Finite Group Databasebeta

← C61×#24512 #29527945

Subgroups — C61×#24512 #29527945

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#447C211yesmaximal, characteristic
2C2×C61×#433C211yesmaximal, characteristic, complemented
3C61×#2624C211yesmaximal, characteristic, complemented
4C61×#2309C211yesmaximal, characteristic, complemented
5C61×#2067C211yesmaximal, characteristic, complemented
6C61×#2065C211yesmaximal, characteristic, complemented
7C61×#2054C211yesmaximal, characteristic, complemented
8C61×#2054C211yesmaximal, characteristic, complemented
9C61×#1972C211yesmaximal, characteristic, complemented
10C61×#1970C211yesmaximal, characteristic, complemented
11C61×#1936C211yesmaximal, characteristic, complemented
12C61×#1934C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×D8×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×#117×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C61×#447—24no—
23C61×#433—24no—
24C2×#107×C61C2211yescharacteristic, complemented
25C2×#106×C61C2211yescharacteristic, complemented
26C2×C4⋊C8×C61C2211yescharacteristic, complemented
27C2×C4⋊C8×C61C2211yescharacteristic, complemented
28C2×#102×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic, complemented
35C2×#102×C61C2211yescharacteristic, complemented
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic, complemented
39C2×C4×C8×C61C2211yescharacteristic, complemented
40C61×#399—21no—
41C61×#397—21no—
42C61×#394—21no—
43C61×#394—21no—
44C61×#390—21no—
45C61×#390—21no—
46C61×#390C2211yescharacteristic
47C61×#390C2211yescharacteristic
48C61×#390C2211yescharacteristic
49C61×#390C2211yescharacteristic
50C61×#390C2211yescharacteristic, complemented
51C61×#390C2211yescharacteristic, complemented
52C61×#389C2211yescharacteristic, complemented
53C61×#389C2211yescharacteristic, complemented
54C61×#380C2211yescharacteristic
55C61×#379—21no—
56C61×#379—21no—
57C61×#340C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C25×C61—21no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—41no—
69C22×D4×C61—41no—
70C22×D4×C61C2311yescharacteristic
71C22×D4×C61C2311yescharacteristic
72C22×D4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C2×D8×C61—22no—
75C2×D8×C61—22no—
76C2×D8×C61—22no—
77C2×D8×C61—22no—
78C2×D8×C61—41no—
79C2×D8×C61—41no—
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84#121×C61—22no—
85#121×C61—22no—
86#117×C61—22no—
87#117×C61—22no—
88#117×C61—41no—
89#117×C61—41no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61D411yescharacteristic
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#107×C61—41no—
120#106×C61—41no—
121C4⋊C8×C61—22no—
122C4⋊C8×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—22no—
126#102×C61—22no—
127#102×C61—41no—
128#102×C61—41no—
129#102×C61—41no—
130#102×C61—41no—
131C22⋊C8×C61—22no—
132C22⋊C8×C61D414yes—
133#97×C61—22no—
134C4×C8×C61—22no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—24no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—44no—
169C2×D4×C61—44no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61#4112yes—
176C2×D4×C61#4112yes—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61#4112yes—
193C22×C4×C61C2411yescharacteristic
194D8×C61—44no—
195D8×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61C2×D412yes—
207C2×C8×C61C2×D412yes—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—81no—
221C4⋊C4×C61—81no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61—81no—
228C22⋊C4×C61—81no—
229C22⋊C4×C61—81no—
230C22⋊C4×C61—81no—
231C22⋊C4×C61—81no—
232C22⋊C4×C61—81no—
233C22⋊C4×C61—81no—
234C22⋊C4×C61—81no—
235C22⋊C4×C61—81no—
236C22⋊C4×C61—81no—
237C22⋊C4×C61—81no—
238C22⋊C4×C61—81no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61—42no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—48no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61—84no—
278C23×C61#12112yes—
279C23×C61C22×D411yescharacteristic
