Finite Group Databasebeta

← #30608738

Subgroups — #30608738

Order 15616.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840709C211yesmaximal, characteristic
2C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×#6923C211yesmaximal, characteristic
4C2×C22⋊C4×#6923C211yesmaximal, characteristic
5C2×C4×C22⋊#6923C211yesmaximal, characteristic
6C22×(C2×#6923)⋊C4C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic, complemented
8#21460999C211yesmaximal, characteristic, complemented
9#21460998C211yesmaximal, characteristic, complemented
10#21460998C211yesmaximal, characteristic, complemented
11#21460996C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460992C211yesmaximal, characteristic
14#95×#6923C211yesmaximal, characteristic, complemented
15#385×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C24×#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26C22×C4×#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840709C418yescomplemented
29C4⋊C4×#6923—24no—
30C22⋊C4×#6923—24no—
31C22⋊C4×#6923C418yescomplemented
32C4×C22⋊#6923—24no—
33C2×(C2×#6923)⋊C4—24no—
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×(C2×#6923)⋊C4C2211yescharacteristic
49C2×(C2×#6923)⋊C4C2211yescharacteristic
50C23×C4×D61C2211yescharacteristic
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C4⋊C4×D61C2211yescharacteristic
53C2×C22⋊C4×D61C2211yescharacteristic
54C2×C22⋊C4×D61C2211yescharacteristic
55#16839637C411yescharacteristic, complemented
56#16839636C411yescharacteristic, complemented
57#16839636C411yescharacteristic, complemented
58#16839635C411yescharacteristic, complemented
59#16839634C411yescharacteristic, complemented
60#16839633C411yescharacteristic, complemented
61#16839633C411yescharacteristic, complemented
62#95×D61C2211yescharacteristic
63#95×D61C2211yescharacteristic
64C61×#385C411yescharacteristic, complemented
65C23×#6923—22no—
66C23×#6923—22no—
67C23×#6923—22no—
68C23×#6923—22no—
69C23×#6923—22no—
70C23×#6923—22no—
71C23×#6923—22no—
72C23×#6923—22no—
73C23×#6923—41no—
74C23×#6923—41no—
75C23×#6923—41no—
76C23×#6923—41no—
77C23×#6923C2×C414yes—
78C23×#6923C2×C414yes—
79C23×#6923C2311yescharacteristic
80C23×#6923C2311yescharacteristic
81C23×#6923C2311yescharacteristic
82C23×#6923C2311yescharacteristic
83C23×#6923C2311yescharacteristic
84C23×#6923C2311yescharacteristic
85C23×#6923C2311yescharacteristic
86C23×#6923C2311yescharacteristic
87C2×C4⋊#6923—22no—
88C2×C4⋊#6923—22no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923—41no—
91C2×C4⋊#6923C2×C414yescomplemented
92C2×C4⋊#6923C2×C414yescomplemented
93C2×C22⋊#6923—22no—
94C2×C22⋊#6923—22no—
95C2×C22⋊#6923C2×C414yes—
96C2×C22⋊#6923C2×C414yes—
97C2×C22⋊#6923D414yes—
98C2×C22⋊#6923Q814yes—
99C2×C4×#6923—22no—
100C2×C4×#6923—22no—
101C2×C4×#6923—22no—
102C2×C4×#6923—22no—
103C2×C4×#6923—22no—
104C2×C4×#6923—22no—
105C2×C4×#6923—22no—
106C2×C4×#6923—22no—
107C2×C4×#6923—22no—
108C2×C4×#6923—22no—
109C2×C4×#6923—41no—
110C2×C4×#6923—41no—
111C2×C4×#6923—41no—
112C2×C4×#6923—41no—
113C2×C4×#6923—41no—
114C2×C4×#6923—41no—
115C2×C4×#6923C2×C414yescomplemented
116C2×C4×#6923C2×C414yescomplemented
117(C2×#6923)⋊C4—22no—
