Finite Group Databasebeta

← #29715629

Subgroups — #29715629

Order 15616.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839981C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C2×#16839862C211yesmaximal, characteristic, complemented
5#21450741C211yesmaximal, characteristic, complemented
6#21447019C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446636C211yesmaximal, characteristic, complemented
11#21446618C211yesmaximal, characteristic, complemented
12#21445819C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic, complemented
21C2×C4×Dic122C2211yescharacteristic, complemented
22#16839981—24no—
23#16839924—24no—
24#16839913—24no—
25#16839862—24no—
26C2×#14519710C2211yescharacteristic, complemented
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519700C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519688C2211yescharacteristic, complemented
43#16839685—21no—
44#16839685—21no—
45#16839665—21no—
46#16839658—21no—
47#16839632C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#546—24no—
55C61×#546—24no—
56C2×#124×C61C2211yescharacteristic
57C2×#123×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C22×C22⋊C4×C61—21no—
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—41no—
74C2×#11758200D414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519756—22no—
80#14519756—22no—
81#14519756—41no—
82#14519756—41no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C4×Dic61—21no—
98#14519710—22no—
99C4⋊#92418—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519700—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113C22⋊#92418—41no—
114#14519688—22no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—41no—
123C2×#41×C61—41no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61—21no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—22no—
130C22×D4×C61—22no—
131C22×D4×C61—21no—
132C22×D4×C61—41no—
133C22×D4×C61—41no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141#124×C61—22no—
142#124×C61D414yes—
143#123×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146#121×C61—28no—
147#121×C61—22no—
148#121×C61—22no—
149#120×C61—28no—
150C4×D4×C61—22no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C4×D4×C61D414yes—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61D411yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—28no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61—24no—
168C24×C61—21no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177#41×C61—44no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—22no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—41no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—44no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—44no—
209C2×D4×C61—81no—
210C2×D4×C61—81no—
211C2×D4×C61C2×D412yes—
212C2×D4×C61C2×D412yes—
213C2×D4×C61C2×D412yes—
214C2×D4×C61#4112yes—
215C22×C4×C61—24no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—24no—
231C22×C4×C61—42no—
232C22×C4×C61—42no—
233C22×C4×C61—81no—
234C22×C4×C61—81no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122C2×D412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—22no—
261C42×C61C2×D412yes—
262C42×C61C2×D412yes—
263C22⋊Dic61—42no—
264C22⋊Dic61—42no—
265C22⋊Dic61—81no—
266C22⋊Dic61—81no—
267#11758202—44no—
268#11758200—28no—
269#11758200—44no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—42no—
277C4⋊Dic61—81no—
278#11758196—42no—
279#11758196—42no—
280#11758196—42no—
281C4×Dic61—42no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418C2×D412yes—
294C23×C61—21no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—48no—
312C23×C61—48no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61—84no—
328C23×C61#13712yes—
329C23×C61C22×D411yescharacteristic
330Q8×C61—22no—
331Q8×C61—22no—
332Q8×C61—41no—
333Q8×C61—41no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—44no—
340D4×C61—48no—
341D4×C61—48no—
342D4×C61—41no—
343D4×C61—41no—
344D4×C61—84no—
345D4×C61#12114yes—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—22no—
