Finite Group Databasebeta

← C61×#24235 #29527668

Subgroups — C61×#24235 #29527668

Order 15616.

1376 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3500C211yesmaximal, characteristic
2C61×#3037C211yesmaximal, characteristic, complemented
3C2×C61×#456C211yesmaximal, characteristic, complemented
4C2×C61×#455C211yesmaximal, characteristic, complemented
5C4×#137×C61C211yesmaximal, characteristic, complemented
6C61×#2545C211yesmaximal, characteristic, complemented
7C61×#2038C211yesmaximal, characteristic, complemented
8C61×#2037C211yesmaximal, characteristic, complemented
9C61×#2005C211yesmaximal, characteristic, complemented
10C61×#2004C211yesmaximal, characteristic, complemented
11C61×#1980C211yesmaximal, characteristic, complemented
12C61×#1967C211yesmaximal, characteristic, complemented
13C61×#1806C211yesmaximal, characteristic, complemented
14C61×#1793C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C2×H(5,𝔽2)×C61C2211yescharacteristic
18C2×#137×C61C2211yescharacteristic
19C2×#137×C61C2211yescharacteristic
20C2×#137×C61C2211yescharacteristic, complemented
21C61×#548—21no—
22C61×#548—21no—
23C61×#546—21no—
24C61×#546—21no—
25C61×#546—22no—
26C61×#546—22no—
27C61×#536—21no—
28C61×#536C2211yescharacteristic
29C61×#535—21no—
30C61×#535C2211yescharacteristic
31C61×#532—21no—
32C61×#532C2211yescharacteristic
33C2×C4⋊Q8×C61C2211yescharacteristic, complemented
34C2×#124×C61—21no—
35C2×#124×C61C2211yescharacteristic
36C2×#124×C61C2211yescharacteristic
37C4×#41×C61C2211yescharacteristic
38C2×C4×Q8×C61C2211yescharacteristic, complemented
39C61×#464—21no—
40C61×#464—21no—
41C61×#462—21no—
42C61×#460—21no—
43C61×#456—24no—
44C61×#455—24no—
45C61×#441—21no—
46C61×#440—21no—
47C4×Q16×C61—21no—
48C4×SD16×C61—21no—
49C61×#428C2211yescharacteristic, complemented
50C61×#423C2211yescharacteristic, complemented
51C2×#104×C61C2211yescharacteristic
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C2×#104×C61C2211yescharacteristic
55C2×#104×C61C2211yescharacteristic, complemented
56C2×#104×C61C2211yescharacteristic, complemented
57C61×#419C2211yescharacteristic, complemented
58C61×#417C2211yescharacteristic
59C61×#417C2211yescharacteristic
60C61×#417C2211yescharacteristic, complemented
61C2×#101×C61C2211yescharacteristic, complemented
62C2×#101×C61C2211yescharacteristic, complemented
63C2×#100×C61C2211yescharacteristic
64C2×#100×C61C2211yescharacteristic
65C4×M16×C61C2211yescharacteristic, complemented
66C61×#396—22no—
67C61×#391C2211yescharacteristic, complemented
68C61×#390C2211yescharacteristic
69C61×#388—22no—
70C4×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#339C2211yescharacteristic, complemented
72C61×#339C2211yescharacteristic, complemented
732−1+4×C61—22no—
742−1+4×C61—22no—
752−1+4×C61—41no—
762−1+4×C61—41no—
77H(5,𝔽2)×C61—22no—
78H(5,𝔽2)×C61—22no—
79H(5,𝔽2)×C61—41no—
80H(5,𝔽2)×C61—41no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—21no—
84C2×#41×C61—21no—
85C2×#41×C61—22no—
86C2×#41×C61C2311yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61C2311yescharacteristic
92C22×Q8×C61C2311yescharacteristic
93C22×D4×C61—22no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61C2311yescharacteristic
97#137×C61—22no—
98#137×C61—22no—
99#137×C61—22no—
100#137×C61—41no—
101#137×C61—41no—
102#137×C61D414yescomplemented
103C2×Q16×C61—21no—
104C2×Q16×C61—21no—
105C2×Q16×C61—21no—
106C2×SD16×C61—21no—
107C2×SD16×C61—21no—