118(C2×#6923)⋊C4—22no—
119(C2×#6923)⋊C4—22no—
120(C2×#6923)⋊C4—22no—
121(C2×#6923)⋊C4—22no—
122(C2×#6923)⋊C4—22no—
123(C2×#6923)⋊C4—22no—
124(C2×#6923)⋊C4—22no—
125(C2×#6923)⋊C4—22no—
126(C2×#6923)⋊C4—41no—
127(C2×#6923)⋊C4—41no—
128(C2×#6923)⋊C4C2×C414yescomplemented
129(C2×#6923)⋊C4C2×C414yescomplemented
130(C2×#6923)⋊C4C2×C414yescomplemented
131(C2×#6923)⋊C4C2×C414yescomplemented
132(C2×#6923)⋊C4D414yes—
133C24×D61C2311yescharacteristic
134C23×Dic61C2×C411yescharacteristic
135C22×C4×D61—22no—
136C22×C4×D61—22no—
137C22×C4×D61—22no—
138C22×C4×D61—22no—
139C22×C4×D61—41no—
140C22×C4×D61—41no—
141C22×C4×D61C2×C411yescharacteristic
142C22×C4×D61C2×C411yescharacteristic
143C22×C4×D61C2311yescharacteristic
144C22×C4×D61C2311yescharacteristic
145C22×C4×D61C2311yescharacteristic
146C22×C4×D61C2311yescharacteristic
147C22×C4×D61C2311yescharacteristic
148C22×C4×D61C2311yescharacteristic
149C2×C4⋊Dic61C2×C411yescharacteristic, complemented
150C2×C4⋊Dic61C2×C411yescharacteristic, complemented
151C2×#11758196C2×C411yescharacteristic, complemented
152C2×#11758196C2×C411yescharacteristic, complemented
153C2×#11758196C2×C411yescharacteristic, complemented
154C2×#11758196C2×C411yescharacteristic, complemented
155C4⋊C4×D61—22no—
156C4⋊C4×D61—22no—
157C4⋊C4×D61—41no—
158C4⋊C4×D61—41no—
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×C22⋊Dic61C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic
165C22⋊C4×D61—22no—
166C22⋊C4×D61—22no—
167C22⋊C4×D61C2×C414yes—
168C22⋊C4×D61C2×C414yes—
169#14519684C2×C411yescharacteristic, complemented
170#14519684C2×C411yescharacteristic, complemented
171#14519684C2×C411yescharacteristic, complemented
172#14519684C2×C411yescharacteristic, complemented
173#14519684C2×C411yescharacteristic, complemented
174#14519684C2×C411yescharacteristic, complemented
175C23×C4×C61C2×C411yescharacteristic
176C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
177C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
178C2×C22⋊C4×C61C2×C411yescharacteristic
179C2×C22⋊C4×C61C2×C411yescharacteristic
180#95×C61C2×C411yescharacteristic, complemented
181#95×C61C2×C411yescharacteristic, complemented
182C24×C61C22×C411yescharacteristic
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61C22×C411yescharacteristic
192C23×D61C22×C412yes—
193C23×D61C22×C412yes—
194C23×D61C2×D412yes—
195C23×D61C2×Q812yes—
196C23×D61#4112yes—
197C23×D61#4112yes—
198C23×D61C2411yescharacteristic
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—28no—
216C22×#6923—28no—
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×#6923—21no—
232C22×#6923—21no—
233C22×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—28no—
242C22×#6923—28no—
243C22×#6923—44no—
244C22×#6923—44no—
245C22×#6923—44no—
246C22×#6923—44no—
247C22×#6923—44no—
248C22×#6923—44no—
249C22×#6923—44no—
250C22×#6923—44no—
251C22×#6923—44no—
252C22×#6923—44no—
253C22×#6923C22×C412yes—
254C22×#6923C22×C412yes—
255C22×#6923C22×C412yes—
256C22×#6923C22×C412yes—
257C22×#6923C22×C412yes—
258C22×#6923C22×C412yes—
259C22×#6923C22×C412yes—
260C22×#6923C22×C412yes—
261C22×#6923C2×D412yes—
262C22×#6923C2×D412yes—
263C22×#6923C2×D412yes—
