Finite Group Databasebeta

← D61×#1508 #29647131

Subgroups — D61×#1508 #29647131

Order 15616.

1554 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3C4×C22⋊C4×D61C211yesmaximal, characteristic
4#21444340C211yesmaximal, characteristic, complemented
5#21444339C211yesmaximal, characteristic, complemented
6#21444338C211yesmaximal, characteristic, complemented
7#21444337C214yesmaximal, complemented
8#328×D61C214yesmaximal, complemented
9C61×#1508C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13C2×#14519757C411yescharacteristic, complemented
14C2×#14519756C2211yescharacteristic
15C2×#14519755—21no—
16C2×#14519754—21no—
17C2×#14519753C411yescharacteristic, complemented
18C22⋊Q8×D61—21no—
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61C412yescomplemented
23C22⋊Q8×D61C412yescomplemented
24C22⋊Q8×D61C2212yes—
25C22⋊Q8×D61C2212yes—
26C2×C4⋊C4×D61—21no—
27C2×C4⋊C4×D61C411yescharacteristic, complemented
28C2×C22⋊C4×D61—21no—
29C2×C22⋊C4×D61—21no—
30C2×C42×D61—21no—
31#16839726C2211yescharacteristic
32#16839725—21no—
33#16839724—21no—
34#16839724C2212yes—
35C22⋊C8×D61—21no—
36C22⋊C8×D61C2212yes—
37C22⋊C4×Dic61—21no—
38C4×#11758198—21no—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839609C2212yes—
41#95×D61C2212yes—
42#16839500C2214yescomplemented
43#16839499C2214yescomplemented
44#16839498C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#328C2214yescomplemented
49C24×D61D411yescharacteristic
50C22×Dic122—21no—
51C22×Dic122C2×C411yescharacteristic, complemented
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—44no—
55C2×Q8×D61C2×C412yes—
56C2×Q8×D61C2×C412yescomplemented
57C23×Dic61D411yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—21no—
75C2×#11758189—22no—
76M16×D61—44no—
77C2×C8×D61—22no—
78#14519757—21no—
79#14519757—21no—
80#14519757C2×C412yes—
81#14519757C2×C412yescomplemented
82#14519756—21no—
83#14519756—21no—
84#14519756C2×C412yescomplemented
85#14519756C2312yes—
86#14519755—22no—
87#14519755—22no—
88#14519755—22no—
89#14519755—22no—
90#14519754—22no—
91#14519754—22no—
92#14519754—22no—
93#14519754—22no—
94#14519753—21no—
95#14519753—21no—
96#14519753C2×C412yes—
97#14519753C2×C412yescomplemented
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2×C411yescharacteristic, complemented
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61C2×C412yes—
110C4⋊C4×D61C2×C412yescomplemented
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—22no—
116C22⋊C4×D61—28no—
117C22⋊C4×D61—22no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—22no—
123C42×D61—44no—
124C22⋊#92418—21no—
125C22⋊#92418C2312yes—
126#14519689—22no—
127#14519689—22no—
128#14519684—22no—
129#14519684C2312yes—
130C22×Q8×C61C2×C411yescharacteristic, complemented
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61C2×C412yescomplemented
136C22⋊Q8×C61C2312yes—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61C2×D411yescharacteristic
146C23×D61—24no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×Q8×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—42no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—42no—
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181Q8×D61—44no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—28no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—44no—
202C2×C4×D61—44no—
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22×C411yescharacteristic
212C2×C4×D61C22×C411yescharacteristic
213C2×C4×D61C22×C411yescharacteristic
214C2×C4×D61C22×C411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×Dic122—21no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—44no—
223C2×Dic122—42no—
224C2×Dic122C22×C412yes—
225M16×C61—42no—
226C2×C8×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61C22×C412yes—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C42×C61—42no—
235C22⋊Dic61—24no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238#11758198—28no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243C4⋊Dic61—21no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61C22×C412yes—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253C4×Dic61—44no—
