Finite Group Databasebeta

← #29717604

Subgroups — #29717604

Order 15616.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840001C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21449270C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446913C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic, complemented
22C22×C4⋊Dic61C2211yescharacteristic
23#16840001—24no—
24#16839924—24no—
25#16839913—24no—
26C2×#14519710C2211yescharacteristic, complemented
27C2×#14519701C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519700C2211yescharacteristic, complemented
31C2×#14519698—24no—
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41#16839695—21no—
42#16839685—21no—
43#16839668C2211yescharacteristic, complemented
44#16839660C2211yescharacteristic, complemented
45#16839642—21no—
46#16839622C2211yescharacteristic, complemented
47#16839620—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, 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
66C23×Dic61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—41no—
75C2×#11758200—41no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519756—22no—
84#14519756—22no—
85#14519756—22no—
86#14519756—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99#14519710—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#14519698D414yescomplemented
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
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—22no—
126C22×D4×C61—22no—
127C22×D4×C61—21no—
128C22×D4×C61—21no—
129C22×D4×C61—22no—
130C22×D4×C61—21no—
131C22×D4×C61—41no—
132C22×D4×C61—41no—
133C22×D4×C61D411yescharacteristic
134C22×D4×C61D414yes—
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×C61—22no—
143#123×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61D414yes—
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×C61—22no—
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—21no—
168C24×C61—24no—
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—28no—
188C2×D4×C61—24no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
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—21no—
201C2×D4×C61—21no—
202C2×D4×C61—44no—
203C2×D4×C61—44no—
204C2×D4×C61—44no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
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—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—24no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
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—42no—
230C22×C4×C61—42no—
231C22×C4×C61—81no—
232C22×C4×C61—81no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—42no—
245C22×Dic61—42no—
246C22×Dic61—81no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122—21no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—22no—
264C42×C61—21no—
265C42×C61—21no—
266C22⋊Dic61—42no—
267C22⋊Dic61—42no—
268C22⋊Dic61—81no—
269#11758202—44no—
270#11758200—44no—
271#11758200—44no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—42no—
278C4⋊Dic61C2×D412yes—
279#11758196—42no—
280#11758196—42no—
281#11758196—81no—
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×#92418—44no—
294C2×#92418C2×D412yes—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—48no—
311C23×C61—41no—
312C23×C61—41no—
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—48no—
322C23×C61—84no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61#12012yes—
328C23×C61#13512yes—
329C23×C61#13712yes—
330C23×C61C22×D411yescharacteristic
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—41no—
334Q8×C61—41no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—48no—
341D4×C61—48no—
342D4×C61—44no—
343D4×C61—41no—
344D4×C61—41no—
345D4×C61—84no—
346D4×C61#12114yes—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—22no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—48no—
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—41no—
372C2×C4×C61—41no—
373C2×C4×C61—84no—
374C2×C4×C61#12012yes—
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C2×#4111yescharacteristic
379C2×C4×C61H(5,𝔽2)11yescharacteristic