264C22×#6923C2×D412yes—
265C22×#6923C2×Q812yes—
266C22×#6923C2×Q812yes—
267C22×#6923#4112yes—
268C22×#6923#4112yes—
269C22×C4×C61—22no—
270C22×C4×C61—22no—
271C22×C4×C61—41no—
272C22×C4×C61C22×C411yescharacteristic
273C22×C4×C61C22×C411yescharacteristic
274C22×C4×C61C22×C411yescharacteristic
275C22×C4×C61C22×C411yescharacteristic
276C22×C4×C61C22×C411yescharacteristic
277C22×C4×C61C22×C411yescharacteristic
278C22×Dic61—22no—
279C22×Dic61—22no—
280C22×Dic61—41no—
281C22×Dic61C22×C411yescharacteristic
282C22×Dic61C22×C411yescharacteristic
283C22×Dic61C22×C411yescharacteristic
284C22×Dic61C22×C411yescharacteristic
285C22×Dic61C22×C411yescharacteristic
286C22×Dic61C22×C411yescharacteristic
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—21no—
294C2×C4×D61—21no—
295C2×C4×D61—21no—
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—22no—
300C2×C4×D61—22no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—21no—
307C2×C4×D61—21no—
308C2×C4×D61—21no—
309C2×C4×D61—21no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—21no—
313C2×C4×D61—21no—
314C2×C4×D61—21no—
315C2×C4×D61—21no—
316C2×C4×D61—21no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—22no—
320C2×C4×D61—22no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—41no—
326C2×C4×D61—41no—
327C2×C4×D61C22×C412yes—
328C2×C4×D61C22×C412yes—
329C2×C4×D61C22×C412yes—
330C2×C4×D61C22×C412yes—
331C2×C4×D61C2×D412yes—
332C2×C4×D61#4112yes—
333C22⋊#6923—28no—
334C22⋊#6923C4⋊C4116yescomplemented
335C4⋊#6923—28no—
336C4⋊#6923—44no—
337C4×#6923—28no—
338C4×#6923—44no—
339C4×#6923—44no—
340C4×#6923—44no—
341C4×#6923—44no—
342C4×#6923—44no—
343C4⋊C4×C61—22no—
344C4⋊C4×C61—41no—
345C22⋊C4×C61—22no—
346C22⋊C4×C61C4214yescomplemented
347C22⋊Dic61—22no—
348C22⋊Dic61C4214yescomplemented
349#11758198—22no—
350#11758198—22no—
351#11758198C4214yescomplemented
352#11758198C4214yescomplemented
353C4⋊Dic61—22no—
354C4⋊Dic61—41no—
355#11758196—22no—
356#11758196—22no—
357#11758196—41no—
358#11758196—41no—
359C23×C61—21no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—21no—
363C23×C61C2×C4212yes—
364C23×C61C4×D412yes—
365C23×C61C4×Q812yes—
366C23×C61C23×C411yescharacteristic
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61C2×C4212yes—
396C22×D61C2×C4⋊C414yes—
397C22×D61#11714yes—
398C22×D61C4×D414yes—
399C22×D61C4×D412yes—
400C22×D61C4×Q814yes—
401C22×D61C4×Q812yes—
402C22×D61C23×C411yescharacteristic
403C22×D61C23×C411yescharacteristic
404C22×D61C22×D411yescharacteristic
405C22×D61C22×D411yescharacteristic
406C22×D61C22×Q811yescharacteristic
407C22×D61C2×#4111yescharacteristic
408C22×D61C2×#4111yescharacteristic
409C22×D61C2×#4111yescharacteristic
410C22×D61C2×#4111yescharacteristic
411C22×D61C2×#4111yescharacteristic
412C22×D61H(5,𝔽2)11yescharacteristic
413C22×D61H(5,𝔽2)11yescharacteristic
414C22×D61H(5,𝔽2)11yescharacteristic
415C22×D612−1+411yescharacteristic
416C2×#6923—22no—
417C2×#6923—22no—
418C2×#6923—22no—
419C2×#6923—22no—
420C2×#6923—22no—
421C2×#6923—22no—
422C2×#6923—22no—
423C2×#6923—22no—
424C2×#6923—22no—
425C2×#6923—22no—
426C2×#6923—22no—
427C2×#6923—22no—
428C2×#6923—22no—
429C2×#6923—22no—
430C2×#6923—22no—
431C2×#6923—22no—
