Finite Group Databasebeta

← #29717643

Subgroups — #29717643

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×#16839991C211yesmaximal, characteristic, complemented
3C2×#16839902C211yesmaximal, characteristic, complemented
4C2×#16839901C211yesmaximal, characteristic, complemented
5#21449253C211yesmaximal, characteristic
6#21447064C211yesmaximal, characteristic, complemented
7#21447014C211yesmaximal, characteristic, complemented
8#21446903C211yesmaximal, characteristic, complemented
9#21446821C211yesmaximal, characteristic, complemented
10#21446172C211yesmaximal, characteristic, complemented
11#21446126C211yesmaximal, characteristic, complemented
12#21446111C211yesmaximal, characteristic, complemented
13#21446089C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C22×#103×C61C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20Q8×C22⋊D61—24no—
21Q8×C22⋊D61—24no—
22C2×#14519775—21no—
23C2×#14519775C2211yescharacteristic
24C2×#14519756—21no—
25C2×#14519756C2211yescharacteristic
26C2×#14519753—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519752C2211yescharacteristic
29C2×#14519751—21no—
30C2×#14519751C2211yescharacteristic
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×C22⋊D61—21no—
33C2×C4×C22⋊D61C2211yescharacteristic
34#16839991—24no—
35#16839902—24no—
36#16839901—24no—
37C2×#14519709C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47#16839684—21no—
48#16839679—21no—
49#16839663C2211yescharacteristic
50#16839661C2211yescharacteristic
51#16839641—21no—
52#16839619C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C23×C8×C61C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C2×#103×C61—24no—
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#103×C61C2211yescharacteristic
64C2×#103×C61C2211yescharacteristic
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—41no—
72C2×Q8×D61—41no—
73C22×D244—21no—
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C2×#11758190—22no—
80C2×#11758190—22no—
81C2×#11758190—41no—
82C2×#11758201—22no—
83C2×#11758201—22no—
84C2×#11758201—22no—
85C2×#11758201—22no—
86C2×#11758201—41no—
87C2×#11758201—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519775—28no—
91#14519775—22no—
92#14519775—22no—
93#14519756—28no—
94#14519756—22no—
95#14519756D414yescomplemented
96#14519753—28no—
97#14519753—22no—
98#14519753—22no—
99#14519752—22no—
100#14519752—41no—
101#14519751—22no—
102#14519751—22no—
103#14519751—44no—
104Q8×Dic61—22no—
105Q8×Dic61—22no—
106C4×C22⋊D61—28no—
107C4×C22⋊D61—22no—
108C4×C22⋊D61—22no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×#11758196D411yescharacteristic
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61D411yescharacteristic
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198D411yescharacteristic
127C2×C4×Dic61—21no—
128C2×C4×Dic61C2311yescharacteristic
129#14519709—22no—
130#14519702—22no—
131#14519701—22no—
132#14519701—22no—
133#14519700—22no—
134#14519700—41no—
135#14519699—22no—
136C22⋊#92418—22no—
137#14519689—22no—
138#14519689—41no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61—21no—
142C22×Q8×C61—22no—
143C22×Q8×C61—22no—
144C22×Q8×C61—22no—
145C22×Q8×C61—41no—
146C22×Q8×C61—41no—
147C22×Q8×C61D414yescomplemented
148C22×Q8×C61C2311yescharacteristic
149C22×Q8×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C23×C4×C61—21no—
152C23×C4×C61C2311yescharacteristic
153C22×C8×C61—22no—
154C22×C8×C61—22no—
155C22×C8×C61—41no—
156C22×C8×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C2×C4⋊C4×C61—22no—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61—41no—
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C4⋊C4×C61C2311yescharacteristic
163#103×C61—22no—
164#103×C61—22no—
165#103×C61—22no—
166#103×C61D414yescomplemented
167C24×C61C2×D411yescharacteristic
168C23×D61—21no—
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—28no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—42no—
181C2×Q8×C61—42no—
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—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—42no—
199C22×C4×C61—42no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—81no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61SD1614yescomplemented
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219Q8×D61—44no—
220Q8×D61—44no—
221Q8×D61—44no—
222Q8×D61—44no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—42no—
230C2×D244—42no—
231C2×D244—81no—
232C2×C4×D61—24no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
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×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—24no—
246C2×Dic122—21no—
247C2×Dic122—42no—
248C2×Dic122—42no—
