Finite Group Databasebeta

← #29715187

Subgroups — #29715187

Order 15616.

1364 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839981C211yesmaximal, characteristic, complemented
2C2×#16839969C211yesmaximal, characteristic, complemented
3C2×#16839924C211yesmaximal, characteristic
4C2×#16839918C211yesmaximal, characteristic, complemented
5#21448501C211yesmaximal, characteristic, complemented
6#21447062C211yesmaximal, characteristic, complemented
7#21447055C211yesmaximal, characteristic, complemented
8#21446919C211yesmaximal, characteristic, complemented
9#21446913C211yesmaximal, characteristic, complemented
10#21446752C211yesmaximal, characteristic, complemented
11#21446743C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#536C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22#16839981—24no—
23#16839969—24no—
24#16839924—24no—
25#16839918—24no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839660C2211yescharacteristic
44#16839657—21no—
45#16839656—21no—
46#16839650—21no—
47#16839643—21no—
48#16839622C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C61×#536—24no—
55C61×#536—24no—
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C2×#124×C61C2211yescharacteristic
59C2×#124×C61C2211yescharacteristic
60C2×#123×C61—21no—
61C2×#123×C61—21no—
62C2×C22⋊Q8×C61—21no—
63C2×C22⋊Q8×C61—21no—
64C2×#117×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—41no—
73C2×#11758202—41no—
74C2×#11758202—41no—
75C2×#11758200—22no—
76C2×#11758200—22no—
77C2×#11758200—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519756—22no—
83#14519756D414yes—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C4⋊#92418—22no—
97C4⋊#92418—22no—
98#14519701—22no—
99#14519701—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519701—41no—
106#14519701—41no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61—22no—
124C22×Q8×C61—22no—
125C22×Q8×C61—21no—
126C22×Q8×C61—22no—
127C22×Q8×C61—22no—
128C22×Q8×C61—41no—
129C22×Q8×C61—41no—
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C4⋊Q8×C61—22no—
139C4⋊Q8×C61—22no—
140C4⋊Q8×C61—22no—
141C4⋊Q8×C61D414yes—
142#124×C61—22no—
143#124×C61—22no—
144#124×C61—22no—
145#124×C61D414yes—
146#123×C61—28no—
147#123×C61—28no—
148C22⋊Q8×C61—28no—
149C22⋊Q8×C61—28no—
150#117×C61—22no—
151#117×C61—22no—
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61D411yescharacteristic
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168#41×C61—44no—
169#41×C61—44no—
170#41×C61—44no—
171#41×C61—44no—
172C2×Q8×C61—24no—
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—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—44no—
189C2×Q8×C61—44no—
190C2×Q8×C61—44no—
191C2×Q8×C61—44no—
192C2×Q8×C61—42no—
193C2×Q8×C61—42no—
194C2×Q8×C61C2×D412yes—
195C2×Q8×C61C2×D412yes—
196C2×Q8×C61C2×D412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61C2×D412yes—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
211C22×C4×C61—24no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61#4112yes—
226C22×C4×C61C2411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C2×D412yes—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—22no—
242C4⋊C4×C61—22no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61C2×D412yes—
252C42×C61C2×D412yes—
253C22⋊Dic61—24no—
254C22⋊Dic61—81no—
255#11758202—44no—
256#11758202—44no—
257#11758202—44no—
258#11758200—44no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C2×D412yes—
265#11758196—24no—
266#11758196—42no—
267#11758196—81no—
268C4×Dic61—42no—
269C4×Dic61—81no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61#12112yes—
296C23×C61C22×D411yescharacteristic
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—48no—
304Q8×C61—41no—
305Q8×C61—41no—
306Q8×C61—41no—
307Q8×C61—41no—
308Q8×C61—41no—
309Q8×C61—41no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—48no—
313D4×C61—41no—
314D4×C61—41no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—48no—
335C2×C4×C61—48no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61#12012yes—
343C2×C4×C61#12012yes—
344C2×C4×C61#12112yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363Dic122—22no—
364Dic122—22no—
365Dic122—41no—
366Dic122—41no—
367#92418—41no—
368#92418—41no—
369#92418—41no—
370#92418—41no—
371#24221—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61C2×#12011yescharacteristic
387C22×C61C2×#12111yescharacteristic
388C22×C61#53511yescharacteristic
389C22×C61#57711yescharacteristic
390C22×C61#57811yescharacteristic
391C22×C61#57811yescharacteristic
392C22×C61#57811yescharacteristic
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—22no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61D4211yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404C4×C61#54611yescharacteristic
405Dic61—42no—
406Dic61—42no—
407Dic61—81no—
408Dic61—81no—
409C2×#536D6111yescharacteristic
410C2×#464—611no—
411C2×#462—611no—
412C2×#452—611no—
413C2×#451—611no—
414#2323—611no—
415#2043—611no—
416#2042—611no—
417#2016—611no—
418#2015—611no—
419#1983—611no—
420#1981—611no—
421#1798—611no—
422#1788—611no—
423#1787—611no—
424C2×C61—42no—
425C2×C61—82no—
426C2×C61#240811yescharacteristic
427C2×C61#301111yescharacteristic
428C2×C61#301311yescharacteristic
429C2×C61#304411yescharacteristic
430C2×C61#304611yescharacteristic
431C2×C61#322311yescharacteristic
432C2×C61#322511yescharacteristic
433C22×#41C2×D6111yescharacteristic