432C2×#6923—22no—
433C2×#6923—22no—
434C2×#6923—22no—
435C2×#6923—22no—
436C2×#6923—22no—
437C2×#6923—22no—
438C2×#6923—22no—
439C2×#6923—22no—
440C2×#6923—22no—
441C2×#6923—22no—
442C2×#6923—22no—
443C2×#6923—22no—
444C2×#6923—22no—
445C2×#6923—22no—
446C2×#6923—22no—
447C2×#6923—22no—
448C2×#6923—22no—
449C2×#6923—22no—
450C2×#6923—22no—
451C2×#6923—22no—
452C2×#6923—416no—
453C2×#6923—416no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461C2×#6923—41no—
462C2×#6923—41no—
463C2×#6923—41no—
464C2×#6923—41no—
465C2×#6923—41no—
466C2×#6923—41no—
467C2×#6923—41no—
468C2×#6923—41no—
469C2×#6923—41no—
470C2×#6923C2×C4⋊C414yes—
471C2×#6923C2×C4⋊C414yes—
472C2×#6923C4×D414yes—
473C2×#6923C4×D414yes—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—21no—
481C2×C4×C61—21no—
482C2×C4×C61—21no—
483C2×C4×C61—21no—
484C2×C4×C61—21no—
485C2×C4×C61—21no—
486C2×C4×C61—21no—
487C2×C4×C61—21no—
488C2×C4×C61—21no—
489C2×C4×C61—44no—
490C2×C4×C61C2×C4212yes—
491C2×C4×C61C2×C4212yes—
492C2×C4×C61C4×D412yes—
493C2×Dic61—21no—
494C2×Dic61—21no—
495C2×Dic61—21no—
496C2×Dic61—21no—
497C2×Dic61—21no—
498C2×Dic61—21no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—21no—
506C2×Dic61—21no—
507C2×Dic61—21no—
508C2×Dic61—44no—
509C2×Dic61C2×C4212yes—
510C2×Dic61C2×C4212yes—
511C2×Dic61C4×D412yes—
512C4×D61—22no—
513C4×D61—22no—
514C4×D61—22no—
515C4×D61—22no—
516C4×D61—22no—
517C4×D61—22no—
518C4×D61—22no—
519C4×D61—22no—
520C4×D61—22no—
521C4×D61—22no—
522C4×D61—22no—
523C4×D61—22no—
524C4×D61—44no—
525C4×D61—44no—
526C4×D61—41no—
527C4×D61—41no—
528C4×D61—41no—
529C4×D61—41no—
530C4×D61—41no—
531C4×D61—41no—
532C4×D61—41no—
533C4×D61—41no—
534C4×D61—41no—
535C4×D61—41no—
536C4×D61—41no—
537C4×D61—41no—
538#13814—611nomaximal, Sylow
539C22×C61—22no—
540C22×C61—22no—
541C22×C61—22no—
542C22×C61—22no—
543C22×C61—22no—
544C22×C61—22no—
545C22×C61C4×C4⋊C414yescomplemented
546C22×C61C22×C4211yescharacteristic
547C22×C61C2×C4×D411yescharacteristic
548C22×C61C2×C4×D411yescharacteristic
549C22×C61C2×C4×Q811yescharacteristic
550C22×C61C4×#4111yescharacteristic
551C22×C61#51811yescharacteristic
552C22×C61#52011yescharacteristic
553C2×D61—22no—
554C2×D61—22no—
555C2×D61—22no—
556C2×D61—22no—
557C2×D61—22no—
558C2×D61—22no—
559C2×D61—24no—
560C2×D61—24no—
561C2×D61—24no—
562C2×D61—24no—
563C2×D61—24no—
564C2×D61—24no—
565C2×D61—24no—
566C2×D61—24no—
567C2×D61C4×C4⋊C414yescomplemented
568C2×D61C22×C4⋊C411yescharacteristic
569C2×D61C2×#11711yescharacteristic
570C2×D61C2×C4×D411yescharacteristic
571C2×D61C2×C4×D411yescharacteristic
572C2×D61C2×C4×D411yescharacteristic
573C2×D61C2×C4×Q811yescharacteristic
574C2×D61C4×#4111yescharacteristic
575C2×D61C4×#4111yescharacteristic
576C2×D61#51811yescharacteristic
577C2×D61#51811yescharacteristic
578C2×D61#52011yescharacteristic
579C2×D61#52011yescharacteristic
580C2×D61D4211yescharacteristic
581C2×D61#54611yescharacteristic
582C2×D61#54611yescharacteristic
583C2×D61#54611yescharacteristic
584C2×D61#54611yescharacteristic
585C2×D61#54711yescharacteristic
586C2×D61D4×Q811yescharacteristic
587C2×D61#55111yescharacteristic
588C2×D61#55111yescharacteristic
