Finite Group Databasebeta

← C61×#17597 #29521030

Subgroups — C61×#17597 #29521030

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3519C211yesmaximal, characteristic
2C61×#2974C211yesmaximal, characteristic, complemented
3C61×#2318C211yesmaximal, characteristic, complemented
4C61×#1521C211yesmaximal, characteristic, complemented
5C61×#1519C211yesmaximal, characteristic, complemented
6C61×#1517C211yesmaximal, characteristic, complemented
7C61×#1516C211yesmaximal, characteristic, complemented
8C61×#1514C211yesmaximal, characteristic, complemented
9C61×#1513C211yesmaximal, characteristic, complemented
10C61×#1512C211yesmaximal, characteristic, complemented
11C61×#1510C211yesmaximal, characteristic, complemented
12C61×#1507C211yesmaximal, characteristic, complemented
13C61×#1504C211yesmaximal, characteristic, complemented
14C61×#1501C211yesmaximal, characteristic, complemented
15C2×C61×#327C211yesmaximal, characteristic, complemented
16C61×#555C411yescharacteristic, complemented
17C61×#554C411yescharacteristic, complemented
18C61×#553—21no—
19C61×#553C411yescharacteristic, complemented
20C61×#553C411yescharacteristic, complemented
21C61×#550C411yescharacteristic, complemented
22C61×#546—21no—
23C61×#546—21no—
24C61×#546C411yescharacteristic, complemented
25C61×#546C411yescharacteristic, complemented
26D42×C61—21no—
27D42×C61C411yescharacteristic, complemented
28C61×#540—21no—
29C61×#538—21no—
30C61×#538—21no—
31C61×#532C2211yescharacteristic
32C61×#529C2211yescharacteristic
33C61×#525C2211yescharacteristic
34C61×#525C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic
36C2×#121×C61C2211yescharacteristic
37C61×#518—21no—
38C2×C4×D4×C61C2211yescharacteristic
39C61×#436—21no—
40C61×#435—21no—
41C61×#435—21no—
42C8×D4×C61—21no—
43C61×#432C2211yescharacteristic, complemented
44C61×#431C2211yescharacteristic, complemented
45C61×#407C2211yescharacteristic, complemented
46C61×#407C2211yescharacteristic, complemented
47C2×C22⋊C8×C61C2211yescharacteristic, complemented
48C2×C22⋊C8×C61C2211yescharacteristic, complemented
49C61×#388—21no—
50C61×#387—21no—
51C61×#386—21no—
52C61×#385—21no—
53C61×#383C2211yescharacteristic, complemented
54C61×#382C2211yescharacteristic, complemented
55C61×#381C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C61C2211yescharacteristic, complemented
58C2×#95×C61C2211yescharacteristic, complemented
59C61×#328C2211yescharacteristic, complemented
60C61×#328C2211yescharacteristic, complemented
61C61×#328C2211yescharacteristic, complemented
62C61×#328C2211yescharacteristic, complemented
63C61×#327C2211yescharacteristic
64C61×#327C2211yescharacteristic
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic, complemented
68C61×#327C2211yescharacteristic, complemented
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic, complemented
72C61×#327C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61C2×C411yescharacteristic
77C2×#41×C61C2×C411yescharacteristic, complemented
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61C2×C411yescharacteristic
82C22×D4×C61C2×C411yescharacteristic, complemented
83C22×D4×C61D411yescharacteristic
84C23×C4×C61—21no—
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C2×M16×C61—21no—
88C2×M16×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C4⋊Q8×C61C2×C411yescharacteristic, complemented
92#127×C61—21no—
93#127×C61C2×C411yescharacteristic, complemented
94#126×C61—21no—
95#126×C61—21no—
96#126×C61—21no—
97#125×C61—21no—
98#125×C61C2×C411yescharacteristic, complemented
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—21no—
