Finite Group Databasebeta

← #29718005

Subgroups — #29718005

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D61C211yesmaximal, characteristic
2C2×#16840017C211yesmaximal, characteristic, complemented
3C2×#16839916C211yesmaximal, characteristic, complemented
4C2×#16839769C211yesmaximal, characteristic, complemented
5#21449244C211yesmaximal, characteristic
6#21447064C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21446917C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21446128C211yesmaximal, characteristic, complemented
12#21446113C211yesmaximal, characteristic
13#21446089C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#451C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19Q8×C22⋊D61—24no—
20Q8×C22⋊D61—24no—
21C2×#14519775—21no—
22C2×#14519775C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519753—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519753C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61—21no—
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32#16840017—24no—
33#16839916—24no—
34C2×#14519709C2211yescharacteristic
35#16839769—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839688—21no—
47#16839678—21no—
48#16839669C2211yescharacteristic
49#16839661C2211yescharacteristic
50#16839658—21no—
51#16839650—21no—
52#16839622C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C22×Q16×C61C2211yescharacteristic
59C22×Q16×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C61×#451—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×D61D414yes—
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×#11758202—22no—
77C2×#11758202—41no—
78C2×#11758202—41no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519775—28no—
85#14519775—22no—
86#14519775—22no—
87#14519756—28no—
88#14519756—22no—
89#14519756—22no—
90#14519753—28no—
91#14519753—22no—
92#14519753—22no—
93#14519753—22no—
94#14519753D414yes—
95Q8×Dic61—22no—
96Q8×Dic61—22no—
97C4×C22⋊D61—28no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100#14519735—22no—
101#14519735—41no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196D411yescharacteristic
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519709—22no—
124#14519702—22no—
125#14519702—22no—
126#14519701—22no—
127#14519701—22no—
128#14519701—22no—
129#14519701—22no—
130#14519701—41no—
131#14519700—22no—
132C22⋊#92418—41no—
133#14519689—22no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×Q8×C61—22no—
139C22×Q8×C61—22no—
140C22×Q8×C61—21no—
141C22×Q8×C61—22no—
142C22×Q8×C61—22no—
143C22×Q8×C61—41no—
144C22×Q8×C61—41no—
145C22×Q8×C61C2311yescharacteristic
146C22×Q8×C61C2311yescharacteristic
147C22×Q8×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61C2311yescharacteristic
150C2×Q16×C61—22no—
151C2×Q16×C61—22no—
152C2×Q16×C61—22no—
153C2×Q16×C61—22no—
154C2×Q16×C61—22no—
155C2×Q16×C61—41no—
156C22×C8×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22⋊Q8×C61—22no—
159C22⋊Q8×C61—41no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C22⋊C4×C61—21no—
163#103×C61—22no—
164#103×C61D414yescomplemented
165C22⋊C8×C61—22no—
166C24×C61C2×D411yescharacteristic
167C23×D61C2×D411yescharacteristic
168C2×Q8×C61—24no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
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—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—42no—
184C2×Q8×C61—42no—
185C2×Q8×C61—44no—
186C2×Q8×C61—44no—
187C2×Q8×C61—44no—
188C2×Q8×C61—44no—
189C2×Q8×C61C2×D412yes—
190C2×Q8×C61C2×D412yes—
191C2×Q8×C61C2×D412yes—
192C2×Q8×C61#4112yes—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—22no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218Q8×D61—28no—
219Q8×D61—44no—
220Q8×D61—44no—
221Q8×D61—44no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—24no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2×D412yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—24no—
237C2×Dic122—42no—
238C2×Dic122—42no—
239C2×Dic122C2×D412yes—
240Q16×C61—44no—
241Q16×C61—44no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61C2×D412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61C2×D412yes—
251C22⋊C4×C61—42no—
252C22⋊Dic61—24no—
253C22⋊Dic61—22no—
254C22⋊Dic61—42no—
255#11758202—44no—
256#11758198—24no—
257#11758198—22no—
