Finite Group Databasebeta

← #29695492

Subgroups — #29695492

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840405C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448719C211yesmaximal, characteristic, complemented
6#21446752C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446239C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21445816C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1959C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19C22×C8×D61C2211yescharacteristic
20#16840405—24no—
21#16840405C418yescomplemented
22C2×#14519759—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519747—21no—
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519739—21no—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32C2×C22⋊C4×D61—21no—
33#16839835—24no—
34C2×C4⋊#92418C2211yescharacteristic, complemented
35#16839762—24no—
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44#102×D61—24no—
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic, complemented
47#16839658—21no—
48#16839633—21no—
49#16839633—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic, complemented
52C4×C4⋊Dic61C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#124×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic, complemented
63C61×#384C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yescomplemented
71C22×D244—21no—
72C22×D244D411yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yescomplemented
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—41no—
96#14519759—28no—
97#14519753—22no—
98#14519753C2×C414yescomplemented
99#14519750—28no—
100#14519748—22no—
101#14519748C2×C414yescomplemented
102#14519747—28no—
103C4×D244—22no—
104C4×D244C2×C414yes—
105C4×D244C2×C414yescomplemented
106C4×D244D414yes—
107#14519739—44no—
108C2×C4⋊Dic61D411yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C4⋊C4×D61—41no—
119C2×C22⋊Dic61—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198D411yescharacteristic
125C2×#11758198D411yescharacteristic
126C22⋊C4×D61—28no—
127C2×C4×Dic61—21no—
128C4⋊#92418—22no—
129#14519701—22no—
130#14519701—41no—
131#14519699—22no—
132#14519699D414yescomplemented
133#14519698—22no—
134#14519698—41no—
135#14519697—22no—
136#14519697—22no—
137#14519689—22no—
138#14519689—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146#124×C61—22no—
147#124×C61C2×C414yescomplemented
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C42×C61C2311yescharacteristic
155#103×C61—22no—
156#103×C61—41no—
157#102×C61—22no—
158#102×C61—41no—
159#97×C61—22no—
160C24×C61—21no—
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C22×C412yes—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61C22×C412yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200#11758226—28no—
201#11758226—44no—
202#11758226—44no—
203#11758226—44no—
204D4×D61—28no—
205D4×D61—44no—
206D4×D61—44no—
207D4×D61—44no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—24no—
214C2×D244—42no—
215C2×D244—42no—
216C2×D244C22⋊C414yes—
217C2×D244C22×C412yes—
218C2×D244C2×D412yes—
219C2×D244#4112yes—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×C4×D61—81no—
239C2×C4×D61—81no—
240C2×C4×D61C22×C412yes—
241C2×C4×D61C22×C412yes—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D412yes—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C2×D412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61—81no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C42×C61C22×C412yes—
259C42×C61C2×D412yes—
260C22⋊Dic61—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—42no—
264#11758198—42no—
265#11758198C22⋊C414yes—
266#11758198C22⋊C414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C22⋊C414yes—
272C4⋊Dic61C22×C412yes—
273C4⋊Dic61C2×D412yes—
274#11758196—24no—
275#11758196—42no—
276#11758196—42no—
277C4×Dic61—42no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284#11758189—44no—
285C8×D61—44no—
286C23×C61—22no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C22×D411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—48no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—48no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61C2×C22⋊C412yes—
319C22×D61C2×C22⋊C412yes—
320C22×D61AGL(1,ℤ/8)12yes—
321C22×D61#13712yes—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—41no—
329D4×C61—41no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61C2×C22⋊C412yes—
344C2×C4×C61C2×C22⋊C412yes—
345C2×C4×C61C23×C411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C22⋊D61—48no—
352C22⋊D61—84no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61C2×C22⋊C412yes—
367C2×Dic61C2×C22⋊C412yes—
368D244—28no—
369D244—22no—
370D244—22no—
371D244—22no—
372D244—48no—
373D244C4×D414yescomplemented
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—48no—
383C4×D61—84no—
384C4×D61—84no—
385C4×D61—84no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C22×C22⋊C411yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61#54611yescharacteristic
401C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C61C2×#13711yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—24no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—41no—
418C2×D61—42no—
419C2×D61—41no—
420C2×D61—42no—
421C2×D61—41no—
422C2×D61—42no—
423C2×D61—41no—
424C2×D61—42no—
425C2×D61—816no—
426C2×D61#41714yescomplemented
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—42no—
430C4×C61—81no—
431C4×C61—81no—
432C4×C61C2×C4×D411yescharacteristic
433C4×C61#51811yescharacteristic
434C4×C61D4211yescharacteristic
435C4×C61#54611yescharacteristic
436Dic61—22no—
437Dic61—22no—
438Dic61—42no—
439Dic61—42no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959D6111yescharacteristic, complemented
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—82no—
457C2×C61D4×C22⋊C411yescharacteristic
458C2×C61C2×#41711yescharacteristic
459C2×C61#289711yescharacteristic
460C2×C61#326411yescharacteristic
461C2×C61#326611yescharacteristic
462C2×C61#330611yescharacteristic
463C2×C61#331411yescharacteristic
464D61—24no—
465D61—42no—
466D61—44no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16—611no—
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124C2×D6111yescharacteristic
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—611no—
481C2×C4×D4—1221no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103C2×D6111yescharacteristic, complemented