102#124×C61C2×C411yescharacteristic, complemented
103#123×C61—21no—
104#123×C61—21no—
105#123×C61—21no—
106#123×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61—21no—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61—21no—
112C22⋊Q8×C61C2×C411yescharacteristic
113C22⋊Q8×C61C2×C411yescharacteristic, complemented
114C22⋊Q8×C61C2311yescharacteristic
115#121×C61—21no—
116#121×C61—21no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61—21no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#121×C61C2×C411yescharacteristic
129#121×C61C2×C411yescharacteristic
130#121×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic, complemented
132#121×C61C2×C411yescharacteristic, complemented
133#121×C61C2×C411yescharacteristic, complemented
134#121×C61C2311yescharacteristic
135#121×C61C2311yescharacteristic
136#121×C61C2311yescharacteristic
137#120×C61—21no—
138#120×C61—21no—
139#120×C61—21no—
140#120×C61—21no—
141#120×C61—21no—
142#120×C61—21no—
143C4×Q8×C61C2×C411yescharacteristic, complemented
144C4×D4×C61—21no—
145C4×D4×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C4×D4×C61C2×C411yescharacteristic
155C4×D4×C61C2×C411yescharacteristic
156C4×D4×C61C2×C411yescharacteristic
157C4×D4×C61C2×C411yescharacteristic
158C4×D4×C61C2×C411yescharacteristic, complemented
159C4×D4×C61C2×C411yescharacteristic, complemented
160C4×D4×C61C2×C411yescharacteristic, complemented
161C4×D4×C61D411yescharacteristic
162C4×D4×C61D411yescharacteristic
163C4×D4×C61D411yescharacteristic
164C4×D4×C61D411yescharacteristic
165#117×C61—21no—
166#117×C61—21no—
167#117×C61C2×C411yescharacteristic
168#117×C61C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2×C411yescharacteristic
172C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61—21no—
186C4⋊C8×C61—21no—
187C22⋊C8×C61—21no—
188C22⋊C8×C61—21no—
189C22⋊C8×C61—21no—
190C22⋊C8×C61—21no—
191C22⋊C8×C61C2311yescharacteristic
192C22⋊C8×C61C2311yescharacteristic
193C22⋊C8×C61C2311yescharacteristic
194C22⋊C8×C61C2311yescharacteristic
195#97×C61—21no—
196C4×C8×C61—21no—
197#95×C61—21no—
198#95×C61—21no—
199#95×C61—21no—
200#95×C61—21no—
201#95×C61—21no—
202#95×C61C2311yescharacteristic
203#95×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D411yescharacteristic
210#41×C61—81no—
211#41×C61—81no—
212#41×C61—81no—
213#41×C61—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61C22×C411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—42no—
232C2×D4×C61—44no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61C22⋊C411yescharacteristic
240C2×D4×C61C22⋊C411yescharacteristic
241C2×D4×C61C22⋊C411yescharacteristic
242C2×D4×C61C22⋊C411yescharacteristic
243C2×D4×C61C22×C411yescharacteristic
244C2×D4×C61C22×C411yescharacteristic
245C2×D4×C61C22×C411yescharacteristic
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—42no—
258C22×C4×C61—81no—
259C22×C4×C61—81no—
260C22×C4×C61—81no—
261C22×C4×C61—81no—
262C22×C4×C61C22×C411yescharacteristic
263C22×C4×C61C22×C411yescharacteristic
264C22×C4×C61C22×C411yescharacteristic
265C22×C4×C61C22×C411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2411yescharacteristic
275M16×C61—81no—
276M16×C61—81no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—81no—
282C2×C8×C61—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—81no—
293C4⋊C4×C61—81no—
294C4⋊C4×C61C22⋊C411yescharacteristic
295C4⋊C4×C61C22⋊C411yescharacteristic
296C4⋊C4×C61C22⋊C411yescharacteristic
297C4⋊C4×C61C22⋊C411yescharacteristic
298C4⋊C4×C61C22×C411yescharacteristic
299C4⋊C4×C61C22×C411yescharacteristic
300C4⋊C4×C61C22×C411yescharacteristic
301C4⋊C4×C61C22×C411yescharacteristic