258#11758198—42no—
259#11758198—42no—
260C4⋊Dic61—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—42no—
267C4⋊Dic61C2×D412yes—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271#11758196—24no—
272#11758196—22no—
273#11758196—42no—
274C4×Dic61—24no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—42no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284#11758189—44no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61#13712yes—
292C23×C61C22×D411yescharacteristic
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61#12012yes—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—48no—
306Q8×C61—41no—
307Q8×C61—41no—
308Q8×C61—41no—
309Q8×C61—41no—
310Q8×C61—41no—
311Q8×C61—41no—
312Q8×C61#12114yes—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—48no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C22⋊D61—28no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61#12012yes—
360C2×Dic61#13712yes—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—48no—
366Dic122—22no—
367Dic122—22no—
368Dic122—48no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—22no—
372C8×C61—41no—
373#92418—41no—
374#92418—41no—
375#24453—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61C2×#12011yescharacteristic
384C22×C61D4211yescharacteristic
385C22×C61#54611yescharacteristic
386C22×C61C2×#13711yescharacteristic
387C22×C61C2×#13711yescharacteristic
388C22×C61#57811yescharacteristic
389C22×C61#57811yescharacteristic
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C4×C61—24no—
398C4×C61—41no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61—81no—
402C4×C61C2×#12111yescharacteristic
403C4×C61#53411yescharacteristic
404C4×C61D4211yescharacteristic
405C4×C61#54611yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—41no—
410Dic61—42no—
411Dic61—81no—
412Dic61—81no—
413C2×D4×Q8—611no—
414C2×#470—611no—
415C2×#451—611no—
416C2×#451D6111yescharacteristic, complemented
417C2×#419—611no—
418#2415—611no—
419#2043—611no—
420#2035—611no—
421#2016—611no—
422#2001—611no—
423#1878—611no—
424#1873—611no—
425#1870—611no—
426#1865—611no—
427#1787—611no—
428C2×C61—42no—
429C2×C61#241011yescharacteristic
430C2×C61#300411yescharacteristic
431C2×C61#301111yescharacteristic
432C2×C61#327011yescharacteristic
433C2×C61#327611yescharacteristic
434C2×C61#331211yescharacteristic
435C2×C61#332811yescharacteristic
436D61—42no—
437C23×Q8—611no—
438C23×Q8C2×D6111yescharacteristic
439C22×Q16—611no—
440C22×Q16C2×D6111yescharacteristic
441C22×Q16C2×D6111yescharacteristic
442C22×M16—611no—
443D4×Q8—1224no—
444D4×Q8—1224no—
445C2×C4⋊Q8—611no—
446C2×C4⋊Q8—1221no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8—611no—
449C2×C22⋊Q8—611no—
450C2×C22⋊Q8—1221no—
451C2×C22⋊Q8—1221no—
452C2×C22⋊Q8C2×D6111yescharacteristic
453C2×C4×Q8—611no—
454C2×C4×D4—611no—
455C2×C4×D4—1221no—
456C2×#117—611no—
457#470—1224no—
458#451—24no—
459#451—1224no—
460C2×#106—611no—
461#419—1224no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103C2×D6111yescharacteristic
471C2×#103C2×D6111yescharacteristic
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8C2×D6111yescharacteristic
475#397—1221no—
476#394—1221no—
477#391—611no—
478#389—611no—
479#389—1221no—
480#388—1221no—
481#380—611no—
482#340—611no—
483#340—611no—
484#336—611no—
485#336—611no—
486C61#2445311yescharacteristic, complemented, Sylow
487C22×Q8—22no—
488C22×Q8—22no—
489C22×Q8—21no—
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8—614no—
495C22×Q8—611no—
496C22×Q8—1221no—
497C22×Q8—1222no—
498C22×Q8—1222no—
499C22×Q8—1222no—
500C22×Q8—2441no—
501C22×Q8—2441no—
502C22×Q8C22×D6111yescharacteristic
503C22×Q8C22×D6111yescharacteristic
504C22×Q8C22×D6111yescharacteristic
505C22×D4—611no—
506C23×C4—21no—
507C23×C4—611no—
508C23×C4—1221no—
509C23×C4C22×D6111yescharacteristic
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—41no—
516C2×Q16—1222no—
517C2×Q16—2441no—
518C2×Q16—2441no—
519C2×M16—1222no—
520C2×M16—1222no—
521C2×M16—2441no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C4⋊Q8—1222no—
527C4⋊Q8—1228no—
528C4⋊Q8—1222no—
529C22⋊Q8—22no—
530C22⋊Q8—41no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1228no—
535C22⋊Q8—1222no—
536C22⋊Q8—1228no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C4×Q8—1222no—