589C2×D61#55111yescharacteristic
590C2×D61#55111yescharacteristic
591C2×D61#55211yescharacteristic
592C2×D61#55211yescharacteristic
593C2×D61#55411yescharacteristic
594C2×D61#55411yescharacteristic
595C2×D61#55411yescharacteristic
596#6923—24no—
597#6923—24no—
598#6923—24no—
599#6923—24no—
600#6923—42no—
601#6923—42no—
602#6923—42no—
603#6923—42no—
604C4×C61—22no—
605C4×C61—22no—
606C4×C61—22no—
607C4×C61—41no—
608C4×C61—41no—
609C4×C61—41no—
610Dic61—22no—
611Dic61—22no—
612Dic61—22no—
613Dic61—41no—
614Dic61—41no—
615Dic61—41no—
616C2×#385—611no—
617C2×#385—611no—
618C2×C4×C4⋊C4—611no—
619C2×C4×C22⋊C4—611no—
620C2×C4×C22⋊C4—611no—
621C2×C4×C22⋊C4—611no—
622C22×#95—611no—
623#1436—611no—
624#1436—611no—
625#1436—611no—
626#1436—611no—
627C4⋊#95—611no—
628#1434—611no—
629C22⋊#95—611no—
630C4×#95—611no—
631C2×C61—24no—
632C2×C61C2×C4×C4⋊C411yescharacteristic
633C2×C61C42×D411yescharacteristic
634C2×C61#227511yescharacteristic
635C2×C61#235811yescharacteristic
636C2×C61#235911yescharacteristic
637C2×C61#236011yescharacteristic
638C2×C61#236811yescharacteristic
639D61—24no—
640D61#234211yescharacteristic
641D61#234311yescharacteristic
642D61D4×C4⋊C411yescharacteristic
643D61#234911yescharacteristic
644D61#235811yescharacteristic
645D61#235911yescharacteristic
646D61#236011yescharacteristic
647D61#236811yescharacteristic
648C24×C4—611no—
649C24×C4—611no—
650C24×C4—611no—
651C22×C4⋊C4—611no—
652C22×C4⋊C4—611no—
653C22×C4⋊C4—611no—
654C22×C4⋊C4—611no—
655C22×C22⋊C4—611no—
656C22×C22⋊C4—611no—
657C22×C22⋊C4—611no—
658C22×C22⋊C4—611no—
659C22×C42—611no—
660C22×C42—611no—
661C22×C42—611no—
662C22×C42—611no—
663C22×C42—611no—
664C22×C42—611no—
665#385—618no—
666#385—611no—
667#385—611no—
668#385—611no—
669#385—611no—
670#385—611no—
671#385—611no—
672#385—611no—
673#385#692311yescharacteristic, complemented
674C4×C4⋊C4—1224no—
675C4×C22⋊C4—618no—
676C4×C22⋊C4—1224no—
677C4×C22⋊C4—1224no—
678C2×#95—611no—
679C2×#95—611no—
680C2×#95—611no—
681C2×#95—611no—
682C2×#95—611no—
683C2×#95—611no—
684C2×#95—611no—
685C2×#95—611no—
686C2×#95—611no—
687C2×#95—611no—
688C2×#95—611no—
689C2×#95—611no—
690C2×#95—611no—
691C2×#95—611no—
692C2×#95—611no—
693C2×#95—611no—
694C2×#95—611no—
695C2×#95—611no—
696C2×#95—1224no—
697C61#1381411yescharacteristic, complemented, Sylow
698C25—611no—
699C23×C4—611no—
700C23×C4—611no—
701C23×C4—611no—
702C23×C4—611no—
703C23×C4—611no—
704C23×C4—611no—
705C23×C4—611no—
706C23×C4—611no—
707C23×C4—611no—
708C23×C4—611no—
709C23×C4—611no—
710C23×C4—614no—
711C23×C4—614no—
712C23×C4—611no—
713C23×C4—611no—
714C23×C4—611no—
715C23×C4—611no—
716C23×C4—611no—
717C23×C4—611no—
718C23×C4—1222no—
719C23×C4—1222no—
720C23×C4—1222no—
721C23×C4—1222no—
722C23×C4—1222no—
723C23×C4—1222no—
724C23×C4—1222no—
725C23×C4—1222no—
726C23×C4—1222no—
727C23×C4—1222no—
728C23×C4—1222no—
729C23×C4—1222no—
730C23×C4—2441no—
731C23×C4—2441no—
732C23×C4—2441no—
733C23×C4—2441no—
734C23×C4—2441no—
735C23×C4—2441no—
736C23×C4C2×#692311yescharacteristic
737C2×C4⋊C4—614no—
738C2×C4⋊C4—611no—
739C2×C4⋊C4—611no—
740C2×C4⋊C4—611no—
741C2×C4⋊C4—614no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—1222no—
