
286C2×C4×D13—21no—
287C2×C4×D13—21no—
288C2×C4×D13—21no—
289C2×C4×D13—21no—
290C2×C4×D13—21no—
291C2×C4×D13C22×C412yes—
292C2×C4×D13C22×C412yes—
293C2×C4×D13C22×C412yes—
294C2×C4×D13C22×C412yes—
295C22⋊#261—28no—
296C22⋊#261—44no—
297C22⋊#261—44no—
298C4⋊#261—44no—
299C4×#261—44no—
300C4×#261—44no—
301C4×#261—44no—
302C4×#261—44no—
303C4×#261—44no—
304C13×C4⋊C4—41no—
305C13×C22⋊C4—41no—
306C13×C22⋊C4—41no—
307C13×C22⋊C4C4214yescomplemented
308C42×C13—41no—
309C22⋊Dic13—41no—
310C22⋊Dic13—41no—
311C22⋊Dic13C4214yescomplemented
312#6103—41no—
313#6103—41no—
314#6103—41no—
315#6103—41no—
316#6103C4214yescomplemented
317#6103C4214yescomplemented
318C4⋊Dic13—41no—
319#6101—41no—
320#6101—41no—
321C4×Dic13—41no—
322C4×Dic13—41no—
323C4×Dic13—41no—
324C2×#388—131no—
325C2×#388—131no—
326C2×C4×C22⋊C4—131no—
327#1437—131no—
328#1437—131no—
329#1436—131no—
330#1436—131no—
331C4⋊#95—131no—
332#1434—131no—
333#1434—131no—
334#1434—131no—
335C22⋊#95—131no—
336C22⋊#95—131no—
337C4×#95—131no—
338C4×#95—131no—
339C23×C13—21no—
340C23×C13—21no—
341C23×C13—21no—
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—21no—
345C23×C13C2×C4212yes—
346C23×C13C23×C411yescharacteristic
347C22×D13—21no—
348C22×D13—21no—
349C22×D13—21no—
350C22×D13—21no—
351C22×D13—21no—
352C22×D13—21no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—22no—
361C22×D13—22no—
362C22×D13—22no—
363C22×D13—22no—
364C22×D13—22no—
365C22×D13—41no—
366C22×D13—41no—
367C22×D13—41no—
368C22×D13—41no—
369C22×D13—41no—
370C22×D13—41no—
371C22×D13—41no—
372C22×D13—41no—
373C22×D13—41no—
374C22×D13—41no—
375C22×D13—41no—
376C22×D13—41no—
377C22×D13—41no—
378C22×D13—41no—
379C22×D13—41no—
380C22×D13—41no—
381C22×D13C2×C4212yes—
382C22×D13C23×C411yescharacteristic
383C22×D13C23×C411yescharacteristic
384C22×D13C2×#4111yescharacteristic
385C22×D13C2×#4111yescharacteristic
386C22×D13C2×#4111yescharacteristic
387C22×D13C2×#4111yescharacteristic
388C22×D13H(5,𝔽2)11yescharacteristic
389C22×D13H(5,𝔽2)11yescharacteristic
390C22×D13H(5,𝔽2)11yescharacteristic
391C22×D13H(5,𝔽2)11yescharacteristic
392C22×D13H(5,𝔽2)11yescharacteristic
393C22×D13H(5,𝔽2)11yescharacteristic
394C22×D132−1+411yescharacteristic
395C22×D132−1+411yescharacteristic
396C2×#261—22no—
397C2×#261—22no—
398C2×#261—22no—
399C2×#261—22no—
400C2×#261—22no—
401C2×#261—22no—
402C2×#261—22no—
403C2×#261—22no—
404C2×#261—22no—
405C2×#261—22no—
406C2×#261—22no—
407C2×#261—22no—
408C2×#261—22no—
409C2×#261—22no—
410C2×#261—22no—
411C2×#261—22no—
412C2×#261—22no—
413C2×#261—22no—
414C2×#261—22no—
415C2×#261—22no—
416C2×#261—22no—
