Finite Group Databasebeta

← #29602805

Subgroups — #29602805

Order 15616.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519757C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3C2×#16839668C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444071C212yesmaximal, complemented
7#21444063C212yesmaximal
8#21444055C212yesmaximal
9#21444053C212yesmaximal, complemented
10#21444048C211yesmaximal, characteristic, complemented
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×#14519757—24no—
15C2×#14519757—24no—
16C2×#14519757C418yescomplemented
17C2×#14519742—24no—
18C2×#14519742—24no—
19C2×#14519742—24no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2212yes—
22C22×#11758196C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839668—24no—
30#16839619—24no—
31C4×#11758198—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2212yes—
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C4⋊C4×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—22no—
48C22×Dic122—22no—
49C22×Dic122C2×C414yes—
50C22×Dic122D414yes—
51C22×Dic122D414yes—
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61C2×C414yes—
64#14519757—232no—
65#14519742—232no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61—24no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61C2×C418yes—
72C2×#11758196—24no—
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—42no—
85C2×#11758198C2×C418yes—
86C2×#11758198Q814yescomplemented
87C2×C4×Dic61—24no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—24no—
91C2×C4×Dic61—24no—
92C2×C4×Dic61D414yes—
93#14519684—24no—
94#14519684—22no—
95#14519684—22no—
96#14519684—24no—
97#14519684—24no—
98#14519684—24no—
99#14519684—42no—
100C23×C4×C61C2312yes—
101C23×C4×C61C2312yes—
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61C2×C414yes—
110C2×C4⋊C4×C61D414yes—
111C2×C42×C61—22no—
112C2×C42×C61—22no—
113C2×C42×C61—22no—
114#95×C61—24no—
115#95×C61—42no—
116C24×C61C2411yescharacteristic
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61C22×C412yes—
130C23×D61C2×Q812yes—
131C23×D61#4112yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C414yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×Q812yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4112yes—
166C22×C4×C61#4112yes—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61C22×C412yes—
195C22×Dic61C22×C414yes—
196C22×Dic61C2×D412yes—
197C22×Dic61C2×D414yes—
198C22×Dic61C2×D414yes—
199C22×Dic61C2×D412yes—
200C22×Dic61C2×Q812yes—
201C22×Dic61#4112yes—
202C2×C4×D61—28no—
203C2×C4×D61—28no—
204C2×C4×D61—28no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61—44no—
208C2×C4×D61—44no—
209C2×Dic122—28no—
210C2×Dic122—28no—
211C2×Dic122—28no—
212C2×Dic122—28no—
213C2×Dic122—28no—
214C2×Dic122—28no—
215C2×Dic122C22⋊C4116yescomplemented
216C4⋊C4×C61—28no—
217C4⋊C4×C61—28no—
218C42×C61—44no—
219#11758198—28no—
220#11758198—216no—
221#11758198—28no—
222#11758198—48no—
223C4⋊Dic61—216no—
224C4⋊Dic61—44no—
225#11758196—216no—
226C4×Dic61—216no—
227C4×Dic61—28no—
228C23×C61C23×C411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C23×C61C22×Q811yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61C2×#4111yescharacteristic
239C23×C61H(5,𝔽2)11yescharacteristic
240C23×C612−1+411yescharacteristic
241C23×C612−1+411yescharacteristic
242C23×C612−1+411yescharacteristic
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61C4×Q814yescomplemented
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61C2×C22⋊C414yes—
307C2×C4×C61C4×D414yes—
308C2×C4×C61C4×D414yes—
309C2×C4×C61#12014yes—
310C2×C4×C61#12114yes—
311C2×C4×C61#12114yes—
312C2×C4×C61#12314yes—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C22⋊C418yes—
347C2×Dic61C22⋊Q814yescomplemented
348C4×D61—416no—
349Dic122—232no—
350#13969—611nomaximal, Sylow
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×C4×Q811yescharacteristic
355C22×C61C4×#4111yescharacteristic
356C22×C61#51911yescharacteristic
357C22×C61#52011yescharacteristic
358C22×C61C2×#12011yescharacteristic
359C22×C61C2×#12111yescharacteristic
360C22×C61C2×#12111yescharacteristic
