Finite Group Databasebeta

← #29601480

Subgroups — #29601480

Order 15616.

3562 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C22×#14519737C212yesmaximal
3C22×#14519684C211yesmaximal, characteristic, complemented
4C2×#95×D61C211yesmaximal, characteristic, complemented
5#21444047C212yesmaximal, complemented
6#21444047C211yesmaximal, characteristic, complemented
7#21444041C212yesmaximal, complemented
8#21444040C211yesmaximal, characteristic, complemented
9#21444040C212yesmaximal, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2212yes—
14C23×C4×D61C2212yes—
15C23×C4×D61C2211yescharacteristic
16C2×C4×C22⋊D61—28no—
17C2×C4×C22⋊D61C418yescomplemented
18C2×#14519737—28no—
19C2×#14519737—28no—
20C2×#14519737C4116yescomplemented
21C22×#11758196C2212yes—
22C22×#11758196C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C2212yes—
25C22×#11758198C2211yescharacteristic
26C22×C4×Dic61C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28C2×#14519684—24no—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36#95×D61—24no—
37C24×C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C24×D61C2311yescharacteristic
43C22×C22⋊D61C2×C418yes—
44C22×C22⋊D61C2×C414yes—
45C22×C22⋊D61D414yes—
46C22×C22⋊D61D418yes—
47C22×C22⋊D61Q814yes—
48C23×Dic61—24no—
49C23×Dic61—24no—
50C23×Dic61—24no—
51C23×Dic61—24no—
52C23×Dic61—42no—
53C23×Dic61—42no—
54C23×Dic61C2×C418yescomplemented
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2312yes—
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—24no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—24no—
66C22×C4×D61—24no—
67C22×C4×D61—42no—
68C22×C4×D61—42no—
69C22×C4×D61—42no—
70C22×C4×D61C2×C418yescomplemented
71C22×C4×D61C2×C414yescomplemented
72C4×C22⋊D61—232no—
73#14519737—264no—
74C2×#11758196—24no—
75C2×#11758196—24no—
76C2×#11758196—24no—
77C2×#11758196C2×C418yescomplemented
78C2×#11758196C2×C414yescomplemented
79C2×C22⋊Dic61—24no—
80C2×C22⋊Dic61C2×C414yescomplemented
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198C2×C418yescomplemented
85C2×#11758198C2×C414yescomplemented
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61—24no—
89C2×C4×Dic61C2×C418yescomplemented
90C2×C4×Dic61C2×C414yescomplemented
91#14519684—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95#14519684—42no—
96#14519684—42no—
97#14519684D414yescomplemented
98C25×C61C2311yescharacteristic
99C23×C4×C61—24no—
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—42no—
103C23×C4×C61C2×C414yescomplemented
104C23×C4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61C2×C418yescomplemented
111#95×C61—22no—
112#95×C61—22no—
113#95×C61—42no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—22no—
119C24×C61—21no—
120C24×C61C22×C414yes—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D414yes—
124C24×C61C2×Q812yes—
125C24×C61C2411yescharacteristic
126C23×D61—21no—
127C23×D61—22no—
128C23×D61—21no—
129C23×D61—22no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61C22×C414yes—
133C23×D61C22×C412yes—
134C23×D61C2×D412yes—
135C23×D61C2×D414yes—
136C23×D61C2×Q812yes—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—28no—
157C22×C4×C61—44no—
158C22×C4×C61—48no—
159C22×C4×C61—48no—
160C22×C4×C61C22×C414yes—
161C22×C4×C61C22×C414yes—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61#4112yes—
166C2×C22⋊D61C42116yes—
167C2×C22⋊D61C22⋊C4132yes—
168C2×C22⋊D61C22⋊C4116yes—
169C2×C22⋊D61C4⋊C4132yes—
170C2×C22⋊D61C4⋊C4116yes—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—216no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—216no—
191C22×Dic61—48no—
192C22×Dic61—48no—
193C22×Dic61—48no—
194C22×Dic61—48no—
195C22×Dic61—48no—
196C22×Dic61C22×C412yes—
197C22×Dic61C22×C414yes—
198C22×Dic61C22×C412yes—
199C22×Dic61C22×C414yes—
200C22×Dic61C22×C414yes—
