Finite Group Databasebeta

← #16792252

Subgroups — #16792252

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719083C211yesmaximal, characteristic
2C2×#11719083C211yesmaximal, characteristic
3C2×#11719082C211yesmaximal, characteristic
4C2×#11719059C211yesmaximal, characteristic
5#13130024C211yesmaximal, characteristic
6#13130024C211yesmaximal, characteristic
7#13130024C211yesmaximal, characteristic
8#13130024C211yesmaximal, characteristic
9#13130022C211yesmaximal, characteristic
10#13130021C211yesmaximal, characteristic
11#13130016C211yesmaximal, characteristic
12#13130016C211yesmaximal, characteristic
13#13130016C211yesmaximal, characteristic
14#13130012C211yesmaximal, characteristic
15D13×#387C211yesmaximal, characteristic
16C22×C4⋊#261C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18C22×C4⋊#261C2211yescharacteristic
19C22×C4⋊#261C2211yescharacteristic
20C22×C4⋊#261C2211yescharacteristic
21C22×C4⋊#261C2211yescharacteristic
22C22×C4⋊#261C2211yescharacteristic
23C22×C4⋊#261C2211yescharacteristic
24C22×C4⋊#261C2211yescharacteristic
25C22×C4⋊#261C2211yescharacteristic
26C22×C4×#261C2211yescharacteristic
27C22×C4×#261C2211yescharacteristic
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×C4⋊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
47#11719083—24no—
48#11719083—24no—
49#11719082—24no—
50#11719059—24no—
51C13×#387C411yescharacteristic, complemented
52#11718642C411yescharacteristic, complemented
53#11718639C411yescharacteristic, complemented
54#11718594C411yescharacteristic, complemented
55D13×#95C2211yescharacteristic
56D13×#95C2211yescharacteristic
57D13×#95C2211yescharacteristic
58D13×#95C2211yescharacteristic
59#11718316C411yescharacteristic, complemented
60#11718315C411yescharacteristic, complemented
61#11718314C411yescharacteristic, complemented
62#11718313C411yescharacteristic, complemented
63C23×#261C2311yescharacteristic
64C23×#261C2311yescharacteristic
65C23×#261C2311yescharacteristic
66C23×#261C2311yescharacteristic
67C23×#261C2311yescharacteristic
68C23×#261C2311yescharacteristic
69C23×#261C2311yescharacteristic
70C23×#261C2311yescharacteristic
71C22×C4×D13C2311yescharacteristic
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×C4×D13C2311yescharacteristic
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2311yescharacteristic
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—41no—
92C2×C4⋊#261—41no—
93C2×C4⋊#261—41no—
94C2×C4⋊#261—41no—
95C2×C4⋊#261—41no—
96C2×C4⋊#261—41no—
97C2×C4⋊#261—41no—
98C2×C4⋊#261—41no—
99C2×C4⋊#261—41no—
100C2×C4⋊#261—41no—
101C2×C4⋊#261—41no—
102C2×C4⋊#261—41no—
103C2×C4⋊#261—41no—
104C2×C4⋊#261—41no—
105C2×C4⋊#261—41no—
106C2×C4⋊#261—41no—
107C2×C4⋊#261D414yes—
108C2×C4×#261—22no—
109C2×C4×#261—22no—
110C2×C4×#261—22no—
111C2×C4×#261—41no—
112C2×C4×#261—41no—
113C2×C4×#261—41no—
114C2×C13×C4⋊C4C2×C411yescharacteristic
