Finite Group Databasebeta

← C61×#22371 #29525804

Subgroups — C61×#22371 #29525804

Order 15616.

774 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#123×C61C211yesmaximal, characteristic
2C61×#1955C211yesmaximal, characteristic
3C61×#1940C211yesmaximal, characteristic, complemented
4C61×#1924C211yesmaximal, characteristic, complemented
5C61×#1924C211yesmaximal, characteristic, complemented
6C61×#1923C211yesmaximal, characteristic, complemented
7C61×#1923C211yesmaximal, characteristic, complemented
8C61×#1917C211yesmaximal, characteristic, complemented
9C61×#1917C211yesmaximal, characteristic, complemented
10C61×#1869C211yesmaximal, characteristic
11C61×#1850C211yesmaximal, characteristic, complemented
12C61×#1797C211yesmaximal, characteristic, complemented
13C61×#1770C211yesmaximal, characteristic, complemented
14C61×#1752C211yesmaximal, characteristic, complemented
15C61×#1749C211yesmaximal, characteristic, complemented
16C23×C8×C61C2211yescharacteristic
17C2×#123×C61C411yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C22×C42×C61C2211yescharacteristic
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×C22⋊C8×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×#97×C61C2211yescharacteristic
33C2×#97×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic
35C2×#97×C61C2211yescharacteristic
36C2×C4×C8×C61C2211yescharacteristic
37C61×#388C411yescharacteristic
38C61×#388C411yescharacteristic
39C61×#387C411yescharacteristic
40C61×#387C411yescharacteristic
41C61×#386C411yescharacteristic
42C61×#385C411yescharacteristic
43C61×#381C411yescharacteristic
44C4×C4⋊C4×C61C2211yescharacteristic
45C4×C4⋊C4×C61C2211yescharacteristic
46C4×C22⋊C4×C61C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C61×#336C2211yescharacteristic
50C61×#336C2211yescharacteristic
51C61×#336C2211yescharacteristic
52C61×#336C2211yescharacteristic
53C61×#336C2211yescharacteristic
54C61×#336C2211yescharacteristic
55C61×#336C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D4×C61C2×C411yescharacteristic
60C23×C4×C61C2×C411yescharacteristic
61C23×C4×C61C2×C411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C22×C8×C61—22no—
65C22×C8×C61—41no—
66C22×C8×C61—41no—
67C22×C8×C61C2311yescharacteristic
68C22×C8×C61C2311yescharacteristic
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75#123×C61—24no—
76C4×D4×C61—41no—
77C4×D4×C61—41no—
78C2×C4⋊C4×C61C2×C411yescharacteristic
79C2×C4⋊C4×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81C2×C4⋊C4×C61C2×C411yescharacteristic
82C2×C4⋊C4×C61C2×C411yescharacteristic
83C2×C22⋊C4×C61C2×C411yescharacteristic
84C2×C22⋊C4×C61C2×C411yescharacteristic
85C2×C22⋊C4×C61C2×C411yescharacteristic
86C2×C22⋊C4×C61C2×C411yescharacteristic
87C2×C22⋊C4×C61C2×C411yescharacteristic
88C2×C22⋊C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C42×C61—41no—
92C2×C42×C61—41no—
93C2×C42×C61C2×C411yescharacteristic
94C2×C42×C61C2×C411yescharacteristic
95C2×C42×C61C2311yescharacteristic
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2311yescharacteristic
98C2×C42×C61C2311yescharacteristic
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61—22no—
101C4⋊C8×C61—41no—
102C4⋊C8×C61—41no—
103C4⋊C8×C61—41no—
104C4⋊C8×C61—41no—
