Finite Group Databasebeta

← #29695499

Subgroups — #29695499

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×#16840403C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C22×#14519699C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446632C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446135C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19#16840403—24no—
20#16840403C418yescomplemented
21C2×#14519766C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519752—21no—
24C2×#14519752C2211yescharacteristic
25C2×#14519747—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C2×C22⋊C4×D61—21no—
32#16839833—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839762—24no—
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519699—24no—
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×#14519689C2211yescharacteristic, complemented
48C2×#14519687C2211yescharacteristic, complemented
49#16839659—21no—
50#16839636—21no—
51#16839634—21no—
52#16839631C2211yescharacteristic, complemented
53#16839619C2211yescharacteristic, complemented
54C4⋊C4×Dic61C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yescomplemented
71C22×D244—22no—
72C22×D244—22no—
73C22×D244—21no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—21no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244C2×C414yescomplemented
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519766—22no—
94#14519766C2×C414yescomplemented
95#14519762—28no—
96#14519752—22no—
97#14519752—28no—
98#14519752C2×C414yescomplemented
99#14519747—28no—
100#14519739—22no—
101#14519739C2×C414yescomplemented
102C4×C22⋊D61C2×C414yes—
103C4×C22⋊D61D414yes—
104#14519737—44no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C4⋊C4×D61—22no—
115C4⋊C4×D61—41no—
116C2×C22⋊Dic61D411yescharacteristic
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C22⋊C4×D61—28no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519706—22no—
127#14519701—22no—
128#14519701—41no—
129#14519699—22no—
130#14519699—22no—
131#14519699—22no—
132#14519699D414yescomplemented
133#14519697—22no—
134#14519697—22no—
135#14519697—41no—
136#14519697—41no—
137C22⋊#92418—22no—
138#14519689—22no—
139#14519687—22no—
140#14519684—21no—
141#14519684—21no—
142C22×Q8×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22⋊Q8×C61—22no—
150C22⋊Q8×C61C2×C414yescomplemented
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157#103×C61—22no—
158#103×C61—41no—
159#95×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
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
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C22×C412yes—
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×C61C22×C412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61C22⋊C414yes—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—81no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200#11758226—28no—
201#11758226—44no—
202#11758226—44no—
203#11758226—44no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—28no—
212C2×D244—24no—
213C2×D244—24no—
214C2×D244—21no—
215C2×D244—24no—
216C2×D244—44no—
217C2×D244—44no—
218C2×D244—44no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244—42no—
222C2×D244—42no—
223C2×D244—81no—
224C2×D244—81no—
225C2×D244C22×C412yes—
226C2×D244C22×C412yes—
227C2×D244C2×D412yes—
228C2×D244#4112yes—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—81no—
240C2×C4×D61—81no—
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—44no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22×C412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—42no—
260C22⋊Dic61C22⋊C414yes—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—42no—
266#11758198C22⋊C414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—42no—
271C4⋊Dic61C2×D412yes—
272#11758196—42no—
273#11758196—42no—
274#11758196—81no—
275#11758196C22⋊C414yes—
276C4×Dic61—42no—
277C4×Dic61C22×C412yes—
278C4×Dic61C2×D412yes—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285#11758189—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61C2×C22⋊C412yes—
291C23×C61AGL(1,ℤ/8)12yes—
292C23×C61#13712yes—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—21no—
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—22no—
304C22×D61—48no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—48no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61C2×C22⋊C412yes—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—41no—
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×C61—41no—
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—28no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—84no—
365C2×Dic61C2×C22⋊C412yes—
366C2×Dic61C2×C22⋊C412yes—
367C2×Dic61C2×C22⋊C412yes—
368D244—22no—
369D244—22no—
370D244—22no—
371D244—22no—
372D244—22no—
373D244—48no—
374D244—48no—
375D244—41no—
376D244—41no—
377D244—84no—
378D244C4×D414yescomplemented
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—48no—
384C4×D61—84no—
385C4×D61—84no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61#41714yescomplemented
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—24no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—41no—
414C2×D61—42no—
415C2×D61—41no—
416C2×D61—42no—
417C2×D61—41no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C4×C61—22no—
428C4×C61—42no—
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—22no—
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#1892D6111yescharacteristic, complemented
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—24no—
457C2×C61D4×C22⋊C411yescharacteristic
458C2×C61C2×#41711yescharacteristic
459C2×C61#289711yescharacteristic
460C2×C61#326411yescharacteristic
461C2×C61#326611yescharacteristic
462C2×C61#330611yescharacteristic
463C2×C61#331411yescharacteristic
464D61—42no—
465D61—44no—
466D61—82no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16—611no—
470C23×C8C2×D6111yescharacteristic
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8C2×D6111yescharacteristic