115C2×C13×C4⋊C4C2×C411yescharacteristic
116C2×C42×C13C2×C411yescharacteristic
117C2×C4⋊Dic13C2×C411yescharacteristic
118C2×C4⋊Dic13C2×C411yescharacteristic
119C2×#6101C2×C411yescharacteristic
120C2×#6101C2×C411yescharacteristic
121C2×#6101C2×C411yescharacteristic
122C2×#6101C2×C411yescharacteristic
123C2×C4×Dic13C2×C411yescharacteristic
124C2×C4×Dic13C2×C411yescharacteristic
125C2×C4×Dic13C2×C411yescharacteristic
126C4⋊C4×D13—22no—
127C4⋊C4×D13—22no—
128C4⋊C4×D13D414yes—
129C4⋊C4×D13Q814yes—
130C42×D13—22no—
131C42×D13—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—
138(C2×#261)⋊C4—22no—
139(C2×#261)⋊C4—22no—
140(C2×#261)⋊C4—22no—
141(C2×#261)⋊C4—22no—
142(C2×#261)⋊C4—41no—
143(C2×#261)⋊C4—41no—
144(C2×#261)⋊C4—41no—
145(C2×#261)⋊C4—41no—
146(C2×#261)⋊C4—41no—
147(C2×#261)⋊C4Q814yes—
148C13×#95C2×C411yescharacteristic
149C13×#95C2×C411yescharacteristic
150C13×#95C2×C411yescharacteristic
151C13×#95C2×C411yescharacteristic
152#88071C2×C411yescharacteristic
153#88071C2×C411yescharacteristic
154#88071C2×C411yescharacteristic
155#88071C2×C411yescharacteristic
156#88071C2×C411yescharacteristic
157#88071C2×C411yescharacteristic
158#88071C2×C411yescharacteristic
159#88071C2×C411yescharacteristic
160#88071C2×C411yescharacteristic
161#88071C2×C411yescharacteristic
162#88071C2×C411yescharacteristic
163#88071C2×C411yescharacteristic
164#14406—131nomaximal, Sylow
165C23×D13C2411yescharacteristic
166C22×#261—21no—
167C22×#261—21no—
168C22×#261—21no—
169C22×#261—21no—
170C22×#261—21no—
171C22×#261—21no—
172C22×#261—21no—
173C22×#261—21no—
174C22×#261—21no—
175C22×#261—21no—
176C22×#261—21no—
177C22×#261—21no—
178C22×#261—21no—
179C22×#261—21no—
180C22×#261—21no—
181C22×#261—21no—
182C22×#261—21no—
183C22×#261—21no—
184C22×#261—21no—
185C22×#261—21no—
186C22×#261—21no—
187C22×#261—21no—
188C22×#261—21no—
189C22×#261—21no—
190C22×#261—21no—
191C22×#261—21no—
192C22×#261—21no—
193C22×#261—21no—
194C22×#261—21no—
195C22×#261—21no—
196C22×#261—21no—
197C22×#261—21no—
198C22×#261—21no—
199C22×#261—21no—
200C22×#261—21no—
201C22×#261—21no—
202C22×#261—21no—
203C22×#261—21no—
204C22×#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×#261C2×D412yes—
219C22×#261C2×D412yes—
220C22×#261C2×Q812yes—
221C22×#261C2×Q812yes—
222C22×C4×C13C22×C411yescharacteristic
223C22×C4×C13C22×C411yescharacteristic
224C22×C4×C13C22×C411yescharacteristic
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C411yescharacteristic
227C22×C4×C13C22×C411yescharacteristic
228C22×C4×C13C22×C411yescharacteristic
229C22×Dic13C22×C411yescharacteristic
230C22×Dic13C22×C411yescharacteristic
231C22×Dic13C22×C411yescharacteristic
232C22×Dic13C22×C411yescharacteristic
233C22×Dic13C22×C411yescharacteristic
234C22×Dic13C22×C411yescharacteristic
235C22×Dic13C22×C411yescharacteristic
236C2×C4×D13—21no—
237C2×C4×D13—21no—
