Finite Group Databasebeta

← #30609323

Subgroups — #30609323

Order 15616.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840705C211yesmaximal, characteristic
3#21461008C211yesmaximal, characteristic, complemented
4#21461006C211yesmaximal, characteristic, complemented
5#21461004C211yesmaximal, characteristic, complemented
6#21461004C211yesmaximal, characteristic, complemented
7#21461003C211yesmaximal, characteristic
8#21461002C211yesmaximal, characteristic
9#21461000C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic, complemented
11#21460996C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460994C211yesmaximal, characteristic, complemented
14#21460993C211yesmaximal, characteristic
15#385×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C22⋊#6923C2211yescharacteristic
19C22×C22⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24#16840712—24no—
25#16840705—24no—
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
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
46C23×C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C4⋊C4×D61C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C22⋊C4×D61C2211yescharacteristic
51#16839637C411yescharacteristic, complemented
52#16839636C411yescharacteristic, complemented
53#16839636C411yescharacteristic, complemented
54#16839635C411yescharacteristic, complemented
55#16839634C411yescharacteristic, complemented
56#16839633C411yescharacteristic, complemented
57#16839633C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#385C411yescharacteristic, 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—41no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C22⋊#6923—22no—
76C2×C22⋊#6923—22no—
77C2×C22⋊#6923—22no—
78C2×C22⋊#6923—22no—
79C2×C22⋊#6923—22no—
80C2×C22⋊#6923—41no—
81C2×C22⋊#6923—41no—
82C2×C22⋊#6923—41no—
83C2×C22⋊#6923—41no—
84C2×C22⋊#6923—41no—
85C2×C22⋊#6923—41no—
86C2×C22⋊#6923D414yes—
87C2×C4×#6923—22no—
88C2×C4×#6923—22no—
89C2×C4×#6923—22no—
90C2×C4×#6923—22no—
91C2×C4×#6923—41no—
92C2×C4×#6923—41no—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—22no—
96(C2×#6923)⋊C4—22no—
97(C2×#6923)⋊C4—22no—
98(C2×#6923)⋊C4—22no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—41no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
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—
113C24×D61C2311yescharacteristic
114C23×Dic61C2×C411yescharacteristic
115C22×C4×D61—22no—
116C22×C4×D61—22no—
117C22×C4×D61—41no—
118C22×C4×D61—41no—
119C22×C4×D61—41no—
120C22×C4×D61—41no—
121C22×C4×D61C2×C411yescharacteristic
122C22×C4×D61C2×C411yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C22×C4×D61C2311yescharacteristic
129C2×C4⋊Dic61C2×C411yescharacteristic
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C2×#11758196C2×C411yescharacteristic
135C4⋊C4×D61—41no—
136C4⋊C4×D61—41no—
137C4⋊C4×D61—41no—
138C4⋊C4×D61—41no—
139C2×C22⋊Dic61C2×C411yescharacteristic
140C2×C22⋊Dic61C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2×C411yescharacteristic
145C22⋊C4×D61—22no—
146C22⋊C4×D61—22no—
147C22⋊C4×D61—22no—
148C22⋊C4×D61—22no—
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153#14519684C2×C411yescharacteristic
154#14519684C2×C411yescharacteristic
155C23×C4×C61C2×C411yescharacteristic
156C2×C4⋊C4×C61C2×C411yescharacteristic
157C2×C4⋊C4×C61C2×C411yescharacteristic
158C2×C22⋊C4×C61C2×C411yescharacteristic
159C2×C22⋊C4×C61C2×C411yescharacteristic
160#95×C61C2×C411yescharacteristic
161#95×C61C2×C411yescharacteristic
162C24×C61C22×C411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61C22×C411yescharacteristic
176C23×D61C2×D412yes—
177C23×D61#4112yes—
178C23×D61C2411yescharacteristic
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×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923C2×D412yes—
232C22×#6923C2×D412yes—
233C22×#6923#4112yes—
234C22×#6923#4112yes—