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—42no—
322C22⋊C4×C61—81no—
323C22⋊C4×C61—81no—
324C22⋊C4×C61C22⋊C411yescharacteristic
325C22⋊C4×C61C22⋊C411yescharacteristic
326C22⋊C4×C61C22⋊C411yescharacteristic
327C22⋊C4×C61C22⋊C411yescharacteristic
328C22⋊C4×C61C22⋊C411yescharacteristic
329C22⋊C4×C61C22⋊C411yescharacteristic
330C22⋊C4×C61C22⋊C411yescharacteristic
331C22⋊C4×C61C22⋊C411yescharacteristic
332C42×C61—21no—
333C42×C61—21no—
334C42×C61—21no—
335C42×C61—81no—
336C42×C61C22×C411yescharacteristic
337C42×C61C22×C411yescharacteristic
338C42×C61C2×D411yescharacteristic
339C42×C61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—22no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—81no—
354C23×C61—81no—
355C23×C61—81no—
356C23×C61—81no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C23×C61C2×C22⋊C411yescharacteristic
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C22×D411yescharacteristic
362Q8×C61—41no—
363Q8×C61—81no—
364D4×C61—22no—
365D4×C61—22no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—41no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—42no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383D4×C61—81no—
384D4×C61—81no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—81no—
388D4×C61—81no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—81no—
422C2×C4×C61—81no—
423C2×C4×C61—81no—
424C2×C4×C61—81no—
425C2×C4×C61—81no—
426C2×C4×C61—81no—
427C2×C4×C61—84no—
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C2×C22⋊C411yescharacteristic
431C2×C4×C61C2×C22⋊C411yescharacteristic
432C2×C4×C61C2×C22⋊C411yescharacteristic
433C2×C4×C61C2×C22⋊C411yescharacteristic
434C2×C4×C61C2×C22⋊C411yescharacteristic
435C2×C4×C61C2×C22⋊C411yescharacteristic
436C2×C4×C61C23×C411yescharacteristic
437C2×C4×C61C22×D411yescharacteristic
438C8×C61—41no—
439C8×C61—41no—
440C8×C61—41no—
441C8×C61—41no—
442#17597C6111yesmaximal, characteristic, direct product factor, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—162no—
470C22×C61—162no—
471C22×C61#42112yes—
472C22×C61C22×C22⋊C411yescharacteristic
473C22×C61#57611yescharacteristic
474C22×C61#57711yescharacteristic
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—21no—
485C4×C61—41no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—41no—
490C4×C61—81no—
491C4×C61—81no—
492C4×C61—81no—
493C4×C61—81no—
494#3519C2×C6111yescharacteristic
495#2974C2×C6111yescharacteristic, complemented
496#2318C2×C6111yescharacteristic, complemented
497#1521C2×C6111yescharacteristic, complemented
498#1519C2×C6111yescharacteristic, complemented
499#1517C2×C6111yescharacteristic, complemented
500#1516C2×C6111yescharacteristic, complemented
501#1514C2×C6111yescharacteristic, complemented
502#1513C2×C6111yescharacteristic, complemented
503#1512C2×C6111yescharacteristic, complemented
504#1510C2×C6111yescharacteristic, complemented
505#1507C2×C6111yescharacteristic, complemented
506#1504C2×C6111yescharacteristic, complemented
507#1501C2×C6111yescharacteristic, complemented
508C2×#327C2×C6111yescharacteristic, complemented
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—22no—
512C2×C61—41no—
513C2×C61—41no—
514C2×C61—41no—
515C2×C61—81no—
516C2×C61—81no—
517C2×C61—81no—
518C2×C61#288311yescharacteristic
519C2×C61#289711yescharacteristic
520C2×C61C2×#42111yescharacteristic
521#555C4×C6111yescharacteristic, complemented
522#554C4×C6111yescharacteristic, complemented
523#553—21no—
524#553C4×C6111yescharacteristic, complemented
525#553C4×C6111yescharacteristic, complemented
526#550C4×C6111yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546C4×C6111yescharacteristic, complemented
