Finite Group Databasebeta

← #29695486

Subgroups — #29695486

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×#16840400C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446632C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446239C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic, complemented
18C22×C8×D61C2211yescharacteristic
19#16840400—24no—
20#16840400C418yescomplemented
21C2×#14519766C2211yescharacteristic
22C2×#14519760—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519749—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C22×C4⋊Dic61C2211yescharacteristic, complemented
31C2×C4⋊C4×D61C2211yescharacteristic
32C22×#11758198—21no—
33#16839836—24no—
34C2×#14519706C2211yescharacteristic, complemented
35#16839763—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×#14519687C2211yescharacteristic, complemented
47#16839659—21no—
48#16839636—21no—
49#16839634—21no—
50#16839631C2211yescharacteristic, complemented
51#16839619C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61D411yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—41no—
73C2×D4×D61—41no—
74C2×D4×D61C2×C414yescomplemented
75C23×Dic61—21no—
76C23×Dic61—21no—
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C2×#11758194—22no—
80C2×#11758194—22no—
81C2×#11758194—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61—41no—
87#14519766—22no—
88#14519766C2×C414yescomplemented
89#14519760—28no—
90#14519753—22no—
91#14519753C2×C414yescomplemented
92#14519751—22no—
93#14519751C2×C414yescomplemented
94#14519749—28no—
95#14519745—28no—
96D4×Dic61—22no—
97D4×Dic61C2×C414yescomplemented
98C4×C22⋊D61C2×C414yes—
99C4×C22⋊D61D414yes—
100#14519737—44no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C4⋊C4×D61—22no—
113C4⋊C4×D61—41no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—28no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519701—22no—
127#14519701—22no—
128#14519699—22no—
129#14519699—41no—
130#14519698—22no—
131#14519698D414yescomplemented
132#14519697—22no—
133#14519697—41no—
134#14519689—22no—
135#14519687—22no—
136#14519684—21no—
137#14519684—21no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—41no—
142C2×#41×C61—41no—
143C2×#41×C61C2×C414yescomplemented
144C22×Q8×C61C2311yescharacteristic
145C22×D4×C61—21no—
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154#103×C61—41no—
155#103×C61—41no—
156#102×C61—22no—
157#102×C61—22no—
158C22⋊C8×C61—22no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C23×D61C2×D411yescharacteristic
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61C22×C412yes—
188C2×D4×C61C2×D412yes—
189C2×D4×C61#4112yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—42no—
199C22×C4×C61—42no—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61—81no—
212C2×C22⋊D61C22⋊C414yes—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—21no—
217C22×Dic61—42no—
218C22×Dic61—42no—
219C22×Dic61—81no—
220C22×Dic61—81no—
221C22×Dic61—81no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225D4×D61—28no—
226D4×D61—44no—
227D4×D61—44no—
228D4×D61—44no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22×C412yes—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—81no—
242C2×C4×D61C22×C412yes—
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×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C22⋊C4×C61—42no—
255C22⋊Dic61—24no—
256C22⋊Dic61C22⋊C414yes—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—42no—
262#11758198C22⋊C414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—42no—
268C4⋊Dic61C22×C412yes—
269C4⋊Dic61C2×D412yes—
270#11758196—24no—
271#11758196—42no—
272#11758196—42no—
273#11758196—81no—
274#11758196C22⋊C414yes—
275C4×Dic61—42no—
276C4×Dic61C22×C412yes—
277C4×Dic61C2×D412yes—
278#11758194—44no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418C2×D412yes—
285C8×D61—44no—
286C23×C61—22no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—48no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—84no—
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—22no—
329D4×C61—48no—
330D4×C61C4×D414yescomplemented
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—48no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61C2×C22⋊C412yes—
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C22⋊D61—28no—
355C22⋊D61—48no—
356C22⋊D61—84no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—84no—
373C2×Dic61—84no—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61C2×C22⋊C412yes—
376C2×Dic61C2×C22⋊C412yes—
377D244—22no—
378D244—22no—
379D244—41no—
380D244—41no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—84no—
386C8×C61—41no—
387C8×C61—41no—
388#92418—22no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—24no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—41no—
403C22×C61—42no—
404C22×C61—41no—
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61C2×#13711yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—816no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61#41714yescomplemented
427C4×C61—22no—
428C4×C61—42no—
429C4×C61—81no—
430C4×C61—81no—
431C4×C61C2×C4×D411yescharacteristic
432C4×C61#51811yescharacteristic
433C4×C61D4211yescharacteristic
434C4×C61#54611yescharacteristic
435Dic61—22no—
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#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788D6111yescharacteristic, complemented
454#1786—611no—
455#1762—611no—
456C2×C61—44no—
457C2×C61—42no—
458C2×C61D4×C22⋊C411yescharacteristic
459C2×C61C2×#41711yescharacteristic
460C2×C61#289711yescharacteristic
461C2×C61#326411yescharacteristic
462C2×C61#326611yescharacteristic
463C2×C61#330611yescharacteristic
464C2×C61#331411yescharacteristic
465D61—24no—
466D61—82no—
467C22×#41C2×D6111yescharacteristic