417C2×#261—22no—
418C2×#261—22no—
419C2×#261—22no—
420C2×#261—22no—
421C2×#261—22no—
422C2×#261—22no—
423C2×#261—22no—
424C2×#261—22no—
425C2×#261—22no—
426C2×#261—416no—
427C2×#261—41no—
428C2×#261—41no—
429C2×#261—41no—
430C2×#261—41no—
431C2×#261—41no—
432C2×#261—41no—
433C2×#261—41no—
434C2×#261—41no—
435C2×#261—41no—
436C2×#261—41no—
437C2×#261—41no—
438C2×#261—41no—
439C2×#261—41no—
440C2×#261—41no—
441C2×#261—41no—
442C2×#261—41no—
443C2×#261—41no—
444C2×#261—41no—
445C2×#261—41no—
446C2×#261—41no—
447C2×#261—41no—
448C2×#261—41no—
449C2×#261—41no—
450C2×#261—41no—
451C2×#261#11714yes—
452C2×#261#11714yes—
453C2×C4×C13—21no—
454C2×C4×C13—21no—
455C2×C4×C13—21no—
456C2×C4×C13—21no—
457C2×C4×C13—21no—
458C2×C4×C13—21no—
459C2×C4×C13—21no—
460C2×C4×C13—21no—
461C2×C4×C13—21no—
462C2×C4×C13—21no—
463C2×C4×C13—21no—
464C2×C4×C13—21no—
465C2×C4×C13—21no—
466C2×C4×C13—21no—
467C2×C4×C13—21no—
468C2×C4×C13—21no—
469C2×C4×C13C2×C4212yes—
470C2×C4×C13C2×C4212yes—
471C2×Dic13—21no—
472C2×Dic13—21no—
473C2×Dic13—21no—
474C2×Dic13—21no—
475C2×Dic13—21no—
476C2×Dic13—21no—
477C2×Dic13—21no—
478C2×Dic13—21no—
479C2×Dic13—21no—
480C2×Dic13—21no—
481C2×Dic13—21no—
482C2×Dic13—21no—
483C2×Dic13—21no—
484C2×Dic13—21no—
485C2×Dic13—21no—
486C2×Dic13—21no—
487C2×Dic13C2×C4212yes—
488C2×Dic13C2×C4212yes—
489C4×D13—22no—
490C4×D13—22no—
491C4×D13—22no—
492C4×D13—22no—
493C4×D13—22no—
494C4×D13—22no—
495C4×D13—22no—
496C4×D13—22no—
497C4×D13—41no—
498C4×D13—41no—
499C4×D13—41no—
500C4×D13—41no—
501C4×D13—41no—
502C4×D13—41no—
503C4×D13—41no—
504C4×D13—41no—
505C4×D13—41no—
506C4×D13—41no—
507C4×D13—41no—
508C4×D13—41no—
509C4×D13—41no—
510C4×D13—41no—
511C4×D13—41no—
512C4×D13—41no—
513C24×C4—131no—
514C22×C4⋊C4—131no—
515C22×C4⋊C4—131no—
516C22×C22⋊C4—131no—
517C22×C22⋊C4—131no—
518C22×C22⋊C4—131no—
519C22×C22⋊C4—131no—
520C22×C22⋊C4—131no—
521C22×C22⋊C4—131no—
522C22×C42—131no—
523C22×C42—131no—
524C22×C42—131no—
525C22×C42—131no—
526C22×C42—131no—
527C22×C42—131no—
528#388—138no—
529#388—131no—
530#388—131no—
531#388—131no—
532#388—131no—
533#388—131no—
534#388—131no—
535#388—131no—
536#388#26111yescharacteristic, complemented
537C4×C22⋊C4—138no—
538C2×#95—131no—
539C2×#95—131no—
540C2×#95—131no—
541C2×#95—131no—
542C2×#95—131no—
543C2×#95—131no—
544C2×#95—131no—
545C2×#95—131no—
546C2×#95—131no—
547C2×#95—131no—
548C2×#95—131no—
549C2×#95—131no—
550C2×#95—131no—
551C2×#95—131no—
552C2×#95—131no—
553C2×#95—131no—
554C2×#95—131no—
555C2×#95—131no—
556C2×#95—131no—
557C2×#95—131no—
558C22×C13—22no—
559C22×C13—22no—
560C22×C13—22no—