540C4×Q8—1222no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1228no—
544#117—1222no—
545#117—2441no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C42—611no—
568C2×C42—1221no—
569C2×C42—1221no—
570#106—1222no—
571#103—22no—
572#103—1222no—
573#103—1222no—
574#103—1222no—
575#103—1222no—
576#103—1222no—
577#103—1222no—
578#103—1222no—
579#103—2441no—
580#103C22⋊D6114yescomplemented
581C22⋊C8—22no—
582C22⋊C8—1222no—
583C22⋊C8—2441no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588C24—611no—
589C24D4×D6111yescharacteristic
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—612no—
612C2×Q8—1224no—
613C2×Q8—1221no—
614C2×Q8—1228no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—2442no—
620C2×Q8—2442no—
621C2×Q8—2444no—
622C2×Q8—2444no—
623C2×Q8—2444no—
624C2×Q8D4×D6112yes—
625C2×Q8D4×D6112yes—
626C2×Q8#1175822412yes—
627C2×Q8C2×C22⋊D6112yes—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1222no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—611no—
649C22×C4—1224no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4D4×D6111yescharacteristic
661C22×C4C23×D6111yescharacteristic
662Q16—44no—
663Q16—44no—
664Q16—2444no—
665M16—2444no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8C2×C22⋊D6112yes—
678C4⋊C4—21no—
679C4⋊C4—42no—
680C4⋊C4—612no—
681C4⋊C4—1222no—
682C4⋊C4—1224no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—2442no—
693C4⋊C4—2442no—
694C4⋊C4C2×C22⋊D6112yes—
695C22⋊C4—42no—
696C22⋊C4—1222no—
697C22⋊C4—1224no—
698C22⋊C4—1222no—
699C22⋊C4—1224no—
700C22⋊C4—2442no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C42—1224no—
704C42—1221no—
705C42—1221no—
706C42—2442no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—612no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23#1451980912yes—
721C23C2×D4×D6111yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—48no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—1222no—
735Q8—1222no—
736Q8—2448no—
737Q8—2441no—
738Q8—2441no—
739Q8#1451974814yes—
740D4—1228no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—612no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1221no—
773C2×C4—1222no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—2448no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4C2×D4×D6111yescharacteristic
789C2×C4C22×C22⋊D6111yescharacteristic
790C2×C4C2×#1175822411yescharacteristic
791C2×C4#1451982211yescharacteristic
792C2×C4#1451982211yescharacteristic
793C8—22no—
794C8—41no—
795C8—2441no—
796C8—2441no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—2441no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22#120×D6111yescharacteristic
812C22D4×C22⋊D6111yescharacteristic
813C22#1684039911yescharacteristic
814C22#137×D6111yescharacteristic
815C22C2×#1451980911yescharacteristic
816C22#1684057511yescharacteristic
817C22#1684057811yescharacteristic
818C4—24no—
819C4—42no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—1222no—
824C4—1222no—
825C4—4881no—
826C4—4881no—
827C4—2441no—
828C4—2442no—
829C4—2442no—
830C4C2×#1451974811yescharacteristic
831C4#1684032211yescharacteristic
832C4D4×C22⋊D6111yescharacteristic
833C4#1684039911yescharacteristic
834C2—42no—
835C2—2442no—
836C2#2144918911yescharacteristic
837C2#2145505411yescharacteristic
838C2#2145510911yescharacteristic
839C2#2145738911yescharacteristic
840C2#2145745911yescharacteristic
841C2#2145787411yescharacteristic
842C2#2145809511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#451D61
hypocenterC61#24453
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#16840017C2semidirect
3. C2×#16839916C2semidirect
4. C2×#16839769C2semidirect
6. #21447064C2semidirect
7. #21447016C2semidirect
8. #21446917C2semidirect
9. #21446827C2semidirect
10. #21446162C2semidirect
11. #21446128C2semidirect
13. #21446089C2semidirect
14. #21445754C2semidirect
15. C2×C61×#451C2semidirect
164. #103×C61D4semidirect
416. C2×#451D61semidirect
486. C61#24453semidirect
580. #103C22⋊D61semidirect

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×#168400172
C2×#168399162
C2×#168397692
#214492442
#214470642
#214470162
#214469172
#214468272
#214461622
#214461282
#214461132
#214460892
#214457542
C2×C61×#4512
#2445361