491C2×#103C2×D6111yescharacteristic, complemented
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—1224no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97C2×D6111yescharacteristic, complemented
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384C2×D6111yescharacteristic, complemented
508#380—611no—
509#380—611no—
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8C22×D6111yescharacteristic
524C22×D4—614no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1222no—
529C22×D4—1221no—
530C22×D4—1222no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—2441no—
534C22×D4—2441no—
535C22×D4C22×D6111yescharacteristic
536C23×C4—611no—
537C23×C4—611no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1222no—
548C22×C8—1222no—
549C22×C8—2441no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—22no—
553#124C4×D6114yescomplemented
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1228no—
559#121—1222no—
560#120—1228no—
561C4×D4—614no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4—2444no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—1222no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1228no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—1222no—
594#103—22no—
595#103—41no—
596#103—1222no—
597#103—2441no—
598#102—22no—
599#102—41no—
600#102—614no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—1222no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—22no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24—611no—
615C24—1224no—
616C24—1221no—
617C24—4881no—
618C24—4881no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24—2442no—
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D6112yes—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—612no—
639C2×D4—612no—
640C2×D4—612no—
641C2×D4—614no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—1228no—
647C2×D4—1224no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2442no—
654C2×D4—2442no—
655C2×D4—2444no—
656C2×D4—2444no—
657C2×D4—2444no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4C2×C4×D6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—1224no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1224no—
682C22×C4—1221no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—4881no—
686C22×C4—4881no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4—2442no—
693C22×C4D4×D6111yescharacteristic
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2444no—
709C2×C8D4×D6112yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—81no—
716C4⋊C4—614no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1224no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—2442no—
725C4⋊C4—2442no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—614no—
729C22⋊C4—614no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C42—2442no—
736C42C2×C4×D6112yes—
737C42D4×D6112yes—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—612no—
746C23—612no—
747C23—612no—
748C23—612no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1222no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1222no—
760C23—1221no—
761C23—1222no—
762C23—4884no—
763C23—4884no—
764C23—4884no—
765C23—4884no—
766C23—4884no—
767C23—2448no—
768C23—2448no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23C2×D4×D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—614no—
783D4—1228no—
784D4—1222no—
785D4—1222no—
786D4—1222no—
787D4—4884no—
788D4—2448no—
789D4—2448no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—4884no—
820C2×C4—4884no—
821C2×C4—4884no—
822C2×C4—2448no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4C22⋊C4×D6112yes—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—614no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1224no—
859C22—1222no—
860C22—48816no—
861C22—2442no—
862C22—2441no—
863C22—2442no—
864C22—2441no—
865C22—2442no—
866C22—2441no—
867C22—2442no—
868C22—2441no—
869C22—2442no—
870C22—2442no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684039711yescharacteristic
873C22#1684040511yescharacteristic
874C22AGL(1,ℤ/8)×D6111yescharacteristic
875C22#137×D6111yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057111yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—1222no—
884C4—1222no—
885C4—4881no—
886C4—2442no—
887C4—2442no—
888C4C4×D4×D6111yescharacteristic
889C4#1684023411yescharacteristic
890C4#1684039611yescharacteristic
891C4#1684040911yescharacteristic
892C2—82no—
893C2—1224no—
894C2—2442no—
895C2—2444no—
896C2#2144864011yescharacteristic
897C2#417×D6111yescharacteristic
898C2#2145434311yescharacteristic
899C2#2145729811yescharacteristic
900C2#2145732811yescharacteristic
901C2#2145777911yescharacteristic
902C2#2145789911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1959C2
socleC23×C61C22×D4
prime radicalC2×#16840405C2
cosocleC22×C4×C61C24
hypercenter#1959D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839762C2semidirect
4. C2×#102×D61C2semidirect
5. #21448719C2semidirect
6. #21446752C2semidirect
7. #21446254C2semidirect
8. #21446239C2semidirect
9. #21446133C2semidirect
10. #21446123C2semidirect
11. #21445816C2semidirect
12. #21445758C2semidirect
13. #21445748C2semidirect
14. #21445645C2semidirect
15. C61×#1959C2semidirect
18. C22×#11758189C22semidirect
21. #16840405C4semidirect
31. C2×C4⋊C4×D61C22semidirect
34. C2×C4⋊#92418C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519701C22semidirect
46. C2×#14519689C22semidirect
51. #16839619C22semidirect
52. C4×C4⋊Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#103×C61C22semidirect
59. C2×#103×C61C22semidirect
62. C2×#97×C61C22semidirect
63. C61×#384C22semidirect
70. C2×#11758226C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
98. #14519753C2×C4semidirect
101. #14519748C2×C4semidirect
105. C4×D244C2×C4semidirect
132. #14519699D4semidirect
147. #124×C61C2×C4semidirect
373. D244C4×D4semidirect
426. C2×D61#417semidirect
447. #1959D61semidirect
490. C2×#103C2×D61semidirect
491. C2×#103C2×D61semidirect
503. C2×#97C2×D61semidirect
507. #384C2×D61semidirect
515. C61#22419semidirect
553. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404052
C2×#168398352
C2×#168397622
C2×#102×D612
#214487192
#214467522
#214462542
#214462392
#214461332
#214461232
#214458162
#214457582
#214457482
#214456452
C61×#19592
#2241961