561C22×C13—41no—
562C22×C13—41no—
563C22×C13—41no—
564C22×C13—41no—
565C22×C13C22×C4211yescharacteristic
566C22×C13C4×#4111yescharacteristic
567C22×C13C4×#4111yescharacteristic
568C22×C13#51811yescharacteristic
569C22×C13#51811yescharacteristic
570C22×C13#52011yescharacteristic
571C22×C13#52011yescharacteristic
572C2×D13—22no—
573C2×D13—22no—
574C2×D13—22no—
575C2×D13—41no—
576C2×D13—41no—
577C2×D13—41no—
578C2×D13—41no—
579C2×D13—42no—
580C2×D13—42no—
581C2×D13—42no—
582C2×D13—42no—
583C2×D13—42no—
584C2×D13—42no—
585C2×D13—42no—
586C2×D13—42no—
587C2×D13C2×#11711yescharacteristic
588C2×D13C2×#11711yescharacteristic
589C2×D13C4×#4111yescharacteristic
590C2×D13C4×#4111yescharacteristic
591C2×D13#51811yescharacteristic
592C2×D13#51811yescharacteristic
593C2×D13#51811yescharacteristic
594C2×D13#51811yescharacteristic
595C2×D13#52011yescharacteristic
596C2×D13#52011yescharacteristic
597C2×D13#52011yescharacteristic
598C2×D13#52011yescharacteristic
599C2×D13#53811yescharacteristic
600C2×D13#53811yescharacteristic
601C2×D13#53811yescharacteristic
602C2×D13#53811yescharacteristic
603C2×D13#53811yescharacteristic
604C2×D13#53811yescharacteristic
605C2×D13#53911yescharacteristic
606C2×D13#53911yescharacteristic
607C2×D13#54011yescharacteristic
608C2×D13#54011yescharacteristic
609C2×D13#54011yescharacteristic
610C2×D13#54111yescharacteristic
611C2×D13#54211yescharacteristic
612C2×D13#54211yescharacteristic
613C2×D13#54211yescharacteristic
614C2×D13#54211yescharacteristic
615#261—24no—
616#261—24no—
617#261—42no—
618#261—42no—
619#261—42no—
620#261—42no—
621#261—42no—
622#261—42no—
623C4×C13—22no—
624C4×C13—22no—
625C4×C13—41no—
626C4×C13—41no—
627C4×C13—41no—
628C4×C13—41no—
629Dic13—22no—
630Dic13—22no—
631Dic13—41no—
632Dic13—41no—
633Dic13—41no—
634Dic13—41no—
635C25—131no—
636C23×C4—131no—
637C23×C4—131no—
638C23×C4—131no—
639C23×C4—131no—
640C23×C4—131no—
641C23×C4—131no—
642C23×C4—131no—
643C23×C4—131no—
644C23×C4—131no—
645C23×C4—131no—
646C23×C4—134no—
647C23×C4—131no—
648C23×C4—131no—
649C23×C4—131no—
650C23×C4—131no—
651C23×C4—262no—
652C23×C4—262no—
653C23×C4—521no—
654C23×C4—521no—
655C23×C4—521no—
656C23×C4—521no—
657C2×C4⋊C4—134no—
658C2×C4⋊C4—131no—
659C2×C4⋊C4—131no—
660C2×C4⋊C4—131no—
661C2×C4⋊C4—521no—
662C2×C4⋊C4—521no—
663C2×C4⋊C4—521no—
664C2×C4⋊C4—521no—
665C2×C4⋊C4C2×#26111yescharacteristic, complemented
666C2×C22⋊C4—131no—
667C2×C22⋊C4—131no—
668C2×C22⋊C4—131no—
669C2×C22⋊C4—134no—
670C2×C22⋊C4—134no—
671C2×C22⋊C4—134no—
672C2×C22⋊C4—134no—
673C2×C22⋊C4—134no—
674C2×C22⋊C4—131no—
675C2×C22⋊C4—131no—
676C2×C22⋊C4—131no—
