Finite Group Databasebeta

← #29696220

Subgroups — #29696220

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840413C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3#21448715C211yesmaximal, characteristic, complemented
4#21446778C211yesmaximal, characteristic, complemented
5#21446769C211yesmaximal, characteristic, complemented
6#21446246C211yesmaximal, characteristic, complemented
7#21446245C211yesmaximal, characteristic, complemented
8#21446135C211yesmaximal, characteristic, complemented
9#21446134C211yesmaximal, characteristic, complemented
10#21445904C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445633C211yesmaximal, characteristic, complemented
13C2×#16839524C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1823C211yesmaximal, characteristic, complemented
16C22×#11758222—21no—
17C23×#92418C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840413—24no—
20#16840413C418yescomplemented
21C2×#14519776C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519760—21no—
24C2×#14519755—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33#16839825—24no—
34C2×#14519706C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839659—21no—
42#16839636—21no—
43#16839634—21no—
44#16839631C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—28no—
63C2×#11758222—44no—
64C2×#11758222—44no—
65C22×Dic122—21no—
66C22×D244—21no—
67C22×D244C2311yescharacteristic
68C22×C22⋊D61—21no—
69C22×C22⋊D61D411yescharacteristic
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—41no—
83#14519776—22no—
84#14519776C2×C414yescomplemented
85#14519762—28no—
86#14519760—28no—
87#14519755—28no—
88#14519752—22no—
89#14519752C2×C414yescomplemented
90#14519751—22no—
91#14519751C2×C414yescomplemented
92#14519739—22no—
93#14519739C2×C414yescomplemented
94C4×C22⋊D61C2×C414yes—
95C4×C22⋊D61D414yes—
96#14519737—44no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—41no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—41no—
112C4⋊C4×D61C2×C414yescomplemented
113C2×C22⋊Dic61D411yescharacteristic
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519706—22no—
122#14519699—22no—
123#14519699—41no—
124#14519697—22no—
125#14519697—41no—
126#14519689—22no—
127C8×Dic61—22no—
128#14519684—21no—
129#14519684—21no—
130C23×C4×C61—21no—
131C23×C4×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61C2×C414yescomplemented
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142C22⋊C8×C61—22no—
143#95×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61—24no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61C22⋊C414yes—
166C2×C22⋊D61D814yes—
167C2×C22⋊D61SD1614yes—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—42no—
173C22×Dic61—81no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177#11758222—432no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—24no—
183C2×D244—21no—
184C2×D244—42no—
185C2×D244—42no—
186C2×D244C22×C412yes—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
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—81no—
200C2×C4×D61C22×C412yes—
201C2×C4×D61C2×D412yes—
202C2×Dic122—24no—
203C2×Dic122—42no—
204C2×Dic122—42no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C22×C412yes—
219C4⋊C4×C61C22×C412yes—
220C22⋊C4×C61—42no—
221C22⋊Dic61C22⋊C414yes—
222#11758198—24no—
223#11758198—24no—
224#11758198—24no—
225#11758198—42no—
226#11758198C22⋊C414yes—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—42no—
232C4⋊Dic61C22×C412yes—
233C4⋊Dic61#4112yescomplemented
234#11758196—24no—
235#11758196—24no—
236#11758196—42no—
237#11758196—42no—
238#11758196—81no—
239#11758196C22⋊C414yes—
240C4×Dic61—42no—
241C4×Dic61C22×C412yes—
242C4×Dic61C2×D412yes—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—44no—
249C2×#92418#4112yescomplemented
250C8×D61—44no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C2×C22⋊C412yes—
256C23×C61C2×D812yes—
257C23×C61C2×SD1612yes—
258C23×C61C22×D411yescharacteristic
