Finite Group Databasebeta

← #16792301

Subgroups — #16792301

Order 3328.

1146 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130024C211yesmaximal, characteristic
2#13130023C211yesmaximal, characteristic
3#13130022C211yesmaximal, characteristic
4#13130022C211yesmaximal, characteristic
5#13130021C211yesmaximal, characteristic
6#13130021C211yesmaximal, characteristic
7#13130016C211yesmaximal, characteristic
8#13130016C211yesmaximal, characteristic
9#13130016C211yesmaximal, characteristic
10#13130015C211yesmaximal, characteristic
11#13130015C211yesmaximal, characteristic
12#13130014C211yesmaximal, characteristic
13#13130012C211yesmaximal, characteristic
14#13130011C211yesmaximal, characteristic
15D13×#382C211yesmaximal, characteristic
16C22×C4⋊#261C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18C22×C4⋊#261C2211yescharacteristic
19C22×C4⋊#261C2211yescharacteristic
20C22×C4×#261C2211yescharacteristic
21C22×C4×#261C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C4⋊C4×D13C2211yescharacteristic
24C2×C42×D13C2211yescharacteristic
25C2×(C2×#261)⋊C4C2211yescharacteristic
26C2×(C2×#261)⋊C4C2211yescharacteristic
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
47C13×#382C411yescharacteristic, complemented
48#11718638C411yescharacteristic, complemented
49#11718638C411yescharacteristic, complemented
50#11718597C411yescharacteristic, complemented
51D13×#95C2211yescharacteristic
52D13×#95C2211yescharacteristic
53D13×#95C2211yescharacteristic
54D13×#95C2211yescharacteristic
55#11718311C411yescharacteristic, complemented
56#11718311C411yescharacteristic, complemented
57#11718311C411yescharacteristic, complemented
58#11718311C411yescharacteristic, complemented
59C23×#261C2311yescharacteristic
60C23×#261C2311yescharacteristic
61C23×#261C2311yescharacteristic
62C23×#261C2311yescharacteristic
63C23×#261C2311yescharacteristic
64C23×#261C2311yescharacteristic
65C23×#261C2311yescharacteristic
66C23×#261C2311yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×C4×D13C2311yescharacteristic
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C2×C4⋊#261—22no—
75C2×C4⋊#261—22no—
76C2×C4⋊#261—22no—
77C2×C4⋊#261—22no—
78C2×C4⋊#261—22no—
79C2×C4⋊#261—41no—
80C2×C4⋊#261—41no—
81C2×C4⋊#261—41no—
82C2×C4⋊#261—41no—
83C2×C4⋊#261—41no—
84C2×C4⋊#261—41no—
85C2×C4⋊#261—41no—
86C2×C4×#261—22no—
87C2×C4×#261—41no—
88C2×C4×#261—41no—
89C2×C4×#261—41no—
90C2×C4×#261—41no—
91C2×C4×#261—41no—
92C2×C13×C4⋊C4C2×C411yescharacteristic
93C2×C13×C4⋊C4C2×C411yescharacteristic
94C2×C42×C13C2×C411yescharacteristic
95C2×C4⋊Dic13C2×C411yescharacteristic
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×C4×Dic13C2×C411yescharacteristic
102C2×C4×Dic13C2×C411yescharacteristic
103C2×C4×Dic13C2×C411yescharacteristic
104C4⋊C4×D13—41no—
105C4⋊C4×D13—41no—
106C4⋊C4×D13—41no—
107C4⋊C4×D13—41no—
108C42×D13—22no—
109C42×D13—22no—
110(C2×#261)⋊C4—22no—
111(C2×#261)⋊C4—22no—
112(C2×#261)⋊C4—22no—
113(C2×#261)⋊C4—22no—
114(C2×#261)⋊C4—22no—
115(C2×#261)⋊C4—22no—
116(C2×#261)⋊C4—22no—
117(C2×#261)⋊C4—41no—
118(C2×#261)⋊C4—41no—
119(C2×#261)⋊C4—41no—
120(C2×#261)⋊C4—41no—
121(C2×#261)⋊C4—41no—
122(C2×#261)⋊C4—41no—
123(C2×#261)⋊C4—41no—
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)⋊C4Q814yes—
132C13×#95C2×C411yescharacteristic
133C13×#95C2×C411yescharacteristic
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#88071C2×C411yescharacteristic
143#88071C2×C411yescharacteristic
144#88071C2×C411yescharacteristic
145#88071C2×C411yescharacteristic
146#88071C2×C411yescharacteristic
147#88071C2×C411yescharacteristic
148#14455—131nomaximal, Sylow
149C23×D13C2411yescharacteristic
150C22×#261—21no—
151C22×#261—21no—