468C23×D4—611no—
469C22×M16—611no—
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124—611no—
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⋊C8C2×D6111yescharacteristic, complemented
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380C2×D6111yescharacteristic, complemented
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C4×D6114yescomplemented
523C22×Q8C22×D6111yescharacteristic
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—614no—
527C22×D4—611no—
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—21no—
537C23×C4—611no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
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—614no—
553#124—1222no—
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—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
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—611no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—1228no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—41no—
595#103—41no—
596#103—1222no—
597#103—1222no—
598#102—22no—
599#102—22no—
600#102—614no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—22no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—21no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24—1224no—
615C24—1221no—
616C24—4881no—
617C24—4881no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24D4×D6111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D6112yes—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—614no—
640C2×D4—612no—
641C2×D4—1224no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1228no—
645C2×D4—1224no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4C2×C4×D6112yes—
659C2×D4D4×D6112yes—
660C2×D4#1175822412yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—1224no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—4881no—
685C22×C4—4881no—
686C22×C4—4881no—
687C22×C4—4881no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4C2×C4×D6112yes—
693C22×C4D4×D6112yes—
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—21no—
703C2×C8—612no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2444no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—614no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—1224no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—4881no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4—2442no—
726C22⋊C4—42no—
727C22⋊C4—614no—
728C22⋊C4—614no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—612no—
752C23—612no—
753C23—612no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1222no—
759C23—4884no—
760C23—4884no—
761C23—4884no—
762C23—4884no—
763C23—4884no—
764C23—2448no—
765C23—2448no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23C22⋊C4×D6112yes—
773C23C2×D4×D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—1228no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—2448no—
787D4—2441no—
788D4—2441no—
789D4#1451973714yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—4884no—
822C2×C4—4884no—
823C2×C4—4884no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4C2×#1175822411yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982211yescharacteristic
838C8—41no—
839C8—41no—
840C8—1222no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—24no—
845C22—22no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—41no—
850C22—42no—
851C22—41no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—42no—
856C22—614no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—48816no—
864C22—4881no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684039411yescharacteristic
873C22#1684039911yescharacteristic
874C22AGL(1,ℤ/8)×D6111yescharacteristic
875C22#137×D6111yescharacteristic
876C22#1684056411yescharacteristic
877C22#1684056911yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—1222no—
883C4—1222no—
884C4—1222no—
885C4—4881no—
886C4—2442no—
887C4—2442no—
888C4C2×#1451973711yescharacteristic
889C4#1684023511yescharacteristic
890C4#1684039411yescharacteristic
891C4#1684039911yescharacteristic
892C2—42no—
893C2—44no—
894C2—1224no—
895C2—4882no—
896C2#2144863511yescharacteristic
897C2#417×D6111yescharacteristic
898C2#2145434111yescharacteristic
899C2#2145730211yescharacteristic
900C2#2145732711yescharacteristic
901C2#2145777311yescharacteristic
902C2#2145789311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839836C2semidirect
3. C2×#16839763C2semidirect
4. C2×#102×D61C2semidirect
5. #21448715C2semidirect
6. #21446748C2semidirect
7. #21446632C2semidirect
8. #21446255C2semidirect
9. #21446239C2semidirect
10. #21446134C2semidirect
11. #21446123C2semidirect
12. #21445817C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C61×#1788C2semidirect
17. C22×#11758194C22semidirect
20. #16840400C4semidirect
30. C22×C4⋊Dic61C22semidirect
34. C2×#14519706C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519701C22semidirect
46. C2×#14519687C22semidirect
50. #16839631C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#103×C61C22semidirect
59. C2×#103×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
74. C2×D4×D61C2×C4semidirect
88. #14519766C2×C4semidirect
91. #14519753C2×C4semidirect
93. #14519751C2×C4semidirect
97. D4×Dic61C2×C4semidirect
131. #14519698D4semidirect
143. C2×#41×C61C2×C4semidirect
330. D4×C61C4×D4semidirect
426. C2×D61#417semidirect
453. #1788D61semidirect
490. C2×#103C2×D61semidirect
491. C2×#103C2×D61semidirect
502. C2×C22⋊C8C2×D61semidirect
509. #380C2×D61semidirect
515. C61#22419semidirect
522. C2×#41C4×D61semidirect
789. D4#14519737semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#168398362
C2×#168397632
C2×#102×D612
#214487152
#214467482
#214466322
#214462552
#214462392
#214461342
#214461232
#214458172
#214457482
#214456462
C61×#17882
#2241961