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—48no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—84no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61#12112yes—
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C8×C61—22no—
335C8×C61—22no—
336C8×C61—41no—
337C8×C61—41no—
338#24512C6111yesmaximal, characteristic, direct product factor, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—816no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61C2×#12111yescharacteristic
369C22×C61#52511yescharacteristic
370C22×C61#53511yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C22×C61#57711yescharacteristic
375C4×C61—22no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61—81no—
383C4×C61—81no—
384C4×C61—81no—
385C4×C61#54611yescharacteristic
386C4×C61#54611yescharacteristic
387C4×C61#55111yescharacteristic
388C4×C61#55111yescharacteristic
389C2×#447C2×C6111yescharacteristic
390C2×#433C2×C6111yescharacteristic, complemented
391#2624C2×C6111yescharacteristic, complemented
392#2309C2×C6111yescharacteristic, complemented
393#2067C2×C6111yescharacteristic, complemented
394#2065C2×C6111yescharacteristic, complemented
395#2054C2×C6111yescharacteristic, complemented
396#2054C2×C6111yescharacteristic, complemented
397#1972C2×C6111yescharacteristic, complemented
398#1970C2×C6111yescharacteristic, complemented
399#1936C2×C6111yescharacteristic, complemented
400#1934C2×C6111yescharacteristic, complemented
401#1875C2×C6111yescharacteristic, complemented
402#1854C2×C6111yescharacteristic, complemented
403#1786C2×C6111yescharacteristic, complemented
404C2×C61—42no—
405C2×C61—82no—
406C2×C61—82no—
407C2×C61—161no—
408C2×C61#241111yescharacteristic
409C2×C61#305811yescharacteristic
410C2×C61#306211yescharacteristic
411C2×C61#311811yescharacteristic
412C2×C61#312211yescharacteristic
413C2×C61#322011yescharacteristic
414C2×C61#322411yescharacteristic
415C23×D4C22×C6111yescharacteristic
416C22×D8C22×C6111yescharacteristic
417C22×D8C22×C6111yescharacteristic
418C2×#121C22×C6111yescharacteristic
419C2×#117C22×C6111yescharacteristic
420C2×#117C22×C6111yescharacteristic
421#447—24no—
422#433—24no—
423C2×#107C22×C6111yescharacteristic, complemented
424C2×#106C22×C6111yescharacteristic, complemented
425C2×C4⋊C8C22×C6111yescharacteristic, complemented
426C2×C4⋊C8C22×C6111yescharacteristic, complemented
427C2×#102C22×C6111yescharacteristic
428C2×#102C22×C6111yescharacteristic
429C2×#102C22×C6111yescharacteristic
430C2×#102C22×C6111yescharacteristic
431C2×#102C22×C6111yescharacteristic
432C2×#102C22×C6111yescharacteristic
433C2×#102C22×C6111yescharacteristic, complemented
434C2×#102C22×C6111yescharacteristic, complemented
435C2×C22⋊C8C22×C6111yescharacteristic
436C2×C22⋊C8C22×C6111yescharacteristic
437C2×#97C22×C6111yescharacteristic, complemented
438C2×C4×C8C22×C6111yescharacteristic, complemented
439#399—21no—
440#397—21no—
441#394—21no—
442#394—21no—
443#390—21no—
444#390—21no—
445#390C22×C6111yescharacteristic
446#390C22×C6111yescharacteristic
447#390C22×C6111yescharacteristic
448#390C22×C6111yescharacteristic
449#390C22×C6111yescharacteristic, complemented
450#390C22×C6111yescharacteristic, complemented
451#389C22×C6111yescharacteristic, complemented
452#389C22×C6111yescharacteristic, complemented
453#380C22×C6111yescharacteristic
454#379—21no—
455#379—21no—
456#340C22×C6111yescharacteristic, complemented
457#340C22×C6111yescharacteristic, complemented
458#340C22×C6111yescharacteristic, complemented
459#340C22×C6111yescharacteristic, complemented
460C61#2451211yescharacteristic, direct product factor, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C6111yescharacteristic
471C22×D4C23×C6111yescharacteristic
472C22×D4C23×C6111yescharacteristic
473C23×C4C23×C6111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C6111yescharacteristic
481C22×C8C23×C6111yescharacteristic
482C22×C8C23×C6111yescharacteristic
483C22×C8C23×C6111yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C6111yescharacteristic