152C22×#261—21no—
153C22×#261—21no—
154C22×#261—21no—
155C22×#261—21no—
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×#261—21no—
201C22×#261—21no—
202C22×#261C2×Q812yes—
203C22×#261C2×Q812yes—
204C22×#261#4112yes—
205C22×#261#4112yes—
206C22×C4×C13C22×C411yescharacteristic
207C22×C4×C13C22×C411yescharacteristic
208C22×C4×C13C22×C411yescharacteristic
209C22×C4×C13C22×C411yescharacteristic
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×Dic13C22×C411yescharacteristic
214C22×Dic13C22×C411yescharacteristic
215C22×Dic13C22×C411yescharacteristic
216C22×Dic13C22×C411yescharacteristic
217C22×Dic13C22×C411yescharacteristic
218C22×Dic13C22×C411yescharacteristic
219C22×Dic13C22×C411yescharacteristic
220C2×C4×D13—21no—
221C2×C4×D13—21no—
222C2×C4×D13—21no—
223C2×C4×D13—21no—
224C2×C4×D13—21no—
225C2×C4×D13—21no—
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×D13C2×Q812yes—
259C2×C4×D13#4112yes—
260C2×C4×D13#4112yes—
261C2×C4×D13#4112yes—
262C4⋊#261—44no—
263C4⋊#261—44no—
264C4⋊#261—44no—
265C4⋊#261—44no—
266C4×#261—44no—
267C4×#261—44no—
268C13×C4⋊C4—41no—
269C13×C4⋊C4—41no—
270C42×C13—22no—
271C4⋊Dic13—41no—
272C4⋊Dic13—41no—
273#6101—41no—
274#6101—41no—
275#6101—41no—
276#6101—41no—
277C4×Dic13—22no—
278C4×Dic13—22no—
279C4×Dic13—22no—
280C2×#382—131no—
281#1444—131no—
282#1443—131no—
283#1442—131no—
284#1442—131no—
285#1441—131no—
286#1441—131no—
287#1436—131no—
288#1436—131no—
289#1436—131no—
290#1436—131no—
291#1436—131no—
292C4⋊#95—131no—
293#1434—131no—
294#1434—131no—
295C23×C13C23×C411yescharacteristic
296C22×D13C22×Q811yescharacteristic
297C22×D13C2×#4111yescharacteristic
298C22×D13C2×#4111yescharacteristic
299C22×D13C2×#4111yescharacteristic
300C22×D13C2×#4111yescharacteristic
301C22×D13C2×#4111yescharacteristic
302C22×D13H(5,𝔽2)11yescharacteristic
303C22×D13H(5,𝔽2)11yescharacteristic
304C22×D13H(5,𝔽2)11yescharacteristic
305C22×D13H(5,𝔽2)11yescharacteristic
306C22×D13H(5,𝔽2)11yescharacteristic
307C22×D132−1+411yescharacteristic
308C22×D132−1+411yescharacteristic
309C22×D132−1+411yescharacteristic
310C2×#261—22no—
311C2×#261—22no—
312C2×#261—22no—
313C2×#261—22no—
314C2×#261—22no—
315C2×#261—22no—
316C2×#261—22no—
317C2×#261—22no—
318C2×#261—22no—
319C2×#261—22no—
320C2×#261—22no—
321C2×#261—22no—
322C2×#261—41no—
323C2×#261—41no—
324C2×#261—41no—
325C2×#261—41no—
326C2×#261—41no—
327C2×#261—41no—
328C2×#261—41no—
329C2×#261—41no—
330C2×#261—41no—
331C2×#261—41no—
332C2×#261—41no—
333C2×#261—41no—
334C2×#261—41no—
335C2×#261—41no—
336C2×#261—41no—
337C2×#261—41no—
338C2×#261—41no—
339C2×#261—41no—
340C2×#261—41no—
341C2×#261—41no—
342C2×#261—41no—
343C2×#261—41no—
344C2×#261—41no—
345C2×#261—41no—
346C2×#261—41no—
347C2×#261—41no—
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×C4×C13—21no—
367C2×C4×C13—21no—
368C2×C4×C13—21no—
369C2×C4×C13—21no—
370C2×C4×C13—21no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
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#11712yes—
386C2×C4×C13C4×Q812yes—
387C2×Dic13—21no—
388C2×Dic13—21no—
389C2×Dic13—21no—
390C2×Dic13—21no—
391C2×Dic13—21no—
392C2×Dic13—21no—
393C2×Dic13—21no—
394C2×Dic13—21no—
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#11712yes—
407C2×Dic13C4×Q812yes—
408C4×D13—22no—
409C4×D13—22no—
410C4×D13—22no—
411C4×D13—22no—
412C4×D13—22no—
413C4×D13—22no—
414C4×D13—22no—
415C4×D13—22no—
416C4×D13—41no—
417C4×D13—41no—
418C4×D13—41no—
419C4×D13—41no—
420C4×D13—41no—
421C4×D13—41no—
422C4×D13—41no—
423C4×D13—41no—
424C4×D13—41no—
425C4×D13—41no—
426C4×D13—41no—
427C4×D13—41no—
428C4×D13—41no—
429C4×D13—41no—
430C4×D13—41no—
431C4×D13—41no—
432C4×D13—41no—
433C4×D13—41no—
434C4×D13—41no—
435C4×D13—41no—