238C2×C4×D13—21no—
239C2×C4×D13—21no—
240C2×C4×D13—21no—
241C2×C4×D13—21no—
242C2×C4×D13—21no—
243C2×C4×D13—21no—
244C2×C4×D13—21no—
245C2×C4×D13—21no—
246C2×C4×D13—21no—
247C2×C4×D13—21no—
248C2×C4×D13—21no—
249C2×C4×D13—21no—
250C2×C4×D13—21no—
251C2×C4×D13—21no—
252C2×C4×D13—21no—
253C2×C4×D13—21no—
254C2×C4×D13—21no—
255C2×C4×D13—21no—
256C2×C4×D13—21no—
257C2×C4×D13—21no—
258C2×C4×D13—21no—
259C2×C4×D13—21no—
260C2×C4×D13—21no—
261C2×C4×D13—21no—
262C2×C4×D13—21no—
263C2×C4×D13—21no—
264C2×C4×D13—21no—
265C2×C4×D13—21no—
266C2×C4×D13—21no—
267C2×C4×D13—21no—
268C2×C4×D13C2×D412yes—
269C2×C4×D13C2×D412yes—
270C2×C4×D13C2×D412yes—
271C2×C4×D13C2×D412yes—
272C2×C4×D13C2×Q812yes—
273C2×C4×D13C2×Q812yes—
274C2×C4×D13C2×Q812yes—
275C2×C4×D13C2×Q812yes—
276C2×C4×D13#4112yes—
277C2×C4×D13#4112yes—
278C4⋊#261—44no—
279C4⋊#261—44no—
280C4⋊#261—44no—
281C4⋊#261—44no—
282C4⋊#261—44no—
283C4⋊#261—44no—
284C4⋊#261—44no—
285C4⋊#261—44no—
286C4⋊#261—44no—
287C4⋊#261—44no—
288C4×#261—44no—
289C4×#261—44no—
290C13×C4⋊C4—22no—
291C13×C4⋊C4C4⋊C414yescomplemented
292C42×C13—22no—
293C4⋊Dic13—22no—
294C4⋊Dic13C4⋊C414yescomplemented
295#6101—22no—
296#6101—22no—
297#6101C4⋊C414yescomplemented
298#6101C4⋊C414yescomplemented
299C4×Dic13—22no—
300C4×Dic13—22no—
301C4×Dic13—22no—
302C2×#389—131no—
303C2×#389—131no—
304C2×#387—131no—
305C2×#387—131no—
306C2×#384—131no—
307#1444—131no—
308#1444—131no—
309#1444—131no—
310#1444—131no—
311#1442—131no—
312#1441—131no—
313#1436—131no—
314#1436—131no—
315#1436—131no—
316#1434—131no—
317C23×C13C23×C411yescharacteristic
318C22×D13C22×D411yescharacteristic
319C22×D13C22×D411yescharacteristic
320C22×D13C22×Q811yescharacteristic
321C22×D13C22×Q811yescharacteristic
322C22×D13C2×#4111yescharacteristic
323C22×D13C2×#4111yescharacteristic
324C22×D13H(5,𝔽2)11yescharacteristic
325C22×D13H(5,𝔽2)11yescharacteristic
326C22×D13H(5,𝔽2)11yescharacteristic
327C22×D13H(5,𝔽2)11yescharacteristic
328C22×D132−1+411yescharacteristic
329C22×D132−1+411yescharacteristic
330C22×D132−1+411yescharacteristic
331C22×D132−1+411yescharacteristic
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—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×#261—41no—
371C2×#261—41no—
372C2×#261—41no—
373C2×#261—41no—
374C2×#261—41no—
375C2×#261—41no—
376C2×#261—41no—
377C2×#261—41no—
378C2×#261—41no—
379C2×#261—41no—
380C2×#261—41no—
381C2×#261—41no—
382C2×#261—41no—
383C2×#261—41no—
384C2×#261—41no—
385C2×#261—41no—
386C2×#261—41no—
387C2×#261—41no—
388C2×C4×C13—21no—
389C2×C4×C13—21no—
390C2×C4×C13—21no—
391C2×C4×C13—21no—
392C2×C4×C13—21no—
393C2×C4×C13—21no—
394C2×C4×C13—21no—
395C2×C4×C13—21no—
396C2×C4×C13—21no—
397C2×C4×C13—21no—
398C2×C4×C13—21no—
399C2×C4×C13—21no—
400C2×C4×C13—21no—
401C2×C4×C13—21no—
402C2×C4×C13—21no—
403C2×C4×C13—21no—
404C2×C4×C13C2×C4⋊C412yes—
405C2×C4×C13C2×C4⋊C412yes—
