Finite Group Databasebeta

← #29708710

Subgroups — #29708710

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839801C211yesmaximal, characteristic, complemented
2C2×#16839784C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic
4C2×#16839765C211yesmaximal, characteristic
5#21448300C211yesmaximal, characteristic, complemented
6#390×D61C211yesmaximal, characteristic
7#21447208C211yesmaximal, characteristic, complemented
8#21447207C211yesmaximal, characteristic, complemented
9#21447206C211yesmaximal, characteristic, complemented
10#21447205C211yesmaximal, characteristic, complemented
11#21447190C211yesmaximal, characteristic, complemented
12#21447189C211yesmaximal, characteristic, complemented
13#21447188C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#2065C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C22⋊C4×D61—21no—
24C2×C42×D61C2211yescharacteristic
25#16839801—24no—
26C2×#14519711C2211yescharacteristic, complemented
27C2×#14519710C2211yescharacteristic, complemented
28C2×#14519708C2211yescharacteristic, complemented
29#16839784—24no—
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519706C2211yescharacteristic, complemented
32C2×#14519706C2211yescharacteristic, complemented
33#16839765—24no—
34#16839765—24no—
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41#16839665C2211yescharacteristic
42#16839664C2211yescharacteristic
43#16839663C2211yescharacteristic
44#16839662—21no—
45#16839662—21no—
46#16839661C2211yescharacteristic, complemented
47#16839660C2211yescharacteristic, complemented
48#16839658C2211yescharacteristic, complemented
49#16839636—21no—
50#16839633—21no—
51C4⋊C4×Dic61—21no—
52#16839613—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C2×#106×C61C2211yescharacteristic, complemented
57C2×C4⋊C8×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#389C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C24×D61—21no—
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61Q814yes—
72C22×C4×D61—21no—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189D414yes—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519735—22no—
85#14519735—22no—
86#14519735—22no—
87#14519735D414yes—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C22⋊C4×D61—44no—
106C22⋊C4×D61—44no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—22no—
113C42×D61—22no—
114#14519711—22no—
115#14519710—22no—
116#14519708—22no—
117C4⋊#92418—22no—
118#14519706—22no—
119#14519706—22no—
120#14519699—22no—
121#14519699—22no—
122#14519698—22no—
123#14519698—22no—
124#14519697—22no—
125#14519697—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129C22×D4×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61C2311yescharacteristic
139#106×C61—22no—
140C4⋊C8×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#95×C61—21no—
144C24×C61—21no—
145C23×D61—21no—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61C2×D411yescharacteristic
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61C2×Q812yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175D4×D61—28no—
176D4×D61—28no—
177D4×D61—44no—
178D4×D61—44no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244C2×Q812yes—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61C2×D412yes—
195C2×C4×D61C2×D412yes—
196C2×C4×D61C2×Q812yes—
197C2×C4×D61#4112yes—
198C2×C4×D61#4112yes—
199C2×C4×D61#4112yes—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61C2×D412yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61C2×D412yes—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219#11758198—24no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—42no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231C4⋊Dic61C2×D412yes—
232#11758196—42no—
233#11758196—42no—
234#11758196—42no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—22no—
238C4×Dic61—22no—
239C4×Dic61—24no—
240C4×Dic61—42no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C2×D412yes—
247#11758189—28no—
248#11758189—44no—
249C23×C61—22no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C22×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—22no—
262C22×D61—48no—
263C22×D61—48no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—48no—
271C22×D61—84no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61#12112yes—
276C22×D61#12112yes—