436C22×C4⋊C4—131no—
437C22×C4⋊C4—131no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C42—131no—
443C22×C42—131no—
444C22×C42—131no—
445#382—131no—
446#382—131no—
447#382—131no—
448#382—131no—
449#382—131no—
450#382—131no—
451#382—131no—
452#382#26111yescharacteristic, complemented
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
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—
479C22×C13C2×#11711yescharacteristic
480C22×C13C2×C4×Q811yescharacteristic
481C22×C13C4×#4111yescharacteristic
482C22×C13#51811yescharacteristic
483C22×C13#52011yescharacteristic
484C22×C13#52011yescharacteristic
485C22×C13#52011yescharacteristic
486C2×D13#53811yescharacteristic
487C2×D13#53811yescharacteristic
488C2×D13#54011yescharacteristic
489C2×D13#54011yescharacteristic
490C2×D13#54111yescharacteristic
491C2×D13#54111yescharacteristic
492C2×D13#54211yescharacteristic
493C2×D13#54211yescharacteristic
494C2×D13#54211yescharacteristic
495C2×D13#54211yescharacteristic
496C2×D13#54411yescharacteristic
497C2×D13#54411yescharacteristic
498C2×D13#55111yescharacteristic
499C2×D13#55111yescharacteristic
500C2×D13#55211yescharacteristic
501C2×D13#55211yescharacteristic
502C2×D13#55211yescharacteristic
503C2×D13#55311yescharacteristic
504C2×D13#55311yescharacteristic
505C2×D13#55311yescharacteristic
506C2×D13#55411yescharacteristic
507C2×D13#55411yescharacteristic
508C2×D13#55411yescharacteristic
509C2×D13#55711yescharacteristic
510C2×D13H(3,𝔽4)11yescharacteristic
511C2×D13#56211yescharacteristic
512C2×D13#56211yescharacteristic
513C2×D13#56311yescharacteristic
514#261—42no—
515#261—42no—
516#261—42no—
517#261—42no—
518#261—81no—
519#261—81no—
520#261—81no—
521#261—81no—
522C4×C13—22no—
523C4×C13—22no—
524C4×C13—41no—
525C4×C13—41no—
526C4×C13—41no—
527C4×C13—41no—
528C4×C13—41no—
529Dic13—22no—
530Dic13—22no—
531Dic13—41no—
532Dic13—41no—
533Dic13—41no—
534Dic13—41no—
535Dic13—41no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C2×C4⋊C4—131no—
552C2×C4⋊C4—131no—
553C2×C4⋊C4—131no—
554C2×C4⋊C4—131no—
555C2×C4⋊C4—131no—
556C2×C4⋊C4—131no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4—521no—
568C2×C4⋊C4—521no—
569C2×C4⋊C4—521no—
570C2×C4⋊C4—521no—
571C2×C4⋊C4—521no—
572C2×C4⋊C4—521no—
573C2×C4⋊C4C2×#26111yescharacteristic
574C2×C4⋊C4C2×#26111yescharacteristic
575C2×C42—131no—
576C2×C42—131no—
577C2×C42—131no—
578C2×C42—262no—
579C2×C42—262no—
580C2×C42—262no—
581C2×C42—521no—
582C2×C42—521no—
583C2×C42—521no—
584C2×C42—521no—
585C2×C42—521no—
586C2×C42C2×#26111yescharacteristic
587#95—134no—
588#95—131no—
589#95—131no—
590#95—131no—
591#95—131no—
592#95—131no—
593#95—131no—
594#95—131no—
595#95—131no—
596#95—131no—
597#95—131no—
598#95—131no—
599#95—131no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—262no—
606#95—262no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614#95—521no—
615#95—521no—
616#95—521no—
617#95—521no—
618#95—521no—
619#95—521no—
620#95—521no—
621#95C2×#26111yescharacteristic
622#95C2×#26111yescharacteristic
623#95C2×#26111yescharacteristic
624#95C2×#26111yescharacteristic
625C2×C13#231411yescharacteristic
626C2×C13#233011yescharacteristic
627C2×C13#233711yescharacteristic
628C2×C13#234311yescharacteristic
629C2×C13#234511yescharacteristic
630C2×C13#237011yescharacteristic
631C2×C13#237911yescharacteristic
632D13#275311yescharacteristic
633D13#275511yescharacteristic
634D13#276111yescharacteristic
635D13#276311yescharacteristic
636D13#276611yescharacteristic
637D13#276811yescharacteristic
638D13#277211yescharacteristic
639D13#277411yescharacteristic
640C24—131no—
641C22×C4—131no—
642C22×C4—131no—
643C22×C4—132no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—131no—