406C2×C4×C13C2×C4⋊C412yes—
407C2×C4×C13C4×D412yes—
408C2×C4×C13C4×Q812yes—
409C2×Dic13—21no—
410C2×Dic13—21no—
411C2×Dic13—21no—
412C2×Dic13—21no—
413C2×Dic13—21no—
414C2×Dic13—21no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—21no—
418C2×Dic13—21no—
419C2×Dic13—21no—
420C2×Dic13—21no—
421C2×Dic13—21no—
422C2×Dic13—21no—
423C2×Dic13—21no—
424C2×Dic13—21no—
425C2×Dic13C2×C4⋊C412yes—
426C2×Dic13C2×C4⋊C412yes—
427C2×Dic13C2×C4⋊C412yes—
428C2×Dic13C4×D412yes—
429C2×Dic13C4×Q812yes—
430C4×D13—22no—
431C4×D13—22no—
432C4×D13—22no—
433C4×D13—22no—
434C4×D13—22no—
435C4×D13—22no—
436C4×D13—22no—
437C4×D13—22no—
438C4×D13—22no—
439C4×D13—22no—
440C4×D13—22no—
441C4×D13—22no—
442C4×D13—22no—
443C4×D13—22no—
444C4×D13—22no—
445C4×D13—22no—
446C4×D13—22no—
447C4×D13—22no—
448C4×D13—22no—
449C4×D13—22no—
450C4×D13—41no—
451C4×D13—41no—
452C4×D13—41no—
453C4×D13—41no—
454C4×D13—41no—
455C4×D13—41no—
456C4×D13—41no—
457C4×D13—41no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4—131no—
463C22×C4⋊C4—131no—
464C22×C4⋊C4—131no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4—131no—
470C22×C42—131no—
471C22×C42—131no—
472C22×C42—131no—
473#389—264no—
474#389—264no—
475#387—131no—
476#387—131no—
477#387—131no—
478#387—131no—
479#387—131no—
480#387—131no—
481#387—131no—
482#387—264no—
483#387#26111yescharacteristic, complemented
484#384—264no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
502C2×#95—131no—
503C2×#95—131no—
504C2×#95—131no—
505C22×C13C22×C4⋊C411yescharacteristic
506C22×C13C2×C4×D411yescharacteristic
507C22×C13C2×C4×Q811yescharacteristic
508C22×C13#52011yescharacteristic
509C22×C13#52011yescharacteristic
510C22×C13#52011yescharacteristic
511C22×C13#52011yescharacteristic
512C2×D13#53411yescharacteristic
513C2×D13#53511yescharacteristic
514C2×D13#53611yescharacteristic
515C2×D13#53611yescharacteristic
516C2×D13#53911yescharacteristic
517C2×D13#53911yescharacteristic
518C2×D13#54011yescharacteristic
519C2×D13#54111yescharacteristic
520C2×D13#54411yescharacteristic
521C2×D13#54411yescharacteristic
522C2×D13#54411yescharacteristic
523C2×D13#54411yescharacteristic
524C2×D13D4211yescharacteristic
525C2×D13#54611yescharacteristic
526C2×D13#54711yescharacteristic
527C2×D13D4×Q811yescharacteristic
528C2×D13D4×Q811yescharacteristic
529C2×D13D4×Q811yescharacteristic
530C2×D13#55011yescharacteristic
531C2×D13#55211yescharacteristic
532C2×D13#55411yescharacteristic
533C2×D13#55411yescharacteristic
534C2×D13#55711yescharacteristic
535C2×D13Q8211yescharacteristic
536C2×D13#56011yescharacteristic
537C2×D13#56311yescharacteristic
538C2×D13#56311yescharacteristic
539C2×D13#56311yescharacteristic
540#261—42no—
541#261—42no—
542#261—42no—
543#261—42no—
544#261—81no—
545#261—81no—
546#261—81no—
547#261—81no—
548C4×C13—22no—
549C4×C13—22no—
550C4×C13—22no—
551C4×C13—22no—
552C4×C13—22no—