493C2×C4⋊C4D4×C6111yescharacteristic
494C2×C4⋊C4C23×C6111yescharacteristic
495C2×C4⋊C4C23×C6111yescharacteristic
496C2×C4⋊C4C23×C6111yescharacteristic
497C2×C4⋊C4C23×C6111yescharacteristic
498C2×C4⋊C4C23×C6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4D4×C6111yescharacteristic
515C2×C22⋊C4D4×C6111yescharacteristic
516C2×C42—21no—
517C2×C42C23×C6111yescharacteristic
518C2×C42C23×C6111yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C6114yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C6111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C6112yes—
576C2×D4#41×C6112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4C2×D4×C6111yescharacteristic
587C22×C4C2×D4×C6111yescharacteristic
588C22×C4C2×D4×C6111yescharacteristic
589C22×C4C2×D4×C6111yescharacteristic
590C22×C4C2×D4×C6111yescharacteristic
591C22×C4C2×D4×C6112yes—
592C22×C4#41×C6112yes—
593C22×C4C24×C6111yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C6112yes—
607C2×C8C2×D4×C6112yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C6112yes—
679C23C22×D4×C6111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4#121×C6112yes—
728C2×C4C22×D4×C6111yescharacteristic
729C2×C4C2×#41×C6111yescharacteristic
730C2×C4C2×#41×C6111yescharacteristic
731C2×C4C2×#41×C6111yescharacteristic
732C2×C4H(5,𝔽2)×C6111yescharacteristic
733C2×C4H(5,𝔽2)×C6111yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C6111yescharacteristic
768C22C61×#52511yescharacteristic
769C22C61×#53511yescharacteristic
770C22C61×#57611yescharacteristic
771C22C61×#57611yescharacteristic
772C22C61×#57611yescharacteristic
773C22C61×#57711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C61×#54611yescharacteristic
785C4C61×#54611yescharacteristic
786C4C61×#55111yescharacteristic
787C4C61×#55111yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C61×#241111yescharacteristic
793C2C61×#305811yescharacteristic
794C2C61×#306211yescharacteristic
795C2C61×#311811yescharacteristic
796C2C61×#312211yescharacteristic
797C2C61×#322011yescharacteristic
798C2C61×#322411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#433C2semidirect
3. C61×#2624C2semidirect
4. C61×#2309C2semidirect
5. C61×#2067C2semidirect
6. C61×#2065C2semidirect
7. C61×#2054C2semidirect
8. C61×#2054C2semidirect
9. C61×#1972C2semidirect
10. C61×#1970C2semidirect
11. C61×#1936C2semidirect
12. C61×#1934C2semidirect
13. C61×#1875C2semidirect
14. C61×#1854C2semidirect
15. C61×#1786C2semidirect
24. C2×#107×C61C22semidirect
25. C2×#106×C61C22semidirect
26. C2×C4⋊C8×C61C22semidirect
27. C2×C4⋊C8×C61C22semidirect
34. C2×#102×C61C22semidirect
35. C2×#102×C61C22semidirect
38. C2×#97×C61C22semidirect
39. C2×C4×C8×C61C22semidirect
50. C61×#390C22semidirect
51. C61×#390C22semidirect
52. C61×#389C22semidirect
53. C61×#389C22semidirect
57. C61×#340C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
338. #24512C61direct (N × H)
390. C2×#433C2×C61semidirect
391. #2624C2×C61semidirect
392. #2309C2×C61semidirect
393. #2067C2×C61semidirect
394. #2065C2×C61semidirect
395. #2054C2×C61semidirect
396. #2054C2×C61semidirect
397. #1972C2×C61semidirect
398. #1970C2×C61semidirect
399. #1936C2×C61semidirect
400. #1934C2×C61semidirect
401. #1875C2×C61semidirect
402. #1854C2×C61semidirect
403. #1786C2×C61semidirect
423. C2×#107C22×C61semidirect
424. C2×#106C22×C61semidirect
425. C2×C4⋊C8C22×C61semidirect
426. C2×C4⋊C8C22×C61semidirect
433. C2×#102C22×C61semidirect
434. C2×#102C22×C61semidirect
437. C2×#97C22×C61semidirect
438. C2×C4×C8C22×C61semidirect
449. #390C22×C61semidirect
450. #390C22×C61semidirect
451. #389C22×C61semidirect
452. #389C22×C61semidirect
456. #340C22×C61semidirect
457. #340C22×C61semidirect
458. #340C22×C61semidirect
459. #340C22×C61semidirect
460. C61#24512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4472
C2×C61×#4332
C61×#26242
C61×#23092
C61×#20672
C61×#20652
C61×#20542
C61×#19722
C61×#19702
C61×#19362
C61×#19342
C61×#18752
C61×#18542
C61×#17862
#2451261