652C22×C4—131no—
653C22×C4—131no—
654C22×C4—131no—
655C22×C4—131no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
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×C4C22×#26111yescharacteristic
747C22×C4C22×#26111yescharacteristic
748C22×C4C22×#26111yescharacteristic
749C22×C4C22×#26111yescharacteristic
750C22×C4C22×#26111yescharacteristic
751C22×C4C22×#26111yescharacteristic
752C22×C4C22×#26111yescharacteristic
753C4⋊C4—41no—
754C4⋊C4—41no—
755C4⋊C4—521no—
756C4⋊C4—521no—
757C4⋊C4—521no—
758C4⋊C4—521no—
759C4⋊C4—521no—
760C4⋊C4—521no—
761C4⋊C4—524no—
762C4⋊C4—524no—
763C4⋊C4—524no—
764C4⋊C4—524no—
765C42—22no—
766C42—262no—
767C42—262no—
768C42—262no—
769C42—524no—
770C42—524no—
771C13#1445511yescharacteristic, complemented, Sylow
772C23—131no—
773C23—131no—
774C23—131no—
775C23—131no—
776C23—131no—
777C23—131no—
778C23—131no—
779C23—131no—
780C23—131no—
781C23—131no—
782C23—131no—
783C23—131no—
784C23—131no—
785C23—131no—
786C23C23×#26111yescharacteristic
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—132no—
807C2×C4—132no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—262no—
812C2×C4—262no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—261no—
817C2×C4—261no—
818C2×C4—261no—
819C2×C4—261no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—261no—
833C2×C4—261no—
834C2×C4—261no—
835C2×C4—261no—
836C2×C4—261no—
837C2×C4—261no—
838C2×C4—261no—
839C2×C4—261no—
840C2×C4—261no—
841C2×C4—261no—
842C2×C4—261no—
843C2×C4—261no—
844C2×C4—261no—
845C2×C4—261no—
846C2×C4—261no—
847C2×C4—521no—
848C2×C4—521no—
849C2×C4—521no—
850C2×C4—521no—
851C2×C4—521no—
852C2×C4—521no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
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#8823712yes—
912C2×C4Q8×#26112yes—
913C22—131no—
914C22—131no—
915C22—131no—
916C22—131no—
917C22—131no—
918C22—131no—
919C22—131no—
920C22—131no—
921C22—131no—
922C22—131no—
923C22—131no—
924C22—131no—
925C22—131no—
926C22—131no—
927C22—131no—
928C22—131no—
929C22—131no—
930C22—131no—
931C22—131no—
932C22—131no—
933C22—131no—
934C22—131no—
935C22—131no—
936C22—131no—
937C22—131no—
938C22—131no—
939C22—131no—
940C22—131no—
941C22C2×#8823711yescharacteristic
942C22#1171962311yescharacteristic
943C22C2×Q8×#26111yescharacteristic
944C22#41×#26111yescharacteristic
945C22#1171963111yescharacteristic
946C22#1171963111yescharacteristic
947C22#1171963111yescharacteristic
948C4—22no—
949C4—22no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—262no—
956C4—262no—
957C4—522no—
958C4—522no—
959C4—522no—
960C4—522no—
961C4—521no—
962C4—521no—
963C4—521no—
964C4—521no—
965C4—521no—
966C4—1041no—
967C4—1041no—
968C4—1041no—
969C4—1041no—
970C2—131no—
971C2—131no—
972C2—131no—
973C2—131no—
974C2—131no—
975C2—131no—
976C2—131no—
977C2—131no—
978C2#1313131411yescharacteristic
979C2#1313133011yescharacteristic
980C2#1313133711yescharacteristic
981C2#1313134311yescharacteristic
982C2#1313134511yescharacteristic
983C2#1313137011yescharacteristic
984C2#1313137911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#382C4
prime radical, cosocleC23×D13C24
hypercenter#382#261
hypocenterC13#14455
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
47. C13×#382C4semidirect
48. #11718638C4semidirect
49. #11718638C4semidirect
50. #11718597C4semidirect
55. #11718311C4semidirect
56. #11718311C4semidirect
57. #11718311C4semidirect
58. #11718311C4semidirect
452. #382#261semidirect
771. C13#14455semidirect

Maximal subgroups

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

subgroupindex
#131300242
#131300232
#131300222
#131300212
#131300162
#131300152
#131300142
#131300122
#131300112
D13×#3822
#1445513