Finite Group Databasebeta

← #30609344

Subgroups — #30609344

Order 15616.

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×#16840713C211yesmaximal, characteristic
2C2×#16840713C211yesmaximal, characteristic
3C2×#16840711C211yesmaximal, characteristic
4C2×#16840706C211yesmaximal, characteristic
5#21461007C211yesmaximal, characteristic
6#21461007C211yesmaximal, characteristic
7#21461005C211yesmaximal, characteristic
8#21461005C211yesmaximal, characteristic
9#21461005C211yesmaximal, characteristic
10#21461004C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic
12#21460999C211yesmaximal, characteristic
13#21460999C211yesmaximal, characteristic
14#21460997C211yesmaximal, 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#16840713—24no—
28#16840711—24no—
29#16840706—24no—
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×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D61C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839649C411yescharacteristic, complemented
52#16839648C411yescharacteristic, complemented
53#16839647C411yescharacteristic, complemented
54#16839646C411yescharacteristic, complemented
55#16839645C411yescharacteristic, complemented
56#16839644C411yescharacteristic, complemented
57#16839643C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#387C411yescharacteristic, complemented
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
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—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—22no—
83C2×C4⋊#6923—22no—
84C2×C4⋊#6923—22no—
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⋊#6923—41no—
93C2×C4⋊#6923—41no—
94C2×C4⋊#6923—41no—
95C2×C4×#6923—22no—
96C2×C4×#6923—22no—
97C2×C4×#6923—22no—
98C2×C4×#6923—41no—
99C2×C4×#6923—41no—
100C2×C4×#6923—41no—
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—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—22no—
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117(C2×#6923)⋊C4—41no—
118(C2×#6923)⋊C4D414yes—
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C2×C4⋊Dic61C2×C411yescharacteristic
127C2×C4⋊Dic61C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61D414yes—
135C4⋊C4×D61Q814yes—
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C42×D61—22no—
140C42×D61—22no—
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
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153C2×C4⋊C4×C61C2×C411yescharacteristic
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C42×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157#95×C61C2×C411yescharacteristic
158#95×C61C2×C411yescharacteristic
159#95×C61C2×C411yescharacteristic
160C23×D61C2411yescharacteristic
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×#6923—21no—
212C22×#6923—21no—
213C22×#6923C2×D412yes—
214C22×#6923C2×D412yes—
215C22×#6923#4112yes—
216C22×#6923#4112yes—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
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×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2×D412yes—
269C2×C4×D61C2×Q812yes—
270C2×C4×D61C2×Q812yes—
271C2×C4×D61C2×Q812yes—
272C2×C4×D61#4112yes—
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×#6923—44no—
282C4×#6923—44no—
283C4⋊C4×C61—22no—
284C4⋊C4×C61C4⋊C414yescomplemented
285C42×C61—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61C4⋊C414yescomplemented
288#11758196—22no—
289#11758196—22no—
290#11758196C4⋊C414yescomplemented
291#11758196C4⋊C414yescomplemented
292C4×Dic61—22no—
293C4×Dic61—22no—
294C4×Dic61—22no—
295C23×C61C23×C411yescharacteristic
296C22×D61C22×D411yescharacteristic
297C22×D61C22×D411yescharacteristic
298C22×D61C22×Q811yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
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
308C22×D612−1+411yescharacteristic
309C22×D612−1+411yescharacteristic
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—22no—
321C2×#6923—22no—
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×#6923—41no—
365C2×#6923—41no—
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×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61C2×C4⋊C412yes—
384C2×C4×C61C2×C4⋊C412yes—
385C2×C4×C61C2×C4⋊C412yes—
386C2×C4×C61C4×D412yes—
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×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61C2×C4⋊C412yes—
405C2×Dic61C2×C4⋊C412yes—
406C2×Dic61C2×C4⋊C412yes—
407C2×Dic61C4×D412yes—
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—22no—
423C4×D61—22no—
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—
434C4×D61—41no—
435C4×D61—41no—
436#14404—611nomaximal, Sylow
437C22×C61C22×C4⋊C411yescharacteristic
438C22×C61C2×C4×D411yescharacteristic
439C22×C61C4×#4111yescharacteristic
440C22×C61#51911yescharacteristic
441C22×C61#52011yescharacteristic
442C22×C61#52011yescharacteristic
443C22×C61#52011yescharacteristic
444C2×D61#53511yescharacteristic
445C2×D61#53611yescharacteristic
446C2×D61#53611yescharacteristic
447C2×D61#53711yescharacteristic
448C2×D61#53811yescharacteristic
449C2×D61#53911yescharacteristic
450C2×D61#54111yescharacteristic
451C2×D61#54111yescharacteristic
452C2×D61#54211yescharacteristic
453C2×D61#54211yescharacteristic
454C2×D61#54411yescharacteristic
455C2×D61#54411yescharacteristic
456C2×D61D4211yescharacteristic
457C2×D61#54611yescharacteristic
458C2×D61#54711yescharacteristic
459C2×D61#54711yescharacteristic
460C2×D61#54811yescharacteristic
461C2×D61#54811yescharacteristic
462C2×D61D4×Q811yescharacteristic
463C2×D61#55111yescharacteristic
464C2×D61#55211yescharacteristic
465C2×D61#55411yescharacteristic
466C2×D61#55711yescharacteristic
467C2×D61#55711yescharacteristic
468C2×D61#56211yescharacteristic
469C2×D61#56311yescharacteristic
470C2×D61#56311yescharacteristic
471C2×D61#56411yescharacteristic
472#6923—42no—