380C2×C4×C61H(5,𝔽2)11yescharacteristic
381C2×Dic61—22no—
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—
392C2×Dic61—41no—
393C2×Dic61—84no—
394Dic122—41no—
395Dic122—41no—
396Dic122—41no—
397Dic122—41no—
398#92418—22no—
399#92418—41no—
400#92418—41no—
401#92418—41no—
402#24426—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—24no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—41no—
417C22×C61—42no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—42no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—816no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61#45214yescomplemented
432C22×C61C2×#12011yescharacteristic
433C22×C61D4211yescharacteristic
434C22×C61#54611yescharacteristic
435C22×C61C2×#13511yescharacteristic
436C22×C61C2×#13711yescharacteristic
437C22×C61#57611yescharacteristic
438C22×C61#57711yescharacteristic
439C4×C61—22no—
440C4×C61—41no—
441C4×C61—42no—
442C4×C61—41no—
443C4×C61—41no—
444C4×C61—42no—
445C4×C61C2×#12111yescharacteristic
446C4×C61#53411yescharacteristic
447C4×C61D4211yescharacteristic
448C4×C61#54611yescharacteristic
449Dic61—42no—
450Dic61—81no—
451Dic61—81no—
452Dic61—81no—
453C2×#546D6111yescharacteristic
454C2×#467—611no—
455C2×#452—611no—
456C2×#450—611no—
457C22×#102—611no—
458#2417—611no—
459#2042—611no—
460#2033—611no—
461#2015—611no—
462#2000—611no—
463#1877—611no—
464#1872—611no—
465#1869—611no—
466#1862—611no—
467#1788—611no—
468C2×C61—24no—
469C2×C61—44no—
470C2×C61—81no—
471C2×C61—82no—
472C2×C61#241011yescharacteristic
473C2×C61C2×#45211yescharacteristic
474C2×C61#301211yescharacteristic
475C2×C61#326611yescharacteristic
476C2×C61#328011yescharacteristic
477C2×C61#329611yescharacteristic
478C2×C61#331411yescharacteristic
479C22×#41C2×D6111yescharacteristic
480C23×D4C2×D6111yescharacteristic
481C22×Q16—611no—
482C22×SD16—611no—
483C22×SD16—611no—
484C23×C8—611no—
485#546—24no—
486#546—24no—
487C2×#124C2×D6111yescharacteristic
488C2×#123—21no—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8—611no—
491C2×C22⋊Q8C2×D6111yescharacteristic
492C2×#121—21no—
493C2×#121C2×D6111yescharacteristic
494C2×#120—21no—
495C2×C4×D4C2×D6111yescharacteristic
496C2×C4×D4C2×D6111yescharacteristic
497C22×C4⋊C4—611no—
498C22×C22⋊C4—21no—
499#467—1224no—
500#452—1224no—
501#450—1224no—
502C2×#107—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—1224no—
514C2×C22⋊C8—611no—
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517#398—1221no—
518#396—1221no—
519#391—611no—
520#389—611no—
521#386—1221no—
522#380—611no—
523#380—1221no—
524#340—611no—
525#340—611no—
526#336—611no—
527#336—611no—
528C61#2442611yescharacteristic, complemented, Sylow
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8—611no—
537C22×Q8C22×D6111yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4C22⋊D6111yescharacteristic
547C22×D4C22⋊D6114yes—
548C22×D4C22×D6111yescharacteristic
549C22×D4C22×D6111yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—1221no—
553C23×C4C22×D6111yescharacteristic
554C23×C4C22×D6111yescharacteristic
555C2×Q16—1222no—
556C2×Q16—1222no—
557C2×Q16—2441no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—1222no—
561C2×SD16—1222no—
562C2×SD16—2441no—
563C2×SD16—2441no—
564C22×C8—611no—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—611no—
568C22×C8—1222no—
569C22×C8—1222no—
570C22×C8—2441no—
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—1222no—
576C22⋊Q8—1222no—
577C22⋊Q8—1222no—
578C22⋊Q8—2441no—
579C22⋊Q8C22⋊D6114yes—
580#121—28no—
581#121—22no—
582#121—22no—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4—2441no—
598C2×C4⋊C4C22⋊D6111yescharacteristic
599C2×C4⋊C4C22×D6111yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4C22⋊D6111yescharacteristic
610C2×C22⋊C4C22⋊D6111yescharacteristic
611C2×C42C22×D6111yescharacteristic
612#107—1222no—
613#103—1222no—
614#103—1222no—
615#103—1222no—
616#103—2441no—
617#102—614no—
618#102—1222no—
619#102—1222no—
620#102—1222no—
621#102—1222no—
622#102—1222no—
623C22⋊C8—1222no—
624C22⋊C8—1222no—
625C22⋊C8—2441no—
626#95—1221no—
627#95—1221no—
628#95—1221no—