553C4×C13—41no—
554C4×C13—41no—
555Dic13—22no—
556Dic13—22no—
557Dic13—22no—
558Dic13—22no—
559Dic13—22no—
560Dic13—41no—
561Dic13—41no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—131no—
574C23×C4—131no—
575C23×C4—131no—
576C23×C4—131no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—131no—
583C2×C4⋊C4—131no—
584C2×C4⋊C4—131no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—521no—
602C2×C4⋊C4—521no—
603C2×C4⋊C4—521no—
604C2×C4⋊C4—521no—
605C2×C4⋊C4—521no—
606C2×C4⋊C4—521no—
607C2×C4⋊C4—521no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4—521no—
612C2×C4⋊C4—521no—
613C2×C4⋊C4—521no—
614C2×C4⋊C4—521no—
615C2×C4⋊C4—521no—
616C2×C4⋊C4—521no—
617C2×C4⋊C4C2×#26111yescharacteristic
618C2×C4⋊C4C2×#26111yescharacteristic
619C2×C42—131no—
620C2×C42—131no—
621C2×C42—131no—
622C2×C42—262no—
623C2×C42—262no—
624C2×C42—262no—
625C2×C42—262no—
626C2×C42—262no—
627C2×C42—521no—
628C2×C42—521no—
629C2×C42—521no—
630C2×C42C2×#26111yescharacteristic
631#95—134no—
632#95—131no—
633#95—131no—
634#95—131no—
635#95—131no—
636#95—131no—
637#95—131no—
638#95—131no—
639#95—131no—
640#95—131no—
641#95—131no—
642#95—131no—
643#95—131no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—262no—
654#95—521no—
655#95—521no—
656#95—521no—
657#95—521no—
658#95—521no—
659#95C2×#26111yescharacteristic
660#95C2×#26111yescharacteristic
661#95C2×#26111yescharacteristic
662#95C2×#26111yescharacteristic
663C2×C13#231711yescharacteristic
664C2×C13#232211yescharacteristic
665C2×C13#233011yescharacteristic
666C2×C13D4×C4⋊C411yescharacteristic
667C2×C13Q8×C4⋊C411yescharacteristic
668C2×C13#236011yescharacteristic
669C2×C13#238311yescharacteristic
670D13#267311yescharacteristic
671D13#267711yescharacteristic
672D13#271311yescharacteristic
673D13#272011yescharacteristic
674D13#272111yescharacteristic
675D13#273411yescharacteristic
676D13#279111yescharacteristic
677D13#279211yescharacteristic
678C24—131no—
679C22×C4—131no—
680C22×C4—131no—
681C22×C4—131no—
682C22×C4—131no—
683C22×C4—131no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—131no—
699C22×C4—131no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4C22×#26111yescharacteristic
785C22×C4C22×#26111yescharacteristic
786C22×C4C22×#26111yescharacteristic
787C22×C4C22×#26111yescharacteristic
788C22×C4C22×#26111yescharacteristic
789C22×C4C22×#26111yescharacteristic
790C22×C4C22×#26111yescharacteristic
791C4⋊C4—22no—
792C4⋊C4—134no—
793C4⋊C4—134no—
794C4⋊C4—134no—
795C4⋊C4—262no—
796C4⋊C4—262no—
797C4⋊C4—262no—
798C4⋊C4—524no—
799C4⋊C4—524no—
800C4⋊C4—524no—
801C4⋊C4—524no—
802C4⋊C4—524no—
803C4⋊C4—524no—
804C4⋊C4—524no—
805C4⋊C4—524no—
806C4⋊C4—524no—
807C4⋊C4—524no—
808C4⋊C4C4⋊#26114yescomplemented
809C42—22no—
810C42—262no—
811C42—262no—
812C42—262no—
813C42—524no—
814C42—524no—
815C13#1440611yescharacteristic, complemented, Sylow
