Finite Group Databasebeta

← #29713988

Subgroups — #29713988

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21450720C211yesmaximal, characteristic, complemented
4#21447005C211yesmaximal, characteristic, complemented
5#21446998C211yesmaximal, characteristic, complemented
6#21446815C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446785C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21446007C211yesmaximal, characteristic, complemented
14#21445829C211yesmaximal, characteristic, complemented
15C2×C61×#553C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840059—24no—
21C4×#11758199—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839688—21no—
38#16839670—21no—
39#16839638—21no—
40#16839638—21no—
41#16839628C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C61×#553—24no—
51C61×#553—24no—
52C2×#126×C61—21no—
53C2×#125×C61C2211yescharacteristic
54C2×#123×C61—21no—
55C2×#121×C61—21no—
56C2×#121×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×C4×D4×C61—21no—
59C2×C4×D4×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519751—22no—
75#14519751—22no—
76#14519751—41no—
77#14519751—41no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88#14519710—22no—
89#14519710—22no—
90#14519708—22no—
91C4⋊#92418—22no—
92#14519698—22no—
93#14519698—41no—
94#14519698—41no—
95#14519697—22no—
96#14519697—22no—
97#14519697—22no—
98C22⋊#92418—22no—
99C22⋊#92418—22no—
100C22⋊#92418—41no—
101C22⋊#92418—41no—
102C4×#92418—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×D4×C61—21no—
108C22×D4×C61—21no—
109C22×D4×C61D411yescharacteristic
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61—21no—
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#126×C61—28no—
116#125×C61—22no—
117#125×C61D414yescomplemented
118#123×C61—28no—
119#121×C61—28no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—22no—
124C4×D4×C61—28no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61D414yescomplemented
129#117×C61—22no—
130#117×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C23×D61—21no—
152C2×D4×C61—24no—
153C2×D4×C61—22no—
154C2×D4×C61—24no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—41no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—81no—
165C2×D4×C61—81no—
166C2×D4×C61C2×D412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—24no—
184C22×C4×C61—81no—
185C22×C4×C61—81no—
186C22×C4×C61—81no—
187C22×C4×C61—81no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61—81no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244#4112yes—
208C2×C4×D61—42no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—24no—
213C4⋊C4×C61—24no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C2×D412yes—
219C4⋊C4×C61C2×D412yes—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—24no—
222C22⋊C4×C61—24no—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C42×C61—24no—
228C42×C61C2×D412yes—
229C42×C61C2×D412yes—
230C22⋊Dic61—81no—
231C22⋊Dic61—81no—
232#11758199—28no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418#4112yes—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61#13512yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—44no—
286D4×C61—48no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—84no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—84no—
318C2×C4×C61—84no—
319C2×C4×C61#12012yes—
320C2×C4×C61#12012yes—
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C2×C4×C612−1+411yescharacteristic
327C22⋊D61—84no—
328C22⋊D61—84no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338D244—22no—
339D244—22no—
340D244—41no—
341D244—41no—
342C4×D61—84no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#24124—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61C2×#12011yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54711yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C22×C61#57511yescharacteristic
374C22×C61#57611yescharacteristic
375C22×C61#57611yescharacteristic
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61#52511yescharacteristic
391C4×C61#53711yescharacteristic
392C4×C61#54811yescharacteristic
393C4×C61#55011yescharacteristic
394Dic61—81no—
395Dic61—81no—
396Dic61—81no—
397C2×#553D6111yescharacteristic, complemented
398C2×#478—611no—
399C2×C4×D8—611no—
400#2535—611no—
401#2034—611no—
402#2033—611no—
403#1999—611no—
404#1999—611no—
405#1991—611no—
406#1954—611no—
407#1875—611no—
408#1874—611no—
409#1854—611no—
410#1852—611no—
411#1804—611no—
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—82no—
415C2×C61#240711yescharacteristic
416C2×C61#300211yescharacteristic
417C2×C61#300811yescharacteristic
418C2×C61#329711yescharacteristic
419C2×C61#332211yescharacteristic
420C2×C61#333911yescharacteristic
421C2×C61#335511yescharacteristic
422D61—82no—
423C22×D8—611no—
424#553—24no—
425#553—24no—
426C2×#126—21no—
427C2×#125C2×D6111yescharacteristic
428C2×#123—21no—
429C2×#121—21no—
430C2×#121—611no—
431C2×#121—611no—
432C2×#121C2×D6111yescharacteristic
433C2×#121C2×D6111yescharacteristic
434C2×C4×D4—21no—