201C22×Dic61C22×C412yes—
202C22×Dic61C2×D414yes—
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D414yes—
205C22×Dic61C2×Q812yes—
206C22×Dic61#4114yes—
207C2×C4×D61—216no—
208C2×C4×D61—28no—
209C2×C4×D61—28no—
210C2×C4×D61—216no—
211C2×C4×D61—48no—
212C2×C4×D61—44no—
213C2×C4×D61—48no—
214C2×C4×D61—48no—
215C2×C4×D61—48no—
216C2×C4×D61—48no—
217C2×C4×D61—48no—
218C2×C4×D61—48no—
219C22⋊C4×C61—216no—
220C22⋊Dic61—28no—
221#11758198—216no—
222#11758198—28no—
223#11758196—216no—
224#11758196—28no—
225C4×Dic61—216no—
226C4×Dic61—28no—
227C23×C61—24no—
228C23×C61—22no—
229C23×C61—24no—
230C23×C61—22no—
231C23×C61—24no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—24no—
244C23×C61—22no—
245C23×C61C2×C4214yes—
246C23×C61C2×C22⋊C414yes—
247C23×C61C2×C22⋊C418yes—
248C23×C61C2×C4⋊C418yes—
249C23×C61C2×C4⋊C414yes—
250C23×C61C23×C412yes—
251C23×C61C23×C411yescharacteristic
252C23×C61C22×D412yes—
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×Q811yescharacteristic
256C23×C61C2×#4112yes—
257C23×C61C2×#4111yescharacteristic
258C23×C61H(5,𝔽2)12yes—
259C23×C61H(5,𝔽2)11yescharacteristic
260C23×C612−1+411yescharacteristic
261C22×D61—24no—
262C22×D61—22no—
263C22×D61—24no—
264C22×D61—22no—
265C22×D61—24no—
266C22×D61—22no—
267C22×D61—24no—
268C22×D61—22no—
269C22×D61—24no—
270C22×D61—22no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—24no—
278C22×D61—22no—
279C22×D61C2×C4214yes—
280C22×D61C2×C22⋊C418yes—
281C22×D61C2×C22⋊C414yes—
282C22×D61C2×C4⋊C414yes—
283C22×D61C2×C4⋊C418yes—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—24no—
297C2×C4×C61—416no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C4×D414yescomplemented
309C22⋊D61#95164yescomplemented
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—24no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—24no—
324C2×Dic61—22no—
325C2×Dic61—432no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61C2×C4214yes—
335C2×Dic61C2×C22⋊C418yes—
336C2×Dic61C2×C22⋊C414yes—
337C2×Dic61C2×C4⋊C414yes—
338C2×Dic61C2×C4⋊C418yes—
339C2×Dic61C4×D418yescomplemented
340C4×D61—432no—
341C4×D61—416no—
342D4×#95—611nomaximal, Sylow
343C22×C61—28no—
344C22×C61—24no—
345C22×C61—24no—
346C22×C61—28no—
347C22×C61—24no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—28no—
351C22×C61—24no—
352C22×C61—24no—
353C22×C61C2×#9518yescomplemented
354C22×C61C22×C4211yescharacteristic
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C22×C22⋊C412yes—
357C22×C61C22×C4⋊C411yescharacteristic
358C22×C61C22×C4⋊C412yes—
359C22×C61C2×C4×D412yes—
360C22×C61C2×C4×D411yescharacteristic
361C22×C61C4×#4112yes—
362C22×C61C4×#4111yescharacteristic
363C22×C61#51812yes—
364C22×C61#51811yescharacteristic
365C22×C61#52012yes—
366C22×C61#52011yescharacteristic
367C22×C61D4212yes—
368C22×C61D4211yescharacteristic
369C22×C61#54612yes—
370C22×C61#54612yes—
371C22×C61#54612yes—
372C22×C61#54712yes—
373C22×C61#54711yescharacteristic
374C22×C61D4×Q811yescharacteristic
375C22×C61#55412yes—
376C22×C61#55411yescharacteristic
377C2×D61—24no—
378C2×D61—28no—
379C2×D61—24no—
380C2×D61—28no—
381C2×D61—24no—
382C2×D61—28no—
383C2×D61—24no—
384C2×D61—28no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61C2×#9518yescomplemented
388C4×C61—24no—
389C4×C61—44no—
390C4×C61—42no—
391C4×C61—44no—
392Dic61—28no—
393Dic61—42no—
394Dic61—44no—
395Dic61—42no—
396Dic61C2×#9518yescomplemented
397C22×C4×D4—611no—
398C22×C4×D4—612no—
399C22×#95—611no—
400C22×#95—611no—
401C4⋊#95—612no—
402C4⋊#95—611no—
403C22⋊#95—612no—
404C22⋊#95—611no—
405C22⋊#95—612no—
406C22⋊#95D6111yescharacteristic, complemented
407C4×#95—611no—
408C2×C61—28no—
409C2×C61C22×#9511yescharacteristic
410C2×C61C42×D411yescharacteristic
411C2×C61#227511yescharacteristic
412C2×C61D4×C22⋊C411yescharacteristic
