Finite Group Databasebeta

← #16792250

Subgroups — #16792250

Order 3328.

1346 conjugacy classes of subgroups.

The subgroup lattice has 1018 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×#11719060C211yesmaximal, characteristic
5#13130024C211yesmaximal, characteristic
6#13130024C211yesmaximal, characteristic
7#13130022C211yesmaximal, characteristic
8#13130022C211yesmaximal, characteristic
9#13130022C211yesmaximal, characteristic
10#13130021C211yesmaximal, characteristic
11#13130016C211yesmaximal, characteristic
12#13130016C211yesmaximal, characteristic
13#13130016C211yesmaximal, characteristic
14#13130014C211yesmaximal, 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
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×C42×D13C2211yescharacteristic
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#11719083—24no—
48#11719083—24no—
49#11719082—24no—
50#11719060—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—22no—
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—22no—
103C2×C4×#261—22no—
104C2×C4×#261—22no—
105C2×C4×#261—41no—
106C2×C4×#261—41no—
107C2×C4×#261—41no—
108C2×C13×C4⋊C4C2×C411yescharacteristic
109C2×C13×C4⋊C4C2×C411yescharacteristic
110C2×C42×C13C2×C411yescharacteristic
111C2×C4⋊Dic13C2×C411yescharacteristic
112C2×C4⋊Dic13C2×C411yescharacteristic
113C2×#6101C2×C411yescharacteristic
114C2×#6101C2×C411yescharacteristic
115C2×#6101C2×C411yescharacteristic
116C2×#6101C2×C411yescharacteristic
117C2×C4×Dic13C2×C411yescharacteristic
118C2×C4×Dic13C2×C411yescharacteristic
119C2×C4×Dic13C2×C411yescharacteristic
120C4⋊C4×D13—22no—
121C4⋊C4×D13—22no—
122C4⋊C4×D13D414yes—
123C4⋊C4×D13Q814yes—
124C42×D13—22no—
125C42×D13—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—
138(C2×#261)⋊C4—41no—
139(C2×#261)⋊C4—41no—
140(C2×#261)⋊C4—41no—
141(C2×#261)⋊C4—41no—
142(C2×#261)⋊C4—41no—
143(C2×#261)⋊C4D414yes—
144C13×#95C2×C411yescharacteristic
145C13×#95C2×C411yescharacteristic
146C13×#95C2×C411yescharacteristic
147C13×#95C2×C411yescharacteristic
148#88071C2×C411yescharacteristic
149#88071C2×C411yescharacteristic
150#88071C2×C411yescharacteristic
151#88071C2×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#14404—131nomaximal, Sylow
161C23×D13C2411yescharacteristic
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×#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×#261C2×D412yes—
215C22×#261C2×D412yes—
216C22×#261#4112yes—
217C22×#261#4112yes—
218C22×C4×C13C22×C411yescharacteristic
219C22×C4×C13C22×C411yescharacteristic
220C22×C4×C13C22×C411yescharacteristic
221C22×C4×C13C22×C411yescharacteristic
222C22×C4×C13C22×C411yescharacteristic
223C22×C4×C13C22×C411yescharacteristic
224C22×C4×C13C22×C411yescharacteristic
225C22×Dic13C22×C411yescharacteristic
226C22×Dic13C22×C411yescharacteristic
227C22×Dic13C22×C411yescharacteristic
228C22×Dic13C22×C411yescharacteristic
229C22×Dic13C22×C411yescharacteristic
230C22×Dic13C22×C411yescharacteristic
231C22×Dic13C22×C411yescharacteristic
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×D13—21no—
263C2×C4×D13—21no—
264C2×C4×D13—21no—
265C2×C4×D13—21no—
266C2×C4×D13C2×D412yes—
267C2×C4×D13C2×D412yes—
268C2×C4×D13C2×D412yes—