105C22⋊C8×C61—22no—
106C22⋊C8×C61—22no—
107C22⋊C8×C61—22no—
108C22⋊C8×C61—41no—
109C22⋊C8×C61—41no—
110C22⋊C8×C61—41no—
111C22⋊C8×C61—41no—
112#97×C61—41no—
113#97×C61—41no—
114#97×C61—41no—
115#97×C61—41no—
116C4×C8×C61—22no—
117#95×C61C2×C411yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120#95×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C24×C61C22×C411yescharacteristic
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—41no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—41no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—44no—
186C2×C8×C61#4112yes—
187C2×C8×C61#4112yes—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61M1614yes—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—41no—
212C42×C61—41no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61C2×M1612yes—
226C23×C61#13112yes—
227C23×C61C23×C411yescharacteristic
228D4×C61—44no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—44no—
264C2×C4×C61—44no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61C2×M1612yes—
274C2×C4×C61C2×M1612yes—
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61H(5,𝔽2)11yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C8×C61—22no—
282C8×C61—22no—
283C8×C61—41no—
284C8×C61—41no—
285C8×C61—41no—
286C8×C61—41no—
287C8×C61—41no—
288C8×C61—41no—
289#22371C6111yesmaximal, characteristic, direct product factor, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61C4×#4111yescharacteristic
305C22×C61#51811yescharacteristic
306C22×C61#52011yescharacteristic
307C22×C61C22×M1611yescharacteristic
308C22×C61C2×#13111yescharacteristic
309C22×C61#56811yescharacteristic
310C22×C61#56811yescharacteristic
311C4×C61—22no—
312C4×C61—22no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61#53811yescharacteristic
324C4×C61#53911yescharacteristic
325C4×C61#54011yescharacteristic
326C4×C61#54211yescharacteristic
327C4×#123C2×C6111yescharacteristic
328#1955C2×C6111yescharacteristic
329#1940C2×C6111yescharacteristic, complemented
330#1924C2×C6111yescharacteristic, complemented
331#1924C2×C6111yescharacteristic, complemented
332#1923C2×C6111yescharacteristic, complemented
333#1923C2×C6111yescharacteristic, complemented
334#1917C2×C6111yescharacteristic, complemented
335#1917C2×C6111yescharacteristic, complemented
336#1869C2×C6111yescharacteristic
337#1850C2×C6111yescharacteristic, complemented
338#1797C2×C6111yescharacteristic, complemented
339#1770C2×C6111yescharacteristic, complemented
340#1752C2×C6111yescharacteristic, complemented
341#1749C2×C6111yescharacteristic, complemented
342C2×C61—42no—
343C2×C61—42no—
344C2×C61#233511yescharacteristic
345C2×C61#296811yescharacteristic
346C2×C61#297011yescharacteristic
347C2×C61#297411yescharacteristic
348C2×C61#297811yescharacteristic
349C2×C61#298911yescharacteristic
350C2×C61#299211yescharacteristic
351C23×C8C22×C6111yescharacteristic
352C2×#123C4×C6111yescharacteristic
353C2×C4×D4C22×C6111yescharacteristic
354C22×C42C22×C6111yescharacteristic
355C2×C4⋊C8C22×C6111yescharacteristic
356C2×C4⋊C8C22×C6111yescharacteristic
357C2×C4⋊C8C22×C6111yescharacteristic
358C2×C4⋊C8C22×C6111yescharacteristic
359C2×C4⋊C8C22×C6111yescharacteristic
360C2×C22⋊C8C22×C6111yescharacteristic