235C22×C4×C61—22no—
236C22×C4×C61—41no—
237C22×C4×C61—41no—
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×Dic61—22no—
245C22×Dic61—41no—
246C22×Dic61—41no—
247C22×Dic61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
251C22×Dic61C22×C411yescharacteristic
252C22×Dic61C22×C411yescharacteristic
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
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×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—41no—
290C2×C4×D61—41no—
291C2×C4×D61—41no—
292C2×C4×D61—41no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61#4112yes—
298C2×C4×D61#4112yes—
299C22⋊#6923—44no—
300C22⋊#6923—44no—
301C22⋊#6923—44no—
302C22⋊#6923—44no—
303C4⋊#6923—44no—
304C4⋊#6923—44no—
305C4×#6923—44no—
306C4×#6923—44no—
307C4⋊C4×C61—41no—
308C4⋊C4×C61—41no—
309C22⋊C4×C61—22no—
310C22⋊C4×C61—22no—
311C22⋊Dic61—22no—
312C22⋊Dic61—22no—
313#11758198—22no—
314#11758198—22no—
315#11758198—22no—
316#11758198—22no—
317C4⋊Dic61—41no—
318C4⋊Dic61—41no—
319#11758196—41no—
320#11758196—41no—
321#11758196—41no—
322#11758196—41no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61C4×D412yes—
330C23×C61C23×C411yescharacteristic
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61C4×D412yes—
366C22×D61C22×D411yescharacteristic
367C22×D61C2×#4111yescharacteristic
368C22×D61C2×#4111yescharacteristic
369C22×D61C2×#4111yescharacteristic
370C22×D61C2×#4111yescharacteristic
371C22×D61C2×#4111yescharacteristic
372C22×D61H(5,𝔽2)11yescharacteristic
373C22×D61H(5,𝔽2)11yescharacteristic
374C22×D61H(5,𝔽2)11yescharacteristic
375C22×D61H(5,𝔽2)11yescharacteristic
376C22×D61H(5,𝔽2)11yescharacteristic
377C22×D612−1+411yescharacteristic
378C22×D612−1+411yescharacteristic
379C22×D612−1+411yescharacteristic
380C2×#6923—22no—
381C2×#6923—22no—
382C2×#6923—22no—
383C2×#6923—22no—
384C2×#6923—22no—
385C2×#6923—22no—
386C2×#6923—22no—
387C2×#6923—22no—
388C2×#6923—22no—
389C2×#6923—22no—
390C2×#6923—22no—
391C2×#6923—22no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—41no—
428C2×#6923—41no—
429C2×#6923—41no—
430C2×#6923—41no—
431C2×#6923—41no—
432C2×#6923—41no—
433C2×#6923—41no—
434C2×#6923—41no—
435C2×#6923—41no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
453C2×C4×C61—44no—
454C2×C4×C61#11712yes—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—21no—
472C2×Dic61—44no—
473C2×Dic61#11712yes—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—22no—
477C4×D61—22no—
478C4×D61—44no—
479C4×D61—44no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486C4×D61—41no—
487C4×D61—41no—
488C4×D61—41no—
489C4×D61—41no—
490C4×D61—41no—
491C4×D61—41no—
492C4×D61—41no—
493C4×D61—41no—
494C4×D61—41no—
495C4×D61—41no—
496C4×D61—41no—
497C4×D61—41no—
498C4×D61—41no—
499C4×D61—41no—
500#14383—611nomaximal, Sylow
501C22×C61—22no—
502C22×C61—22no—
503C22×C61—22no—
504C22×C61—41no—
505C22×C61—41no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61C2×#11711yescharacteristic
509C22×C61C2×C4×D411yescharacteristic
510C22×C61C4×#4111yescharacteristic
511C22×C61#51811yescharacteristic
512C22×C61#51811yescharacteristic
513C22×C61#51911yescharacteristic
514C22×C61#52011yescharacteristic
515C2×D61—22no—
516C2×D61—22no—
517C2×D61—22no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61—41no—
521C2×D61—41no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61#53411yescharacteristic
531C2×D61#53511yescharacteristic
532C2×D61#53811yescharacteristic
533C2×D61#53811yescharacteristic
534C2×D61#53911yescharacteristic
535C2×D61#53911yescharacteristic
536C2×D61#54011yescharacteristic
537C2×D61#54011yescharacteristic
538C2×D61#54211yescharacteristic
539C2×D61#54211yescharacteristic
540C2×D61#54211yescharacteristic
541C2×D61#54211yescharacteristic
542C2×D61#54611yescharacteristic
543C2×D61#54711yescharacteristic
544C2×D61#54711yescharacteristic