269C2×C4×D13C2×D412yes—
270C2×C4×D13C2×Q812yes—
271C2×C4×D13C2×Q812yes—
272C2×C4×D13C2×Q812yes—
273C2×C4×D13#4112yes—
274C4⋊#261—44no—
275C4⋊#261—44no—
276C4⋊#261—44no—
277C4⋊#261—44no—
278C4⋊#261—44no—
279C4⋊#261—44no—
280C4⋊#261—44no—
281C4⋊#261—44no—
282C4×#261—44no—
283C4×#261—44no—
284C13×C4⋊C4—22no—
285C13×C4⋊C4C4⋊C414yescomplemented
286C42×C13—22no—
287C4⋊Dic13—22no—
288C4⋊Dic13C4⋊C414yescomplemented
289#6101—22no—
290#6101—22no—
291#6101C4⋊C414yescomplemented
292#6101C4⋊C414yescomplemented
293C4×Dic13—22no—
294C4×Dic13—22no—
295C4×Dic13—22no—
296C2×#389—131no—
297C2×#389—131no—
298C2×#387—131no—
299C2×#387—131no—
300C2×#382—131no—
301#1444—131no—
302#1444—131no—
303#1442—131no—
304#1442—131no—
305#1442—131no—
306#1441—131no—
307#1436—131no—
308#1436—131no—
309#1436—131no—
310C4⋊#95—131no—
311C23×C13C23×C411yescharacteristic
312C22×D13C22×D411yescharacteristic
313C22×D13C22×D411yescharacteristic
314C22×D13C22×Q811yescharacteristic
315C22×D13C2×#4111yescharacteristic
316C22×D13C2×#4111yescharacteristic
317C22×D13C2×#4111yescharacteristic
318C22×D13H(5,𝔽2)11yescharacteristic
319C22×D13H(5,𝔽2)11yescharacteristic
320C22×D13H(5,𝔽2)11yescharacteristic
321C22×D132−1+411yescharacteristic
322C22×D132−1+411yescharacteristic
323C22×D132−1+411yescharacteristic
324C22×D132−1+411yescharacteristic
325C22×D132−1+411yescharacteristic
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—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×#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×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—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×C13C2×C4⋊C412yes—
400C2×C4×C13C2×C4⋊C412yes—
401C2×C4×C13C2×C4⋊C412yes—
402C2×C4×C13C4×D412yes—
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—21no—
414C2×Dic13—21no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—21no—
418C2×Dic13—21no—
419C2×Dic13—21no—
420C2×Dic13C2×C4⋊C412yes—
421C2×Dic13C2×C4⋊C412yes—
422C2×Dic13C2×C4⋊C412yes—
423C2×Dic13C4×D412yes—
424C4×D13—22no—
425C4×D13—22no—
426C4×D13—22no—
427C4×D13—22no—
428C4×D13—22no—
429C4×D13—22no—
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—41no—
441C4×D13—41no—
442C4×D13—41no—
443C4×D13—41no—
444C4×D13—41no—
445C4×D13—41no—
446C4×D13—41no—
447C4×D13—41no—
448C4×D13—41no—
449C4×D13—41no—
450C4×D13—41no—
451C4×D13—41no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C42—131no—
463C22×C42—131no—
464C22×C42—131no—
465#389—264no—
466#389—264no—
467#387—131no—
468#387—131no—
469#387—131no—
470#387—131no—
471#387—131no—
472#387—131no—
473#387—131no—
474#387—264no—
475#387#26111yescharacteristic, complemented
476#382—264no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
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—
499C22×C13C22×C4⋊C411yescharacteristic
500C22×C13C2×C4×D411yescharacteristic
501C22×C13C4×#4111yescharacteristic
502C22×C13#51911yescharacteristic
503C22×C13#52011yescharacteristic
504C22×C13#52011yescharacteristic
505C22×C13#52011yescharacteristic
506C2×D13#53511yescharacteristic
507C2×D13#53611yescharacteristic
508C2×D13#53611yescharacteristic
509C2×D13#53711yescharacteristic
510C2×D13#53811yescharacteristic