361C2×C22⋊C8C22×C6111yescharacteristic
362C2×C22⋊C8C22×C6111yescharacteristic
363C2×C22⋊C8C22×C6111yescharacteristic
364C2×C22⋊C8C22×C6111yescharacteristic
365C2×C22⋊C8C22×C6111yescharacteristic
366C2×C22⋊C8C22×C6111yescharacteristic
367C2×#97C22×C6111yescharacteristic
368C2×#97C22×C6111yescharacteristic
369C2×#97C22×C6111yescharacteristic
370C2×#97C22×C6111yescharacteristic
371C2×C4×C8C22×C6111yescharacteristic
372#388C4×C6111yescharacteristic
373#388C4×C6111yescharacteristic
374#387C4×C6111yescharacteristic
375#387C4×C6111yescharacteristic
376#386C4×C6111yescharacteristic
377#385C4×C6111yescharacteristic
378#381C4×C6111yescharacteristic
379C4×C4⋊C4C22×C6111yescharacteristic
380C4×C4⋊C4C22×C6111yescharacteristic
381C4×C22⋊C4C22×C6111yescharacteristic
382C4×C22⋊C4C22×C6111yescharacteristic
383C4×C22⋊C4C22×C6111yescharacteristic
384#336C22×C6111yescharacteristic
385#336C22×C6111yescharacteristic
386#336C22×C6111yescharacteristic
387#336C22×C6111yescharacteristic
388#336C22×C6111yescharacteristic
389#336C22×C6111yescharacteristic
390#336C22×C6111yescharacteristic
391#336C22×C6111yescharacteristic
392#336C22×C6111yescharacteristic
393#336C22×C6111yescharacteristic
394C61#2237111yescharacteristic, direct product factor, Sylow
395C22×D4C2×C4×C6111yescharacteristic
396C23×C4C2×C4×C6111yescharacteristic
397C23×C4C2×C4×C6111yescharacteristic
398C23×C4C23×C6111yescharacteristic
399C23×C4C23×C6111yescharacteristic
400C22×C8—22no—
401C22×C8—41no—
402C22×C8—41no—
403C22×C8C23×C6111yescharacteristic
404C22×C8C23×C6111yescharacteristic
405C22×C8C23×C6111yescharacteristic
406C22×C8C23×C6111yescharacteristic
407C22×C8C23×C6111yescharacteristic
408C22×C8C23×C6111yescharacteristic
409C22×C8C23×C6111yescharacteristic
410C22×C8C23×C6111yescharacteristic
411#123—24no—
412C4×D4—41no—
413C4×D4—41no—
414C2×C4⋊C4C2×C4×C6111yescharacteristic
415C2×C4⋊C4C2×C4×C6111yescharacteristic
416C2×C4⋊C4C2×C4×C6111yescharacteristic
417C2×C4⋊C4C2×C4×C6111yescharacteristic
418C2×C4⋊C4C2×C4×C6111yescharacteristic
419C2×C22⋊C4C2×C4×C6111yescharacteristic
420C2×C22⋊C4C2×C4×C6111yescharacteristic
421C2×C22⋊C4C2×C4×C6111yescharacteristic
422C2×C22⋊C4C2×C4×C6111yescharacteristic
423C2×C22⋊C4C2×C4×C6111yescharacteristic
424C2×C22⋊C4C2×C4×C6111yescharacteristic
425C2×C22⋊C4C2×C4×C6111yescharacteristic
426C2×C22⋊C4C2×C4×C6111yescharacteristic
427C2×C42—41no—
428C2×C42—41no—
429C2×C42C2×C4×C6111yescharacteristic
430C2×C42C2×C4×C6111yescharacteristic
431C2×C42C23×C6111yescharacteristic
432C2×C42C23×C6111yescharacteristic
433C2×C42C23×C6111yescharacteristic
434C2×C42C23×C6111yescharacteristic
435C2×C42C23×C6111yescharacteristic
436C4⋊C8—22no—
437C4⋊C8—41no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440C4⋊C8—41no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443C22⋊C8—22no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447C22⋊C8—41no—
448#97—41no—
449#97—41no—
450#97—41no—
451#97—41no—
452C4×C8—22no—
453#95C2×C4×C6111yescharacteristic
454#95C2×C4×C6111yescharacteristic
455#95C2×C4×C6111yescharacteristic
456#95C2×C4×C6111yescharacteristic
457#95C2×C4×C6111yescharacteristic
458#95C2×C4×C6111yescharacteristic
459#95C2×C4×C6111yescharacteristic
460#95C2×C4×C6111yescharacteristic