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61C2×C22⋊C412yes—
271C22×D61C2×D812yes—
272C22×D61C2×SD1612yes—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—48no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61C2×C22⋊C412yes—
293C2×C4×C61C23×C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C612−1+411yescharacteristic
299C22⋊D61—48no—
300C22⋊D61#102116yescomplemented
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—84no—
315C2×Dic61C2×C22⋊C412yes—
316C2×Dic61C2×C22⋊C412yes—
317C2×Dic61C2×C22⋊C412yes—
318C2×Dic61C2×D812yes—
319C2×Dic61C2×SD1612yes—
320D244—22no—
321D244—22no—
322D244—48no—
323D244—41no—
324D244—41no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—48no—
330C4×D61—48no—
331C4×D61—84no—
332Dic122—48no—
333C8×C61—41no—
334C8×C61—41no—
335#92418—22no—
336#92418—41no—
337#22485—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61C2×#10214yes—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61#54611yescharacteristic
347C22×C61#54711yescharacteristic
348C22×C61C22×D811yescharacteristic
349C22×C61C22×SD1611yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57811yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61C2×#10214yes—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—81no—
370C4×C61—81no—
371C4×C61C4×#4111yescharacteristic
372C4×C61#52011yescharacteristic
373C4×C61#54611yescharacteristic
374C4×C61#54711yescharacteristic
375Dic61—22no—
376Dic61—22no—
377Dic61—42no—
378Dic61—42no—
379Dic61—81no—
380Dic61C2×#10214yes—
381C2×#547—611no—
382C2×C8×D4—611no—
383D4×C4⋊C4—611no—
384#1990—611no—
385#1988—611no—
386#1893—611no—
387#1893—611no—
388#1874—611no—
389#1874—611no—
390#1823—611no—
391#1823D6111yescharacteristic, complemented
392#1802—611no—
393C4×#102—611no—
394C2×#340—611no—
395C2×#340—611no—
396C2×C61—24no—
397C2×C61#233911yescharacteristic
398C2×C61C22×#10211yescharacteristic
399C2×C61#289811yescharacteristic
400C2×C61#329411yescharacteristic
401C2×C61#329811yescharacteristic
402C2×C61#333411yescharacteristic
403C2×C61#333511yescharacteristic
404D61—24no—
405D61—82no—
406C22×#41—1221no—
407C23×C8—611no—
408C23×C8—611no—
409#547—618no—
410#547—1224no—
411C2×C4⋊Q8—611no—
412C2×#123—1221no—
413C2×#123—1221no—
414C2×C22⋊Q8—1221no—
415C2×#121—611no—
416C2×#121—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C2×C4×D4—1221no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4C2×D6111yescharacteristic
424C8×D4—1224no—
425C2×C4⋊C8—611no—
426C2×#102—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8C2×D6111yescharacteristic
432C2×C4×C8—611no—
433#389—1221no—
434#385—1221no—
435#385—1221no—
436#384—611no—
437#380—611no—
438#380C2×D6111yescharacteristic
439C4×C4⋊C4—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340C2×D6111yescharacteristic
449#340C2×D6111yescharacteristic
450#340C2×D6111yescharacteristic
451#340C2×D6111yescharacteristic
452C61#2248511yescharacteristic, complemented, Sylow
453C2×#41—1228no—
454C2×#41—2444no—
455C2×#41—2444no—
456C22×Q8—1221no—
457C22×D4—611no—
458C22×D4—611no—
459C22×D4—1221no—
460C22×D4—1221no—
461C23×C4—21no—
462C23×C4—611no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4C22×D6111yescharacteristic
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C22×C8—2441no—
475C22×C8—2441no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478C4⋊Q8—614no—
479C4⋊Q8—1222no—
480#123—1228no—
481#123—1228no—
482C22⋊Q8—1228no—
483#121—614no—
484#121—614no—
485#121—1222no—
486#121—1222no—
487C4×D4—614no—
488C4×D4—614no—
489C4×D4—614no—
490C4×D4—1222no—
491C4×D4—2444no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—2441no—
509C2×C4⋊C4—2441no—
510C2×C4⋊C4C4×D6114yescomplemented
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C42—611no—
523C2×C42—1221no—
524C4⋊C8—1222no—
525#102—1222no—
526#102—1222no—
527#102—2441no—
528#102—2441no—
529C22⋊C8—22no—
530C22⋊C8—1222no—
531C4×C8—1222no—
532#95—21no—
533#95—1221no—
534#95—1221no—
535C24—611no—
536C24—1221no—
537C24D4×D6111yescharacteristic