254C4×Dic61—42no—
255#11758194—42no—
256C2×#92418—22no—
257#11758189—44no—
258C8×D61—44no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—41no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—416no—
282C22×D61#10414yes—
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61C2×C22⋊C411yescharacteristic
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61C2×C22⋊C411yescharacteristic
287C22×D61#13714yes—
288Q8×C61—42no—
289Q8×C61—42no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—24no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C23×C411yescharacteristic
306C2×C4×C61C22×D411yescharacteristic
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—416no—
340C4×D61—44no—
341C4×D61—44no—
342C4×D61—44no—
343C4×D61—44no—
344C4×D61#9914yes—
345Dic122—44no—
346Dic122—42no—
347Dic122—44no—
348Dic122—42no—
349C8×C61—42no—
350#92418—42no—
351C2×#1508—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—44no—
360C22×C61C2×#10412yes—
361C22×C61C22×C22⋊C411yescharacteristic
362C22×C61C2×#13712yes—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—28no—
368C2×D61—28no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61C2×#9912yes—
377C2×D61#41912yes—
378C2×D61#41912yes—
379C2×D61C2×#10412yes—
380C2×D61C2×#10412yes—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—44no—
385C4×C61—42no—
386C4×C61—42no—
387C4×C61C2×#9912yes—
388Dic61—21no—
389Dic61—21no—
390Dic61—21no—
391Dic61—44no—
392Dic61—42no—
393Dic61—42no—
394Dic61C2×#9912yes—
395C22×C22⋊Q8—611no—
396C2×#407—611no—
397C2×C4×C22⋊C4—611no—
398#1508—611no—
399#1508—611no—
400#1508—614no—
401#1508—611no—
402#1508D6111yescharacteristic, direct product factor
403C2×#328—614no—
404C2×C61—22no—
405C2×C61—22no—
406C2×C61—41no—
407C2×C61C22×#9911yescharacteristic
408C2×C61C2×#41911yescharacteristic
409C2×C61C22×#10411yescharacteristic
410D61—22no—
411D61—22no—
412D61—41no—
413D61#150814yesdirect product factor
414C23×Q8—611no—
415C24×C4—611no—
416C22×M16—1221no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×C22⋊Q8—612no—
420C2×C22⋊Q8—612no—
421C2×C22⋊Q8—612no—
422C2×C22⋊Q8—612no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—1221no—
425C2×C22⋊Q8—1221no—
426C2×C22⋊Q8—1221no—
427C2×C22⋊Q8—1221no—
428C2×C22⋊Q8—1221no—
429C2×C22⋊Q8—1221no—
430C2×C22⋊Q8C2×D6111yescharacteristic
431C22×C4⋊C4—611no—
432C22×C4⋊C4—1221no—
433C22×C22⋊C4—1221no—
434C22×C22⋊C4—1221no—
435C22×C42—1221no—
436#407—611no—
437#407—612no—
438#407—1221no—
439#407—1221no—
440#407C2×D6111yescharacteristic
441C2×C22⋊C8—612no—
442C2×C22⋊C8—1221no—
443C4×C22⋊C4—611no—
444C4×C22⋊C4—612no—
445C4×C22⋊C4—1221no—
446C4×C22⋊C4—1221no—
447C4×C22⋊C4C2×D6111yescharacteristic
448C2×#95—612no—
449#328—614no—
450#328—614no—
451#328—614no—
452#328C2×D6114yescomplemented
453C61C2×#150811yescharacteristic, complemented, Sylow
454C25—611no—
455C22×Q8—612no—
456C22×Q8—612no—
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×Q8—1221no—
460C22×Q8—1221no—
461C22×Q8—2444no—
462C22×Q8C4×D6111yescharacteristic, complemented
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1222no—
479C23×C4—2444no—
480C23×C4C22×D6111yescharacteristic
481C2×M16—21no—
482C2×M16—1222no—
483C2×M16—1221no—
484C2×M16—2444no—
485C22×C8—1222no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—612no—
489C22⋊Q8—612no—
490C22⋊Q8—612no—
491C22⋊Q8—612no—
492C22⋊Q8—612no—
493C22⋊Q8—612no—
494C22⋊Q8—1222no—
495C22⋊Q8—1222no—
496C22⋊Q8—1222no—
497C22⋊Q8—1222no—
498C22⋊Q8—1222no—
499C22⋊Q8—1222no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502C22⋊Q8—1221no—
503C22⋊Q8—1221no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508C22⋊Q8C4×D6112yescomplemented
509C22⋊Q8C22×D6112yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—612no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C4×D6111yescharacteristic, complemented
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1228no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1222no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—21no—
538C2×C42—1222no—
539C2×C42—1221no—
540C2×C42—2444no—
541C22⋊C8—21no—
