Finite Group Databasebeta

← #16792550

Subgroups — #16792550

Order 3328.

1422 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×C42×#261C211yesmaximal, characteristic
3#13130016C211yesmaximal, characteristic
4#13130016C211yesmaximal, characteristic
5#13130016C211yesmaximal, characteristic
6#13130016C211yesmaximal, characteristic
7#13130016C211yesmaximal, characteristic
8#13130015C211yesmaximal, characteristic
9#13130015C211yesmaximal, characteristic
10#13130015C211yesmaximal, characteristic
11#13130012C211yesmaximal, characteristic
12#13130011C211yesmaximal, characteristic
13#13130011C211yesmaximal, characteristic
14#13130011C211yesmaximal, 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#11719082—24no—
48C42×#261—24no—
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—22no—
79C2×C4⋊#261—22no—
80C2×C4⋊#261—22no—
81C2×C4⋊#261—22no—
82C2×C4×#261—22no—
83C2×C4×#261—22no—
84C2×C4×#261—22no—
85C2×C4×#261—22no—
86C2×C4×#261—22no—
87C2×C4×#261—22no—
88C2×C4×#261—22no—
89C2×C4×#261—22no—
90C2×C4×#261—22no—
91C2×C4×#261—22no—
92C2×C4×#261—22no—
93C2×C4×#261—22no—
94C2×C4×#261—22no—
95C2×C4×#261—22no—
96C2×C4×#261—22no—
97C2×C4×#261—22no—
98C2×C4×#261D414yes—
99C2×C4×#261Q814yes—
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—22no—
113C4⋊C4×D13—22no—
114C4⋊C4×D13—22no—
115C4⋊C4×D13—22no—
116C42×D13—22no—
117C42×D13—22no—
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—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—22no—
131(C2×#261)⋊C4—22no—
132(C2×#261)⋊C4—22no—
133(C2×#261)⋊C4—22no—
134(C2×#261)⋊C4—22no—
135(C2×#261)⋊C4—22no—
136(C2×#261)⋊C4—22no—
137(C2×#261)⋊C4—22no—
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#14704—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×#261C2×D412yes—
201C22×#261C2×D412yes—
202C22×#261C2×Q812yes—
203C22×#261C2×Q812yes—
204C22×#261#4112yes—
205C22×#261#4112yes—
206C22×#261#4112yes—
207C22×#261#4112yes—
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×D13C2×D412yes—
263C2×C4×D13C2×Q812yes—
264C2×C4×D13#4112yes—
265C2×C4×D13#4112yes—
266C2×C4×D13#4112yes—
267C2×C4×D13#4112yes—
268C4⋊#261—44no—
269C4⋊#261—44no—
270C4×#261—28no—
271C4×#261—28no—
272C4×#261—28no—
273C4×#261—28no—
274C4×#261—28no—
275C4×#261—28no—
276C13×C4⋊C4—22no—
277C13×C4⋊C4—22no—
278C42×C13—22no—
279C4⋊Dic13—22no—
280C4⋊Dic13—22no—
281#6101—22no—
282#6101—22no—
283#6101—22no—
284#6101—22no—
285C4×Dic13—22no—
286C4×Dic13—22no—
287C4×Dic13—22no—
288C2×#387—131no—
289C2×#387—131no—
290C2×C43—131no—
291#1436—131no—
292#1436—131no—
293#1436—131no—
294#1436—131no—
295#1436—131no—
296#1436—131no—
297#1436—131no—
298#1436—131no—
299#1434—131no—
300#1434—131no—
301#1434—131no—
302#1434—131no—
303C23×C13C23×C411yescharacteristic
304C22×D13C22×D411yescharacteristic
305C22×D13C22×Q811yescharacteristic
306C22×D13C2×#4111yescharacteristic
307C22×D13C2×#4111yescharacteristic
308C22×D13C2×#4111yescharacteristic
309C22×D13C2×#4111yescharacteristic
310C22×D13C2×#4111yescharacteristic
311C22×D13C2×#4111yescharacteristic
312C22×D13C2×#4111yescharacteristic
313C22×D13C2×#4111yescharacteristic
314C22×D13C2×#4111yescharacteristic
315C22×D13C2×#4111yescharacteristic
316C22×D13C2×#4111yescharacteristic
317C22×D13C2×#4111yescharacteristic
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—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×#261—41no—
367C2×#261—41no—
368C2×#261—41no—
369C2×#261—41no—
370C2×#261C22⋊Q814yes—
371C2×#261#12314yes—
372C2×#261#12514yes—
373C2×#261#12614yes—
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×C13#11712yes—
393C2×C4×C13C4×D412yes—
394C2×C4×C13C4×Q812yes—
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×Dic13#11712yes—
414C2×Dic13C4×D412yes—
415C2×Dic13C4×Q812yes—
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—131no—
456#387—131no—
457#387—131no—
458#387—131no—
459#387—131no—
460#387—131no—
461#387—131no—
462#387—264no—
463#387#26111yescharacteristic, complemented
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—
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—
488C43—264no—
489C22×C13C2×#11711yescharacteristic
490C22×C13C2×C4×D411yescharacteristic
491C22×C13C2×C4×Q811yescharacteristic
492C22×C13C4×#4111yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13C4×#4111yescharacteristic
496C2×D13C2×C22⋊Q811yescharacteristic
497C2×D13C2×#12311yescharacteristic
498C2×D13#52511yescharacteristic
499C2×D13#52511yescharacteristic
500C2×D13#52511yescharacteristic
501C2×D13#52511yescharacteristic
502C2×D13C2×#12511yescharacteristic
503C2×D13C2×#12611yescharacteristic
504C2×D13#52911yescharacteristic
505C2×D13#52911yescharacteristic
506C2×D13#52911yescharacteristic
507C2×D13#52911yescharacteristic