677C2×C22⋊C4—131no—
678C2×C22⋊C4—131no—
679C2×C22⋊C4—131no—
680C2×C22⋊C4—262no—
681C2×C22⋊C4—262no—
682C2×C22⋊C4—521no—
683C2×C22⋊C4—521no—
684C2×C22⋊C4—521no—
685C2×C22⋊C4—521no—
686C2×C22⋊C4—521no—
687C2×C22⋊C4—521no—
688C2×C22⋊C4—521no—
689C2×C22⋊C4—521no—
690C2×C22⋊C4C2×#26111yescharacteristic
691C2×C22⋊C4C2×#26111yescharacteristic
692C2×C22⋊C4C2×#26111yescharacteristic
693C2×C42—134no—
694C2×C42—134no—
695C2×C42—134no—
696C2×C42—131no—
697C2×C42—131no—
698C2×C42—131no—
699C2×C42—262no—
700C2×C42—262no—
701C2×C42—521no—
702C2×C42—521no—
703C2×C42—521no—
704C2×C42—521no—
705C2×C42—521no—
706C2×C42—521no—
707C2×C42—521no—
708C2×C42—521no—
709C2×C42—521no—
710C2×C42—521no—
711C2×C42—521no—
712C2×C42—521no—
713C2×C42C2×#26111yescharacteristic, complemented
714#95—134no—
715#95—134no—
716#95—134no—
717#95—134no—
718#95—131no—
719#95—131no—
720#95—131no—
721#95—131no—
722#95—131no—
723#95—131no—
724#95—262no—
725#95—262no—
726#95—262no—
727#95—262no—
728#95—262no—
729#95—262no—
730#95—521no—
731#95—521no—
732#95—521no—
733#95—521no—
734#95—521no—
735#95—521no—
736#95—521no—
737#95—521no—
738#95C2×#26111yescharacteristic, complemented
739#95C2×#26111yescharacteristic, complemented
740C2×C13—42no—
741C2×C13C4×#11711yescharacteristic
742C2×C13#227511yescharacteristic
743C2×C13#227511yescharacteristic
744C2×C13#233311yescharacteristic
745C2×C13#233411yescharacteristic
746C2×C13#233511yescharacteristic
747C2×C13#233711yescharacteristic
748D13—42no—
749D13#231211yescharacteristic
750D13#231411yescharacteristic
751D13#231811yescharacteristic
752D13#231911yescharacteristic
753D13#233311yescharacteristic
754D13#233411yescharacteristic
755D13#233511yescharacteristic
756D13#233711yescharacteristic
757C24—131no—
758C24—132no—
759C24—132no—
760C24—131no—
761C24—261no—
762C24—261no—
763C24—261no—
764C24—261no—
765C24—261no—
766C24—261no—
767C24—261no—
768C24—261no—
769C24—261no—
770C24—261no—
771C24—261no—
772C24—261no—
773C24C22×#26111yescharacteristic
774C22×C4—132no—
775C22×C4—132no—
776C22×C4—132no—
777C22×C4—132no—
778C22×C4—132no—
779C22×C4—132no—
780C22×C4—131no—
781C22×C4—131no—
782C22×C4—132no—
783C22×C4—132no—
784C22×C4—132no—
785C22×C4—132no—
786C22×C4—132no—
787C22×C4—132no—
788C22×C4—132no—
789C22×C4—132no—
790C22×C4—132no—
791C22×C4—132no—
792C22×C4—131no—
793C22×C4—131no—
794C22×C4—131no—
795C22×C4—131no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—261no—
807C22×C4—261no—
808C22×C4—261no—
809C22×C4—261no—
810C22×C4—261no—
811C22×C4—261no—
812C22×C4—261no—
813C22×C4—261no—
814C22×C4—261no—
815C22×C4—261no—
