Finite Group Databasebeta

← #29730742

Subgroups — #29730742

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839990C211yesmaximal, characteristic, complemented
2C2×#16839965C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
4#21450769C211yesmaximal, characteristic, complemented
5#21450733C211yesmaximal, characteristic
6#21447017C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446819C211yesmaximal, characteristic, complemented
10#21446619C211yesmaximal, characteristic, complemented
11#21446579C211yesmaximal, characteristic, complemented
12#21446242C211yesmaximal, characteristic, complemented
13#21446239C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#465C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519753C2211yescharacteristic
22C2×#14519749—21no—
23C2×#14519748C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26#16839990—24no—
27#16839965—24no—
28C8×C22⋊D61—24no—
29C2×#14519708C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839698—21no—
41#16839697—21no—
42#16839677—21no—
43#16839676—21no—
44#16839662—21no—
45#16839631—21no—
46#16839631C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839620—21no—
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#465—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—41no—
76#14519775—22no—
77#14519775—22no—
78#14519757—22no—
79#14519757—41no—
80#14519756—22no—
81#14519756—41no—
82#14519753—22no—
83#14519753—41no—
84#14519749—44no—
85#14519748—22no—
86#14519748—41no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198D411yescharacteristic
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519708—22no—
114#14519706D414yescomplemented
115#14519702—22no—
116#14519702—22no—
117#14519701—22no—
118#14519701—41no—
119#14519700—41no—
120#14519698—22no—
121C22⋊#92418—22no—
122#14519689—22no—
123C8×Dic61—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×Q8×C61C2311yescharacteristic
128C22×D4×C61—21no—
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×SD16×C61—22no—
132C2×SD16×C61—22no—
133C2×SD16×C61—41no—
134C22×C8×C61—22no—
135C22×C8×C61—22no—
136C22×C8×C61—41no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—41no—
141#121×C61—22no—
142#121×C61—41no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148#106×C61—22no—
149#103×C61—22no—
150#102×C61D414yescomplemented
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—81no—
168C2×D4×C61C2×D412yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—81no—
185C2×C22⋊D61SD1614yescomplemented
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208SD16×C61—44no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—44no—
214C2×C8×C61C2×D412yes—
215C2×C8×C61C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊Dic61—22no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228#11758200—44no—
229#11758198—22no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—42no—
239C4⋊Dic61#4112yes—
240#11758196—22no—
241#11758196—42no—
242#11758196—42no—
243#11758196—42no—
244#11758196—42no—
245#11758196—42no—
246#11758196—81no—
247C4×Dic61—42no—
248C4×Dic61C2×D412yes—
249C4×Dic61#4112yes—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C2×D412yes—
256C8×D61—44no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—22no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61C2×SD1612yes—
271C23×C61C22×D411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61C2×SD1612yes—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61—41no—
282Q8×C61—41no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—84no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C22⋊D61—28no—
311C22⋊D61—84no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—84no—
330C2×Dic61#12112yes—
331C2×Dic61#12112yes—
332C2×Dic61C2×SD1612yes—
333C2×Dic61#13512yes—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338Dic122—41no—
339Dic122—41no—
340Dic122—41no—
341Dic122—41no—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—41no—
346#25385—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61C2×#12111yescharacteristic
362C22×C61D4211yescharacteristic
363C22×C61#54611yescharacteristic
364C22×C61C22×SD1611yescharacteristic
365C22×C61C2×#13511yescharacteristic
366C22×C61#57711yescharacteristic
367C22×C61#57811yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C4×C61—41no—
376C4×C61—42no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61#53211yescharacteristic
380C4×C61#54011yescharacteristic
381C4×C61D4211yescharacteristic
382C4×C61#55011yescharacteristic
383Dic61—22no—
384Dic61—41no—
385Dic61—42no—
386Dic61—81no—
387Dic61—81no—
388Dic61—81no—
389Dic61#46514yescomplemented
390C2×#465—611no—
391C2×#465D6111yescharacteristic, complemented
392C2×#461—611no—
393C2×C8×D4—611no—
394#2542—611no—
395#2537—611no—
396#2035—611no—
397#2035—611no—
398#2000—611no—
399#2000—611no—
400#1956—611no—
401#1948—611no—
402#1892—611no—
403#1892—611no—
404C4×#102—611no—
405C2×C61—42no—
406C2×C61—82no—
407C2×C61#242811yescharacteristic
408C2×C61C2×#46511yescharacteristic
409C2×C61#306311yescharacteristic
410C2×C61D4×SD1611yescharacteristic
411C2×C61#328311yescharacteristic
412C2×C61#329811yescharacteristic
413C2×C61#330311yescharacteristic
414D61—42no—
415C22×SD16—611no—
416C22×SD16C2×D6111yescharacteristic
417C23×C8—611no—
418C23×C8C2×D6111yescharacteristic
419C2×C4⋊Q8—611no—
