Finite Group Databasebeta

← #29727491

Subgroups — #29727491

Order 15616.

1126 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×#16839984C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21449396C211yesmaximal, characteristic, complemented
6#21447193C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21446895C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14#21446087C211yesmaximal, characteristic, complemented
15C61×#2341C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24#16839984—24no—
25#16839924—24no—
26#16839907—24no—
27C4×#11758201—24no—
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839691—21no—
43#16839677—21no—
44#16839668C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839638—21no—
47#16839621—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#390—21no—
56C61×#390—21no—
57C61×#390C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#380—21no—
60C61×#380C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—41no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201D414yes—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519765—22no—
84#14519765—41no—
85#14519756—22no—
86#14519756—41no—
87#14519751—22no—
88#14519751—41no—
89C4×D244—22no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519708—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701D414yescomplemented
105#14519700—22no—
106#14519700—41no—
107#14519698—22no—
108#14519698—22no—
109#14519697—22no—
110#14519697—22no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C4×Q8×C61—22no—
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C4×Q8×C61—41no—
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×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C42×C61—21no—
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—
153#41×C61—44no—
154#41×C61—44no—
155#41×C61—44no—
156#41×C61—44no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61C2×D412yes—
162C2×Q8×C61#4112yes—
163C2×D4×C61—24no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61#4112yes—
172C22×C4×C61—21no—
173C22×C4×C61—24no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—81no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244C2×D412yes—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—81no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—81no—
222C22⋊C4×C61—81no—
223C22⋊C4×C61—81no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—42no—
229C42×C61—42no—
230C22⋊Dic61—42no—
231#11758202—44no—
232#11758201—28no—
233#11758200—44no—
234#11758199—44no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C2×D412yes—
243#11758196—42no—
244#11758196—81no—
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—22no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
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—22no—
282Q8×C61#12114yes—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—48no—
286D4×C61—41no—
287D4×C61—41no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
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—48no—
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×C61#13512yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—84no—
324C2×Dic61—22no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333D244—22no—
334D244—22no—
335D244—41no—
336D244—41no—
337C4×D61—84no—
338Dic122—41no—
339Dic122—41no—
340Dic122—41no—
341Dic122—41no—
342#92418—22no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#25155—611nomaximal, Sylow
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—41no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61#52511yescharacteristic
362C22×C61D4211yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61C2×#13511yescharacteristic
365C22×C61#57511yescharacteristic
366C22×C61#57711yescharacteristic
367C22×C61#57711yescharacteristic
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C4×C61—24no—
376C4×C61—22no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—81no—
382C4×C61—81no—
383C4×C61C2×#12111yescharacteristic
384C4×C61#53811yescharacteristic
385C4×C61#54611yescharacteristic
386C4×C61#54611yescharacteristic
387Dic61—42no—
388Dic61—81no—
389Dic61—81no—
390C2×#464—611no—
391C2×#452—611no—
392C2×#449—611no—
393C2×C4×SD16—611no—
394#2427—611no—
395#2341D6111yescharacteristic, complemented
396#2065—611no—
397#2035—611no—
398#2034—611no—
399#2012—611no—
400#1968—611no—
401#1923—611no—
402#1879—611no—
403#1878—611no—
404#1865—611no—
405C2×C61—81no—
406C2×C61—82no—
407C2×C61#242411yescharacteristic
408C2×C61#310211yescharacteristic
409C2×C61#312511yescharacteristic
410C2×C61#327111yescharacteristic
411C2×C61#327511yescharacteristic
412C2×C61#328211yescharacteristic
413C2×C61#328411yescharacteristic
414D61—82no—
415C22×#41C2×D6111yescharacteristic
416C22×Q16—611no—
417C22×SD16—611no—
418C22×SD16—611no—
419C22×D8—611no—
420C2×#124—611no—
421C2×C22⋊Q8—611no—
422C2×#121—611no—
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×Q8C2×D6111yescharacteristic
425C2×C4×D4—611no—
426#464—1224no—
427#452—1224no—
428#449—1224no—
429C4×SD16—1224no—
430C2×#106—611no—
431C2×#106—611no—
432C2×C4⋊C8—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444#397—1221no—
445#394—1221no—
