Finite Group Databasebeta

← #30609408

Subgroups — #30609408

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C211yesmaximal, characteristic
2C2×#16840711C211yesmaximal, characteristic
3#21461007C211yesmaximal, characteristic
4#21461007C211yesmaximal, characteristic
5#21461007C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21461005C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic
12#21460997C211yesmaximal, characteristic
13#21460997C211yesmaximal, characteristic
14#21460996C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22C22×C4⋊#6923C2211yescharacteristic
23C22×C4⋊#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26#16840713—24no—
27#16840711—24no—
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839649C411yescharacteristic, complemented
50#16839648C411yescharacteristic, complemented
51#16839647C411yescharacteristic, complemented
52#16839646C411yescharacteristic, complemented
53#16839645C411yescharacteristic, complemented
54#16839644C411yescharacteristic, complemented
55#16839643C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#387C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—22no—
70C2×C4⋊#6923—22no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—22no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923—41no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923—41no—
87C2×C4⋊#6923—41no—
88C2×C4⋊#6923—41no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923—41no—
91C2×C4⋊#6923—41no—
92C2×C4⋊#6923Q814yes—
93C2×C4×#6923—22no—
94C2×C4×#6923—22no—
95C2×C4×#6923—22no—
96C2×C4×#6923—41no—
97C2×C4×#6923—41no—
98C2×C4×#6923—41no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—22no—
106(C2×#6923)⋊C4—22no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4—41no—
112(C2×#6923)⋊C4—41no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C4⋊C4×D61—41no—
131C4⋊C4×D61—41no—
132C4⋊C4×D61D414yes—
133C4⋊C4×D61Q814yes—
134C2×C4×Dic61C2×C411yescharacteristic
135C2×C4×Dic61C2×C411yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C42×D61—41no—
138C42×D61—41no—
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151C2×C4⋊C4×C61C2×C411yescharacteristic
152C2×C4⋊C4×C61C2×C411yescharacteristic
153C2×C42×C61C2×C411yescharacteristic
154#95×C61C2×C411yescharacteristic
155#95×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157#95×C61C2×C411yescharacteristic
158C23×D61C2411yescharacteristic
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923C2×Q812yes—
212C22×#6923C2×Q812yes—
213C22×#6923#4112yes—
214C22×#6923#4112yes—
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2×Q812yes—
267C2×C4×D61C2×Q812yes—
268C2×C4×D61C2×Q812yes—
269C2×C4×D61C2×Q812yes—
270C2×C4×D61#4112yes—
271C4⋊#6923—44no—
272C4⋊#6923—44no—
273C4⋊#6923—44no—
274C4⋊#6923—44no—
275C4⋊#6923—44no—
276C4⋊#6923—44no—
277C4⋊#6923—44no—
278C4⋊#6923—44no—
279C4×#6923—44no—
280C4×#6923—44no—
281C4⋊C4×C61—41no—
282C4⋊C4×C61C4⋊C414yescomplemented
283C42×C61—41no—
284C4⋊Dic61—41no—
285C4⋊Dic61C4⋊C414yescomplemented
286#11758196—41no—
287#11758196—41no—
288#11758196C4⋊C414yescomplemented
289#11758196C4⋊C414yescomplemented
290C4×Dic61—41no—
291C4×Dic61—41no—
292C4×Dic61—41no—
293C23×C61C23×C411yescharacteristic
294C22×D61C22×D411yescharacteristic
295C22×D61C22×Q811yescharacteristic
296C22×D61C22×Q811yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61H(5,𝔽2)11yescharacteristic
301C22×D61H(5,𝔽2)11yescharacteristic
302C22×D61H(5,𝔽2)11yescharacteristic
303C22×D61H(5,𝔽2)11yescharacteristic
304C22×D61H(5,𝔽2)11yescharacteristic