538#41—24432no—
539C2×Q8—1224no—
540C2×Q8—2442no—
541C2×Q8—2442no—
542C2×D4—614no—
543C2×D4—614no—
544C2×D4—614no—
545C2×D4—612no—
546C2×D4—1224no—
547C2×D4—1224no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—2442no—
554C2×D4—2442no—
555C2×D4—2442no—
556C2×D4—2442no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4C2×C4×D6112yes—
593C22×C4D4×D6112yes—
594C22×C4D4×D6111yescharacteristic
595C22×C4C23×D6111yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—612no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—2444no—
609C2×C8—2444no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—614no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—4881no—
627C4⋊C4—2442no—
628C4⋊C4—2442no—
629C4⋊C4—2442no—
630C4⋊C4C2×C4×D6112yes—
631C4⋊C4C2×C4×D6112yes—
632C22⋊C4—42no—
633C22⋊C4—614no—
634C22⋊C4—614no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—2442no—
639C42—612no—
640C42—612no—
641C42—2442no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—612no—
647C23—612no—
648C23—612no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1222no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23C22⋊C4×D6112yes—
661C23D8×D6112yes—
662C23SD16×D6112yes—
663C23C2×D4×D6111yescharacteristic
664Q8—2448no—
665D4—6116no—
666D4—1222no—
667D4—1222no—
668D4—2448no—
669D4—2448no—
670D4—2441no—
671D4—2441no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4884no—
707C2×C4—4884no—
708C2×C4—2448no—
709C2×C4—2448no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4C22⋊C4×D6112yes—
718C2×C4C22×C4×D6111yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4#41×D6111yescharacteristic
721C2×C4#41×D6111yescharacteristic
722C2×C4#1451982311yescharacteristic
723C2×C4#1451982411yescharacteristic
724C8—41no—
725C8—41no—
726C8—1222no—
727C8—2441no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—614no—
735C22—1222no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—4881no—
742C22—4881no—
743C22—4881no—
744C22—4881no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22#102×D6114yes—
749C22C2×C22⋊C4×D6111yescharacteristic
750C22#1684040411yescharacteristic
751C22#1684041011yescharacteristic
752C22C2×D8×D6111yescharacteristic
753C22C2×SD16×D6111yescharacteristic
754C22#1684057111yescharacteristic
755C22#1684057811yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4—614no—
762C4—1222no—
763C4—1222no—
764C4—4881no—
765C4—2442no—
766C4—2442no—
767C4#1684023011yescharacteristic
768C4#1684024211yescharacteristic
769C4#1684040411yescharacteristic
770C4#1684041011yescharacteristic
771C2—24no—
772C2—1224no—
773C2—4882no—
774C2#2144864311yescharacteristic
775C2C2×#102×D6111yescharacteristic
776C2#2145435111yescharacteristic
777C2#2145763011yescharacteristic
778C2#2145768211yescharacteristic
779C2#2145816111yescharacteristic
780C2#2145816911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1823C2
socleC23×C61C22×D4
prime radicalC2×#16840413C2
cosocleC22×C4×C61C24
hypercenter#1823D61
hypocenterC61#22485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. #21448715C2semidirect
4. #21446778C2semidirect
5. #21446769C2semidirect
6. #21446246C2semidirect
7. #21446245C2semidirect
8. #21446135C2semidirect
9. #21446134C2semidirect
10. #21445904C2semidirect
11. #21445818C2semidirect
12. #21445633C2semidirect
13. C2×#16839524C2semidirect
14. #340×D61C2semidirect
15. C61×#1823C2semidirect
20. #16840413C4semidirect
84. #14519776C2×C4semidirect
89. #14519752C2×C4semidirect
91. #14519751C2×C4semidirect
93. #14519739C2×C4semidirect
112. C4⋊C4×D61C2×C4semidirect
136. C2×C4⋊C4×C61C2×C4semidirect
233. C4⋊Dic61#41semidirect
249. C2×#92418#41semidirect
300. C22⋊D61#102semidirect
391. #1823D61semidirect
452. C61#22485semidirect
510. 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×#168404132
C2×#168398252
#214487152
#214467782
#214467692
#214462462
#214462452
#214461352
#214461342
#214459042
#214458182
#214456332
C2×#168395242
#340×D612
C61×#18232
#2248561