413C2×C61D4×C22⋊C412yes—
414C2×C61#233911yescharacteristic
415C2×C61#233912yes—
416C2×C61D4×C4⋊C411yescharacteristic
417C2×C61D4×C4⋊C412yes—
418C2×C61#234911yescharacteristic
419C2×C61#234912yes—
420D61—28no—
421C23×D4—611no—
422C24×C4—612no—
423C24×C4—612no—
424C24×C4—611no—
425C24×C4C2×D6111yescharacteristic
426C2×C4×D4—618no—
427C2×C4×D4—6116no—
428C2×C4×D4—1228no—
429C2×C4×D4—1228no—
430C2×C4×D4—1228no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—612no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4C2×D6112yes—
437C22×C42—612no—
438C22×C42—611no—
439C2×#95—611no—
440C2×#95—612no—
441C2×#95—612no—
442C2×#95—612no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—1224no—
447C2×#95—1224no—
448C2×#95C2×D6111yescharacteristic
449C2×#95C2×D6111yescharacteristic
450C2×#95C2×D6112yes—
451C61D4×#9511yescharacteristic, complemented, Sylow
452C25—611no—
453C25C22×D6111yescharacteristic
454C22×D4—614no—
455C22×D4—618no—
456C22×D4—614no—
457C22×D4—618no—
458C22×D4—614no—
459C23×C4—24no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—42no—
463C23×C4—611no—
464C23×C4—612no—
465C23×C4—611no—
466C23×C4—612no—
467C23×C4—611no—
468C23×C4—618no—
469C23×C4—618no—
470C23×C4—614no—
471C23×C4—1224no—
472C23×C4—1224no—
473C23×C4—1224no—
474C23×C4—1224no—
475C23×C4—1224no—
476C23×C4—1224no—
477C23×C4—1224no—
478C23×C4—1224no—
479C23×C4—1224no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—2442no—
483C23×C4—2442no—
484C23×C4—2442no—
485C23×C4—2442no—
486C23×C4—2442no—
487C23×C4C4×D6114yescomplemented
488C23×C4C22×D6112yes—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492C4×D4—12264no—
493C4×D4—12232no—
494C2×C4⋊C4—614no—
495C2×C4⋊C4—618no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—1224no—
498C2×C4⋊C4—1224no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—614no—
502C2×C22⋊C4—614no—
503C2×C22⋊C4—618no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4C4×D6118yescomplemented
509C2×C42—618no—
510C2×C42—614no—
511C2×C42—1224no—
512C2×C42—1224no—
513C2×C42—1224no—
514#95—22no—
515#95—22no—
516#95—42no—
517#95—614no—
518#95—1224no—
519#95—1224no—
520#95—1224no—
521#95—1222no—
522#95—2442no—
523#95—2442no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—614no—
531C24—612no—
532C24—614no—
533C24—612no—
534C24—612no—
535C24—1221no—
536C24—1222no—
537C24—1221no—
538C24—1222no—
539C24—1221no—
540C24—1221no—
541C24C2×C4×D6112yes—
542C24C2×C4×D6114yes—
543C24D4×D6112yes—
544C24D4×D6114yes—
545C24Q8×D6112yes—
546C24C23×D6111yescharacteristic
547C2×D4—6116no—
548C2×D4—6132no—
549C2×D4—6116no—
550C2×D4—6116no—
551C2×D4—6132no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—614no—
576C22×C4—612no—
577C22×C4—614no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—614no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—612no—
584C22×C4—614no—
585C22×C4—612no—
586C22×C4—12216no—
587C22×C4—1228no—
588C22×C4—12216no—
589C22×C4—12216no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—12216no—
609C22×C4—1228no—
610C22×C4—2444no—
611C22×C4—2448no—
612C22×C4—2448no—
613C22×C4—2448no—
614C22×C4—2448no—
615C22×C4—2448no—
616C22×C4—2448no—
617C22×C4—2448no—
618C22×C4—2448no—
619C22×C4—2448no—
620C22×C4—2448no—
621C22×C4—2448no—
622C22×C4—2448no—
623C22×C4C2×C4×D6114yes—
624C22×C4C2×C4×D6112yes—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×C4×D6112yes—
627C22×C4D4×D6112yes—
628C22×C4#1175822412yes—
629C4⋊C4—12216no—
630C4⋊C4—1228no—
631C22⋊C4—216no—
632C22⋊C4—12216no—
633C22⋊C4—1228no—
634C22⋊C4—1228no—
635C42—1228no—
636C42—12216no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—614no—
656C23—614no—
657C23—618no—
658C23—614no—
659C23—618no—
660C23—1224no—
661C23—1222no—
662C23—1224no—
663C23—1222no—
664C23—1224no—
665C23—1222no—
666C23—1224no—