746C2×C4⋊C4—1222no—
747C2×C4⋊C4—1222no—
748C2×C4⋊C4—1222no—
749C2×C4⋊C4—2441no—
750C2×C4⋊C4—2441no—
751C2×C4⋊C4—2441no—
752C2×C4⋊C4—2441no—
753C2×C4⋊C4C2×#692311yescharacteristic, complemented
754C2×C4⋊C4C2×#692311yescharacteristic, complemented
755C2×C22⋊C4—614no—
756C2×C22⋊C4—614no—
757C2×C22⋊C4—614no—
758C2×C22⋊C4—611no—
759C2×C22⋊C4—611no—
760C2×C22⋊C4—611no—
761C2×C22⋊C4—614no—
762C2×C22⋊C4—614no—
763C2×C22⋊C4—614no—
764C2×C22⋊C4—611no—
765C2×C22⋊C4—611no—
766C2×C22⋊C4—611no—
767C2×C22⋊C4—1222no—
768C2×C22⋊C4—1222no—
769C2×C22⋊C4—1222no—
770C2×C22⋊C4—1222no—
771C2×C22⋊C4C2×#692311yescharacteristic
772C2×C22⋊C4C2×#692311yescharacteristic
773C2×C42—614no—
774C2×C42—614no—
775C2×C42—1222no—
776C2×C42—1222no—
777C2×C42—1222no—
778C2×C42—1222no—
779C2×C42—1222no—
780C2×C42—1222no—
781C2×C42—1222no—
782C2×C42—1222no—
783C2×C42—1222no—
784C2×C42—1222no—
785C2×C42—2441no—
786C2×C42—2441no—
787C2×C42—2441no—
788C2×C42—2441no—
789C2×C42—2441no—
790C2×C42—2441no—
791#95—614no—
792#95—614no—
793#95—614no—
794#95—614no—
795#95—614no—
796#95—611no—
797#95—611no—
798#95—611no—
799#95—611no—
800#95—611no—
801#95—611no—
802#95—1222no—
803#95—1222no—
804#95—1222no—
805#95—1222no—
806#95—1222no—
807#95—1222no—
808#95—1222no—
809#95—1222no—
810#95—1222no—
811#95—2441no—
812#95—2441no—
813#95C2×#692311yescharacteristic, complemented
814#95C2×#692311yescharacteristic, complemented
815C24—611no—
816C24—612no—
817C24—612no—
818C24—612no—
819C24—612no—
820C24—612no—
821C24—612no—
822C24—611no—
823C24—1221no—
824C24—1221no—
825C24—1221no—
826C24—1221no—
827C24—1221no—
828C24—1221no—
829C24—1221no—
830C24—1221no—
831C24C22×#692311yescharacteristic
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—41no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—612no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—612no—
842C22×C4—612no—
843C22×C4—612no—
844C22×C4—612no—
845C22×C4—612no—
846C22×C4—612no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—612no—
858C22×C4—612no—
859C22×C4—612no—
860C22×C4—611no—
861C22×C4—611no—
862C22×C4—611no—
863C22×C4—1222no—
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—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1222no—
892C22×C4—1222no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1222no—
897C22×C4—1228no—
898C22×C4—1228no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—1221no—
915C22×C4—1221no—
916C22×C4—1221no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1221no—
920C22×C4—1221no—
921C22×C4—1221no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—1221no—
928C22×C4—1221no—
929C22×C4—1221no—
930C22×C4—1221no—
931C22×C4—1221no—
932C22×C4—1221no—
933C22×C4—1228no—
934C22×C4—1228no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1222no—
942C22×C4—1222no—
943C22×C4—2441no—
944C22×C4—2441no—
945C22×C4—2444no—
946C22×C4—2444no—
947C22×C4—2444no—
948C22×C4—2444no—
949C22×C4—2441no—
950C22×C4—2444no—
951C22×C4—2444no—
952C22×C4—2444no—
953C22×C4—2444no—
954C22×C4—2444no—
955C22×C4—2444no—
956C22×C4—2444no—
957C22×C4—2444no—
958C22×C4—2444no—
959C22×C4—2444no—
960C22×C4C22×#692311yescharacteristic
961C22×C4C22×#692311yescharacteristic
