Finite Group Databasebeta

← #29717645

Subgroups — #29717645

Order 15616.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
2C2×#16839988C211yesmaximal, characteristic, complemented
3C2×#16839899C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21449255C211yesmaximal, characteristic
6#21447064C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21446900C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446176C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21446108C211yesmaximal, characteristic, complemented
13#21446089C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#448C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19Q8×C22⋊D61—24no—
20Q8×C22⋊D61—24no—
21C2×#14519775—21no—
22C2×#14519775C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519753—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519748—21no—
28C2×#14519748C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×C22⋊D61—21no—
31C2×C4×C22⋊D61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33#16839988—24no—
34#16839899—24no—
35C2×#14519709C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44C2×#14519698C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47#16839685—21no—
48#16839676—21no—
49#16839665C2211yescharacteristic
50#16839661C2211yescharacteristic
51#16839638—21no—
52#16839622C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C22×SD16×C61C2211yescharacteristic
59C22×SD16×C61C2211yescharacteristic
60C2×#121×C61C2211yescharacteristic
61C61×#448—24no—
62C2×#103×C61C2211yescharacteristic
63C2×#103×C61C2211yescharacteristic
64C2×C22⋊C8×C61C2211yescharacteristic
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—41no—
71C2×Q8×D61—41no—
72C2×Q8×D61D414yescomplemented
73C22×C22⋊D61—21no—
74C22×C22⋊D61D411yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758200—22no—
79C2×#11758200—41no—
80C2×#11758200—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86#14519775—28no—
87#14519775—22no—
88#14519775—22no—
89#14519756—28no—
90#14519756—22no—
91#14519756—22no—
92#14519753—28no—
93#14519753—22no—
94#14519753D414yescomplemented
95#14519748—22no—
96#14519748—22no—
97#14519748—44no—
98Q8×Dic61—22no—
99Q8×Dic61—22no—
100C4×C22⋊D61—28no—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C4⋊C4×D61—22no—
115C4⋊C4×D61—41no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×C22⋊Dic61D411yescharacteristic
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519709—22no—
127#14519702—22no—
128#14519702—22no—
129#14519701—22no—
130#14519701—22no—
131#14519701—22no—
132#14519701—41no—
133#14519700—22no—
134#14519698—22no—
135C22⋊#92418—41no—
136#14519689—22no—
137#14519684—21no—
138#14519684—21no—
139C22×Q8×C61—22no—
140C22×Q8×C61—22no—
141C22×Q8×C61—21no—
142C22×Q8×C61—22no—
143C22×Q8×C61—22no—
144C22×Q8×C61—41no—
145C22×Q8×C61—41no—
146C22×Q8×C61C2311yescharacteristic
147C22×Q8×C61C2311yescharacteristic
148C22×D4×C61—21no—
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C23×C4×C61C2311yescharacteristic
152C2×SD16×C61—22no—
153C2×SD16×C61—22no—
154C2×SD16×C61—22no—
155C2×SD16×C61—22no—
156C2×SD16×C61—22no—
157C2×SD16×C61—41no—
158C22×C8×C61C2311yescharacteristic
159C22×C8×C61C2311yescharacteristic
160#121×C61—22no—
161#121×C61—41no—
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—21no—
164#103×C61—22no—
165#103×C61D414yescomplemented
166C22⋊C8×C61—22no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×Q8×C61—24no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—42no—
180C2×Q8×C61—42no—
181C2×Q8×C61—44no—
182C2×Q8×C61—44no—
183C2×Q8×C61—44no—
184C2×Q8×C61—44no—
185C2×Q8×C61C2×D412yes—
186C2×Q8×C61C2×D412yes—
187C2×Q8×C61C2×D412yes—
188C2×Q8×C61#4112yes—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—81no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—22no—
213C2×C22⋊D61—22no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61SD1614yescomplemented
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225Q8×D61—28no—
226Q8×D61—44no—
227Q8×D61—44no—
228Q8×D61—44no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—24no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—81no—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2×D412yes—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—42no—
248C2×Dic122—42no—
249C2×Dic122C2×D412yes—
250SD16×C61—44no—
251SD16×C61—44no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61C2×D412yes—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2×D412yes—
260C22⋊C4×C61—42no—
261C22⋊Dic61—24no—
262C22⋊Dic61—22no—
263C22⋊Dic61—42no—
264C22⋊Dic61—42no—
265C22⋊Dic61—42no—
266C22⋊Dic61—81no—
267#11758200—44no—