530#546C4×C6111yescharacteristic, complemented
531D42—21no—
532D42C4×C6111yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C22×C6111yescharacteristic
537#529C22×C6111yescharacteristic
538#525C22×C6111yescharacteristic
539#525C22×C6111yescharacteristic
540C2×#121C22×C6111yescharacteristic
541C2×#121C22×C6111yescharacteristic
542#518—21no—
543C2×C4×D4C22×C6111yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C22×C6111yescharacteristic, complemented
549#431C22×C6111yescharacteristic, complemented
550#407C22×C6111yescharacteristic, complemented
551#407C22×C6111yescharacteristic, complemented
552C2×C22⋊C8C22×C6111yescharacteristic, complemented
553C2×C22⋊C8C22×C6111yescharacteristic, complemented
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C22×C6111yescharacteristic, complemented
559#382C22×C6111yescharacteristic, complemented
560#381C22×C6111yescharacteristic, complemented
561#380C22×C6111yescharacteristic, complemented
562C4×C22⋊C4C22×C6111yescharacteristic, complemented
563C2×#95C22×C6111yescharacteristic, complemented
564#328C22×C6111yescharacteristic, complemented
565#328C22×C6111yescharacteristic, complemented
566#328C22×C6111yescharacteristic, complemented
567#328C22×C6111yescharacteristic, complemented
568#327C22×C6111yescharacteristic
569#327C22×C6111yescharacteristic
570#327C22×C6111yescharacteristic
571#327C22×C6111yescharacteristic
572#327C22×C6111yescharacteristic, complemented
573#327C22×C6111yescharacteristic, complemented
574#327C22×C6111yescharacteristic, complemented
575#327C22×C6111yescharacteristic, complemented
576#327C22×C6111yescharacteristic, complemented
577#327C22×C6111yescharacteristic, complemented
578#327C22×C6111yescharacteristic, complemented
579#327C22×C6111yescharacteristic, complemented
580C61#1759711yescharacteristic, direct product factor, Sylow
581C2×#41—21no—
582C2×#41C2×C4×C6111yescharacteristic
583C2×#41C2×C4×C6111yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C6111yescharacteristic
588C22×D4C2×C4×C6111yescharacteristic, complemented
589C22×D4D4×C6111yescharacteristic
590C23×C4—21no—
591C23×C4C23×C6111yescharacteristic
592C23×C4C23×C6111yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C6111yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C6111yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C6111yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C6111yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×C4×C6111yescharacteristic
619C22⋊Q8C2×C4×C6111yescharacteristic, complemented
620C22⋊Q8C23×C6111yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×C4×C6111yescharacteristic
635#121C2×C4×C6111yescharacteristic
636#121C2×C4×C6111yescharacteristic
637#121C2×C4×C6111yescharacteristic, complemented
638#121C2×C4×C6111yescharacteristic, complemented
639#121C2×C4×C6111yescharacteristic, complemented
640#121C23×C6111yescharacteristic
641#121C23×C6111yescharacteristic
642#121C23×C6111yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C6111yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×C4×C6111yescharacteristic
661C4×D4C2×C4×C6111yescharacteristic
662C4×D4C2×C4×C6111yescharacteristic
663C4×D4C2×C4×C6111yescharacteristic
664C4×D4C2×C4×C6111yescharacteristic, complemented
665C4×D4C2×C4×C6111yescharacteristic, complemented
666C4×D4C2×C4×C6111yescharacteristic, complemented
667C4×D4D4×C6111yescharacteristic
668C4×D4D4×C6111yescharacteristic
669C4×D4D4×C6111yescharacteristic
670C4×D4D4×C6111yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C6111yescharacteristic