511C2×D13#53911yescharacteristic
512C2×D13#54111yescharacteristic
513C2×D13#54111yescharacteristic
514C2×D13#54211yescharacteristic
515C2×D13#54211yescharacteristic
516C2×D13#54411yescharacteristic
517C2×D13#54411yescharacteristic
518C2×D13D4211yescharacteristic
519C2×D13#54611yescharacteristic
520C2×D13#54711yescharacteristic
521C2×D13#54711yescharacteristic
522C2×D13#54811yescharacteristic
523C2×D13#54811yescharacteristic
524C2×D13D4×Q811yescharacteristic
525C2×D13#55111yescharacteristic
526C2×D13#55211yescharacteristic
527C2×D13#55411yescharacteristic
528C2×D13#55711yescharacteristic
529C2×D13#55711yescharacteristic
530C2×D13#56211yescharacteristic
531C2×D13#56311yescharacteristic
532C2×D13#56311yescharacteristic
533C2×D13#56411yescharacteristic
534#261—42no—
535#261—42no—
536#261—42no—
537#261—42no—
538#261—81no—
539#261—81no—
540#261—81no—
541#261—81no—
542C4×C13—22no—
543C4×C13—22no—
544C4×C13—22no—
545C4×C13—22no—
546C4×C13—41no—
547C4×C13—41no—
548C4×C13—41no—
549Dic13—22no—
550Dic13—22no—
551Dic13—22no—
552Dic13—22no—
553Dic13—41no—
554Dic13—41no—
555Dic13—41no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
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—
571C2×C4⋊C4—131no—
572C2×C4⋊C4—131no—
573C2×C4⋊C4—131no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—131no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
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—521no—
596C2×C4⋊C4—521no—
597C2×C4⋊C4—521no—
598C2×C4⋊C4—521no—
599C2×C4⋊C4—521no—
600C2×C4⋊C4—521no—
601C2×C4⋊C4—521no—
602C2×C4⋊C4—521no—
603C2×C4⋊C4—521no—
604C2×C4⋊C4—521no—
605C2×C4⋊C4C2×#26111yescharacteristic
606C2×C4⋊C4C2×#26111yescharacteristic
607C2×C42—131no—
608C2×C42—131no—
609C2×C42—131no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—262no—
614C2×C42—262no—
615C2×C42—521no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42C2×#26111yescharacteristic
619#95—134no—
620#95—131no—
621#95—131no—
622#95—131no—
623#95—131no—
624#95—131no—
625#95—131no—
626#95—131no—
627#95—131no—
628#95—131no—
629#95—131no—
630#95—131no—
631#95—131no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—262no—
637#95—262no—
638#95—262no—
639#95—262no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—521no—
645#95—521no—
646#95—521no—
647#95—521no—
648#95—521no—
649#95C2×#26111yescharacteristic
650#95C2×#26111yescharacteristic
651#95C2×#26111yescharacteristic
652#95C2×#26111yescharacteristic
653C2×C13#231711yescharacteristic
654C2×C13#232311yescharacteristic
655C2×C13#233411yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13#235111yescharacteristic
658C2×C13#235911yescharacteristic
659C2×C13#238211yescharacteristic
660D13#267411yescharacteristic
661D13#267611yescharacteristic
662D13#271311yescharacteristic
663D13#271911yescharacteristic
664D13#272311yescharacteristic
665D13#272611yescharacteristic
666D13#275511yescharacteristic
667D13#277411yescharacteristic
668C24—131no—
669C22×C4—131no—
670C22×C4—131no—
671C22×C4—131no—
672C22×C4—131no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—131no—
686C22×C4—131no—
687C22×C4—131no—
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×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×C4C22×#26111yescharacteristic