816C22×C4—261no—
817C22×C4—261no—
818C22×C4—261no—
819C22×C4—261no—
820C22×C4—261no—
821C22×C4—261no—
822C22×C4—261no—
823C22×C4—261no—
824C22×C4—261no—
825C22×C4—261no—
826C22×C4—261no—
827C22×C4—261no—
828C22×C4—268no—
829C22×C4—261no—
830C22×C4—261no—
831C22×C4—261no—
832C22×C4—261no—
833C22×C4—261no—
834C22×C4—261no—
835C22×C4—261no—
836C22×C4—261no—
837C22×C4—261no—
838C22×C4—261no—
839C22×C4—261no—
840C22×C4—261no—
841C22×C4—261no—
842C22×C4—261no—
843C22×C4—261no—
844C22×C4—261no—
845C22×C4—261no—
846C22×C4—261no—
847C22×C4—261no—
848C22×C4—261no—
849C22×C4—261no—
850C22×C4—261no—
851C22×C4—261no—
852C22×C4—261no—
853C22×C4—261no—
854C22×C4—261no—
855C22×C4—261no—
856C22×C4—261no—
857C22×C4—261no—
858C22×C4—261no—
859C22×C4—261no—
860C22×C4—261no—
861C22×C4—261no—
862C22×C4—261no—
863C22×C4—261no—
864C22×C4—261no—
865C22×C4—261no—
866C22×C4—261no—
867C22×C4—261no—
868C22×C4—261no—
869C22×C4—261no—
870C22×C4—261no—
871C22×C4—261no—
872C22×C4—261no—
873C22×C4—524no—
874C22×C4—524no—
875C22×C4—524no—
876C22×C4—524no—
877C22×C4—524no—
878C22×C4—524no—
879C22×C4C22×#26111yescharacteristic
880C22×C4C22×#26111yescharacteristic
881C22×C4C22×#26111yescharacteristic
882C22×C4C22×#26111yescharacteristic
883C22×C4C22×#26111yescharacteristic
884C22×C4C22×#26111yescharacteristic
885C4⋊C4—41no—
886C4⋊C4—521no—
887C4⋊C4—521no—
888C4⋊C4—521no—
889C4⋊C4—524no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C22⋊C4—134no—
893C22⋊C4—134no—
894C22⋊C4—134no—
895C22⋊C4—268no—
896C22⋊C4—521no—
897C22⋊C4—521no—
898C22⋊C4—521no—
899C22⋊C4—521no—
900C22⋊C4—521no—
901C22⋊C4—521no—
902C22⋊C4—524no—
903C22⋊C4—524no—
904C22⋊C4C4×#26114yescomplemented
905C42—41no—
906C42—521no—
907C42—521no—
908C42—521no—
909C42—524no—
910C42—524no—
911C42—524no—
912C42—524no—
913C42—524no—
914C13#1378811yescharacteristic, complemented, Sylow
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—131no—
922C23—131no—
923C23—131no—
924C23—131no—
925C23—131no—
926C23—131no—
927C23—131no—
928C23—131no—
929C23—131no—
930C23—131no—
931C23—131no—
932C23—131no—
933C23—131no—
934C23—131no—
935C23—132no—
936C23—262no—
937C23—262no—
938C23—262no—
939C23—262no—
940C23—262no—
941C23—262no—
942C23—262no—
943C23—262no—
944C23—262no—
945C23—262no—
946C23—262no—
947C23—262no—
948C23—261no—
949C23—261no—
950C23—261no—
951C23—261no—
952C23—261no—
953C23—261no—
954C23—521no—
955C23—521no—
956C23—521no—
957C23—521no—
958C23—521no—
959C23—521no—
960C23—521no—
961C23—521no—
962C23—521no—
963C23—521no—
964C23—521no—
965C23—521no—
966C23—521no—
967C23—521no—
968C23—521no—
969C23—521no—