542C22⋊C8—612no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1221no—
546C22⋊C8C22×D6112yes—
547#95—612no—
548#95—1222no—
549#95C22×D6112yes—
550C24—611no—
551C24—611no—
552C24—611no—
553C24—611no—
554C24—611no—
555C24—611no—
556C24—1224no—
557C24—1224no—
558C24—2442no—
559C24D4×D6111yescharacteristic
560C2×Q8—21no—
561C2×Q8—42no—
562C2×Q8—612no—
563C2×Q8—1222no—
564C2×Q8—1222no—
565C2×Q8—1221no—
566C2×Q8—2442no—
567C2×Q8—2444no—
568C2×Q8—2444no—
569C2×Q8—2444no—
570C2×Q8—2444no—
571C2×Q8—2444no—
572C2×Q8C2×C4×D6112yes—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—42no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1228no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2444no—
620C22×C4—2444no—
621C22×C4—2444no—
622C22×C4—2444no—
623C22×C4—2442no—
624C22×C4C2×C4×D6111yescharacteristic
625C22×C4C2×C4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630M16—42no—
631M16—2444no—
632M16—2442no—
633C2×C8—22no—
634C2×C8—1222no—
635C2×C8—2444no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—612no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C4⋊C4—1222no—
644C4⋊C4—1222no—
645C4⋊C4—1222no—
646C4⋊C4—1222no—
647C4⋊C4—1221no—
648C4⋊C4—1222no—
649C4⋊C4C2×C4×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1228no—
658C22⋊C4—1224no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C42—42no—
662C42—2442no—
663C42—2444no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—611no—
668C23—611no—
669C23—611no—
670C23—614no—
671C23—614no—
672C23—611no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—24416no—
690C23C22⋊C4×D6111yescharacteristic
691C23C22⋊C4×D6111yescharacteristic
692C23C2×D4×D6111yescharacteristic
693Q8—42no—
694Q8—42no—
695Q8—2442no—
696Q8—2444no—
697Q8—2444no—
698Q8—2442no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—611no—
713C2×C4—614no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—24416no—
742C2×C4—2444no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4C22⋊C4×D6111yescharacteristic
751C2×C4C22⋊C4×D6111yescharacteristic
752C2×C4C22×C4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C8—42no—
755C8—2442no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—44no—
764C22—612no—
765C22—612no—
766C22—612no—
767C22—612no—
768C22—612no—
769C22—1228no—
770C22—1228no—
771C22—1221no—
772C22—1221no—
773C22—1221no—
774C22—1221no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—2444no—
779C22—2444no—
780C22—2444no—
781C22—2444no—
782C22#104×D6112yes—
783C22C2×C22⋊C4×D6111yescharacteristic
784C22#137×D6112yes—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—612no—
792C4—1221no—
793C4—1221no—
794C4—1221no—
795C4—2444no—
796C4—2442no—
797C4—2442no—
798C4#99×D6112yes—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—614no—
803C2—1222no—
804C2—1222no—
805C2—2441no—
806C2C2×#99×D6111yescharacteristic
807C2#419×D6111yescharacteristic
808C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1508C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1508D61
hypocenterC61C2×#1508
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #21444340C2semidirect
5. #21444339C2semidirect
6. #21444338C2semidirect
7. #21444337C2semidirect
8. #328×D61C2semidirect
9. C61×#1508C2semidirect
10. C22×Q8×D61C4semidirect
13. C2×#14519757C4semidirect
17. C2×#14519753C4semidirect
22. C22⋊Q8×D61C4semidirect
23. C22⋊Q8×D61C4semidirect
27. C2×C4⋊C4×D61C4semidirect
42. #16839500C22semidirect
43. #16839499C22semidirect
44. #16839498C22semidirect
48. C61×#328C22semidirect
51. C22×Dic122C2×C4semidirect
56. C2×Q8×D61C2×C4semidirect
81. #14519757C2×C4semidirect
84. #14519756C2×C4semidirect
97. #14519753C2×C4semidirect
99. C2×C4⋊Dic61C2×C4semidirect
110. C4⋊C4×D61C2×C4semidirect
130. C22×Q8×C61C2×C4semidirect
135. C22⋊Q8×C61C2×C4semidirect
138. C2×C4⋊C4×C61C2×C4semidirect
402. #1508D61direct (N × H)
413. D61#1508direct (N × H)
452. #328C2×D61semidirect
453. C61C2×#1508semidirect
462. C22×Q8C4×D61semidirect
508. C22⋊Q8C4×D61semidirect
524. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
#407×D612
C4×C22⋊C4×D612
#214443402
#214443392
#214443382
#214443372
#328×D612
C61×#15082
C2×#150861