305C22×D612−1+411yescharacteristic
306C22×D612−1+411yescharacteristic
307C22×D612−1+411yescharacteristic
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61C2×C4⋊C412yes—
382C2×C4×C61C2×C4⋊C412yes—
383C2×C4×C61C2×C4⋊C412yes—
384C2×C4×C61C4×Q812yes—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61C2×C4⋊C412yes—
403C2×Dic61C2×C4⋊C412yes—
404C2×Dic61C2×C4⋊C412yes—
405C2×Dic61C4×Q812yes—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434#14468—611nomaximal, Sylow
435C22×C61C22×C4⋊C411yescharacteristic
436C22×C61C2×C4×Q811yescharacteristic
437C22×C61C4×#4111yescharacteristic
438C22×C61#51811yescharacteristic
439C22×C61#52011yescharacteristic
440C22×C61#52011yescharacteristic
441C22×C61#52011yescharacteristic
442C2×D61#53511yescharacteristic
443C2×D61#53611yescharacteristic
444C2×D61#53811yescharacteristic
445C2×D61#53811yescharacteristic
446C2×D61#53911yescharacteristic
447C2×D61#53911yescharacteristic
448C2×D61#54111yescharacteristic
449C2×D61#54211yescharacteristic
450C2×D61#54311yescharacteristic
451C2×D61#54411yescharacteristic
452C2×D61#54411yescharacteristic
453C2×D61#54411yescharacteristic
454C2×D61#54611yescharacteristic
455C2×D61#54611yescharacteristic
456C2×D61D4×Q811yescharacteristic
457C2×D61#55011yescharacteristic
458C2×D61#55211yescharacteristic
459C2×D61#55311yescharacteristic
460C2×D61#55411yescharacteristic
461C2×D61#55411yescharacteristic
462C2×D61#55411yescharacteristic
463C2×D61#55711yescharacteristic
464C2×D61#55711yescharacteristic
465C2×D61Q8211yescharacteristic
466C2×D61#56011yescharacteristic
467C2×D61#56211yescharacteristic
468C2×D61#56211yescharacteristic
469C2×D61#56311yescharacteristic
470#6923—42no—
471#6923—42no—
472#6923—42no—
473#6923—42no—
474#6923—81no—
475#6923—81no—
476#6923—81no—
477#6923—81no—
478C4×C61—22no—
479C4×C61—22no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485Dic61—22no—
486Dic61—22no—
487Dic61—22no—
488Dic61—22no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492C2×#389—611no—
493C2×#387—611no—
494C2×#387—611no—
495#1444—611no—
496#1444—611no—
497#1444—611no—
498#1442—611no—
499#1442—611no—
500#1441—611no—
501#1436—611no—
502#1436—611no—
503#1436—611no—
504C4⋊#95—611no—
505C4⋊#95—611no—
506C4⋊#95—611no—
507C2×C61#231711yescharacteristic
508C2×C61#232911yescharacteristic
509C2×C61#233411yescharacteristic
510C2×C61#234911yescharacteristic
511C2×C61Q8×C4⋊C411yescharacteristic
512C2×C61#237011yescharacteristic
513C2×C61#237611yescharacteristic
514D61#269211yescharacteristic
515D61#269411yescharacteristic
516D61#271311yescharacteristic
517D61#271411yescharacteristic
518D61#277411yescharacteristic
519D61#279211yescharacteristic
520D61#280211yescharacteristic
521D61#280611yescharacteristic
522C22×C4⋊C4—611no—
523C22×C4⋊C4—611no—
524C22×C4⋊C4—611no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C4⋊C4—611no—
529C22×C4⋊C4—611no—
530C22×C4⋊C4—611no—
531C22×C4⋊C4—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535#389—1224no—
536#387—611no—
537#387—611no—
538#387—611no—
539#387—611no—
540#387—611no—
541#387—611no—
542#387—611no—
543#387—1224no—
544#387#692311yescharacteristic, complemented
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C61#1446811yescharacteristic, complemented, Sylow
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—614no—
587C2×C4⋊C4—614no—
588C2×C4⋊C4—614no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—2441no—
602C2×C4⋊C4—2441no—
603C2×C4⋊C4—2441no—
604C2×C4⋊C4—2441no—