473#6923—42no—
474#6923—42no—
475#6923—42no—
476#6923—81no—
477#6923—81no—
478#6923—81no—
479#6923—81no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—22no—
483C4×C61—22no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—22no—
488Dic61—22no—
489Dic61—22no—
490Dic61—22no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494C2×#389—611no—
495C2×#389—611no—
496C2×#387—611no—
497C2×#387—611no—
498C2×#382—611no—
499#1444—611no—
500#1444—611no—
501#1442—611no—
502#1442—611no—
503#1442—611no—
504#1441—611no—
505#1436—611no—
506#1436—611no—
507#1436—611no—
508C4⋊#95—611no—
509C2×C61#231711yescharacteristic
510C2×C61#232311yescharacteristic
511C2×C61#233411yescharacteristic
512C2×C61D4×C4⋊C411yescharacteristic
513C2×C61#235111yescharacteristic
514C2×C61#235911yescharacteristic
515C2×C61#238211yescharacteristic
516D61#267411yescharacteristic
517D61#267611yescharacteristic
518D61#271311yescharacteristic
519D61#271911yescharacteristic
520D61#272311yescharacteristic
521D61#272611yescharacteristic
522D61#275511yescharacteristic
523D61#277411yescharacteristic
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×C4⋊C4—611no—
533C22×C4⋊C4—611no—
534C22×C42—611no—
535C22×C42—611no—
536C22×C42—611no—
537#389—1224no—
538#389—1224no—
539#387—611no—
540#387—611no—
541#387—611no—
542#387—611no—
543#387—611no—
544#387—611no—
545#387—611no—
546#387—1224no—
547#387#692311yescharacteristic, complemented
548#382—1224no—
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—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C61#1440411yescharacteristic, complemented, Sylow
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—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—614no—
591C2×C4⋊C4—614no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
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—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
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⋊C4—2441no—
618C2×C4⋊C4—2441no—
619C2×C4⋊C4—2441no—
620C2×C4⋊C4—2441no—
621C2×C4⋊C4C2×#692311yescharacteristic
622C2×C4⋊C4C2×#692311yescharacteristic
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1222no—
627C2×C42—1222no—
628C2×C42—1222no—
629C2×C42—1222no—
630C2×C42—1222no—
631C2×C42—2441no—
632C2×C42—2441no—
633C2×C42—2441no—
634C2×C42C2×#692311yescharacteristic
635#95—614no—
636#95—611no—
637#95—611no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—611no—
647#95—611no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—1222no—
658#95—1222no—
659#95—1222no—
660#95—2441no—
661#95—2441no—
662#95—2441no—
663#95—2441no—
664#95—2441no—
665#95C2×#692311yescharacteristic
666#95C2×#692311yescharacteristic
667#95C2×#692311yescharacteristic
668#95C2×#692311yescharacteristic
669C24—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
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—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
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×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C22×C4C22×#692311yescharacteristic
779C22×C4C22×#692311yescharacteristic
780C22×C4C22×#692311yescharacteristic
781C22×C4C22×#692311yescharacteristic
782C4⋊C4—22no—
783C4⋊C4—614no—
784C4⋊C4—614no—
785C4⋊C4—614no—
786C4⋊C4—1222no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—2444no—
790C4⋊C4—2444no—
791C4⋊C4—2444no—
792C4⋊C4—2444no—
793C4⋊C4—2444no—
794C4⋊C4—2444no—
795C4⋊C4—2444no—
796C4⋊C4—2444no—
797C4⋊C4C4⋊#692314yescomplemented
798C42—22no—
799C42—1222no—
800C42—1222no—
801C42—1222no—
802C42—2444no—
803C42—2444no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23—611no—
815C23—611no—
816C23—611no—
817C23—611no—
818C23C23×#692311yescharacteristic
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—612no—
837C2×C4—612no—
838C2×C4—612no—
839C2×C4—612no—
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—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
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—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
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×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4C2×C4⋊#692312yes—
942C2×C4C2×C4⋊#692312yes—
943C2×C4C2×C4⋊#692312yes—
944C2×C4D4×#692312yes—
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—
969C22—611no—
970C22—611no—
971C22—611no—
972C22—611no—
973C22C22×C4⋊#692311yescharacteristic
974C22C2×D4×#692311yescharacteristic
975C22#41×#692311yescharacteristic
976C22#1684083011yescharacteristic
977C22#1684083111yescharacteristic
978C22#1684083111yescharacteristic
979C22#1684083111yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—1222no—
988C4—1222no—
989C4—1222no—
990C4—1222no—
991C4—4881no—
992C4—4881no—
993C4—4881no—
994C4—4881no—
995C4—2442no—
996C4—2442no—
997C4—2442no—
998C4—2442no—
999C4—2441no—
1000C4—2441no—
1001C4—2441no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2—611no—
1007C2—611no—
1008C2—611no—
1009C2—611no—
1010C2#2146230011yescharacteristic
1011C2#2146230611yescharacteristic
1012C2#2146231711yescharacteristic
1013C2D4×C4⋊#692311yescharacteristic
1014C2#2146233411yescharacteristic
1015C2#2146234211yescharacteristic
1016C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14404
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
51. #16839649C4semidirect
52. #16839648C4semidirect
53. #16839647C4semidirect
54. #16839646C4semidirect
55. #16839645C4semidirect
56. #16839644C4semidirect
57. #16839643C4semidirect
62. C61×#387C4semidirect
284. C4⋊C4×C61C4⋊C4semidirect
287. C4⋊Dic61C4⋊C4semidirect
290. #11758196C4⋊C4semidirect
291. #11758196C4⋊C4semidirect
547. #387#6923semidirect
571. C61#14404semidirect
797. 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
C2×#168407062
#214610072
#214610052
#214610042
#214609992
#214609972
#387×D612
#1440461