674#117C2×C4×C6111yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C6111yescharacteristic
678C2×C4⋊C4C2×C4×C6111yescharacteristic, complemented
679C2×C4⋊C4D4×C6111yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4D4×C6111yescharacteristic
688C2×C22⋊C4D4×C6111yescharacteristic
689C2×C42—21no—
690C2×C42C23×C6111yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C6111yescharacteristic
698C22⋊C8C23×C6111yescharacteristic
699C22⋊C8C23×C6111yescharacteristic
700C22⋊C8C23×C6111yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C6111yescharacteristic
709#95C23×C6111yescharacteristic
710#95C23×C6111yescharacteristic
711#95C23×C6111yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C6111yescharacteristic
715C24C2×D4×C6111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C6111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C6111yescharacteristic
746C2×D4C22⋊C4×C6111yescharacteristic
747C2×D4C22⋊C4×C6111yescharacteristic
748C2×D4C22⋊C4×C6111yescharacteristic
749C2×D4C22×C4×C6111yescharacteristic
750C2×D4C22×C4×C6111yescharacteristic
751C2×D4C22×C4×C6111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C6111yescharacteristic
769C22×C4C22×C4×C6111yescharacteristic
770C22×C4C22×C4×C6111yescharacteristic
771C22×C4C22×C4×C6111yescharacteristic
772C22×C4C2×D4×C6111yescharacteristic
773C22×C4C2×D4×C6111yescharacteristic
774C22×C4C2×D4×C6111yescharacteristic
775C22×C4C2×D4×C6111yescharacteristic
776C22×C4C2×D4×C6111yescharacteristic
777C22×C4C2×D4×C6111yescharacteristic
778C22×C4C2×D4×C6111yescharacteristic
779C22×C4C2×D4×C6111yescharacteristic
780C22×C4C24×C6111yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C6111yescharacteristic
801C4⋊C4C22⋊C4×C6111yescharacteristic
802C4⋊C4C22⋊C4×C6111yescharacteristic
803C4⋊C4C22⋊C4×C6111yescharacteristic
804C4⋊C4C22×C4×C6111yescharacteristic
805C4⋊C4C22×C4×C6111yescharacteristic
806C4⋊C4C22×C4×C6111yescharacteristic
807C4⋊C4C22×C4×C6111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C6111yescharacteristic
831C22⋊C4C22⋊C4×C6111yescharacteristic
832C22⋊C4C22⋊C4×C6111yescharacteristic
833C22⋊C4C22⋊C4×C6111yescharacteristic
834C22⋊C4C22⋊C4×C6111yescharacteristic
835C22⋊C4C22⋊C4×C6111yescharacteristic
836C22⋊C4C22⋊C4×C6111yescharacteristic
837C22⋊C4C22⋊C4×C6111yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C6111yescharacteristic
843C42C22×C4×C6111yescharacteristic
844C42C2×D4×C6111yescharacteristic
845C42C2×D4×C6111yescharacteristic
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C6111yescharacteristic
864C23C2×C22⋊C4×C6111yescharacteristic
865C23C2×C22⋊C4×C6111yescharacteristic
866C23C2×C22⋊C4×C6111yescharacteristic
867C23C22×D4×C6111yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—42no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C6111yescharacteristic
935C2×C4C2×C22⋊C4×C6111yescharacteristic
936C2×C4C2×C22⋊C4×C6111yescharacteristic
937C2×C4C2×C22⋊C4×C6111yescharacteristic
938C2×C4C2×C22⋊C4×C6111yescharacteristic
939C2×C4C2×C22⋊C4×C6111yescharacteristic
940C2×C4C2×C22⋊C4×C6111yescharacteristic
941C2×C4C2×C22⋊C4×C6111yescharacteristic
942C2×C4C23×C4×C6111yescharacteristic
943C2×C4C22×D4×C6111yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C61×#42112yes—
977C22C22×C22⋊C4×C6111yescharacteristic
978C22C61×#57611yescharacteristic
979C22C61×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C61×#288311yescharacteristic
1009C2C61×#289711yescharacteristic
1010C2C2×C61×#42111yescharacteristic
subgroupG/H
center, socleC22×C61C22×C22⋊C4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2974C2semidirect
3. C61×#2318C2semidirect
4. C61×#1521C2semidirect