605C2×C4⋊C4—2441no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4—2441no—
608C2×C4⋊C4—2441no—
609C2×C4⋊C4—2441no—
610C2×C4⋊C4—2441no—
611C2×C4⋊C4—2441no—
612C2×C4⋊C4—2441no—
613C2×C4⋊C4—2441no—
614C2×C4⋊C4—2441no—
615C2×C4⋊C4—2441no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4C2×#692311yescharacteristic
618C2×C4⋊C4C2×#692311yescharacteristic
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625C2×C42—2441no—
626C2×C42—2441no—
627C2×C42—2441no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42C2×#692311yescharacteristic
631#95—611no—
632#95—611no—
633#95—611no—
634#95—611no—
635#95—611no—
636#95—611no—
637#95—611no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—2441no—
653#95—2441no—
654#95—2441no—
655#95—2441no—
656#95—2441no—
657#95—2441no—
658#95—2441no—
659#95—2441no—
660#95—2441no—
661#95C2×#692311yescharacteristic
662#95C2×#692311yescharacteristic
663#95C2×#692311yescharacteristic
664#95C2×#692311yescharacteristic
665C24—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773C22×C4C22×#692311yescharacteristic
774C22×C4C22×#692311yescharacteristic
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C4⋊C4—41no—
779C4⋊C4—614no—
780C4⋊C4—614no—
781C4⋊C4—614no—
782C4⋊C4—2441no—
783C4⋊C4—2441no—
784C4⋊C4—2441no—
785C4⋊C4—2444no—
786C4⋊C4—2444no—
787C4⋊C4—2444no—
788C4⋊C4—2444no—
789C4⋊C4—2444no—
790C4⋊C4—2444no—
791C4⋊C4—2444no—
792C4⋊C4—2444no—
793C4⋊C4C4⋊#692314yescomplemented
794C42—41no—
795C42—2441no—
796C42—2441no—
797C42—2441no—
798C42—2444no—
799C42—2444no—
800C23—611no—
801C23—611no—
802C23—611no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23C23×#692311yescharacteristic
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
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—612no—
833C2×C4—612no—
834C2×C4—612no—
835C2×C4—612no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4C2×C4⋊#692312yes—
938C2×C4C2×C4⋊#692312yes—
939C2×C4C2×C4⋊#692312yes—
940C2×C4Q8×#692312yes—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—611no—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22C22×C4⋊#692311yescharacteristic
970C22C2×Q8×#692311yescharacteristic
971C22#41×#692311yescharacteristic
972C22#1684082911yescharacteristic
973C22#1684083111yescharacteristic
974C22#1684083111yescharacteristic
975C22#1684083111yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—1222no—
984C4—1222no—
985C4—1222no—
986C4—1222no—
987C4—4881no—
988C4—4881no—
989C4—4881no—
990C4—4881no—
991C4—2442no—
992C4—2442no—
993C4—2442no—
994C4—2442no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C2—611no—
999C2—611no—
1000C2—611no—
1001C2—611no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2#2146230011yescharacteristic
1007C2#2146231211yescharacteristic
1008C2#2146231711yescharacteristic
1009C2#2146233211yescharacteristic
1010C2Q8×C4⋊#692311yescharacteristic
1011C2#2146235311yescharacteristic
1012C2#2146235911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14468
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
49. #16839649C4semidirect
50. #16839648C4semidirect
51. #16839647C4semidirect
52. #16839646C4semidirect
53. #16839645C4semidirect
54. #16839644C4semidirect
55. #16839643C4semidirect
60. C61×#387C4semidirect
282. C4⋊C4×C61C4⋊C4semidirect
285. C4⋊Dic61C4⋊C4semidirect
288. #11758196C4⋊C4semidirect
289. #11758196C4⋊C4semidirect
544. #387#6923semidirect
567. C61#14468semidirect
793. C4⋊C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407112
#214610072
#214610052
#214610042
#214609992
#214609972
#214609962
#387×D612
#1446861