108C2×SD16×C61—21no—
109C2×M16×C61C2311yescharacteristic
110C2×M16×C61C2311yescharacteristic
111C2×M16×C61C2311yescharacteristic
112C2×M16×C61C2311yescharacteristic
113C4⋊Q8×C61—21no—
114C4⋊Q8×C61—22no—
115C4⋊Q8×C61—41no—
116C4⋊Q8×C61D411yescharacteristic
117#127×C61—21no—
118#127×C61D411yescharacteristic
119#124×C61—22no—
120#124×C61—22no—
121#124×C61—21no—
122#124×C61—21no—
123#124×C61—22no—
124#124×C61—21no—
125#124×C61—21no—
126#124×C61—21no—
127#124×C61—21no—
128#124×C61—41no—
129#124×C61D411yescharacteristic
130#124×C61D411yescharacteristic
131#123×C61—22no—
132#123×C61—22no—
133#123×C61—22no—
134C22⋊Q8×C61—22no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#120×C61—22no—
147#120×C61—22no—
148#120×C61—22no—
149C4×Q8×C61—21no—
150C4×Q8×C61—21no—
151C4×Q8×C61—21no—
152C4×Q8×C61—21no—
153C4×Q8×C61D411yescharacteristic
154C4×Q8×C61D411yescharacteristic
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61D411yescharacteristic
162C4×D4×C61D411yescharacteristic
163#117×C61—21no—
164#117×C61C2311yescharacteristic
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61D412yes—
174C2×C22⋊C4×C61D412yes—
175C2×C42×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180#107×C61—21no—
181#106×C61—21no—
182C4⋊C8×C61—21no—
183C4⋊C8×C61—21no—
184#104×C61—22no—
185#104×C61—22no—
186#104×C61—22no—
187#104×C61—22no—
188#104×C61—41no—
189#104×C61—41no—
190#103×C61—21no—
191#103×C61—21no—
192#103×C61—21no—
193#103×C61—21no—
194#103×C61—21no—
195#102×C61—21no—
196#102×C61—21no—
197#102×C61—21no—
198#101×C61—22no—
199#101×C61—41no—
200#100×C61—22no—
201#100×C61—41no—
202#97×C61—21no—
203C4×C8×C61—21no—
204#95×C61—21no—
205#95×C61—22no—
206C24×C61—22no—
207C24×C61C2×D412yes—
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—21no—
212#41×C61—21no—
213#41×C61—21no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61—44no—
221#41×C61—44no—
222#41×C61—42no—
223#41×C61—42no—
224#41×C61—42no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61C2×D412yes—
229#41×C61#4112yes—
230C2×Q8×C61—22no—
231C2×Q8×C61—21no—
232C2×Q8×C61—21no—
233C2×Q8×C61—21no—
234C2×Q8×C61—21no—
235C2×Q8×C61—21no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—42no—
243C2×Q8×C61—42no—
244C2×Q8×C61—42no—
245C2×Q8×C61—42no—
246C2×Q8×C61C2×D411yescharacteristic
247C2×Q8×C61C2×D411yescharacteristic
248C2×Q8×C61C2×D412yes—
249C2×Q8×C61C2×D411yescharacteristic
250C2×D4×C61—21no—
251C2×D4×C61—22no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—21no—
255C2×D4×C61—21no—
256C2×D4×C61—22no—
257C2×D4×C61—22no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—42no—
267C2×D4×C61—42no—
268C2×D4×C61—44no—
269C2×D4×C61—44no—
270C2×D4×C61—42no—
271C2×D4×C61—42no—
272C2×D4×C61C2×D411yescharacteristic
273C2×D4×C61C2×D411yescharacteristic
274C2×D4×C61C2×D411yescharacteristic
275C22×C4×C61—21no—
276C22×C4×C61—22no—
277C22×C4×C61—22no—
278C22×C4×C61—22no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—21no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61C2×D412yes—
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291Q16×C61—24no—
292Q16×C61—42no—
293Q16×C61—42no—
294SD16×C61—24no—
295SD16×C61—42no—
296SD16×C61—42no—
297M16×C61—21no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61—21no—
302M16×C61—21no—
303M16×C61—21no—
304M16×C61C2×D412yes—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—21no—
308C2×C8×C61—21no—
309C4⋊C4×C61—22no—