5. C61×#1519C2semidirect
6. C61×#1517C2semidirect
7. C61×#1516C2semidirect
8. C61×#1514C2semidirect
9. C61×#1513C2semidirect
10. C61×#1512C2semidirect
11. C61×#1510C2semidirect
12. C61×#1507C2semidirect
13. C61×#1504C2semidirect
14. C61×#1501C2semidirect
15. C2×C61×#327C2semidirect
16. C61×#555C4semidirect
17. C61×#554C4semidirect
19. C61×#553C4semidirect
20. C61×#553C4semidirect
21. C61×#550C4semidirect
24. C61×#546C4semidirect
25. C61×#546C4semidirect
27. D42×C61C4semidirect
43. C61×#432C22semidirect
44. C61×#431C22semidirect
45. C61×#407C22semidirect
46. C61×#407C22semidirect
47. C2×C22⋊C8×C61C22semidirect
48. C2×C22⋊C8×C61C22semidirect
53. C61×#383C22semidirect
54. C61×#382C22semidirect
55. C61×#381C22semidirect
56. C61×#380C22semidirect
57. C4×C22⋊C4×C61C22semidirect
58. C2×#95×C61C22semidirect
59. C61×#328C22semidirect
60. C61×#328C22semidirect
61. C61×#328C22semidirect
62. C61×#328C22semidirect
67. C61×#327C22semidirect
68. C61×#327C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#327C22semidirect
72. C61×#327C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
77. C2×#41×C61C2×C4semidirect
82. C22×D4×C61C2×C4semidirect
91. C4⋊Q8×C61C2×C4semidirect
93. #127×C61C2×C4semidirect
98. #125×C61C2×C4semidirect
102. #124×C61C2×C4semidirect
113. C22⋊Q8×C61C2×C4semidirect
131. #121×C61C2×C4semidirect
132. #121×C61C2×C4semidirect
133. #121×C61C2×C4semidirect
143. C4×Q8×C61C2×C4semidirect
158. C4×D4×C61C2×C4semidirect
159. C4×D4×C61C2×C4semidirect
160. C4×D4×C61C2×C4semidirect
168. #117×C61C2×C4semidirect
172. C2×C4⋊C4×C61C2×C4semidirect
442. #17597C61direct (N × H)
495. #2974C2×C61semidirect
496. #2318C2×C61semidirect
497. #1521C2×C61semidirect
498. #1519C2×C61semidirect
499. #1517C2×C61semidirect
500. #1516C2×C61semidirect
501. #1514C2×C61semidirect
502. #1513C2×C61semidirect
503. #1512C2×C61semidirect
504. #1510C2×C61semidirect
505. #1507C2×C61semidirect
506. #1504C2×C61semidirect
507. #1501C2×C61semidirect
508. C2×#327C2×C61semidirect
521. #555C4×C61semidirect
522. #554C4×C61semidirect
524. #553C4×C61semidirect
525. #553C4×C61semidirect
526. #550C4×C61semidirect
529. #546C4×C61semidirect
530. #546C4×C61semidirect
532. D42C4×C61semidirect
548. #432C22×C61semidirect
549. #431C22×C61semidirect
550. #407C22×C61semidirect
551. #407C22×C61semidirect
552. C2×C22⋊C8C22×C61semidirect
553. C2×C22⋊C8C22×C61semidirect
558. #383C22×C61semidirect
559. #382C22×C61semidirect
560. #381C22×C61semidirect
561. #380C22×C61semidirect
562. C4×C22⋊C4C22×C61semidirect
563. C2×#95C22×C61semidirect
564. #328C22×C61semidirect
565. #328C22×C61semidirect
566. #328C22×C61semidirect
567. #328C22×C61semidirect
572. #327C22×C61semidirect
573. #327C22×C61semidirect
574. #327C22×C61semidirect
575. #327C22×C61semidirect
576. #327C22×C61semidirect
577. #327C22×C61semidirect
578. #327C22×C61semidirect
579. #327C22×C61semidirect
580. C61#17597direct (N × H)
583. C2×#41C2×C4×C61semidirect
588. C22×D4C2×C4×C61semidirect
597. C4⋊Q8C2×C4×C61semidirect
599. #127C2×C4×C61semidirect
604. #125C2×C4×C61semidirect
608. #124C2×C4×C61semidirect
619. C22⋊Q8C2×C4×C61semidirect
637. #121C2×C4×C61semidirect
638. #121C2×C4×C61semidirect
639. #121C2×C4×C61semidirect
649. C4×Q8C2×C4×C61semidirect
664. C4×D4C2×C4×C61semidirect
665. C4×D4C2×C4×C61semidirect
666. C4×D4C2×C4×C61semidirect
674. #117C2×C4×C61semidirect
678. C2×C4⋊C4C2×C4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35192
C61×#29742
C61×#23182
C61×#15212
C61×#15192
C61×#15172
C61×#15162
C61×#15142
C61×#15132
C61×#15122
C61×#15102
C61×#15072
C61×#15042
C61×#15012
C2×C61×#3272
#1759761