249C2×Dic122C2×D412yes—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—44no—
256C2×C8×C61C2×D412yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61C2×D412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—22no—
264#11758201—44no—
265#11758201—44no—
266#11758198—24no—
267#11758198—22no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—42no—
272#11758198—81no—
273C4⋊Dic61—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—42no—
278C4⋊Dic61C2×D412yes—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196—22no—
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—
293#11758190—44no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61#12012yes—
299C23×C61C2×SD1612yes—
300C23×C61#13712yes—
301C23×C61C22×D411yescharacteristic
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61C2×SD1612yes—
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
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—48no—
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×C61—84no—
345C2×C4×C61#12012yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C22⋊D61—28no—
353C22⋊D61—84no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—22no—
360C2×Dic61—21no—
361C2×Dic61—21no—
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×Dic61C2×SD1612yes—
372D244—41no—
373D244—41no—
374D244—41no—
375D244—41no—
376D244—84no—
377C4×D61—48no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—41no—
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—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61#44814yescomplemented
399C22×C61C2×#12011yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61C22×SD1611yescharacteristic
403C22×C61C2×#13711yescharacteristic
404C22×C61#57711yescharacteristic
405C22×C61#57811yescharacteristic
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C4×C61—24no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61—81no—
425C4×C61C2×#12111yescharacteristic
426C4×C61#53411yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—22no—
430Dic61—42no—
431Dic61—41no—
432Dic61—41no—
433Dic61—42no—
434Dic61—81no—
435C2×D4×Q8—611no—
436C2×#465—611no—
437C2×#448—611no—
438C2×#448—611no—
439C22×#103D6111yescharacteristic, complemented
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—24no—
451C2×C61#241011yescharacteristic
452C2×C61C2×#44811yescharacteristic
453C2×C61#301311yescharacteristic
454C2×C61#327011yescharacteristic
455C2×C61D4×SD1611yescharacteristic
456C2×C61#329811yescharacteristic
457C2×C61#332011yescharacteristic
458D61—42no—
459D61—161no—
460C23×Q8—611no—
461C23×Q8C2×D6111yescharacteristic
462C22×SD16—611no—
463C22×SD16—611no—
464C22×SD16—611no—
465C23×C8C2×D6111yescharacteristic
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—611no—
476C2×#121—1221no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×C4×D4—1221no—
480C22×C4⋊C4C2×D6111yescharacteristic
481#465—1224no—
482#448—1224no—
483#448—1224no—
484C2×#106—611no—
485C2×#103—24no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103C2×D6111yescharacteristic
492C2×#103C2×D6111yescharacteristic
493C2×#103C2×D6111yescharacteristic
494C2×#103C2×D6111yescharacteristic
495C2×#102—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8—611no—
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—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1222no—
519C22×Q8—1222no—
520C22×Q8—1222no—
521C22×Q8—1222no—
522C22×Q8—2441no—
523C22×Q8—2441no—
524C22×Q8D24414yescomplemented
525C22×Q8C22×D6111yescharacteristic
526C22×Q8C22×D6111yescharacteristic
527C22×D4—611no—
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—611no—
534C23×C4—1221no—
535C23×C4C22×D6111yescharacteristic
536C2×SD16—1222no—
537C2×SD16—1222no—
538C2×SD16—1222no—
539C2×SD16—1222no—
540C2×SD16—1222no—
541C2×SD16—1222no—
542C2×SD16—2441no—
543C2×SD16—2441no—
544C2×SD16—2441no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552C4⋊Q8—1222no—
553C4⋊Q8—1228no—
554C4⋊Q8—1222no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557C22⋊Q8—1228no—
558C22⋊Q8—1228no—
559C22⋊Q8—1222no—
560C22⋊Q8—1222no—
561#121—1222no—
562#121—1222no—
563#121—1222no—
564#121—2441no—
565#121—2444no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×D4—1228no—
569C4×D4—1222no—
570C4×D4—1222no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C22⋊C4—611no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—1221no—
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—22no—
599#103—22no—
600#103—1222no—
601#103—1222no—
602#103—1222no—
603#103—1222no—
604#103—2441no—
605#103C22⋊D6114yescomplemented
606#102—1222no—
607C22⋊C8—1222no—
608C22⋊C8—1222no—
609C22⋊C8—2441no—
610#95—1221no—
611#95—1221no—
612C24—611no—
613C24—1221no—
614C24D4×D6111yescharacteristic