970C23C2×C4×#26112yes—
971C23C23×#26111yescharacteristic
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—134no—
989C2×C4—134no—
990C2×C4—132no—
991C2×C4—132no—
992C2×C4—262no—
993C2×C4—262no—
994C2×C4—262no—
995C2×C4—262no—
996C2×C4—262no—
997C2×C4—262no—
998C2×C4—262no—
999C2×C4—262no—
1000C2×C4—262no—
1001C2×C4—262no—
1002C2×C4—262no—
1003C2×C4—262no—
1004C2×C4—262no—
1005C2×C4—262no—
1006C2×C4—262no—
1007C2×C4—262no—
1008C2×C4—262no—
1009C2×C4—262no—
1010C2×C4—262no—
1011C2×C4—262no—
1012C2×C4—261no—
1013C2×C4—261no—
1014C2×C4—261no—
1015C2×C4—261no—
1016C2×C4—262no—
1017C2×C4—262no—
1018C2×C4—262no—
1019C2×C4—262no—
1020C2×C4—262no—
1021C2×C4—262no—
1022C2×C4—262no—
1023C2×C4—262no—
1024C2×C4—262no—
1025C2×C4—262no—
1026C2×C4—262no—
1027C2×C4—262no—
1028C2×C4—262no—
1029C2×C4—262no—
1030C2×C4—262no—
1031C2×C4—262no—
1032C2×C4—262no—
1033C2×C4—262no—
1034C2×C4—261no—
1035C2×C4—261no—
1036C2×C4—261no—
1037C2×C4—261no—
1038C2×C4—261no—
1039C2×C4—261no—
1040C2×C4—261no—
1041C2×C4—261no—
1042C2×C4—261no—
1043C2×C4—261no—
1044C2×C4—261no—
1045C2×C4—261no—
1046C2×C4—521no—
1047C2×C4—521no—
1048C2×C4—521no—
1049C2×C4—521no—
1050C2×C4—521no—
1051C2×C4—521no—
1052C2×C4—521no—
1053C2×C4—521no—
1054C2×C4—521no—
1055C2×C4—521no—
1056C2×C4—521no—
1057C2×C4—521no—
1058C2×C4—521no—
1059C2×C4—521no—
1060C2×C4—521no—
1061C2×C4—521no—
1062C2×C4—5216no—
1063C2×C4—521no—
1064C2×C4—521no—
1065C2×C4—521no—
1066C2×C4—521no—
1067C2×C4—521no—
1068C2×C4—521no—
1069C2×C4—521no—
1070C2×C4—521no—
1071C2×C4—521no—
1072C2×C4—521no—
1073C2×C4—521no—
1074C2×C4—521no—
1075C2×C4—521no—
1076C2×C4—521no—
1077C2×C4—521no—
1078C2×C4—521no—
1079C2×C4—521no—
1080C2×C4—521no—
1081C2×C4—521no—
1082C2×C4—521no—
1083C2×C4—521no—
1084C2×C4—521no—
1085C2×C4—521no—
1086C2×C4—521no—
1087C2×C4C2×C4×#26112yes—
1088C2×C4C2×C4×#26112yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—131no—
1097C22—131no—
1098C22—131no—
1099C22—131no—
1100C22—131no—
1101C22—131no—
1102C22—131no—
1103C22—131no—
1104C22—131no—
1105C22—131no—
1106C22—131no—
1107C22—131no—
1108C22—131no—
1109C22—131no—
1110C22—131no—
1111C22—131no—
1112C22—131no—
1113C22—131no—
1114C22—131no—
1115C22—131no—
1116C22—131no—
1117C22—131no—
1118C22—131no—
1119C22—131no—
1120C22—131no—
1121C22—131no—
1122C22—131no—
1123C22—131no—
1124C22—262no—
1125C22—262no—
1126C22—262no—
1127C22—522no—
1128C22—522no—
1129C22—522no—
1130C22—522no—
1131C22—522no—
1132C22—522no—
1133C22—522no—
1134C22—522no—
1135C22—521no—
1136C22—521no—
1137C22—521no—
1138C22—521no—
1139C22C22×C4×#26111yescharacteristic