351C2×C4×C61—21no—
352C2×C4×C61—22no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—48no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—84no—
372C2×C4×C61#12012yes—
373C2×C4×C61#12012yes—
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C2×#4111yescharacteristic
378C2×C4×C61H(5,𝔽2)11yescharacteristic
379C2×C4×C61H(5,𝔽2)11yescharacteristic
380C2×Dic61—22no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392Dic122—22no—
393Dic122—22no—
394Dic122—41no—
395Dic122—41no—
396#92418—22no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#24259—611nomaximal, Sylow
401C22×C61—24no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—41no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—816no—
426C22×C61—81no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61C2×#12011yescharacteristic
431C22×C61D4211yescharacteristic
432C22×C61#54611yescharacteristic
433C22×C61C2×#13711yescharacteristic
434C22×C61#57511yescharacteristic
435C22×C61#57611yescharacteristic
436C22×C61#57711yescharacteristic
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—41no—
440C4×C61—41no—
441C4×C61—42no—
442C4×C61—42no—
443C4×C61C2×#12111yescharacteristic
444C4×C61#53511yescharacteristic
445C4×C61D4211yescharacteristic
446C4×C61#54611yescharacteristic
447Dic61—42no—
448Dic61—81no—
449Dic61—81no—
450Dic61—81no—
451C2×#546D6111yescharacteristic
452C2×#464—611no—
453C2×#452—611no—
454C2×#450—611no—
455C2×#440—611no—
456#2538—611no—
457#2036—611no—
458#2033—611no—
459#2001—611no—
460#2000—611no—
461#1959—611no—
462#1955—611no—
463#1802—611no—
464#1788—611no—
465#1786—611no—
466C2×C61—42no—
467C2×C61—44no—
468C2×C61—81no—
469C2×C61—82no—
470C2×C61#240811yescharacteristic
471C2×C61#300711yescharacteristic
472C2×C61#301211yescharacteristic
473C2×C61#326611yescharacteristic
474C2×C61#326811yescharacteristic
475C2×C61#331111yescharacteristic
476C2×C61#331411yescharacteristic
477C22×#41C2×D6111yescharacteristic
478C23×D4C2×D6111yescharacteristic
479C22×Q16—611no—
480C22×SD16—611no—
481C22×SD16—611no—
482#546—24no—
483#546—24no—
484C2×#124C2×D6111yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8—611no—
487C2×C22⋊Q8—611no—
488C2×C22⋊Q8C2×D6111yescharacteristic
489C2×#121—21no—
490C2×#121C2×D6111yescharacteristic
491C2×#120—21no—
492C2×C4×Q8—611no—
493C2×C4×D4C2×D6111yescharacteristic
494C2×C4×D4C2×D6111yescharacteristic
495C22×C22⋊C4—21no—
496#464—1224no—
497#452—1224no—
498#450—1224no—
499#440—1224no—
500C2×#107—611no—
501C2×C4⋊C8—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×C22⋊C8—611no—
513C2×C22⋊C8—611no—
514C2×C22⋊C8—611no—
515C2×C22⋊C8—611no—
516C2×#97—611no—
517#396—1221no—
518#396—1221no—
519#390—1221no—
520#389—1221no—
521#384—611no—
522#380—611no—
523#380—611no—
524#340—611no—
525#340—611no—
526C61#2425911yescharacteristic, complemented, Sylow
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8—611no—
535C22×Q8C22×D6111yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4C22⋊D6111yescharacteristic
546C22×D4C22×D6111yescharacteristic
547C22×D4C22×D6111yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C22×D6111yescharacteristic
551C23×C4C22×D6111yescharacteristic
552C2×Q16—1222no—
553C2×Q16—1222no—
554C2×Q16—2441no—
555C2×SD16—614no—
556C2×SD16—1222no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—2441no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—611no—
565#124—22no—
566#124C22⋊D6114yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—1222no—
571C22⋊Q8—1222no—
572C22⋊Q8—2441no—
573C22⋊Q8—2441no—
574#121—28no—
575#121—22no—
576#121—22no—
577#120—28no—
578C4×Q8—1222no—
579C4×Q8—1222no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4C22⋊D6114yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C22⋊D6111yescharacteristic
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C42—1221no—
608C2×C42C22×D6111yescharacteristic
609#107—1222no—
610C4⋊C8—1222no—
611#103—1222no—
612#103—1222no—
613#103—1222no—
614#103—2441no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—1222no—