962C22×C4C22×#692311yescharacteristic
963C22×C4C22×#692311yescharacteristic
964C22×C4C22×#692311yescharacteristic
965C22×C4C22×#692311yescharacteristic
966C4⋊C4—22no—
967C4⋊C4—41no—
968C4⋊C4—1222no—
969C4⋊C4—1222no—
970C4⋊C4—1228no—
971C4⋊C4—1222no—
972C4⋊C4—2441no—
973C4⋊C4—2441no—
974C4⋊C4—2441no—
975C4⋊C4—2444no—
976C22⋊C4—22no—
977C22⋊C4—6116no—
978C22⋊C4—614no—
979C22⋊C4—614no—
980C22⋊C4—614no—
981C22⋊C4—1222no—
982C22⋊C4—1222no—
983C22⋊C4—1228no—
984C22⋊C4—1222no—
985C22⋊C4C4×#692314yescomplemented
986C42—1228no—
987C42—2444no—
988C42—2444no—
989C42—2444no—
990C42—2444no—
991C42—2444no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—611no—
997C23—611no—
998C23—611no—
999C23—611no—
1000C23—611no—
1001C23—611no—
1002C23—611no—
1003C23—611no—
1004C23—611no—
1005C23—611no—
1006C23—611no—
1007C23—611no—
1008C23—611no—
1009C23—611no—
1010C23—612no—
1011C23—612no—
1012C23—612no—
1013C23—614no—
1014C23—614no—
1015C23—614no—
1016C23—614no—
1017C23—1222no—
1018C23—1222no—
1019C23—1222no—
1020C23—1222no—
1021C23—1222no—
1022C23—1222no—
1023C23—1222no—
1024C23—1222no—
1025C23—1222no—
1026C23—1222no—
1027C23—1222no—
1028C23—1222no—
1029C23—1222no—
1030C23—1222no—
1031C23—1222no—
1032C23—1222no—
1033C23—1222no—
1034C23—1222no—
1035C23—1222no—
1036C23—1222no—
1037C23—1222no—
1038C23—1222no—
1039C23—1222no—
1040C23—1222no—
1041C23—1221no—
1042C23—1221no—
1043C23—1221no—
1044C23—1221no—
1045C23C2×C4×#692312yes—
1046C23D4×#692312yes—
1047C23Q8×#692312yes—
1048C23C23×#692311yescharacteristic
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—44no—
1065C2×C4—614no—
1066C2×C4—614no—
1067C2×C4—614no—
1068C2×C4—614no—
1069C2×C4—612no—
1070C2×C4—612no—
1071C2×C4—612no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1221no—
1109C2×C4—1221no—
1110C2×C4—1221no—
1111C2×C4—1221no—
1112C2×C4—1221no—
1113C2×C4—1221no—
1114C2×C4—1222no—
1115C2×C4—1222no—
1116C2×C4—1222no—
1117C2×C4—1222no—
1118C2×C4—1222no—
1119C2×C4—1222no—
1120C2×C4—1222no—
1121C2×C4—1222no—
1122C2×C4—1222no—
1123C2×C4—1222no—
1124C2×C4—1222no—
1125C2×C4—1222no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—2444no—
1136C2×C4—2444no—
1137C2×C4—2441no—
1138C2×C4—2441no—
1139C2×C4—2441no—
1140C2×C4—2441no—
1141C2×C4—2441no—
1142C2×C4—2441no—
1143C2×C4—2441no—
1144C2×C4—2441no—
1145C2×C4—2441no—
1146C2×C4—2441no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2444no—
1150C2×C4—24416no—
1151C2×C4—24416no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2441no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4—2441no—
1167C2×C4—2441no—
1168C2×C4C2×C4×#692312yes—
1169C2×C4C2×C4×#692312yes—
1170C2×C4D4×#692312yes—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—611no—
1178C22—611no—
1179C22—611no—
1180C22—611no—
1181C22—611no—
1182C22—611no—
1183C22—611no—
1184C22—611no—
1185C22—611no—
1186C22—611no—
1187C22—611no—
1188C22—611no—
1189C22—611no—
1190C22—611no—
1191C22—611no—
1192C22—611no—
1193C22—611no—
1194C22—611no—
1195C22—611no—
1196C22—611no—
1197C22—611no—
1198C22—611no—
1199C22—611no—
1200C22—611no—
1201C22—611no—
1202C22—611no—
1203C22—611no—
1204C22—611no—
1205C22—614no—
1206C22—1224no—
1207C22—1224no—