508C2×D13#52911yescharacteristic
509C2×D13#52911yescharacteristic
510C2×D13#52911yescharacteristic
511C2×D13#52911yescharacteristic
512C2×D13#52911yescharacteristic
513C2×D13#52911yescharacteristic
514C2×D13#52911yescharacteristic
515C2×D13#52911yescharacteristic
516C2×D13#52911yescharacteristic
517C2×D13#52911yescharacteristic
518C2×D13#52911yescharacteristic
519C2×D13#52911yescharacteristic
520C2×D13#53311yescharacteristic
521C2×D13#53311yescharacteristic
522C2×D13#53311yescharacteristic
523C2×D13#53311yescharacteristic
524#261—24no—
525#261—24no—
526#261—24no—
527#261—24no—
528#261—81no—
529#261—81no—
530#261—81no—
531#261—81no—
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—131no—
565C2×C4⋊C4—131no—
566C2×C4⋊C4—131no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4C2×#26111yescharacteristic
578C2×C4⋊C4C2×#26111yescharacteristic
579C2×C42—134no—
580C2×C42—134no—
581C2×C42—131no—
582C2×C42—131no—
583C2×C42—131no—
584C2×C42—262no—
585C2×C42—262no—
586C2×C42—262no—
587C2×C42—262no—
588C2×C42—262no—
589C2×C42—262no—
590C2×C42—262no—
591C2×C42—262no—
592C2×C42—262no—
593C2×C42—262no—
594C2×C42—262no—
595C2×C42—262no—
596C2×C42—262no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42C2×#26111yescharacteristic
603#95—131no—
604#95—131no—
605#95—131no—
606#95—131no—
607#95—131no—
608#95—131no—
609#95—131no—
610#95—131no—
611#95—131no—
612#95—131no—
613#95—131no—
614#95—131no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95C2×#26111yescharacteristic
636#95C2×#26111yescharacteristic
637#95C2×#26111yescharacteristic
638#95C2×#26111yescharacteristic
639C2×C13#229011yescharacteristic
640C2×C13#229511yescharacteristic
641C2×C13#229811yescharacteristic
642C2×C13C4×#12311yescharacteristic
643C2×C13C4×C22⋊Q811yescharacteristic
644C2×C13C4×#12611yescharacteristic
645C2×C13C4×#12511yescharacteristic
646D13#285111yescharacteristic
647D13#285211yescharacteristic
648D13#285311yescharacteristic
649D13#285511yescharacteristic
650D13#286311yescharacteristic
651D13#286411yescharacteristic
652D13#286511yescharacteristic
653D13#286611yescharacteristic
654C24—131no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—132no—
667C22×C4—131no—
668C22×C4—131no—
669C22×C4—131no—
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—22no—
768C4⋊C4—22no—
769C4⋊C4—262no—
770C4⋊C4—262no—
771C4⋊C4—262no—
772C4⋊C4—262no—
773C4⋊C4—262no—
774C4⋊C4—262no—
775C4⋊C4—524no—
776C4⋊C4—524no—
777C42—22no—
778C42—262no—
779C42—262no—
780C42—268no—
781C42—268no—
782C42—268no—
783C42—268no—
784C42—268no—
785C42—268no—
786C42—262no—
787C13#1470411yescharacteristic, 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—134no—
824C2×C4—134no—
825C2×C4—132no—
826C2×C4—132no—
827C2×C4—132no—
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—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—261no—
865C2×C4—261no—
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—261no—
875C2×C4—261no—
876C2×C4—261no—
877C2×C4—261no—
878C2×C4—261no—
879C2×C4—261no—
880C2×C4—261no—
881C2×C4—261no—
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—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#8823712yes—
927C2×C4D4×#26112yes—
928C2×C4Q8×#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—
957C22C2×#8823711yescharacteristic
958C22C2×D4×#26111yescharacteristic
959C22C2×Q8×#26111yescharacteristic
960C22#41×#26111yescharacteristic
961C22#41×#26111yescharacteristic
962C22#41×#26111yescharacteristic
963C22#41×#26111yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—41no—
971C4—264no—
972C4—264no—
973C4—264no—
974C4—264no—
975C4—262no—
976C4—262no—
977C4—262no—
978C4—521no—
979C4—521no—
980C4—521no—
981C4—521no—
982C4—1041no—
983C4—1041no—
984C4—1041no—
985C4—1041no—
986C2—131no—
987C2—131no—
988C2—131no—
989C2—131no—
990C2—131no—
991C2—131no—
992C2—131no—
993C2—131no—
994C2#1313129011yescharacteristic
995C2#1313129511yescharacteristic
996C2#1313129811yescharacteristic
997C2#123×#26111yescharacteristic
998C2C22⋊Q8×#26111yescharacteristic
999C2#126×#26111yescharacteristic
1000C2#125×#26111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#387C4
prime radical, cosocleC23×D13C24
hypercenter#387#261
hypocenterC13#14704
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
49. C13×#387C4semidirect
50. #11718642C4semidirect
51. #11718639C4semidirect
52. #11718594C4semidirect
57. #11718316C4semidirect
58. #11718315C4semidirect
59. #11718314C4semidirect
60. #11718313C4semidirect
463. #387#261semidirect
787. C13#14704semidirect

Maximal subgroups

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

subgroupindex
C2×#117190822
C2×C42×#2612
#131300162
#131300152
#131300122
#131300112
D13×#3872
#1470413