361C22×C61C2×C22⋊Q811yescharacteristic
362C22×C61C2×#12311yescharacteristic
363C22×C61#52511yescharacteristic
364C22×C61#52911yescharacteristic
365C22×C61#53311yescharacteristic
366C22×C61#53611yescharacteristic
367C22×C61#53711yescharacteristic
368C22×C61#54111yescharacteristic
369C22×C61#54211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54711yescharacteristic
372C22×C61#54811yescharacteristic
373C22×C61#54811yescharacteristic
374C22×C61#54811yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61#54811yescharacteristic
377C22×C61D4×Q811yescharacteristic
378C22×C61D4×Q811yescharacteristic
379C22×C61D4×Q811yescharacteristic
380C22×C61#55011yescharacteristic
381C22×C61#55011yescharacteristic
382C22×C61#55211yescharacteristic
383C22×C61#55211yescharacteristic
384C22×C61#55411yescharacteristic
385C22×C61#55611yescharacteristic
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—44no—
402C4×C61—44no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61#38618yes—
406Dic61—24no—
407Dic61—28no—
408Dic61—42no—
409Dic61—42no—
410Dic61—82no—
411C22×C22⋊Q8—611no—
412C22×C4×Q8—611no—
413C2×#391—611no—
414C2×#380—611no—
415C2×C4×C22⋊C4—611no—
416#1441—612no—
417#1439—612no—
418#1437—612no—
419#1436—612no—
420C4⋊#95—611no—
421C4⋊#95D6111yescharacteristic, complemented
422C2×C61C2×#38611yescharacteristic
423C2×C61C4×C22⋊Q811yescharacteristic
424C2×C61#232311yescharacteristic
425C2×C61Q8×C22⋊C411yescharacteristic
426C2×C61#234111yescharacteristic
427C2×C61#236011yescharacteristic
428C2×C61#236211yescharacteristic
429C2×C61#240711yescharacteristic
430C2×C61#240911yescharacteristic
431C2×C61#242111yescharacteristic
432C2×C61#242311yescharacteristic
433C2×C61#242611yescharacteristic
434C2×C61#242911yescharacteristic
435C2×C61#253611yescharacteristic
436C2×C61#253811yescharacteristic
437D61—44no—
438C23×Q8—611no—
439C24×C4—611no—
440C2×C22⋊Q8—618no—
441C2×C22⋊Q8—1224no—
442C2×C22⋊Q8—1224no—
443C2×C4×Q8—1224no—
444C2×C4×Q8—1224no—
445C2×C4×Q8—1224no—
446C22×C4⋊C4—612no—
447C22×C4⋊C4—612no—
448C22×C4⋊C4—611no—
449C22×C4⋊C4C2×D6111yescharacteristic
450C22×C4⋊C4C2×D6111yescharacteristic
451C22×C22⋊C4—612no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—612no—
455C22×C42—611no—
456C22×C42—612no—
457C22×C42C2×D6111yescharacteristic
458#391—1224no—
459#380—1224no—
460C4×C22⋊C4—1224no—
461C2×#95—612no—
462C2×#95—611no—
463C2×#95—612no—
464C2×#95—612no—
465C2×#95—612no—
466C2×#95—611no—
467C2×#95—612no—
468C2×#95C2×D6112yes—
469C2×#95C2×D6112yes—
470C61#1396911yescharacteristic, complemented, Sylow
471C25—611no—
472C22×Q8—614no—
473C22×Q8—614no—
474C22×Q8—614no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C22×Q8—1222no—
479C23×C4—612no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—614no—
484C23×C4—612no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4—1222no—
491C23×C4C22×D6112yes—
492C23×C4C22×D6112yes—
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C22⋊Q8—12232no—
497C4×Q8—12232no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—618no—
503C2×C4⋊C4—1224no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4C4×D6114yes—
512C2×C4⋊C4D24414yes—
513C2×C22⋊C4—618no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—2442no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—614no—
529C2×C42—1224no—
530C2×C42—1224no—
531C2×C42—1224no—
532C2×C42—1222no—
533C2×C42—1222no—
534#95—24no—
535#95—42no—
536#95—1222no—
537#95—1222no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541#95—1224no—
542#95—2442no—
543C24—612no—
544C24—612no—
545C24—612no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24—1221no—
557C24—1221no—
558C24C23×D6111yescharacteristic
559C2×Q8—6116no—
560C2×Q8—1228no—
561C2×Q8—1228no—
562C2×Q8—1228no—
563C2×Q8—1228no—
564C2×Q8—1228no—
565C2×Q8—1228no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—614no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1228no—
619C22×C4—1228no—
620C22×C4—1228no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4C2×C4×D6114yes—
633C22×C4C2×C4×D6112yes—
634C22×C4C2×D24414yes—
635C22×C4C2×D24412yes—