446#391—611no—
447#390—21no—
448#390—21no—
449#390C2×D6111yescharacteristic
450#390C2×D6111yescharacteristic
451#389—611no—
452#386—1221no—
453#380—21no—
454#380—1221no—
455#380C2×D6111yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2×D6111yescharacteristic
458#340—611no—
459#340—611no—
460#336—611no—
461#336—611no—
462C61#2515511yescharacteristic, complemented, Sylow
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—41no—
468C2×#41—41no—
469C22×Q8—611no—
470C22×Q8C22×D6111yescharacteristic
471C22×D4—21no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4C22×D6111yescharacteristic
475C23×C4—21no—
476C23×C4—1221no—
477C23×C4C22×D6111yescharacteristic
478C2×Q16—1222no—
479C2×Q16—1222no—
480C2×Q16—1222no—
481C2×SD16—614no—
482C2×SD16—1222no—
483C2×SD16—1222no—
484C2×SD16—1222no—
485C2×SD16—1222no—
486C2×SD16—2441no—
487C2×D8—1222no—
488C2×D8—1222no—
489C2×D8—2441no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C22×C8—611no—
494#124—1222no—
495#124—2441no—
496C22⋊Q8—1222no—
497C22⋊Q8—2441no—
498#121—1222no—
499#121—2441no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8—41no—
503C4×Q8—41no—
504C4×D4—1222no—
505C4×D4—2441no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
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—21no—
528C2×C42C22×D6111yescharacteristic
529C2×C42C22×D6111yescharacteristic
530#106—1222no—
531#106—2441no—
532C4⋊C8—1222no—
533#103—614no—
534#103—1222no—
535#103—1222no—
536#103—2441no—
537#102—1222no—
538#102—1222no—
539#102—1222no—
540#102—1222no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C4×C8—1222no—
544#95—21no—
545#95—1221no—
546#95—1221no—
547#95—1221no—
548#95C22⋊D6111yescharacteristic
549#95C22⋊D6111yescharacteristic
550C24—21no—
551C24—1221no—
552C24C2×C22⋊D6111yescharacteristic
553#41—44no—
554#41—44no—
555#41—44no—
556#41—44no—
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×Q8#1175822212yes—
567C2×Q8D4×D6112yes—
568C2×Q8D4×D6112yes—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—612no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—4881no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4#1175822212yes—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—4881no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C23×D6111yescharacteristic
611Q16—2444no—
612SD16—1228no—
613SD16—2444no—
614D8—2444no—
615C2×C8—612no—
616C2×C8—612no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—612no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—4881no—
638C4⋊C4—2442no—
639C22⋊C4—22no—
640C22⋊C4—41no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—42no—
656C42—42no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—1222no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23C22×C22⋊D6111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—2441no—
683Q8—2441no—
684Q8—2441no—
685Q8—2441no—
686Q8#1451975014yes—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—1222no—
693D4—1222no—
694D4—4884no—
695D4—2441no—
696D4—2441no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—48no—
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—41no—
725C2×C4—1222no—
726C2×C4—4884no—
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#1451979712yes—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4C2×#1175822211yescharacteristic
739C2×C4C2×#1175822211yescharacteristic
740C2×C4#1451982211yescharacteristic
741C2×C4#1451982211yescharacteristic
742C8—1222no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22#1684027311yescharacteristic
768C22D4×C22⋊D6111yescharacteristic
769C22D4×C22⋊D6111yescharacteristic
770C22C2×#1451979711yescharacteristic
771C22#1684056011yescharacteristic
772C22#1684057011yescharacteristic
773C22#1684057311yescharacteristic
774C4—22no—
775C4—24no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—4881no—
783C4—4881no—
784C4—2442no—
785C4C2×#1451975011yescharacteristic
786C4#1684035011yescharacteristic
787C4#1684040211yescharacteristic
788C4#1684040211yescharacteristic
789C2—81no—
790C2—82no—
791C2—4882no—
792C2#2144935511yescharacteristic
793C2#2145583711yescharacteristic
794C2#2145609611yescharacteristic
795C2#2145740011yescharacteristic
796C2#2145745111yescharacteristic
797C2#2145752711yescharacteristic
798C2#2145754911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2341C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenter#2341D61
hypocenterC61#25155
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#16839984C2semidirect
2. C2×#16839924C2semidirect
4. C2×C4×#11758201C2semidirect
5. #21449396C2semidirect
6. #21447193C2semidirect
7. #21447015C2semidirect
8. #21447008C2semidirect
9. #21446895C2semidirect
10. #21446672C2semidirect
11. #21446427C2semidirect
12. #21446170C2semidirect
13. #21446160C2semidirect
14. #21446087C2semidirect
15. C61×#2341C2semidirect
104. #14519701D4semidirect
395. #2341D61semidirect
462. C61#25155semidirect

Maximal subgroups

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

subgroupindex
C2×#168399842
C2×#168399242
C2×#168399072
C2×C4×#117582012
#214493962
#214471932
#214470152
#214470082
#214468952
#214466722
#214464272
#214461702
#214461602
#214460872
C61×#23412
#2515561