629#95—1221no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×C22⋊D6111yescharacteristic
640C24C2×C22⋊D6111yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1221no—
656C2×Q8C2×C22⋊D6112yes—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—24no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4D4×D6112yes—
682C2×D4#1175822412yes—
683C2×D4C2×C22⋊D6112yes—
684C2×D4C2×C22⋊D6112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
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×C4—4881no—
708C22×C4—2442no—
709C22×C4—2442no—
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C2×C22⋊D6111yescharacteristic
712C22×C4C2×C22⋊D6111yescharacteristic
713C22×C4C2×C22⋊D6112yes—
714C22×C4C2×C22⋊D6112yes—
715C22×C4C2×C22⋊D6111yescharacteristic
716C22×C4C23×D6111yescharacteristic
717Q16—2444no—
718SD16—2444no—
719SD16—2444no—
720C2×C8—612no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—2444no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—612no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—4881no—
743C4⋊C4—2442no—
744C4⋊C4—2442no—
745C4⋊C4—2442no—
746C4⋊C4C2×C22⋊D6112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—22no—
754C22⋊C4—4881no—
755C22⋊C4—2442no—
756C22⋊C4—2442no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—48no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#1451974612yes—
792C23#1451979712yes—
793C23#1451980712yes—
794C23C22×C22⋊D6111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—2441no—
800Q8—2441no—
801Q8—2441no—
802Q8—2441no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#1451974914yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—48no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—84no—
842C2×C4—1222no—
843C2×C4—4884no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4#1451974612yes—
856C2×C4C2×D4×D6111yescharacteristic
857C2×C4C22×C22⋊D6111yescharacteristic
858C2×C4C22×C22⋊D6111yescharacteristic
859C2×C4C2×#1175822411yescharacteristic
860C2×C4#1451982211yescharacteristic
861C2×C4#1451982211yescharacteristic
862C8—1222no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#1683992414yescomplemented
895C22C2×#1451974611yescharacteristic
896C22D4×C22⋊D6111yescharacteristic
897C22#1684040611yescharacteristic
898C22C2×#1451979711yescharacteristic
899C22C2×#1451980711yescharacteristic
900C22#1684056511yescharacteristic
901C22#1684057311yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—4881no—
909C4—4881no—
910C4—4881no—
911C4—2442no—
912C4C2×#1451974911yescharacteristic
913C4#1684032111yescharacteristic
914C4D4×C22⋊D6111yescharacteristic
915C4#1684040611yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2#2144919311yescharacteristic
921C2C2×#1683992411yescharacteristic
922C2#2145512311yescharacteristic
923C2#2145732511yescharacteristic
924C2#2145750011yescharacteristic
925C2#2145765411yescharacteristic
926C2#2145790011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24426
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×#16840001C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839913C2semidirect
4. C22×#14519698C2semidirect
5. #21449270C2semidirect
6. #21447055C2semidirect
7. #21446998C2semidirect
8. #21446913C2semidirect
9. #21446822C2semidirect
10. #21446153C2semidirect
11. #21446127C2semidirect
12. #21446112C2semidirect
13. #21446066C2semidirect
14. #21445759C2semidirect
16. C22×#11758202C22semidirect
21. C2×#14519756C22semidirect
26. C2×#14519710C22semidirect
27. C2×#14519701C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519700C22semidirect
39. C2×C22⋊#92418C22semidirect
40. C2×C22⋊#92418C22semidirect
43. #16839668C22semidirect
44. #16839660C22semidirect
46. #16839622C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
109. #14519698D4semidirect
431. C22×C61#452semidirect
528. C61#24426semidirect
894. C22#16839924semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
C2×#168399242
C2×#168399132
C22×#145196982
#214492702
#214470552
#214469982
#214469132
#214468222
#214461532
#214461272
#214461122
#214460662
#214457592
C2×C61×#5462
#2442661