667C23—1222no—
668C23—1224no—
669C23—1222no—
670C23—1224no—
671C23—1222no—
672C23—1224no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1222no—
677C23—1222no—
678C23C42×D6114yes—
679C23C22⋊C4×D6118yes—
680C23C22⋊C4×D6114yes—
681C23C4⋊C4×D6114yes—
682C23C4⋊C4×D6118yes—
683C23C22×C4×D6112yes—
684C23C22×C4×D6111yescharacteristic
685C23C2×D4×D6112yes—
686C23C2×D4×D6111yescharacteristic
687C23C2×D4×D6111yescharacteristic
688C23C2×Q8×D6111yescharacteristic
689C23#41×D6112yes—
690C23C2×#1175822411yescharacteristic
691C23#1451982212yes—
692C23#1451982311yescharacteristic
693C23#1451982411yescharacteristic
694D4—6164no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—614no—
720C2×C4—614no—
721C2×C4—618no—
722C2×C4—614no—
723C2×C4—618no—
724C2×C4—618no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1224no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—24416no—
741C2×C4—24432no—
742C2×C4—24432no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4#1451973714yescomplemented
752C22—24no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—24no—
757C22—28no—
758C22—24no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—618no—
763C22—1224no—
764C22—1228no—
765C22—1224no—
766C22—1228no—
767C22—1224no—
768C22—1228no—
769C22—1224no—
770C22—1228no—
771C22—1224no—
772C22—1224no—
773C22#95×D6118yescomplemented
774C22C2×C42×D6111yescharacteristic
775C22C2×C22⋊C4×D6111yescharacteristic
776C22C2×C22⋊C4×D6112yes—
777C22C2×C4⋊C4×D6111yescharacteristic
778C22C2×C4⋊C4×D6112yes—
779C22C4×D4×D6112yes—
780C22C2×#1451973711yescharacteristic
781C22C4×#1175822412yes—
782C22#1684023011yescharacteristic
783C22#1684023412yes—
784C22#1684023511yescharacteristic
785C22#1684024112yes—
786C22#1684024211yescharacteristic
787C22#1684039412yes—
788C22#1684039611yescharacteristic
789C22#1684039912yes—
790C22#1684040112yes—
791C22#1684040412yes—
792C22#1684041012yes—
793C22#1684041211yescharacteristic
794C22#1684042511yescharacteristic
795C22#1684046612yes—
796C22#1684047011yescharacteristic
797C4—24no—
798C4—42no—
799C4—44no—
800C4—44no—
801C4—618no—
802C4—1228no—
803C4—2442no—
804C4—2444no—
805C4—2442no—
806C2—28no—
807C2—1228no—
808C2C2×#95×D6111yescharacteristic
809C2C4×#1451973711yescharacteristic
810C2#2144817811yescharacteristic
811C2#2144863511yescharacteristic
812C2#2144863712yes—
813C2#2144864311yescharacteristic
814C2#2144864512yes—
815C2#2144871511yescharacteristic
816C2#2144871712yes—
817C2#2144872311yescharacteristic
818C2#2144872512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61D4×#95
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C22×#14519684C2semidirect
4. C2×#95×D61C2semidirect
5. #21444047C2semidirect
6. #21444047C2semidirect
7. #21444041C2semidirect
8. #21444040C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C61×C22⋊#95C2semidirect
17. C2×C4×C22⋊D61C4semidirect
20. C2×#14519737C4semidirect
54. C23×Dic61C2×C4semidirect
70. C22×C4×D61C2×C4semidirect
71. C22×C4×D61C2×C4semidirect
77. C2×#11758196C2×C4semidirect
78. C2×#11758196C2×C4semidirect
80. C2×C22⋊Dic61C2×C4semidirect
84. C2×#11758198C2×C4semidirect
85. C2×#11758198C2×C4semidirect
89. C2×C4×Dic61C2×C4semidirect
90. C2×C4×Dic61C2×C4semidirect
97. #14519684D4semidirect
103. C23×C4×C61C2×C4semidirect
110. C2×C22⋊C4×C61C2×C4semidirect
308. C2×C4×C61C4×D4semidirect
309. C22⋊D61#95semidirect
339. C2×Dic61C4×D4semidirect
353. C22×C61C2×#95semidirect
387. C2×D61C2×#95semidirect
396. Dic61C2×#95semidirect
406. C22⋊#95D61semidirect
451. C61D4×#95semidirect
487. C23×C4C4×D61semidirect
508. C2×C22⋊C4C4×D61semidirect
751. C2×C4#14519737semidirect
773. C22#95×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C22×#145197372
C22×#145196842
C2×#95×D612
#214440472
#214440412
#214440402
#95×Dic612
C61×C22⋊#952
D4×#9561