1208C22—1224no—
1209C22—1224no—
1210C22—1224no—
1211C22—1224no—
1212C22—1224no—
1213C22—1224no—
1214C22—1222no—
1215C22—1222no—
1216C22—1222no—
1217C22—1222no—
1218C22—1222no—
1219C22—1222no—
1220C22C4⋊C4×#692314yescomplemented
1221C22C22×C4×#692311yescharacteristic
1222C22C2×D4×#692311yescharacteristic
1223C22C2×D4×#692311yescharacteristic
1224C22C2×Q8×#692311yescharacteristic
1225C22#41×#692311yescharacteristic
1226C22#1684082911yescharacteristic
1227C22#1684083111yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—1224no—
1235C4—1224no—
1236C4—1224no—
1237C4—1224no—
1238C4—1222no—
1239C4—1222no—
1240C4—1222no—
1241C4—2442no—
1242C4—2442no—
1243C4—2442no—
1244C4—2442no—
1245C4—2441no—
1246C4—2441no—
1247C4—2441no—
1248C2—24no—
1249C2—611no—
1250C2—611no—
1251C2—611no—
1252C2—611no—
1253C2—611no—
1254C2—611no—
1255C2—611no—
1256C2—611no—
1257C2—1224no—
1258C2C2×C4⋊C4×#692311yescharacteristic
1259C2C4×D4×#692311yescharacteristic
1260C2#2146225811yescharacteristic
1261C2#2146234111yescharacteristic
1262C2#2146234211yescharacteristic
1263C2#2146234311yescharacteristic
1264C2#2146235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#385C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#385#6923
hypocenterC61#13814
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#6923C2semidirect
7. #21460999C2semidirect
8. #21460999C2semidirect
9. #21460998C2semidirect
10. #21460998C2semidirect
11. #21460996C2semidirect
12. #21460994C2semidirect
14. #95×#6923C2semidirect
28. #16840709C4semidirect
31. C22⋊C4×#6923C4semidirect
55. #16839637C4semidirect
56. #16839636C4semidirect
57. #16839636C4semidirect
58. #16839635C4semidirect
59. #16839634C4semidirect
60. #16839633C4semidirect
61. #16839633C4semidirect
64. C61×#385C4semidirect
91. C2×C4⋊#6923C2×C4semidirect
92. C2×C4⋊#6923C2×C4semidirect
115. C2×C4×#6923C2×C4semidirect
116. C2×C4×#6923C2×C4semidirect
128. (C2×#6923)⋊C4C2×C4semidirect
129. (C2×#6923)⋊C4C2×C4semidirect
130. (C2×#6923)⋊C4C2×C4semidirect
131. (C2×#6923)⋊C4C2×C4semidirect
149. C2×C4⋊Dic61C2×C4semidirect
150. C2×C4⋊Dic61C2×C4semidirect
151. C2×#11758196C2×C4semidirect
152. C2×#11758196C2×C4semidirect
153. C2×#11758196C2×C4semidirect
154. C2×#11758196C2×C4semidirect
169. #14519684C2×C4semidirect
170. #14519684C2×C4semidirect
171. #14519684C2×C4semidirect
172. #14519684C2×C4semidirect
173. #14519684C2×C4semidirect
174. #14519684C2×C4semidirect
176. C2×C4⋊C4×C61C2×C4semidirect
177. C2×C4⋊C4×C61C2×C4semidirect
180. #95×C61C2×C4semidirect
181. #95×C61C2×C4semidirect
334. C22⋊#6923C4⋊C4semidirect
346. C22⋊C4×C61C42semidirect
348. C22⋊Dic61C42semidirect
351. #11758198C42semidirect
352. #11758198C42semidirect
545. C22×C61C4×C4⋊C4semidirect
567. C2×D61C4×C4⋊C4semidirect
673. #385#6923semidirect
697. C61#13814semidirect
753. C2×C4⋊C4C2×#6923semidirect
754. C2×C4⋊C4C2×#6923semidirect
813. #95C2×#6923semidirect
814. #95C2×#6923semidirect
985. C22⋊C4C4×#6923semidirect
1220. C22C4⋊C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407092
C2×C4⋊C4×#69232
C2×C22⋊C4×#69232
C2×C4×C22⋊#69232
C22×(C2×#6923)⋊C42
#214609992
#214609982
#214609962
#214609942
#214609922
#95×#69232
#385×D612
#1381461