1140C22#1171962311yescharacteristic
1141C22#1171962311yescharacteristic
1142C22#41×#26111yescharacteristic
1143C22#41×#26111yescharacteristic
1144C22#1171963111yescharacteristic
1145C22#1171963111yescharacteristic
1146C4—22no—
1147C4—22no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—264no—
1153C4—264no—
1154C4—262no—
1155C4—262no—
1156C4—522no—
1157C4—522no—
1158C4—522no—
1159C4—522no—
1160C4—522no—
1161C4—522no—
1162C4—521no—
1163C4—521no—
1164C4—521no—
1165C4—521no—
1166C2—42no—
1167C2—131no—
1168C2—131no—
1169C2—131no—
1170C2—131no—
1171C2—131no—
1172C2—131no—
1173C2—131no—
1174C2—131no—
1175C2—522no—
1176C2#117×#26111yescharacteristic
1177C2#1313127511yescharacteristic
1178C2#1313127511yescharacteristic
1179C2#1313133311yescharacteristic
1180C2#1313133411yescharacteristic
1181C2#1313133511yescharacteristic
1182C2#1313133711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenter#388#261
hypocenterC13#13788
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #13130016C2semidirect
6. #13130015C2semidirect
7. #13130013C2semidirect
8. #13130012C2semidirect
9. #13130011C2semidirect
10. #13130011C2semidirect
13. C4×(C2×#261)⋊C4C2semidirect
14. #95×#261C2semidirect
49. #11719071C4semidirect
50. C22⋊C4×#261C4semidirect
51. C13×#388C4semidirect
52. #11718651C4semidirect
53. #11718612C4semidirect
54. #11718606C4semidirect
55. #11718605C4semidirect
56. #11718601C4semidirect
57. #11718331C4semidirect
58. #11718330C4semidirect
94. C2×C4⋊#261C2×C4semidirect
109. C2×C4×#261C2×C4semidirect
110. C2×C13×C4⋊C4C2×C4semidirect
114. C2×C42×C13C2×C4semidirect
124. C2×C4⋊Dic13C2×C4semidirect
125. C2×#6101C2×C4semidirect
126. C2×#6101C2×C4semidirect
127. C2×C4×Dic13C2×C4semidirect
128. C2×C4×Dic13C2×C4semidirect
129. C2×C4×Dic13C2×C4semidirect
156. (C2×#261)⋊C4C2×C4semidirect
157. (C2×#261)⋊C4C2×C4semidirect
158. C13×#95C2×C4semidirect
159. C13×#95C2×C4semidirect
160. #88071C2×C4semidirect
161. #88071C2×C4semidirect
162. #88071C2×C4semidirect
163. #88071C2×C4semidirect
164. #88071C2×C4semidirect
165. #88071C2×C4semidirect
307. C13×C22⋊C4C42semidirect
311. C22⋊Dic13C42semidirect
316. #6103C42semidirect
317. #6103C42semidirect
536. #388#261semidirect
665. C2×C4⋊C4C2×#261semidirect
713. C2×C42C2×#261semidirect
738. #95C2×#261semidirect
739. #95C2×#261semidirect
904. C22⋊C4C4×#261semidirect
914. C13#13788semidirect

Maximal subgroups

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

subgroupindex
C2×#117190712
C2×C22⋊C4×#2612
#131300172
#131300162
#131300152
#131300132
#131300122
#131300112
#131300092
C4×(C2×#261)⋊C42
#95×#2612
D13×#3882
#1378813