277C22×D61C22⋊Q812yes—
278D4×C61—22no—
279D4×C61—22no—
280D4×C61—41no—
281D4×C61—41no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61AGL(1,ℤ/8)12yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×Q811yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C22⋊D61—48no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—22no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61#12112yes—
319C2×Dic61#12112yes—
320C2×Dic61C22⋊Q812yes—
321C2×Dic61AGL(1,ℤ/8)12yes—
322D244—22no—
323D244—22no—
324D244—41no—
325D244—41no—
326C4×D61—44no—
327C4×D61—44no—
328C4×D61—84no—
329C4×D61#12114yes—
330C4×D61C22⋊Q814yes—
331C4×D61C22⋊Q814yes—
332C4×D61#12614yes—
333C8×C61—22no—
334C8×C61—41no—
335#92418—22no—
336#92418—41no—
337#23618—611nomaximal, Sylow
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C2×#12111yescharacteristic
346C22×C61C2×#12111yescharacteristic
347C22×C61C2×C22⋊Q811yescharacteristic
348C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61#57511yescharacteristic
351C22×C61#57511yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—816no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61#39614yes—
367C4×C61—22no—
368C4×C61—42no—
369C4×C61—41no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61C2×#12111yescharacteristic
373C4×C61C2×C22⋊Q811yescharacteristic
374C4×C61C2×C22⋊Q811yescharacteristic
375C4×C61C2×#12611yescharacteristic
376Dic61—22no—
377Dic61—42no—
378Dic61—41no—
379Dic61—81no—
380Dic61—81no—
381Dic61#39614yes—
382C2×#428—611no—
383C2×#423—611no—
384C2×#418—611no—
385C2×#418—611no—
386#2296—611no—
387C2×#390—611no—
388#2067—611no—
389#2067—611no—
390#2067—611no—
391#2067—611no—
392#2065—611no—
393#2065—611no—
394#2065—611no—
395#2065D6111yescharacteristic, complemented
396#1736—611no—
397C2×C61—82no—
398C2×C61C2×#39611yescharacteristic
399C2×C61#303811yescharacteristic
400C2×C61#304011yescharacteristic
401C2×C61#305511yescharacteristic
402C2×C61#305511yescharacteristic
403C2×C61#307711yescharacteristic
404C2×C61#307711yescharacteristic
405D61—24no—
406D61—82no—
407C23×D4—611no—
408C22×M16—611no—
409C22×M16—611no—
410C2×#117—611no—
411C2×#117—611no—
412C22×C4⋊C4—611no—
413C22×C22⋊C4—1221no—
414C22×C22⋊C4—1221no—
415C22×C42—611no—
416#428—1224no—
417C2×#107—611no—
418C2×#107—611no—
419C2×#106—611no—
420C2×#106C2×D6111yescharacteristic, complemented
421#423—1224no—
422C2×C4⋊C8—611no—
423C2×C4⋊C8—611no—
424C2×C4⋊C8—611no—
425C2×C4⋊C8C2×D6111yescharacteristic, complemented
426#418—1224no—
427#418—1224no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102C2×D6111yescharacteristic
435C2×#102C2×D6111yescharacteristic
436#390—611no—
437#390—611no—
438#390—611no—
439#390—1221no—
440#390—1221no—
441#390C2×D6111yescharacteristic
442#389—611no—
443#389—611no—
444#389—611no—
445#389C2×D6111yescharacteristic, complemented
446#385—1221no—
447#385—1221no—
448C4×C4⋊C4—1221no—
449C4×C4⋊C4—1221no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340C2×D6111yescharacteristic, complemented
454C61#2361811yescharacteristic, complemented, Sylow
455C25—1221no—
456C22×D4—614no—
457C22×D4—611no—
458C22×D4—1222no—
459C22×D4—1222no—
460C22×D4—1222no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1221no—
464C22×D4C22×D6111yescharacteristic
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—1221no—
469C2×M16—614no—
470C2×M16—1222no—
471C2×M16—1222no—
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479#117—614no—
480#117—1222no—
481#117—1222no—
482#117—1222no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—2444no—
507C2×C22⋊C4—2444no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1222no—
512C2×C42—1222no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42C22×D6111yescharacteristic
516#107—1222no—
517#107—1222no—
518#106—22no—
519#106—1222no—
520C4⋊C8—22no—
521C4⋊C8—1222no—
522C4⋊C8—1222no—
523C4⋊C8—1222no—
524#102—22no—
525#102—22no—
526#102—1222no—
527#102—1222no—
528#102—1222no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532#95—21no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536C24—21no—
537C24—611no—
538C24—1224no—
539C24—1221no—
540C24—2442no—
541C24—2442no—
542C24—2442no—
543C24—2442no—
544C24—2442no—
545C24—2442no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—612no—
552C2×D4—1228no—
553C2×D4—1228no—