310C4⋊C4×C61—22no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—44no—
318C4⋊C4×C61—42no—
319C4⋊C4×C61—41no—
320C4⋊C4×C61—41no—
321C4⋊C4×C61C2×D411yescharacteristic
322C4⋊C4×C61C2×D411yescharacteristic
323C22⋊C4×C61—22no—
324C22⋊C4×C61—22no—
325C22⋊C4×C61—22no—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—22no—
331C22⋊C4×C61—22no—
332C22⋊C4×C61—22no—
333C22⋊C4×C61—22no—
334C22⋊C4×C61—21no—
335C22⋊C4×C61—21no—
336C22⋊C4×C61—21no—
337C22⋊C4×C61—21no—
338C22⋊C4×C61—44no—
339C22⋊C4×C61—44no—
340C42×C61—21no—
341C42×C61—21no—
342C42×C61—21no—
343C42×C61—21no—
344C42×C61—21no—
345C42×C61—21no—
346C42×C61—21no—
347C42×C61—41no—
348C42×C61—41no—
349C42×C61C2×D411yescharacteristic
350C42×C61C2×D411yescharacteristic
351C42×C61C2×D411yescharacteristic
352C42×C61C2×D411yescharacteristic
353C23×C61—21no—
354C23×C61—22no—
355C23×C61—21no—
356C23×C61—21no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—44no—
360C23×C61—42no—
361C23×C61—42no—
362C23×C61—82no—
363C23×C61—82no—
364C23×C61C22×D411yescharacteristic
365Q8×C61—21no—
366Q8×C61—22no—
367Q8×C61—22no—
368Q8×C61—21no—
369Q8×C61—21no—
370Q8×C61—21no—
371Q8×C61—21no—
372Q8×C61—44no—
373Q8×C61—41no—
374Q8×C61—41no—
375Q8×C61—41no—
376Q8×C61—41no—
377Q8×C61—41no—
378Q8×C61—41no—
379Q8×C61#12112yes—
380D4×C61—22no—
381D4×C61—22no—
382D4×C61—21no—
383D4×C61—21no—
384D4×C61—21no—
385D4×C61—21no—
386D4×C61—21no—
387D4×C61—44no—
388D4×C61—44no—
389D4×C61—44no—
390D4×C61—41no—
391D4×C61—41no—
392D4×C61—41no—
393D4×C61—41no—
394D4×C61—41no—
395D4×C61—41no—
396D4×C61—41no—
397D4×C61—41no—
398D4×C61—81no—
399D4×C61—81no—
400D4×C61—82no—
401D4×C61—82no—
402D4×C61#12112yes—
403C2×C4×C61—21no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—22no—
411C2×C4×C61—21no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—44no—
418C2×C4×C61—44no—
419C2×C4×C61—41no—
420C2×C4×C61—44no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—42no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—81no—
434C2×C4×C61—81no—
435C2×C4×C61#12011yescharacteristic
436C2×C4×C61#12011yescharacteristic
437C2×C4×C61#12011yescharacteristic
438C2×C4×C61#12011yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C2×#4111yescharacteristic
443C2×C4×C61H(5,𝔽2)11yescharacteristic
444C2×C4×C61H(5,𝔽2)11yescharacteristic
445C8×C61—22no—
446C8×C61—41no—
447C8×C61—41no—
448C8×C61—41no—
449#24235C6111yesmaximal, characteristic, direct product factor, Sylow
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—22no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—42no—
458C22×C61—41no—
459C22×C61—42no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—42no—
463C22×C61—41no—
464C22×C61—82no—
465C22×C61—82no—
466C22×C61—164no—
467C22×C61C2×#12011yescharacteristic
468C22×C61D4211yescharacteristic
469C22×C61#54611yescharacteristic
470C4×C61—22no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—21no—
475C4×C61—42no—
476C4×C61—42no—
477C4×C61—41no—
478C4×C61—41no—
479C4×C61—42no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—81no—
483C4×C61—81no—
484C4×C61C2×#12111yescharacteristic
485C4×C61#53511yescharacteristic
486C4×C61D4211yescharacteristic
487C4×C61#54611yescharacteristic
488#3500C2×C6111yescharacteristic
489#3037C2×C6111yescharacteristic, complemented
490C2×#456C2×C6111yescharacteristic, complemented
491C2×#455C2×C6111yescharacteristic, complemented
492C4×#137C2×C6111yescharacteristic, complemented