268#11758198—24no—
269#11758198—22no—
270C4⋊Dic61—24no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—42no—
277C4⋊Dic61C2×D412yes—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—22no—
283#11758196—42no—
284C4×Dic61—24no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C8×D61—44no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61C2×SD1612yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61#12012yes—
314C22×D61C2×SD1612yes—
315C22×D61#13712yes—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61—48no—
322Q8×C61—41no—
323Q8×C61—41no—
324Q8×C61#12114yescomplemented
325D4×C61—41no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—84no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
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×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C22⋊D61—28no—
354C22⋊D61—84no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61#12012yes—
375C2×Dic61C2×SD1612yes—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—48no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—48no—
385Dic122—41no—
386Dic122—41no—
387C8×C61—22no—
388C8×C61—41no—
389#92418—41no—
390#92418—41no—
391#24429—611nomaximal, Sylow
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61C2×#12011yescharacteristic
407C22×C61D4211yescharacteristic
408C22×C61#54611yescharacteristic
409C22×C61C22×SD1611yescharacteristic
410C22×C61C2×#13711yescharacteristic
411C22×C61#57711yescharacteristic
412C22×C61#57811yescharacteristic
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61#44814yescomplemented
420C4×C61—24no—
421C4×C61—41no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61C2×#12111yescharacteristic
425C4×C61#53411yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—42no—
431Dic61—41no—
432Dic61—42no—
433Dic61—81no—
434Dic61—81no—
435C2×D4×Q8—611no—
436C2×#465—611no—
437C2×#448—611no—
438C2×#448D6111yescharacteristic, complemented
439C22×#103—611no—
440#2416—611no—
441#2043—611no—
442#2035—611no—
443#2013—611no—
444#2000—611no—
445#1880—611no—
446#1872—611no—
447#1869—611no—
448#1865—611no—
449#1787—611no—
450C2×C61—42no—
451C2×C61—161no—
452C2×C61#241011yescharacteristic
453C2×C61C2×#44811yescharacteristic
454C2×C61#301311yescharacteristic
455C2×C61#327011yescharacteristic
456C2×C61D4×SD1611yescharacteristic
457C2×C61#329811yescharacteristic
458C2×C61#332011yescharacteristic
459D61—24no—
460C23×Q8—611no—
461C23×Q8C2×D6111yescharacteristic
462C22×SD16—611no—
463C22×SD16C2×D6111yescharacteristic
464C22×SD16C2×D6111yescharacteristic
465C23×C8—611no—
466D4×Q8—1224no—
467D4×Q8—1224no—
468C2×C4⋊Q8—611no—
469C2×C4⋊Q8—1221no—
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—611no—
472C2×C22⋊Q8—1221no—
473C2×C22⋊Q8—1221no—
474C2×#121—611no—
475C2×#121—1221no—
476C2×#121C2×D6111yescharacteristic
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×C4×D4—1221no—
480C22×C4⋊C4—611no—
481#465—1224no—
482#448—24no—
483#448—1224no—
484C2×#106—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#103—1224no—
493C2×#103C2×D6111yescharacteristic
494C2×#103C2×D6111yescharacteristic
495C2×#102—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8C2×D6111yescharacteristic
499#396—1221no—
500#394—1221no—
501#390—611no—
502#389—611no—
503#386—1221no—
504#380—611no—
505#340—611no—
506#340—611no—
507#336—611no—
508#336—611no—
509C61#2442911yescharacteristic, complemented, Sylow
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—21no—
513C22×Q8—22no—
514C22×Q8—22no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—614no—
518C22×Q8—611no—
519C22×Q8—1221no—
520C22×Q8—1222no—
521C22×Q8—1222no—
522C22×Q8—1222no—
523C22×Q8—2441no—
524C22×Q8—2441no—
525C22×Q8C22×D6111yescharacteristic
526C22×Q8C22×D6111yescharacteristic
527C22×D4—21no—
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4C22×D6111yescharacteristic
531C23×C4—21no—
532C23×C4—611no—
533C23×C4—1221no—
534C23×C4—1221no—
535C23×C4C22×D6111yescharacteristic
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—1222no—
543C2×SD16—2441no—
544C2×SD16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1222no—
548C22×C8—1222no—
549C22×C8—2441no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552C4⋊Q8—1222no—
553C4⋊Q8—1228no—
554C4⋊Q8—1222no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557C22⋊Q8—1222no—
558C22⋊Q8—1228no—
559C22⋊Q8—1222no—
560C22⋊Q8—1228no—
561#121—22no—
562#121—41no—
563#121—1222no—
564#121—1222no—
565#121—2444no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×D4—1222no—
569C4×D4—1222no—
570C4×D4—1228no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—2441no—