420C2×C22⋊Q8—611no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—611no—
423C2×C22⋊Q8C2×D6111yescharacteristic
424C2×#121—611no—
425C2×#121—1221no—
426C2×#121C2×D6111yescharacteristic
427C2×C4×D4—611no—
428C2×C4×D4—611no—
429#465—24no—
430#465—1224no—
431#461—1224no—
432C8×D4—1224no—
433C2×#106—611no—
434C2×#106C2×D6111yescharacteristic
435C2×C4⋊C8—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#102C2×D6111yescharacteristic
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C4×C8—611no—
447#399—1221no—
448#399—1221no—
449#394—1221no—
450#394—1221no—
451#390—1221no—
452#384—611no—
453#384—1221no—
454#380—611no—
455#380—611no—
456#380—1221no—
457C4×C4⋊C4—611no—
458#340—611no—
459#340—611no—
460#340—611no—
461#340—611no—
462C61#2538511yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×Q8C22×D6111yescharacteristic
465C22×D4—21no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4C22×D6111yescharacteristic
469C23×C4—611no—
470C23×C4—1221no—
471C23×C4C22×D6111yescharacteristic
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16—41no—
475C2×SD16—1222no—
476C2×SD16—1222no—
477C2×SD16—2441no—
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—41no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—2441no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C4⋊Q8—1222no—
489C4⋊Q8—1222no—
490C22⋊Q8—22no—
491C22⋊Q8—41no—
492C22⋊Q8—1222no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495C22⋊Q8—2441no—
496C22⋊Q8—2441no—
497C22⋊Q8—2441no—
498#121—22no—
499#121—41no—
500#121—1222no—
501#121—2441no—
502#121—2444no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C42—611no—
533C2×C42—1221no—
534#106—22no—
535#106—1222no—
536C4⋊C8—614no—
537#103—22no—
538#103—1222no—
539#103—1222no—
540#103—1222no—
541#103—2441no—
542#103—2441no—
543#102—1222no—
544#102C22⋊D6114yescomplemented
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C4×C8—1222no—
548#95—1221no—
549#95—1221no—
550#95—1221no—
551C24—21no—
552C24—611no—
553C24D4×D6111yescharacteristic
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—614no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—4881no—
578C2×D4—2442no—
579C2×D4—2442no—
580C2×D4C2×C22⋊D6112yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608SD16—44no—
609SD16—2444no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—44no—
615C2×C8—612no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—2444no—
622C2×C8D4×D6112yes—
623C2×C8C2×C22⋊D6112yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—612no—
629C4⋊C4—1222no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—4881no—
636C4⋊C4—2442no—
637C4⋊C4—2442no—
638C4⋊C4—2442no—
639C4⋊C4—2442no—
640C4⋊C4—2442no—
641C4⋊C4—2442no—
642C4⋊C4C2×C22⋊D6112yes—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C42—612no—
655C42—612no—
656C42—2442no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—612no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23SD16×D6112yes—
678C23C2×D4×D6111yescharacteristic
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—2441no—
684Q8—2441no—
685Q8—2441no—
686Q8—2441no—
687D4—22no—
688D4—22no—
689D4—41no—
690D4—41no—
691D4—84no—
692D4—1228no—
693D4—4884no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—612no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—4884no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C22×C22⋊D6111yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C2×C4#41×D6111yescharacteristic
740C2×C4#1451982211yescharacteristic
741C2×C4#1451982211yescharacteristic
742C8—22no—
743C8—22no—
744C8—1222no—
745C8—2441no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22#121×D6111yescharacteristic
768C22D4×C22⋊D6111yescharacteristic
769C22#1684040111yescharacteristic
770C22C2×SD16×D6111yescharacteristic
771C22#135×D6111yescharacteristic
772C22#1684056811yescharacteristic
773C22#1684057611yescharacteristic
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—614no—
779C4—1222no—
780C4—4881no—
781C4—4881no—
782C4—4881no—
783C4—2442no—
784C4—2441no—
785C4#1684030811yescharacteristic
786C4#1684036211yescharacteristic
787C4D4×C22⋊D6111yescharacteristic
788C4#1684043011yescharacteristic
789C2—42no—
790C2—82no—
791C2—2442no—
792C2#2144940411yescharacteristic
793C2#465×D6111yescharacteristic
794C2#2145550311yescharacteristic
795C2SD16×C22⋊D6111yescharacteristic
796C2#2145753511yescharacteristic
797C2#2145767911yescharacteristic
798C2#2145774211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radical#21450733C2
hypercenterC2×#465D61
hypocenterC61#25385
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16839990C2semidirect
2. C2×#16839965C2semidirect
3. C2×C8×C22⋊D61C2semidirect
4. #21450769C2semidirect
6. #21447017C2semidirect
7. #21447012C2semidirect
8. #21446822C2semidirect
9. #21446819C2semidirect
10. #21446619C2semidirect
11. #21446579C2semidirect
12. #21446242C2semidirect
13. #21446239C2semidirect
14. #102×Dic61C2semidirect
15. C2×C61×#465C2semidirect
114. #14519706D4semidirect
150. #102×C61D4semidirect
185. C2×C22⋊D61SD16semidirect
389. Dic61#465semidirect
391. C2×#465D61semidirect
462. C61#25385semidirect
544. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399902
C2×#168399652
C2×C8×C22⋊D612
#214507692
#214507332
#214470172
#214470122
#214468222
#214468192
#214466192
#214465792
#214462422
#214462392
#102×Dic612
C2×C61×#4652
#2538561