493#2545C2×C6111yescharacteristic, complemented
494#2038C2×C6111yescharacteristic, complemented
495#2037C2×C6111yescharacteristic, complemented
496#2005C2×C6111yescharacteristic, complemented
497#2004C2×C6111yescharacteristic, complemented
498#1980C2×C6111yescharacteristic, complemented
499#1967C2×C6111yescharacteristic, complemented
500#1806C2×C6111yescharacteristic, complemented
501#1793C2×C6111yescharacteristic, complemented
502#1792C2×C6111yescharacteristic, complemented
503C2×C61—21no—
504C2×C61—21no—
505C2×C61—42no—
506C2×C61—81no—
507C2×C61—82no—
508C2×C61—81no—
509C2×C61#240811yescharacteristic
510C2×C61#301811yescharacteristic
511C2×C61#302211yescharacteristic
512C2×2−1+4C22×C6111yescharacteristic
513C2×H(5,𝔽2)C22×C6111yescharacteristic
514C2×#137C22×C6111yescharacteristic
515C2×#137C22×C6111yescharacteristic
516C2×#137C22×C6111yescharacteristic, complemented
517#548—21no—
518#548—21no—
519#546—21no—
520#546—21no—
521#546—22no—
522#546—22no—
523#536—21no—
524#536C22×C6111yescharacteristic
525#535—21no—
526#535C22×C6111yescharacteristic
527#532—21no—
528#532C22×C6111yescharacteristic
529C2×C4⋊Q8C22×C6111yescharacteristic, complemented
530C2×#124—21no—
531C2×#124C22×C6111yescharacteristic
532C2×#124C22×C6111yescharacteristic
533C4×#41C22×C6111yescharacteristic
534C2×C4×Q8C22×C6111yescharacteristic, complemented
535#464—21no—
536#464—21no—
537#462—21no—
538#460—21no—
539#456—24no—
540#455—24no—
541#441—21no—
542#440—21no—
543C4×Q16—21no—
544C4×SD16—21no—
545#428C22×C6111yescharacteristic, complemented
546#423C22×C6111yescharacteristic, complemented
547C2×#104C22×C6111yescharacteristic
548C2×#104C22×C6111yescharacteristic
549C2×#104C22×C6111yescharacteristic
550C2×#104C22×C6111yescharacteristic
551C2×#104C22×C6111yescharacteristic, complemented
552C2×#104C22×C6111yescharacteristic, complemented
553#419C22×C6111yescharacteristic, complemented
554#417C22×C6111yescharacteristic
555#417C22×C6111yescharacteristic
556#417C22×C6111yescharacteristic, complemented
557C2×#101C22×C6111yescharacteristic, complemented
558C2×#101C22×C6111yescharacteristic, complemented
559C2×#100C22×C6111yescharacteristic
560C2×#100C22×C6111yescharacteristic
561C4×M16C22×C6111yescharacteristic, complemented
562#396—22no—
563#391C22×C6111yescharacteristic, complemented
564#390C22×C6111yescharacteristic
565#388—22no—
566C4×C4⋊C4C22×C6111yescharacteristic, complemented
567#339C22×C6111yescharacteristic, complemented
568#339C22×C6111yescharacteristic, complemented
569C61#2423511yescharacteristic, direct product factor, Sylow
5702−1+4—22no—
5712−1+4—22no—
5722−1+4—41no—
5732−1+4—41no—
574H(5,𝔽2)—22no—
575H(5,𝔽2)—22no—
576H(5,𝔽2)—41no—
577H(5,𝔽2)—41no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—22no—
583C2×#41C23×C6111yescharacteristic
584C2×#41C23×C6111yescharacteristic
585C2×#41C23×C6111yescharacteristic
586C22×Q8—21no—
587C22×Q8—21no—
588C22×Q8C23×C6111yescharacteristic
589C22×Q8C23×C6111yescharacteristic
590C22×D4—22no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4C23×C6111yescharacteristic
594#137—22no—
595#137—22no—
596#137—22no—
597#137—41no—
598#137—41no—
599#137D4×C6114yescomplemented
600C2×Q16—21no—
601C2×Q16—21no—
602C2×Q16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×M16C23×C6111yescharacteristic
607C2×M16C23×C6111yescharacteristic
608C2×M16C23×C6111yescharacteristic
609C2×M16C23×C6111yescharacteristic
610C4⋊Q8—21no—
611C4⋊Q8—22no—