775C22×C4C22×#26111yescharacteristic
776C22×C4C22×#26111yescharacteristic
777C22×C4C22×#26111yescharacteristic
778C22×C4C22×#26111yescharacteristic
779C22×C4C22×#26111yescharacteristic
780C22×C4C22×#26111yescharacteristic
781C4⋊C4—22no—
782C4⋊C4—134no—
783C4⋊C4—134no—
784C4⋊C4—134no—
785C4⋊C4—262no—
786C4⋊C4—262no—
787C4⋊C4—262no—
788C4⋊C4—524no—
789C4⋊C4—524no—
790C4⋊C4—524no—
791C4⋊C4—524no—
792C4⋊C4—524no—
793C4⋊C4—524no—
794C4⋊C4—524no—
795C4⋊C4—524no—
796C4⋊C4C4⋊#26114yescomplemented
797C42—22no—
798C42—262no—
799C42—262no—
800C42—262no—
801C42—524no—
802C42—524no—
803C13#1440411yescharacteristic, complemented, Sylow
804C23—131no—
805C23—131no—
806C23—131no—
807C23—131no—
808C23—131no—
809C23—131no—
810C23—131no—
811C23—131no—
812C23—131no—
813C23—131no—
814C23—131no—
815C23—131no—
816C23—131no—
817C23—131no—
818C23C23×#26111yescharacteristic
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—132no—
837C2×C4—132no—
838C2×C4—132no—
839C2×C4—132no—
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—261no—
857C2×C4—261no—
858C2×C4—261no—
859C2×C4—261no—
860C2×C4—261no—
861C2×C4—261no—
862C2×C4—261no—
863C2×C4—261no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—261no—
877C2×C4—261no—
878C2×C4—261no—
879C2×C4—261no—
880C2×C4—261no—
881C2×C4—261no—
882C2×C4—261no—
883C2×C4—261no—
884C2×C4—261no—
885C2×C4—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—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×C4C2×C4⋊#26112yes—
942C2×C4C2×C4⋊#26112yes—
943C2×C4C2×C4⋊#26112yes—
944C2×C4D4×#26112yes—
945C22—131no—
946C22—131no—
947C22—131no—
948C22—131no—
949C22—131no—
950C22—131no—
951C22—131no—
952C22—131no—
953C22—131no—
954C22—131no—
955C22—131no—
956C22—131no—
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—
973C22C22×C4⋊#26111yescharacteristic
974C22C2×D4×#26111yescharacteristic
975C22#1171962711yescharacteristic
976C22#41×#26111yescharacteristic
977C22#1171963111yescharacteristic
978C22#1171963111yescharacteristic
979C22#1171963111yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—262no—
988C4—262no—
989C4—262no—
990C4—262no—
991C4—522no—
992C4—522no—
993C4—522no—
994C4—522no—
995C4—521no—
996C4—521no—
997C4—521no—
998C4—1041no—
999C4—1041no—
1000C4—1041no—
1001C4—1041no—
1002C2—131no—
1003C2—131no—
1004C2—131no—
1005C2—131no—
1006C2—131no—
1007C2—131no—
1008C2—131no—
1009C2—131no—
1010C2#1313131711yescharacteristic
1011C2#1313132311yescharacteristic
1012C2#1313133411yescharacteristic
1013C2D4×C4⋊#26111yescharacteristic
1014C2#1313135111yescharacteristic
1015C2#1313135911yescharacteristic
1016C2#1313138211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#387C4
prime radical, cosocleC23×D13C24
hypercenter#387#261
hypocenterC13#14404
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
285. C13×C4⋊C4C4⋊C4semidirect
288. C4⋊Dic13C4⋊C4semidirect
291. #6101C4⋊C4semidirect
292. #6101C4⋊C4semidirect
475. #387#261semidirect
796. C4⋊C4C4⋊#261semidirect
803. C13#14404semidirect

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×#117190602
#131300242
#131300222
#131300212
#131300162
#131300142
D13×#3872
#1440413