Finite Group Databasebeta

← #29727788

Subgroups — #29727788

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839981C211yesmaximal, characteristic, complemented
2C2×#16839922C211yesmaximal, characteristic, complemented
3C2×#16839905C211yesmaximal, characteristic
4C2×#16839867C211yesmaximal, characteristic, complemented
5#21448659C211yesmaximal, characteristic, complemented
6#21447190C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21447005C211yesmaximal, characteristic, complemented
9#21446896C211yesmaximal, characteristic, complemented
10#21446694C211yesmaximal, characteristic, complemented
11#21446434C211yesmaximal, characteristic, complemented
12#21446177C211yesmaximal, characteristic, complemented
13#21446174C211yesmaximal, characteristic, complemented
14#21446086C211yesmaximal, characteristic, complemented
15C61×#2426C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16839981—24no—
24#16839922—24no—
25#16839905—24no—
26#16839867—24no—
27C2×#14519708C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839664C2211yescharacteristic
43#16839662—21no—
44#16839662—21no—
45#16839622C2211yescharacteristic
46#16839621—21no—
47#16839609—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#394—21no—
58C61×#390—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73C2×#11758202—22no—
74C2×#11758202—22no—
75C2×#11758202D414yescomplemented
76C2×#11758200—22no—
77C2×#11758200—22no—
78C2×#11758200—22no—
79C2×#11758201—22no—
80C2×#11758201—22no—
81C2×#11758201—41no—
82C2×#11758199—22no—
83C2×#11758199—22no—
84C2×#11758199—41no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—41no—
92C4×Dic122—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104#14519708—22no—
105#14519708—41no—
106C4⋊#92418—22no—
107#14519701—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700D414yes—
111#14519698—22no—
112#14519698—41no—
113#14519697—22no—
114#14519697—22no—
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117#14519688—22no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#124×C61—22no—
124#124×C61—41no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127#121×C61—22no—
128#121×C61—41no—
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C2×C42×C61C2311yescharacteristic
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C23×D61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C2×D412yes—
159C2×D4×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—
168C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189#11758222—44no—
190#11758222—44no—
191#11758222—44no—
192#11758222—44no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244#4112yes—
199C2×C4×D61—24no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C2×D412yes—
206C2×Dic122C2×D412yes—
207C2×Dic122#4112yes—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—81no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—41no—
216C22⋊C4×C61—41no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—42no—
228C22⋊Dic61—81no—
229#11758202—28no—
230#11758201—44no—
231#11758200—44no—
232#11758199—44no—
233#11758198—42no—
234#11758198—42no—
235#11758198—81no—
236#11758198—81no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241#11758196—42no—
242#11758196—42no—
243C4×Dic61—42no—
244C4×Dic61—42no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C2×D412yes—
256C2×#92418C2×D412yes—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61C22×D411yescharacteristic
272C22×D61—22no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—41no—
282Q8×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—84no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—48no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332D244—22no—
333D244—22no—
334D244—41no—
335D244—41no—
336C4×D61—48no—
337Dic122—22no—
338Dic122—22no—
339Dic122—22no—
340Dic122#12114yes—
341#92418—22no—
342#92418—22no—
343#92418—41no—
344#92418—41no—
345#25175—611nomaximal, Sylow
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61#52511yescharacteristic
361C22×C61D4211yescharacteristic
362C22×C61D4211yescharacteristic
363C22×C61#57511yescharacteristic
364C22×C61#57511yescharacteristic
365C22×C61#57711yescharacteristic
366C22×C61#57711yescharacteristic
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—42no—
381C4×C61—81no—
382C4×C61C2×#12111yescharacteristic
383C4×C61#53811yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#54611yescharacteristic
386Dic61—24no—
387Dic61—81no—
388Dic61—81no—
389C2×#464—611no—
390C2×#452—611no—
391C2×#449—611no—
392C2×#441—611no—
393#2426D6111yescharacteristic, complemented
394#2341—611no—
395#2065—611no—
396#2035—611no—
397#2034—611no—
398#2012—611no—
399#1972—611no—
400#1924—611no—
401#1880—611no—
402#1880—611no—
403#1865—611no—
404C2×C61—81no—
405C2×C61—161no—
406C2×C61#242411yescharacteristic
407C2×C61#311111yescharacteristic
408C2×C61#312511yescharacteristic
409C2×C61#327111yescharacteristic
410C2×C61#327111yescharacteristic
411C2×C61#327111yescharacteristic
412C2×C61#327511yescharacteristic
413D61—82no—
414C22×#41—611no—
415C22×Q16—611no—
416C22×SD16—611no—
417C22×SD16—611no—
418C22×D8—611no—
419C2×#124C2×D6111yescharacteristic
420C2×C22⋊Q8C2×D6111yescharacteristic
421C2×#121C2×D6111yescharacteristic