612C4⋊Q8—41no—
613C4⋊Q8D4×C6111yescharacteristic
614#127—21no—
615#127D4×C6111yescharacteristic
616#124—22no—
617#124—22no—
618#124—21no—
619#124—21no—
620#124—22no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—41no—
626#124D4×C6111yescharacteristic
627#124D4×C6111yescharacteristic
628#123—22no—
629#123—22no—
630#123—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635#121—22no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#120—22no—
644#120—22no—
645#120—22no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8D4×C6111yescharacteristic
651C4×Q8D4×C6111yescharacteristic
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4D4×C6111yescharacteristic
659C4×D4D4×C6111yescharacteristic
660#117—21no—
661#117C23×C6111yescharacteristic
662C2×C4⋊C4—21no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4C23×C6111yescharacteristic
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4D4×C6112yes—
671C2×C22⋊C4D4×C6112yes—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42C23×C6111yescharacteristic
675C2×C42C23×C6111yescharacteristic
676C2×C42C23×C6111yescharacteristic
677#107—21no—
678#106—21no—
679C4⋊C8—21no—
680C4⋊C8—21no—
681#104—22no—
682#104—22no—
683#104—22no—
684#104—22no—
685#104—41no—
686#104—41no—
687#103—21no—
688#103—21no—
689#103—21no—
690#103—21no—
691#103—21no—
692#102—21no—
693#102—21no—
694#102—21no—
695#101—22no—
696#101—41no—
697#100—22no—
698#100—41no—
699#97—21no—
700C4×C8—21no—
701#95—21no—
702#95—22no—
703C24—22no—
704C24C2×D4×C6112yes—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—21no—
715#41—42no—
716#41—42no—
717#41—44no—
718#41—44no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41—42no—
725#41C2×D4×C6112yes—
726#41#41×C6112yes—
727C2×Q8—22no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8C2×D4×C6111yescharacteristic
744C2×Q8C2×D4×C6111yescharacteristic
745C2×Q8C2×D4×C6112yes—
746C2×Q8C2×D4×C6111yescharacteristic
747C2×D4—21no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4C2×D4×C6111yescharacteristic
770C2×D4C2×D4×C6111yescharacteristic
771C2×D4C2×D4×C6111yescharacteristic
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4C2×D4×C6112yes—
785C22×C4C2×D4×C6111yescharacteristic
786C22×C4C2×D4×C6111yescharacteristic
787C22×C4C24×C6111yescharacteristic
788Q16—24no—
789Q16—42no—
790Q16—42no—
791SD16—24no—
792SD16—42no—
793SD16—42no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16C2×D4×C6112yes—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—44no—
815C4⋊C4—42no—
816C4⋊C4—41no—
817C4⋊C4—41no—
818C4⋊C4C2×D4×C6111yescharacteristic
819C4⋊C4C2×D4×C6111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C42—21no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—21no—
844C42—41no—
845C42—41no—
846C42C2×D4×C6111yescharacteristic
847C42C2×D4×C6111yescharacteristic
848C42C2×D4×C6111yescharacteristic
849C42C2×D4×C6111yescharacteristic
850C23—21no—
851C23—22no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23—22no—
856C23—44no—
857C23—42no—
858C23—42no—
859C23—82no—
860C23—82no—
861C23C22×D4×C6111yescharacteristic
862Q8—21no—
863Q8—22no—
864Q8—21no—
865Q8—21no—
866Q8—21no—
867Q8—21no—
868Q8—22no—
869Q8—44no—
870Q8—41no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875Q8—41no—
876Q8#121×C6112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—21no—
883D4—21no—
884D4—44no—
885D4—44no—