816C23—131no—
817C23—131no—
818C23—131no—
819C23—131no—
820C23—131no—
821C23—131no—
822C23—131no—
823C23—131no—
824C23—131no—
825C23—131no—
826C23—131no—
827C23—131no—
828C23—131no—
829C23—131no—
830C23C23×#26111yescharacteristic
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—132no—
848C2×C4—132no—
849C2×C4—132no—
850C2×C4—132no—
851C2×C4—132no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
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—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—261no—
895C2×C4—261no—
896C2×C4—261no—
897C2×C4—261no—
898C2×C4—261no—
899C2×C4—261no—
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—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4C2×C4⋊#26112yes—
953C2×C4C2×C4⋊#26112yes—
954C2×C4C2×C4⋊#26112yes—
955C2×C4D4×#26112yes—
956C2×C4Q8×#26112yes—
957C22—131no—
958C22—131no—
959C22—131no—
960C22—131no—
961C22—131no—
962C22—131no—
963C22—131no—
964C22—131no—
965C22—131no—
966C22—131no—
967C22—131no—
968C22—131no—
969C22—131no—
970C22—131no—
971C22—131no—
972C22—131no—
973C22—131no—
974C22—131no—
975C22—131no—
976C22—131no—
977C22—131no—
978C22—131no—
979C22—131no—
980C22—131no—
981C22—131no—
982C22—131no—
983C22—131no—
984C22—131no—
985C22C22×C4⋊#26111yescharacteristic
986C22C2×D4×#26111yescharacteristic
987C22C2×Q8×#26111yescharacteristic
988C22#1171963111yescharacteristic
989C22#1171963111yescharacteristic
990C22#1171963111yescharacteristic
991C22#1171963111yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—262no—
1000C4—262no—
1001C4—262no—
1002C4—262no—
1003C4—262no—
1004C4—522no—
1005C4—522no—
1006C4—522no—
1007C4—522no—
1008C4—521no—
1009C4—521no—
1010C4—1041no—
1011C4—1041no—
1012C4—1041no—
1013C4—1041no—
1014C2—131no—
1015C2—131no—
1016C2—131no—
1017C2—131no—
1018C2—131no—
1019C2—131no—
1020C2—131no—
1021C2—131no—
1022C2#1313131711yescharacteristic
1023C2#1313132211yescharacteristic
1024C2#1313133011yescharacteristic
1025C2D4×C4⋊#26111yescharacteristic
1026C2Q8×C4⋊#26111yescharacteristic
1027C2#1313136011yescharacteristic
1028C2#1313138311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#387C4
prime radical, cosocleC23×D13C24
hypercenter#387#261
hypocenterC13#14406
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
51. C13×#387C4semidirect
52. #11718642C4semidirect
53. #11718639C4semidirect
54. #11718594C4semidirect
59. #11718316C4semidirect
60. #11718315C4semidirect
61. #11718314C4semidirect
62. #11718313C4semidirect
291. C13×C4⋊C4C4⋊C4semidirect
294. C4⋊Dic13C4⋊C4semidirect
297. #6101C4⋊C4semidirect
298. #6101C4⋊C4semidirect
483. #387#261semidirect
808. C4⋊C4C4⋊#261semidirect
815. C13#14406semidirect

Maximal subgroups

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

subgroupindex
C2×#117190832
C2×#117190822
C2×#117190592
#131300242
#131300222
#131300212
#131300162
#131300122
D13×#3872
#1440613