434C23×Q8C2×D6111yescharacteristic
435C22×Q16—611no—
436C22×Q16—611no—
437C22×Q16—611no—
438C22×SD16—611no—
439#536—24no—
440#536—24no—
441C2×C4⋊Q8C2×D6111yescharacteristic
442C2×C4⋊Q8C2×D6111yescharacteristic
443C2×#124C2×D6111yescharacteristic
444C2×#124C2×D6111yescharacteristic
445C2×#123—21no—
446C2×#123—21no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—611no—
450C2×C4×Q8—611no—
451C2×#117C2×D6111yescharacteristic
452#464—1224no—
453#462—1224no—
454#452—1224no—
455#451—1224no—
456C2×C4⋊C8—611no—
457C2×C4⋊C8—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472#391—611no—
473#389—611no—
474#389—1221no—
475#388—1221no—
476#388—1221no—
477#387—1221no—
478#380—611no—
479C4×C4⋊C4—611no—
480#336—611no—
481#336—611no—
482C61#2422111yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—611no—
497C22×Q8C22×D6111yescharacteristic
498C22×Q8C22×D6111yescharacteristic
499C22×Q8C22×D6111yescharacteristic
500C22×D4—21no—
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C22×D6111yescharacteristic
505C2×Q16—1222no—
506C2×Q16—1222no—
507C2×Q16—1222no—
508C2×Q16—1222no—
509C2×Q16—1222no—
510C2×Q16—1222no—
511C2×Q16—2441no—
512C2×Q16—2441no—
513C2×Q16—2441no—
514C2×SD16—1222no—
515C2×SD16—1222no—
516C2×SD16—2441no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8C22⋊D6114yes—
525#124—22no—
526#124—22no—
527#124—22no—
528#124C22⋊D6114yes—
529#123—28no—
530#123—28no—
531C22⋊Q8—28no—
532C22⋊Q8—28no—
533C22⋊Q8—614no—
534C22⋊Q8—1222no—
535C4×Q8—1222no—
536C4×Q8—1222no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4C22⋊D6111yescharacteristic
550C2×C4⋊C4C22⋊D6111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4C22⋊D6111yescharacteristic
558C2×C22⋊C4C22⋊D6111yescharacteristic
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562C2×C42C22×D6111yescharacteristic
563C4⋊C8—1222no—
564C4⋊C8—1222no—
565#103—1222no—
566#103—1222no—
567#103—1222no—
568#103—1222no—
569#103—1222no—
570#103—1222no—
571#103—2441no—
572#103—2441no—
573#103—2441no—
574#102—1222no—
575#102—1222no—
576#102—2441no—
577C22⋊C8—1222no—
578C22⋊C8—1222no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584C24—21no—
585C24C2×C22⋊D6111yescharacteristic
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
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—21no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—612no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8C2×C22⋊D6112yes—
619C2×Q8C2×C22⋊D6112yes—
620C2×Q8C2×C22⋊D6112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×C22⋊D6112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4D4×D6112yes—
648C22×C4#1175822412yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C23×D6111yescharacteristic
655Q16—2444no—
656Q16—2444no—
657Q16—2444no—
658SD16—2444no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—612no—
678C4⋊C4—1221no—
679C4⋊C4—1224no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—4881no—
685C4⋊C4—2442no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—1224no—
693C22⋊C4—4881no—
694C42—21no—
695C42—21no—
696C42—4881no—
697C42—2442no—
698C42C2×C22⋊D6112yes—
699C42C2×C22⋊D6112yes—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23#1451974812yes—
714C23C22×C22⋊D6111yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—48no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—1222no—
729Q8—1222no—
730Q8—2441no—
731Q8—2441no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—41no—
736D4—41no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4#1451974612yes—
777C2×C4#1451974612yes—
778C2×C4#1451974812yes—
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C22×C22⋊D6111yescharacteristic
781C2×C4C22×C22⋊D6111yescharacteristic
782C2×C4C2×#1175822411yescharacteristic
783C2×C4#1451982211yescharacteristic
784C2×C4#1451982211yescharacteristic
785C8—2441no—
786C8—2441no—
787C8—2441no—
788C8—2441no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#1451974611yescharacteristic
804C22C2×#1451974811yescharacteristic
805C22#1684032911yescharacteristic
806C22#1684057011yescharacteristic
807C22#1684057711yescharacteristic
808C22#1684057711yescharacteristic
809C22#1684057711yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—4881no—
819C4—4881no—
820C4—2442no—
821C4—2442no—
822C4D4×C22⋊D6111yescharacteristic
823C4D4×C22⋊D6111yescharacteristic
824C4#1684040611yescharacteristic
825C4#1684040611yescharacteristic
826C2—42no—
827C2—82no—
828C2#2144916911yescharacteristic
829C2#2145511411yescharacteristic
830C2#2145513411yescharacteristic
831C2#2145534511yescharacteristic
832C2#2145536511yescharacteristic
833C2#2145690211yescharacteristic
834C2#2145692811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#536C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#536D61
hypocenterC61#24221
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#16839981C2semidirect
2. C2×#16839969C2semidirect
4. C2×#16839918C2semidirect
5. #21448501C2semidirect
6. #21447062C2semidirect
7. #21447055C2semidirect
8. #21446919C2semidirect
9. #21446913C2semidirect
10. #21446752C2semidirect
11. #21446743C2semidirect
12. #21445803C2semidirect
14. #21445754C2semidirect
482. C61#24221semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168399692
C2×#168399242
C2×#168399182
#214485012
#214470622
#214470552
#214469192
#214469132
#214467522
#214467432
#214458032
#214457592
#214457542
C2×C61×#5362
#2422161