545C2×D61#54711yescharacteristic
546C2×D61#55111yescharacteristic
547C2×D61#55111yescharacteristic
548C2×D61#55111yescharacteristic
549C2×D61#55211yescharacteristic
550C2×D61#55211yescharacteristic
551C2×D61#55211yescharacteristic
552C2×D61#55311yescharacteristic
553C2×D61#55311yescharacteristic
554C2×D61#56211yescharacteristic
555C2×D61#56211yescharacteristic
556C2×D61#56311yescharacteristic
557C2×D61#56311yescharacteristic
558#6923—42no—
559#6923—42no—
560#6923—42no—
561#6923—42no—
562#6923—81no—
563#6923—81no—
564#6923—81no—
565#6923—81no—
566C4×C61—22no—
567C4×C61—41no—
568C4×C61—41no—
569C4×C61—41no—
570C4×C61—41no—
571C4×C61—41no—
572Dic61—22no—
573Dic61—41no—
574Dic61—41no—
575Dic61—41no—
576Dic61—41no—
577Dic61—41no—
578C2×#388—611no—
579C2×#385—611no—
580C2×#381—611no—
581#1445—611no—
582#1443—611no—
583#1441—611no—
584#1441—611no—
585#1440—611no—
586#1439—611no—
587#1437—611no—
588#1436—611no—
589C4⋊#95—611no—
590#1434—611no—
591#1434—611no—
592C22⋊#95—611no—
593C2×C61—42no—
594C2×C61#231911yescharacteristic
595C2×C61#232111yescharacteristic
596C2×C61#233211yescharacteristic
597C2×C61#234411yescharacteristic
598C2×C61#235311yescharacteristic
599C2×C61#235911yescharacteristic
600C2×C61#237811yescharacteristic
601D61—42no—
602D61#270111yescharacteristic
603D61#270611yescharacteristic
604D61#271711yescharacteristic
605D61#271811yescharacteristic
606D61#274311yescharacteristic
607D61#276111yescharacteristic
608D61#276411yescharacteristic
609D61#276511yescharacteristic
610C24×C4—611no—
611C22×C4⋊C4—611no—
612C22×C4⋊C4—611no—
613C22×C4⋊C4—611no—
614C22×C4⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C42—611no—
622C22×C42—611no—
623#388—1224no—
624#385—611no—
625#385—611no—
626#385—611no—
627#385—611no—
628#385—611no—
629#385—611no—
630#385—611no—
631#385#692311yescharacteristic, complemented
632#381—1224no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C61#1438311yescharacteristic, complemented, Sylow
656C25—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—611no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4C2×#692311yescharacteristic
681C2×C4⋊C4—611no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—1222no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—2441no—
691C2×C4⋊C4—2441no—
692C2×C4⋊C4—2441no—
693C2×C4⋊C4—2441no—
694C2×C4⋊C4—2441no—
695C2×C4⋊C4—2441no—
696C2×C4⋊C4—2441no—
697C2×C4⋊C4C2×#692311yescharacteristic
698C2×C4⋊C4C2×#692311yescharacteristic
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—611no—
705C2×C22⋊C4—614no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4C2×#692311yescharacteristic
722C2×C22⋊C4C2×#692311yescharacteristic
723C2×C42—1222no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—2441no—
728C2×C42—2441no—
729#95—611no—
730#95—611no—
731#95—611no—
732#95—611no—
733#95—611no—
734#95—611no—
735#95—1222no—
736#95—1222no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—2441no—
745#95—2441no—
746#95—2441no—
747#95—2441no—
748#95—2441no—
749#95—2441no—
750#95—2441no—
751#95—2441no—
752#95—2441no—
753#95—2441no—
754#95—2441no—
755#95C2×#692311yescharacteristic
756#95C2×#692311yescharacteristic
757C24—611no—
758C24—612no—
759C24—612no—
760C24—611no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24C22×#692311yescharacteristic
774C22×C4—22no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—611no—
778C22×C4—612no—
779C22×C4—612no—
780C22×C4—612no—
781C22×C4—612no—
782C22×C4—612no—
783C22×C4—612no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1222no—
822C22×C4—1222no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1222no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—2441no—
879C22×C4—2441no—
880C22×C4—2441no—
881C22×C4—2441no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2441no—
887C22×C4—2441no—
888C22×C4C22×#692311yescharacteristic
889C22×C4C22×#692311yescharacteristic