422C2×C4×Q8—611no—
423C2×C4×Q8—611no—
424C2×C4×Q8C2×D6111yescharacteristic
425#464—1224no—
426#452—1224no—
427#449—1224no—
428#441—1224no—
429C2×#106—611no—
430C2×#106—611no—
431C2×C4⋊C8—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×#97—611no—
443#396—21no—
444#394—21no—
445#390—21no—
446#390—611no—
447#390—611no—
448#390—1221no—
449#390—1221no—
450#390C2×D6111yescharacteristic
451#389C2×D6111yescharacteristic
452#388—21no—
453#380—611no—
454#380—1221no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4C2×D6111yescharacteristic
457#340—611no—
458#340—611no—
459#336—611no—
460#336—611no—
461C61#2517511yescharacteristic, complemented, Sylow
462C2×#41—1222no—
463C2×#41—1222no—
464C2×#41—1222no—
465C2×#41—1222no—
466C2×#41—2441no—
467C2×#41—2441no—
468C22×Q8—611no—
469C22×Q8C22×D6111yescharacteristic
470C22×D4—21no—
471C22×D4—611no—
472C22×D4—1221no—
473C22×D4C22×D6111yescharacteristic
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×Q16—614no—
477C2×Q16—1222no—
478C2×Q16—1222no—
479C2×SD16—1222no—
480C2×SD16—1222no—
481C2×SD16—1222no—
482C2×SD16—1222no—
483C2×SD16—1222no—
484C2×SD16—2441no—
485C2×D8—1222no—
486C2×D8—1222no—
487C2×D8—2441no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492#124—22no—
493#124—41no—
494C22⋊Q8—22no—
495C22⋊Q8—41no—
496#121—22no—
497#121—41no—
498C4×Q8—22no—
499C4×Q8—41no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×Q8—2441no—
503C4×Q8—2441no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4C22⋊D6111yescharacteristic
526C2×C42—21no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42C22×D6111yescharacteristic
530C2×C42C22×D6111yescharacteristic
531#106—1222no—
532#106—2441no—
533C4⋊C8—1222no—
534#103—614no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#102—1222no—
539#102—1222no—
540#102—1222no—
541#102—2441no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544#97—1222no—
545#95—21no—
546#95—1221no—
547#95C22⋊D6111yescharacteristic
548#95C22⋊D6111yescharacteristic
549C24—21no—
550C24—1221no—
551C24C2×C22⋊D6111yescharacteristic
552#41—2444no—
553#41—2444no—
554#41—2444no—
555#41—2444no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—612no—
562C2×Q8—612no—
563C2×Q8—612no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8D4×D6112yes—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—612no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—2442no—
585C2×D4—2442no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C23×D6111yescharacteristic
607Q16—1228no—
608SD16—2444no—
609SD16—2444no—
610D8—2444no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—81no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—2442no—
634C4⋊C4—2442no—
635C4⋊C4D4×D6112yes—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—4881no—
645C22⋊C4—4881no—
646C22⋊C4—4881no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C42—2442no—
655C42—2442no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—1222no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23C22×C22⋊D6111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—614no—
683Q8—1222no—
684Q8—1222no—
685Q8—1222no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—84no—
691D4—1222no—
692D4—1222no—
693D4—2448no—
694D4—2441no—
695D4—2441no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—2448no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×D4×D6111yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C2×C4#41×D6111yescharacteristic
738C2×C4#1451982211yescharacteristic
739C2×C4#1451982211yescharacteristic
740C8—1222no—
741C8—1222no—
742C8—2441no—
743C8—2441no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22#1684026911yescharacteristic
766C22D4×C22⋊D6111yescharacteristic
767C22D4×C22⋊D6111yescharacteristic
768C22#1684056011yescharacteristic
769C22#1684056011yescharacteristic
770C22#1684057011yescharacteristic
771C22#1684057311yescharacteristic
772C4—41no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—1224no—
781C4—4881no—
782C4—4881no—
783C4#121×D6111yescharacteristic
784C4#1684034411yescharacteristic
785C4#1684040111yescharacteristic
786C4#1684040911yescharacteristic
787C2—81no—
788C2—161no—
789C2—4882no—
790C2#2144935211yescharacteristic
791C2#2145592211yescharacteristic
792C2#2145609011yescharacteristic
793C2#2145740011yescharacteristic
794C2#2145740511yescharacteristic
795C2#2145740511yescharacteristic
796C2#2145744611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2426C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenter#2426D61
hypocenterC61#25175
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#16839981C2semidirect
2. C2×#16839922C2semidirect
4. C2×#16839867C2semidirect
5. #21448659C2semidirect
6. #21447190C2semidirect
7. #21447012C2semidirect
8. #21447005C2semidirect
9. #21446896C2semidirect
10. #21446694C2semidirect
11. #21446434C2semidirect
12. #21446177C2semidirect
13. #21446174C2semidirect
14. #21446086C2semidirect
15. C61×#2426C2semidirect
75. C2×#11758202D4semidirect
393. #2426D61semidirect
461. C61#25175semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168399222
C2×#168399052
C2×#168398672
#214486592
#214471902
#214470122
#214470052
#214468962
#214466942
#214464342
#214461772
#214461742
#214460862
C61×#24262
#2517561