461#95C2×C4×C6111yescharacteristic
462#95C2×C4×C6111yescharacteristic
463C24C22×C4×C6111yescharacteristic
464C24C22×C4×C6111yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—41no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4C22×C4×C6111yescharacteristic
487C22×C4C22×C4×C6111yescharacteristic
488C22×C4C22×C4×C6111yescharacteristic
489C22×C4C22×C4×C6111yescharacteristic
490C22×C4C22×C4×C6111yescharacteristic
491C22×C4C22×C4×C6111yescharacteristic
492C22×C4C22×C4×C6111yescharacteristic
493C22×C4C22×C4×C6111yescharacteristic
494C22×C4C22×C4×C6111yescharacteristic
495C22×C4C22×C4×C6111yescharacteristic
496C22×C4C22×C4×C6111yescharacteristic
497C22×C4C22×C4×C6111yescharacteristic
498C22×C4C24×C6111yescharacteristic
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—44no—
522C2×C8#41×C6112yes—
523C2×C8#41×C6112yes—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4M16×C6114yes—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—41no—
548C42—41no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23C2×M16×C6112yes—
562C23#131×C6112yes—
563C23C23×C4×C6111yescharacteristic
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4C2×M16×C6112yes—
610C2×C4C2×M16×C6112yes—
611C2×C4C2×#41×C6111yescharacteristic
612C2×C4C2×#41×C6111yescharacteristic
613C2×C4H(5,𝔽2)×C6111yescharacteristic
614C2×C4H(5,𝔽2)×C6111yescharacteristic
615C2×C4H(5,𝔽2)×C6111yescharacteristic
616C2×C42−1+4×C6111yescharacteristic
617C8—22no—
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C4×#41×C6111yescharacteristic
640C22C61×#51811yescharacteristic
641C22C61×#52011yescharacteristic
642C22C22×M16×C6111yescharacteristic
643C22C2×#131×C6111yescharacteristic
644C22C61×#56811yescharacteristic
645C22C61×#56811yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4C61×#53811yescharacteristic
659C4C61×#53911yescharacteristic
660C4C61×#54011yescharacteristic
661C4C61×#54211yescharacteristic
662C2—42no—
663C2—42no—
664C2C61×#233511yescharacteristic
665C2C61×#296811yescharacteristic
666C2C61×#297011yescharacteristic
667C2C61×#297411yescharacteristic
668C2C61×#297811yescharacteristic
669C2C61×#298911yescharacteristic
670C2C61×#299211yescharacteristic
subgroupG/H
centerC22×C4×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC23×C61C23×C4
prime radicalC22×D4×C61C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1940C2semidirect
4. C61×#1924C2semidirect
5. C61×#1924C2semidirect
6. C61×#1923C2semidirect
7. C61×#1923C2semidirect
8. C61×#1917C2semidirect
9. C61×#1917C2semidirect
11. C61×#1850C2semidirect
12. C61×#1797C2semidirect
13. C61×#1770C2semidirect
14. C61×#1752C2semidirect
15. C61×#1749C2semidirect
289. #22371C61direct (N × H)
329. #1940C2×C61semidirect
330. #1924C2×C61semidirect
331. #1924C2×C61semidirect
332. #1923C2×C61semidirect
333. #1923C2×C61semidirect
334. #1917C2×C61semidirect
335. #1917C2×C61semidirect
337. #1850C2×C61semidirect
338. #1797C2×C61semidirect
339. #1770C2×C61semidirect
340. #1752C2×C61semidirect
341. #1749C2×C61semidirect
394. C61#22371direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#123×C612
C61×#19552
C61×#19402
C61×#19242
C61×#19232
C61×#19172
C61×#18692
C61×#18502
C61×#17972
C61×#17702
C61×#17522
C61×#17492
#2237161