554C2×D4—1224no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—2444no—
561C2×D4—2444no—
562C2×D4—2442no—
563C2×D4—2442no—
564C2×D4Q8×D6112yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—611no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—2441no—
585C22×C4—2441no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4D4×D6111yescharacteristic
590C22×C4D4×D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592M16—1228no—
593M16—2444no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—612no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8D4×D6112yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—612no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4D4×D6112yes—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—1224no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C42—21no—
634C42—21no—
635C42—1222no—
636C42—1222no—
637C42—1224no—
638C42—1221no—
639C42—1221no—
640C42—2442no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—612no—
649C23—612no—
650C23—612no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1222no—
656C23—4884no—
657C23—4884no—
658C23—4884no—
659C23—4884no—
660C23—2448no—
661C23—2448no—
662C23—2448no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23C2×D4×D6111yescharacteristic
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—1222no—
675D4—1222no—
676D4—2448no—
677D4—2441no—
678D4—2441no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—614no—
697C2×C4—614no—
698C2×C4—614no—
699C2×C4—614no—
700C2×C4—612no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1222no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—4884no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4#1451980412yes—
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×Q8×D6111yescharacteristic
722C2×C4#41×D6111yescharacteristic
723C2×C4#41×D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C8—22no—
726C8—41no—
727C8—1222no—
728C8—2441no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—614no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—1222no—
742C22—1222no—
743C22—48816no—
744C22—4881no—
745C22—4881no—
746C22—4881no—
747C22—4881no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22#121×D6111yescharacteristic
752C22#121×D6111yescharacteristic
753C22C22⋊Q8×D6111yescharacteristic
754C22AGL(1,ℤ/8)×D6111yescharacteristic
755C22C2×#1451980411yescharacteristic
756C22#1684055811yescharacteristic
757C22#1684055911yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—81no—
762C4—81no—
763C4—614no—
764C4—1222no—
765C4—4881no—
766C4—4881no—
767C4—2441no—
768C4—2442no—
769C4#121×D6111yescharacteristic
770C4C22⋊Q8×D6111yescharacteristic
771C4C22⋊Q8×D6111yescharacteristic
772C4#126×D6111yescharacteristic
773C2—82no—
774C2—1224no—
775C2—4882no—
776C2#396×D6111yescharacteristic
777C2#2145529611yescharacteristic
778C2#2145530811yescharacteristic
779C2#2145543111yescharacteristic
780C2#2145543711yescharacteristic
781C2#2145561411yescharacteristic
782C2#2145561711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2065C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2065D61
hypocenterC61#23618
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#16839801C2semidirect
2. C2×#16839784C2semidirect
5. #21448300C2semidirect
7. #21447208C2semidirect
8. #21447207C2semidirect
9. #21447206C2semidirect
10. #21447205C2semidirect
11. #21447190C2semidirect
12. #21447189C2semidirect
13. #21447188C2semidirect
14. #21445537C2semidirect
15. C61×#2065C2semidirect
26. C2×#14519711C22semidirect
27. C2×#14519710C22semidirect
28. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519706C22semidirect
32. C2×#14519706C22semidirect
46. #16839661C22semidirect
47. #16839660C22semidirect
48. #16839658C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. C2×#106×C61C22semidirect
57. C2×C4⋊C8×C61C22semidirect
61. C61×#389C22semidirect
62. C61×#340C22semidirect
395. #2065D61semidirect
420. C2×#106C2×D61semidirect
425. C2×C4⋊C8C2×D61semidirect
445. #389C2×D61semidirect
453. #340C2×D61semidirect
454. C61#23618semidirect

Maximal subgroups

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

subgroupindex
C2×#168398012
C2×#168397842
C2×#168397652
#214483002
#390×D612
#214472082
#214472072
#214472062
#214472052
#214471902
#214471892
#214471882
#214455372
C61×#20652
#2361861