636C22×C4#1175822212yes—
637C22×C4D4×D6112yes—
638C22×C4D4×D6112yes—
639C22×C4D4×D6112yes—
640C22×C4#1175822412yes—
641C22×C4Q8×D6112yes—
642C22×C4#1175822612yes—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—12216no—
646C4⋊C4—12216no—
647C4⋊C4—2444no—
648C22⋊C4—1228no—
649C22⋊C4—12216no—
650C22⋊C4—1228no—
651C22⋊C4—2448no—
652C42—44no—
653C42—12216no—
654C42—1228no—
655C23—614no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23C22×C4×D6111yescharacteristic
691C23C2×D4×D6111yescharacteristic
692C23C2×D4×D6111yescharacteristic
693C23C2×D4×D6111yescharacteristic
694C23C22×D24411yescharacteristic
695C23C2×Q8×D6111yescharacteristic
696C23#41×D6111yescharacteristic
697C23#41×D6111yescharacteristic
698C23C2×#1175822411yescharacteristic
699C23C2×#1175822211yescharacteristic
700C23C2×#1175822611yescharacteristic
701C23#1451982211yescharacteristic
702C23#1451982411yescharacteristic
703C23#1451982411yescharacteristic
704C23#1451982511yescharacteristic
705Q8—12232no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—618no—
735C2×C4—614no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1222no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—24416no—
770C2×C4C22⋊C4×D6114yes—
771C2×C4#1451973914yes—
772C2×C4C4×D24414yes—
773C2×C4#1451974714yes—
774C2×C4#1451975014yes—
775C2×C4#1451975214yes—
776C2×C4#1451976214yes—
777C22—1224no—
778C22—1224no—
779C22—1224no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22C2×C22⋊C4×D6111yescharacteristic
793C22C2×#1451973911yescharacteristic
794C22C2×C4×D24411yescharacteristic
795C22C4×Q8×D6111yescharacteristic
796C22C4×#1175822411yescharacteristic
797C22#1684023811yescharacteristic
798C22#1684024111yescharacteristic
799C22C2×#1451974711yescharacteristic
800C22C2×#1451975011yescharacteristic
801C22C2×#1451975211yescharacteristic
802C22C22⋊Q8×D6111yescharacteristic
803C22C2×#1451976211yescharacteristic
804C22#1684027211yescharacteristic
805C22#1684029711yescharacteristic
806C22#1684031711yescharacteristic
807C22#1684033511yescharacteristic
808C22#1684034111yescharacteristic
809C22#1684037511yescharacteristic
810C22#1684038611yescharacteristic
811C22#1684040711yescharacteristic
812C22#1684041611yescharacteristic
813C22#1684041811yescharacteristic
814C22#1684042011yescharacteristic
815C22#1684042011yescharacteristic
816C22#1684042211yescharacteristic
817C22#1684042411yescharacteristic
818C22#1684042511yescharacteristic
819C22#1684042711yescharacteristic
820C22Q8×D24411yescharacteristic
821C22#1684043011yescharacteristic
822C22#1684043211yescharacteristic
823C22#1684044711yescharacteristic
824C22#1684045111yescharacteristic
825C22#1684046711yescharacteristic
826C22#1684048011yescharacteristic
827C4—44no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—1228no—
832C4—1224no—
833C4—4882no—
834C4—2442no—
835C4—2442no—
836C4#1683964018yes—
837C2—2444no—
838C2C2×#1683964011yescharacteristic
839C2#2144834911yescharacteristic
840C2#2144849911yescharacteristic
841C2#2144865311yescharacteristic
842C2#2144865811yescharacteristic
843C2#2144882611yescharacteristic
844C2#2144884811yescharacteristic
845C2#2144916211yescharacteristic
846C2#2144918211yescharacteristic
847C2#2144932511yescharacteristic
848C2#2144934711yescharacteristic
849C2#2144938311yescharacteristic
850C2#2144941611yescharacteristic
851C2#2145073011yescharacteristic
852C2#2145074311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4⋊#95D61
hypocenterC61#13969
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
3. C2×#16839668C2semidirect
6. #21444071C2semidirect
9. #21444053C2semidirect
10. #21444048C2semidirect
11. C61×C4⋊#95C2semidirect
16. C2×#14519757C4semidirect
86. C2×#11758198Q8semidirect
215. C2×Dic122C22⋊C4semidirect
277. C22×D61C4×Q8semidirect
347. C2×Dic61C22⋊Q8semidirect
421. C4⋊#95D61semidirect
470. C61#13969semidirect

Maximal subgroups

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

subgroupindex
C22×#145197572
C22×#145197422
C2×#168396682
C2×#168396192
C2×C4×#117581982
#214440712
#214440632
#214440552
#214440532
#214440482
C61×C4⋊#952
#1396961