620#102—2441no—
621C22⋊C8—1222no—
622C22⋊C8—1222no—
623C22⋊C8—2441no—
624C22⋊C8—2441no—
625#97—1222no—
626#95—1221no—
627#95—1221no—
628C24—21no—
629C24—24no—
630C24—21no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24C2×C22⋊D6111yescharacteristic
638C24C2×C22⋊D6111yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—612no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8C2×C22⋊D6112yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—22no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4D4×D6112yes—
680C2×D4#1175822412yes—
681C2×D4C2×C22⋊D6112yes—
682C2×D4C2×C22⋊D6112yes—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6111yescharacteristic
712Q16—2444no—
713SD16—1228no—
714SD16—2444no—
715C2×C8—612no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—22no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—4881no—
737C4⋊C4—2442no—
738C4⋊C4—2442no—
739C4⋊C4—2442no—
740C4⋊C4—2442no—
741C4⋊C4C2×C22⋊D6112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—4881no—
750C22⋊C4—4881no—
751C22⋊C4—2442no—
752C22⋊C4—2442no—
753C42—2442no—
754C42C2×C22⋊D6112yes—
755C42C2×C22⋊D6112yes—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—22no—
763C23—21no—
764C23—22no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23#1451980712yes—
791C23C22×C22⋊D6111yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—41no—
795Q8—41no—
796Q8—1222no—
797Q8—1222no—
798Q8—2441no—
799Q8—2441no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4#1451974814yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—48no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—84no—
838C2×C4—1222no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4#1451974612yes—
851C2×C4#1451974612yes—
852C2×C4C2×D4×D6111yescharacteristic
853C2×C4C22×C22⋊D6111yescharacteristic
854C2×C4C22×C22⋊D6111yescharacteristic
855C2×C4C2×#1175822411yescharacteristic
856C2×C4#1451982211yescharacteristic
857C2×C4#1451982211yescharacteristic
858C8—1222no—
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—22no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×#1451974611yescharacteristic
892C22D4×C22⋊D6111yescharacteristic
893C22#1684040611yescharacteristic
894C22C2×#1451980711yescharacteristic
895C22#1684056011yescharacteristic
896C22#1684056511yescharacteristic
897C22#1684057311yescharacteristic
898C4—22no—
899C4—22no—
900C4—42no—
901C4—41no—
902C4—41no—
903C4—42no—
904C4—4881no—
905C4—4881no—
906C4—4881no—
907C4—2442no—
908C4C2×#1451974811yescharacteristic
909C4#1684032911yescharacteristic
910C4D4×C22⋊D6111yescharacteristic
911C4#1684040611yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2#2144916911yescharacteristic
917C2#2145507911yescharacteristic
918C2#2145512311yescharacteristic
919C2#2145732511yescharacteristic
920C2#2145735511yescharacteristic
921C2#2145785511yescharacteristic
922C2#2145790011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24259
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16839981C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839913C2semidirect
4. C2×#16839862C2semidirect
5. #21450741C2semidirect
6. #21447019C2semidirect
7. #21446998C2semidirect
8. #21446827C2semidirect
9. #21446822C2semidirect
10. #21446636C2semidirect
11. #21446618C2semidirect
12. #21445819C2semidirect
13. #21445759C2semidirect
14. #21445750C2semidirect
16. C22×#11758202C22semidirect
20. C2×#14519756C22semidirect
21. C2×C4×Dic122C22semidirect
26. C2×#14519710C22semidirect
27. C2×C4⋊#92418C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
31. C2×#14519700C22semidirect
40. C2×C22⋊#92418C22semidirect
41. C2×C22⋊#92418C22semidirect
42. C2×#14519688C22semidirect
47. #16839632C22semidirect
49. #16839622C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
74. C2×#11758200D4semidirect
526. C61#24259semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168399242
C2×#168399132
C2×#168398622
#214507412
#214470192
#214469982
#214468272
#214468222
#214466362
#214466182
#214458192
#214457592
#214457502
C2×C61×#5462
#2425961