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—611no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C42—611no—
595C2×C42—1221no—
596#106—1222no—
597#103—22no—
598#103—1222no—
599#103—1222no—
600#103—1222no—
601#103—1222no—
602#103—1222no—
603#103—1222no—
604#103—2441no—
605#103C22⋊D6114yescomplemented
606#102—1222no—
607C22⋊C8—22no—
608C22⋊C8—1222no—
609C22⋊C8—2441no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24D4×D6111yescharacteristic
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—42no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—612no—
631C2×Q8—1224no—
632C2×Q8—1221no—
633C2×Q8—1228no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8—2442no—
639C2×Q8—2442no—
640C2×Q8—2444no—
641C2×Q8—2444no—
642C2×Q8—2444no—
643C2×Q8D4×D6112yes—
644C2×Q8D4×D6112yes—
645C2×Q8#1175822412yes—
646C2×Q8C2×C22⋊D6112yes—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—81no—
656C2×D4—614no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—2442no—
660C2×D4—2442no—
661C2×D4—2442no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—611no—
679C22×C4—1224no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—4881no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4—2442no—
693C22×C4D4×D6111yescharacteristic
694C22×C4C23×D6111yescharacteristic
695SD16—44no—
696SD16—44no—
697SD16—2444no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2444no—
710C2×C8C2×C22⋊D6112yes—
711C4⋊C4—21no—
712C4⋊C4—612no—
713C4⋊C4—1222no—
714C4⋊C4—1224no—
715C4⋊C4—1224no—
716C4⋊C4—1224no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—2442no—
725C4⋊C4—2442no—
726C4⋊C4C2×C22⋊D6112yes—
727C22⋊C4—42no—
728C22⋊C4—1222no—
729C22⋊C4—1224no—
730C22⋊C4—1222no—
731C22⋊C4—1224no—
732C22⋊C4—4881no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C22⋊C4—2442no—
736C42—1224no—
737C42—1221no—
738C42—1221no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—612no—
753C23—612no—
754C23—612no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23SD16×D6112yes—
760C23C2×D4×D6111yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—48no—
767Q8—41no—
768Q8—41no—
769Q8—1222no—
770Q8—1222no—
771Q8—2448no—
772Q8—2441no—
773Q8—2441no—
774Q8#1451974814yescomplemented
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—84no—
780D4—1228no—
781D4—4884no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1221no—
811C2×C4—1222no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—4884no—
815C2×C4—2448no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4C22×C22⋊D6111yescharacteristic
829C2×C4C2×#1175822411yescharacteristic
830C2×C4#1451982211yescharacteristic
831C2×C4#1451982211yescharacteristic
832C8—22no—
833C8—41no—
834C8—2441no—
835C8—2441no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—614no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22#120×D6111yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684039911yescharacteristic
860C22C2×SD16×D6111yescharacteristic
861C22#137×D6111yescharacteristic
862C22#1684056811yescharacteristic
863C22#1684057811yescharacteristic
864C4—24no—
865C4—42no—
866C4—41no—
867C4—42no—
868C4—1222no—
869C4—1222no—
870C4—4881no—
871C4—4881no—
872C4—2441no—
873C4—2442no—
874C4—2442no—
875C4C2×#1451974811yescharacteristic
876C4#1684032211yescharacteristic
877C4D4×C22⋊D6111yescharacteristic
878C4#1684039911yescharacteristic
879C2—42no—
880C2—161no—
881C2—1224no—
882C2#2144918911yescharacteristic
883C2#448×D6111yescharacteristic
884C2#2145512911yescharacteristic
885C2#2145738311yescharacteristic
886C2SD16×C22⋊D6111yescharacteristic
887C2#2145767711yescharacteristic
888C2#2145798311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radical#21449255C2
hypercenterC2×#448D61
hypocenterC61#24429
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D61C2semidirect
2. C2×#16839988C2semidirect
3. C2×#16839899C2semidirect
4. C2×#103×D61C2semidirect
6. #21447064C2semidirect
7. #21447016C2semidirect
8. #21446900C2semidirect
9. #21446822C2semidirect
10. #21446176C2semidirect
11. #21446123C2semidirect
12. #21446108C2semidirect
13. #21446089C2semidirect
14. #21445754C2semidirect
15. C2×C61×#448C2semidirect
72. C2×Q8×D61D4semidirect
94. #14519753D4semidirect
165. #103×C61D4semidirect
217. C2×C22⋊D61SD16semidirect
324. Q8×C61#121semidirect
419. C2×D61#448semidirect
438. C2×#448D61semidirect
509. C61#24429semidirect
605. #103C22⋊D61semidirect
774. Q8#14519748semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D612
C2×#168399882
C2×#168398992
C2×#103×D612
#214492552
#214470642
#214470162
#214469002
#214468222
#214461762
#214461232
#214461082
#214460892
#214457542
C2×C61×#4482
#2442961