435C2×C4×D4—611no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117C2×D6111yescharacteristic
439C22×C4⋊C4C2×D6111yescharacteristic
440#478—1224no—
441C4×D8—1224no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×C4⋊C8—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C4×C8—611no—
457#397—1221no—
458#392—1221no—
459#386—1221no—
460#386—1221no—
461#382—611no—
462#380—611no—
463#380—611no—
464#340—611no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470C61#2412411yescharacteristic, complemented, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—611no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4C22⋊D6111yescharacteristic
477C22×D4C22×D6111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483C2×D8—1222no—
484C2×D8—1222no—
485C2×D8—1222no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490#126—28no—
491#125—22no—
492#125C22⋊D6114yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—1222no—
500#121—1222no—
501#121—2441no—
502#121—2441no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4C22⋊D6114yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4C22⋊D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4C22⋊D6111yescharacteristic
534C2×C22⋊C4C22⋊D6111yescharacteristic
535C2×C42—21no—
536C2×C42C22×D6111yescharacteristic
537#107—1222no—
538#107—1222no—
539#106—1222no—
540C4⋊C8—1222no—
541#102—1222no—
542#102—1222no—
543#102—1222no—
544#102—1222no—
545#102—2441no—
546#102—2441no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—2441no—
550C22⋊C8—2441no—
551C4×C8—1222no—
552#95—1221no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556C24—21no—
557C24—1221no—
558C24C2×C22⋊D6111yescharacteristic
559C24C2×C22⋊D6111yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—612no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—4881no—
581C2×D4—4881no—
582C2×D4—2442no—
583C2×D4—2442no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4C2×C22⋊D6112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—2442no—
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C22×C4C2×C22⋊D6111yescharacteristic
617C22×C4C2×C22⋊D6111yescharacteristic
618C22×C4C23×D6111yescharacteristic
619D8—1228no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4C2×C22⋊D6112yes—
646C4⋊C4C2×C22⋊D6112yes—
647C4⋊C4C2×C22⋊D6112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—4881no—
655C22⋊C4—4881no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C42—24no—
660C42C2×C22⋊D6112yes—
661C42C2×C22⋊D6112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—1222no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23#1451979712yes—
690C23C22×C22⋊D6111yescharacteristic
691D4—22no—
692D4—22no—
693D4—44no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—84no—
698D4—1222no—
699D4—1222no—
700D4—4884no—
701D4—4884no—
702D4—2441no—
703D4—2441no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—4884no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4#1451974612yes—
744C2×C4#1451974612yes—
745C2×C4C22×C22⋊D6111yescharacteristic
746C2×C4C22×C22⋊D6111yescharacteristic
747C2×C4#41×D6111yescharacteristic
748C2×C4#41×D6111yescharacteristic
749C2×C4#1451982311yescharacteristic
750C2×C4#1451982411yescharacteristic
751C8—1222no—
752C8—2441no—
753C8—2441no—
754C8—2441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—4881no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22C2×#1451974611yescharacteristic
784C22#1684040011yescharacteristic
785C22#1684041111yescharacteristic
786C22C2×#1451979711yescharacteristic
787C22#1684056011yescharacteristic
788C22#1684056511yescharacteristic
789C22#1684056511yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—42no—
797C4—4881no—
798C4—4881no—
799C4—4881no—
800C4#1684026911yescharacteristic
801C4#1684034011yescharacteristic
802C4#1684041911yescharacteristic
803C4#1684043111yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—4882no—
808C2#2144915811yescharacteristic
809C2#2145503711yescharacteristic
810C2#2145508711yescharacteristic
811C2#2145766311yescharacteristic
812C2#2145801411yescharacteristic
813C2#2145821511yescharacteristic
814C2#2145841911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#553C2
socleC23×C61C22×D4
hypercenterC2×#553D61
hypocenterC61#24124
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
2. C2×C4×#11758199C2semidirect
3. #21450720C2semidirect
4. #21447005C2semidirect
5. #21446998C2semidirect
6. #21446815C2semidirect
7. #21446815C2semidirect
8. #21446785C2semidirect
9. #21446614C2semidirect
10. #21446141C2semidirect
11. #21446136C2semidirect
12. #21446018C2semidirect
13. #21446007C2semidirect
14. #21445829C2semidirect
15. C2×C61×#553C2semidirect
117. #125×C61D4semidirect
128. C4×D4×C61D4semidirect
397. C2×#553D61semidirect
470. C61#24124semidirect
492. #125C22⋊D61semidirect
509. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×C4×#117581992
#214507202
#214470052
#214469982
#214468152
#214467852
#214466142
#214461412
#214461362
#214460182
#214460072
#214458292
C2×C61×#5532
#2412461