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—24no—
620C2×Q8—28no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—42no—
626C2×Q8—42no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—612no—
631C2×Q8—1224no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—2442no—
638C2×Q8—2442no—
639C2×Q8—2444no—
640C2×Q8—2444no—
641C2×Q8—2444no—
642C2×Q8—2444no—
643C2×Q8C2×D24412yes—
644C2×Q8C2×D24412yes—
645C2×Q8#1175822212yes—
646C2×Q8C2×C22⋊D6112yes—
647C2×D4—614no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—4881no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4—2442no—
661C2×D4—2442no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—611no—
677C22×C4—611no—
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—1221no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4C2×D24412yes—
692C22×C4D4×D6112yes—
693C22×C4D4×D6111yescharacteristic
694C22×C4C23×D6111yescharacteristic
695SD16—2444no—
696SD16—2444no—
697SD16—2444no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—44no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8C2×C22⋊D6112yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—612no—
716C4⋊C4—1224no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1224no—
720C4⋊C4—1221no—
721C4⋊C4—1222no—
722C4⋊C4—1224no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—2442no—
726C4⋊C4C2×C22⋊D6112yes—
727C22⋊C4—1224no—
728C22⋊C4—1222no—
729C22⋊C4—1224no—
730C22⋊C4—1222no—
731C22⋊C4—4881no—
732C22⋊C4—2442no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C22⋊C4—2442no—
736C42—1224no—
737C42—1221no—
738C42—1221no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—612no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23#1451974712yes—
758C23SD16×D6112yes—
759C23#1451980912yes—
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#1451975114yescomplemented
775D4—1228no—
776D4—4884no—
777D4—4884no—
778D4—2441no—
779D4—2441no—
780D4—2441no—
781D4—2441no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—612no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1222no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1222no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—2448no—
814C2×C4—2441no—
815C2×C4—2441no—
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#1451974712yes—
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C22×C22⋊D6111yescharacteristic
828C2×C4C22×D24411yescharacteristic
829C2×C4C2×#1175822211yescharacteristic
830C2×C4#1451982211yescharacteristic
831C2×C4#1451982211yescharacteristic
832C8—22no—
833C8—41no—
834C8—2441no—
835C8—2441no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—4881no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4881no—
850C22—4881no—
851C22—4881no—
852C22—2441no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22#1683990214yescomplemented
857C22C2×#1451974711yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684040211yescharacteristic
860C22C2×SD16×D6111yescharacteristic
861C22C2×#1451980911yescharacteristic
862C22#1684056811yescharacteristic
863C22#1684057511yescharacteristic
864C4—22no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—1222no—
870C4—4881no—
871C4—2441no—
872C4—2442no—
873C4—2441no—
874C4—2442no—
875C4C2×#1451975111yescharacteristic
876C4#1684032411yescharacteristic
877C4D4×C22⋊D6111yescharacteristic
878C4#1684040211yescharacteristic
879C2—24no—
880C2—9761no—
881C2—2442no—
882C2#2144918711yescharacteristic
883C2C2×#1683990211yescharacteristic
884C2#2145513911yescharacteristic
885C2#2145738911yescharacteristic
886C2SD16×C22⋊D6111yescharacteristic
887C2#2145768011yescharacteristic
888C2#2145798611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC23×C61C22×D4
prime radical#21449253C2
hypercenterC22×#103D61
hypocenterC61#24429
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D61C2semidirect
2. C2×#16839991C2semidirect
3. C2×#16839902C2semidirect
4. C2×#16839901C2semidirect
6. #21447064C2semidirect
7. #21447014C2semidirect
8. #21446903C2semidirect
9. #21446821C2semidirect
10. #21446172C2semidirect
11. #21446126C2semidirect
12. #21446111C2semidirect
13. #21446089C2semidirect
14. #21445752C2semidirect
15. C22×#103×C61C2semidirect
95. #14519756D4semidirect
147. C22×Q8×C61D4semidirect
166. #103×C61D4semidirect
212. C2×C22⋊D61SD16semidirect
324. Q8×C61#121semidirect
398. C22×C61#448semidirect
439. C22×#103D61semidirect
509. C61#24429semidirect
524. C22×Q8D244semidirect
605. #103C22⋊D61semidirect
774. Q8#14519751semidirect
856. C22#16839902semidirect

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×#168399912
C2×#168399022
C2×#168399012
#214492532
#214470642
#214470142
#214469032
#214468212
#214461722
#214461262
#214461112
#214460892
#214457522
C22×#103×C612
#2442961