886D4—44no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4#121×C6112yes—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—41no—
917C2×C4—44no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4#120×C6111yescharacteristic
933C2×C4#120×C6111yescharacteristic
934C2×C4#120×C6111yescharacteristic
935C2×C4#120×C6111yescharacteristic
936C2×C4C22×D4×C6111yescharacteristic
937C2×C4C22×D4×C6111yescharacteristic
938C2×C4C22×D4×C6111yescharacteristic
939C2×C4C2×#41×C6111yescharacteristic
940C2×C4H(5,𝔽2)×C6111yescharacteristic
941C2×C4H(5,𝔽2)×C6111yescharacteristic
942C8—22no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—22no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—42no—
954C22—41no—
955C22—42no—
956C22—41no—
957C22—41no—
958C22—42no—
959C22—41no—
960C22—82no—
961C22—82no—
962C22—164no—
963C22C2×#120×C6111yescharacteristic
964C22D42×C6111yescharacteristic
965C22C61×#54611yescharacteristic
966C4—22no—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—42no—
972C4—42no—
973C4—41no—
974C4—41no—
975C4—42no—
976C4—41no—
977C4—41no—
978C4—81no—
979C4—81no—
980C4C2×#121×C6111yescharacteristic
981C4C61×#53511yescharacteristic
982C4D42×C6111yescharacteristic
983C4C61×#54611yescharacteristic
984C2—21no—
985C2—21no—
986C2—42no—
987C2—82no—
988C2—81no—
989C2—81no—
990C2C61×#240811yescharacteristic
991C2C61×#301811yescharacteristic
992C2C61×#302211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3500C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3037C2semidirect
3. C2×C61×#456C2semidirect
4. C2×C61×#455C2semidirect
5. C4×#137×C61C2semidirect
6. C61×#2545C2semidirect
7. C61×#2038C2semidirect
8. C61×#2037C2semidirect
9. C61×#2005C2semidirect
10. C61×#2004C2semidirect
11. C61×#1980C2semidirect
12. C61×#1967C2semidirect
13. C61×#1806C2semidirect
14. C61×#1793C2semidirect
15. C61×#1792C2semidirect
20. C2×#137×C61C22semidirect
33. C2×C4⋊Q8×C61C22semidirect
38. C2×C4×Q8×C61C22semidirect
49. C61×#428C22semidirect
50. C61×#423C22semidirect
55. C2×#104×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C61×#419C22semidirect
60. C61×#417C22semidirect
61. C2×#101×C61C22semidirect
62. C2×#101×C61C22semidirect
65. C4×M16×C61C22semidirect
67. C61×#391C22semidirect
70. C4×C4⋊C4×C61C22semidirect
71. C61×#339C22semidirect
72. C61×#339C22semidirect
102. #137×C61D4semidirect
449. #24235C61direct (N × H)
489. #3037C2×C61semidirect
490. C2×#456C2×C61semidirect
491. C2×#455C2×C61semidirect
492. C4×#137C2×C61semidirect
493. #2545C2×C61semidirect
494. #2038C2×C61semidirect
495. #2037C2×C61semidirect
496. #2005C2×C61semidirect
497. #2004C2×C61semidirect
498. #1980C2×C61semidirect
499. #1967C2×C61semidirect
500. #1806C2×C61semidirect
501. #1793C2×C61semidirect
502. #1792C2×C61semidirect
516. C2×#137C22×C61semidirect
529. C2×C4⋊Q8C22×C61semidirect
534. C2×C4×Q8C22×C61semidirect
545. #428C22×C61semidirect
546. #423C22×C61semidirect
551. C2×#104C22×C61semidirect
552. C2×#104C22×C61semidirect
553. #419C22×C61semidirect
556. #417C22×C61semidirect
557. C2×#101C22×C61semidirect
558. C2×#101C22×C61semidirect
561. C4×M16C22×C61semidirect
563. #391C22×C61semidirect
566. C4×C4⋊C4C22×C61semidirect
567. #339C22×C61semidirect
568. #339C22×C61semidirect
569. C61#24235direct (N × H)
599. #137D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35002
C61×#30372
C2×C61×#4562
C2×C61×#4552
C4×#137×C612
C61×#25452
C61×#20382
C61×#20372
C61×#20052
C61×#20042
C61×#19802
C61×#19672
C61×#18062
C61×#17932
C61×#17922
#2423561