890C22×C4C22×#692311yescharacteristic
891C22×C4C22×#692311yescharacteristic
892C22×C4C22×#692311yescharacteristic
893C22×C4C22×#692311yescharacteristic
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—2441no—
897C4⋊C4—2441no—
898C4⋊C4—2441no—
899C4⋊C4—2441no—
900C4⋊C4—2441no—
901C4⋊C4—2441no—
902C4⋊C4—2444no—
903C4⋊C4—2444no—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—1222no—
907C22⋊C4—1222no—
908C22⋊C4—1222no—
909C22⋊C4—1222no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C22⋊C4—2444no—
916C42—2444no—
917C42—2444no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—611no—
925C23—611no—
926C23—611no—
927C23—611no—
928C23—611no—
929C23—611no—
930C23—611no—
931C23—611no—
932C23—611no—
933C23—611no—
934C23—611no—
935C23—611no—
936C23—611no—
937C23—611no—
938C23—612no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—1221no—
955C23—1221no—
956C23—1221no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23D4×#692312yes—
974C23C23×#692311yescharacteristic
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—44no—
993C2×C4—612no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
1024C2×C4—1221no—
1025C2×C4—1221no—
1026C2×C4—1221no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2444no—
1048C2×C4—2444no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2444no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4#1451985612yes—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—611no—
1103C22—611no—
1104C22—611no—
1105C22—611no—
1106C22—611no—
1107C22—611no—
1108C22—611no—
1109C22—611no—
1110C22—611no—
1111C22—611no—
1112C22—611no—
1113C22—611no—
1114C22—611no—
1115C22—611no—
1116C22—611no—
1117C22—611no—
1118C22—611no—
1119C22—611no—
1120C22—611no—
1121C22—611no—
1122C22—611no—
1123C22—611no—
1124C22—611no—
1125C22—611no—
1126C22—611no—
1127C22—611no—
1128C22—611no—
1129C22—611no—
1130C22—1222no—
1131C22—1222no—
1132C22—1222no—
1133C22—2442no—
1134C22—2442no—
1135C22—2442no—
1136C22—2442no—
1137C22—2442no—
1138C22—2442no—
1139C22—2442no—
1140C22—2442no—
1141C22—2441no—
1142C22—2441no—
1143C22—2441no—
1144C22—2441no—
1145C22C2×#1451985611yescharacteristic
1146C22C2×D4×#692311yescharacteristic
1147C22#41×#692311yescharacteristic
1148C22#1684082911yescharacteristic
1149C22#1684082911yescharacteristic
1150C22#1684083011yescharacteristic
1151C22#1684083111yescharacteristic
1152C4—22no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—1222no—
1159C4—4881no—
1160C4—4881no—
1161C4—4881no—
1162C4—4881no—
1163C4—2442no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2441no—
1168C4—2441no—
1169C4—2441no—
1170C4—2441no—
1171C4—2441no—
1172C2—42no—
1173C2—611no—
1174C2—611no—
1175C2—611no—
1176C2—611no—
1177C2—611no—
1178C2—611no—
1179C2—611no—
1180C2—611no—
1181C2—2442no—
1182C2#2146230211yescharacteristic
1183C2#2146230411yescharacteristic
1184C2#2146231511yescharacteristic
1185C2#2146232711yescharacteristic
1186C2#2146233611yescharacteristic
1187C2#2146234211yescharacteristic
1188C2#2146236111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#385C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#385#6923
hypocenterC61#14383
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #21461008C2semidirect
4. #21461006C2semidirect
5. #21461004C2semidirect
6. #21461004C2semidirect
10. #21460999C2semidirect
11. #21460996C2semidirect
12. #21460994C2semidirect
13. #21460994C2semidirect
51. #16839637C4semidirect
52. #16839636C4semidirect
53. #16839636C4semidirect
54. #16839635C4semidirect
55. #16839634C4semidirect
56. #16839633C4semidirect
57. #16839633C4semidirect
60. C61×#385C4semidirect
631. #385#6923semidirect
655. C61#14383semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×#168407052
#214610082
#214610062
#214610042
#214610032
#214610022
#214610002
#214609992
#214609962
#214609942
#214609932
#385×D612
#1438361