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—611no—
499C2×#102—611no—
500C2×#102—1224no—
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380C2×D6111yescharacteristic
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340C2×D6111yescharacteristic, complemented
514#340C2×D6111yescharacteristic, complemented
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—611no—
525C22×D4—614no—
526C22×D4—611no—
527C22×D4—611no—
528C22×D4—1222no—
529C22×D4—1222no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1222no—
534C22×D4—2441no—
535C22×D4—2441no—
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—22no—
556C22⋊Q8C4×D6114yescomplemented
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—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—2441no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—22no—
595#103—41no—
596#103—1222no—
597#103—2441no—
598#102—614no—
599#102—1222no—
600#102—1222no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—21no—
610#95—1221no—
611#95—1221no—
612C24—611no—
613C24—1221no—
614C24—1224no—
615C24—1221no—
616C24—4881no—
617C24—4881no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24D4×D6111yescharacteristic
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—614no—
634C2×D4—612no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—1228no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1222no—
642C2×D4—1222no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1224no—
652C2×D4—4881no—
653C2×D4—4881no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2444no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4—2442no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—1224no—
675C22×C4—1224no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—4881no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—4881no—
686C22×C4—2442no—
687C22×C4—2442no—
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—44no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8D4×D6112yes—
710C4⋊C4—21no—
711C4⋊C4—24no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—614no—
717C4⋊C4—612no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—4881no—
722C4⋊C4—2442no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4C2×C4×D6112yes—
726C22⋊C4—24no—
727C22⋊C4—42no—
728C22⋊C4—614no—
729C22⋊C4—614no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—612no—
743C23—1222no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1222no—
750C23—1221no—
751C23—1222no—
752C23—1222no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—4884no—
757C23—4884no—
758C23—2448no—
759C23—2448no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23C22⋊C4×D6112yes—
771C23#1451980412yes—
772C23#1451980912yes—
773C23C2×D4×D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—614no—
779D4—1228no—
780D4—1222no—
781D4—1222no—
782D4—1222no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—2448no—
787D4—2448no—
788D4—2441no—
789D4—2441no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
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—41no—
807C2×C4—41no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—4884no—
823C2×C4—4884no—
824C2×C4—4884no—
825C2×C4—2448no—
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×C4#41×D6111yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—1222no—
849C22—1222no—
850C22—1224no—
851C22—1222no—
852C22—48816no—
853C22—4881no—
854C22—4881no—
855C22—4881no—
856C22—4881no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2441no—
862C22—2442no—
863C22—2441no—
864C22—2442no—
865C22—2441no—
866C22—2442no—
867C22—2441no—
868C22—2442no—
869C22—2442no—
870C22#1683976214yescomplemented
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684039611yescharacteristic
873C22#1684040111yescharacteristic
874C22C2×#1451980411yescharacteristic
875C22C2×#1451980911yescharacteristic
876C22#1684056411yescharacteristic
877C22#1684056911yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—1222no—
884C4—1222no—
885C4—1222no—
886C4—4881no—
887C4—2442no—
888C4C4×D4×D6111yescharacteristic
889C4#1684023411yescharacteristic
890C4#1684039411yescharacteristic
891C4#1684040411yescharacteristic
892C2—24no—
893C2—4882no—
894C2—2442no—
895C2—2444no—
896C2#2144863711yescharacteristic
897C2C2×#1683976211yescharacteristic
898C2#2145434111yescharacteristic
899C2#2145729611yescharacteristic
900C2#2145732611yescharacteristic
901C2#2145778611yescharacteristic
902C2#2145790611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC2×#16840403C2
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839762C2semidirect
4. C22×#14519699C2semidirect
5. #21448715C2semidirect
6. #21446748C2semidirect
7. #21446632C2semidirect
8. #21446256C2semidirect
9. #21446135C2semidirect
10. #21446127C2semidirect
11. #21445818C2semidirect
12. #21445758C2semidirect
13. #21445749C2semidirect
14. #21445643C2semidirect
15. C61×#1892C2semidirect
18. C22×#11758189C22semidirect
20. #16840403C4semidirect
30. C2×C4⋊C4×D61C22semidirect
33. C2×#14519706C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
47. C2×#14519689C22semidirect
48. C2×#14519687C22semidirect
52. #16839631C22semidirect
53. #16839619C22semidirect
54. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
70. C2×#11758226C2×C4semidirect
79. C22×D244C2×C4semidirect
94. #14519766C2×C4semidirect
98. #14519752C2×C4semidirect
101. #14519739C2×C4semidirect
132. #14519699D4semidirect
150. C22⋊Q8×C61C2×C4semidirect
378. D244C4×D4semidirect
397. C22×C61#417semidirect
449. #1892D61semidirect
490. C2×#103C2×D61semidirect
491. C2×#103C2×D61semidirect
513. #340C2×D61semidirect
514. #340C2×D61semidirect
515. C61#22419semidirect
556. C22⋊Q8C4×D61semidirect
870. C22#16839762semidirect

Maximal subgroups

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

subgroupindex
C2×#168404032
C2×#168398332
C2×#168397622
C22×#145196992
#214487152
#214467482
#214466322
#214462562
#214461352
#214461272
#214458182
#214457582
#214457492
#214456432
C61×#18922
#2241961