Finite Group Databasebeta

← #29691356

Subgroups — #29691356

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839898C211yesmaximal, characteristic
2#21448512C211yesmaximal, characteristic, complemented
3#21448399C211yesmaximal, characteristic, complemented
4#21446695C211yesmaximal, characteristic, complemented
5#21446685C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446502C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446440C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446139C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445751C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic, complemented
21C2×#14519736C2211yescharacteristic
22#16839898C418yescomplemented
23C2×#14519711C2211yescharacteristic, complemented
24C2×#14519709C2211yescharacteristic, complemented
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic, complemented
32C2×#14519699C2211yescharacteristic, complemented
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839664C2211yescharacteristic, complemented
38#16839663—21no—
39#16839663—21no—
40#16839662—21no—
41#16839660C2211yescharacteristic, complemented
42#16839652—21no—
43#16839638—21no—
44#16839633—21no—
45#16839622C2211yescharacteristic
46#16839617—21no—
47#16839617—21no—
48C4×C4⋊Dic61C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53C2×#117×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic, complemented
57C2×C4×C8×C61C2211yescharacteristic, complemented
58C61×#336C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244—21no—
62C22×D244—22no—
63C22×D244—41no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244—41no—
67C22×D244C2×C414yescomplemented
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73C2×D488—41no—
74C2×D488—41no—
75C2×D488—41no—
76C2×D488—41no—
77C2×D488C2×C414yes—
78C2×D488C2×C414yes—
79#14519751—22no—
80#14519751C2×C414yes—
81C4×D244—41no—
82C4×D244—41no—
83#14519736—41no—
84#14519736—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107#14519711—41no—
108#14519709—41no—
109#14519699—41no—
110#14519699—41no—
111#14519699—41no—
112#14519699—41no—
113#14519699—41no—
114#14519699—41no—
115#14519699C2×C414yescomplemented
116#14519699C2×C414yescomplemented
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C23×C4×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125#117×C61—41no—
126#117×C61—41no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C22⋊C8×C61—22no—
134C22⋊C8×C61C2×C414yescomplemented
135#97×C61—41no—
136C4×C8×C61—41no—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61—81no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4112yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—24no—
161C2×C22⋊D61—81no—
162C2×C22⋊D61—81no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—24no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—44no—
185C2×D244—44no—
186C2×D244—42no—
187C2×D244—42no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244C22×C412yes—
191C2×D244C22×C412yes—
192C2×D244C22×C412yes—
193C2×C4×D61—42no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61C22×C412yes—
207C2×C8×C61C22×C412yes—
208C4⋊C4×C61—41no—
209C4⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C22⋊C4×C61—41no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—42no—
217C22⋊Dic61—81no—
218#11758198—24no—
219#11758198—42no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226#11758198—81no—
227#11758198—81no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61C22×C412yes—
240#11758196—81no—
241C4×Dic61—42no—
242C4×Dic61—81no—
243D488—44no—
244D488—44no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61C4×D412yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—48no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
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×C61C4×D412yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C22⋊D61—84no—
307C2×Dic61—22no—
308C2×Dic61—41no—
309C2×Dic61—41no—
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—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322D244—22no—
323D244—22no—
324D244—22no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—48no—
329D244—41no—
330D244—41no—
331D244—41no—
332D244—41no—
333D244—41no—
334D244—41no—
335C4×D61—84no—
336C8×C61—22no—
337C8×C61—22no—
338C8×C61—41no—
339C8×C61—41no—
340#22056—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61#53411yescharacteristic
350C22×C61#53511yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57611yescharacteristic
353C22×C61#57611yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—816no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61#51811yescharacteristic
383C4×C61#51811yescharacteristic
384C4×C61#53811yescharacteristic
385C4×C61#53811yescharacteristic
386Dic61—42no—
387Dic61—81no—
388Dic61—81no—
389Dic61—81no—
390Dic61—81no—
391C2×#447—611no—
392#2324—611no—
393#2309—611no—
394#1972—611no—
395#1970—611no—
396#1936—611no—
397#1934—611no—
398#1926—611no—
399#1925—611no—
400#1879—611no—
401#1879—611no—
402#1875—611no—
403#1854—611no—
404#1786—611no—
405#1750D6111yescharacteristic, complemented
406C2×C61—42no—
407C2×C61#232111yescharacteristic
408C2×C61#294611yescharacteristic
409C2×C61#294811yescharacteristic
410C2×C61#319811yescharacteristic
411C2×C61#319911yescharacteristic
412C2×C61#322011yescharacteristic
413C2×C61#322411yescharacteristic
414D61—82no—
415D61—82no—
416D61—82no—
417C23×D4—611no—
418C22×D8—611no—
419C22×D8—611no—
420C2×#121—611no—
421C2×C4×D4—611no—
422C2×#117—611no—
423C2×#117C2×D6111yescharacteristic
424#447—618no—
425C2×#107—611no—
426C2×#106—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×C22⋊C8C2×D6111yescharacteristic
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97C2×D6111yescharacteristic, complemented
438C2×C4×C8C2×D6111yescharacteristic, complemented
439#390—611no—
440#390—611no—
441#390—611no—
442#390—611no—
443#390—611no—
444#390—1221no—
445#390—1221no—
446#390—1221no—
447#389—611no—
448#388—1221no—
449#386—1221no—
450#385—1221no—
451#380—611no—
452#379—1221no—
453#379—1221no—
454C4×C4⋊C4—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459#336C2×D6111yescharacteristic, complemented
460#336C2×D6111yescharacteristic, complemented
461C61#2205611yescharacteristic, complemented, Sylow
462C25—1221no—
463C22×D4—614no—
464C22×D4—611no—
465C22×D4—611no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1222no—
470C22×D4—2441no—
471C22×D4—2441no—
472C22×D4—2441no—
473C22×D4—2441no—
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×D8—614no—
477C2×D8—614no—
478C2×D8—2441no—
479C2×D8—2441no—
480C2×D8—2441no—
481C2×D8—2441no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—614no—
487#121—1222no—
488C4×D4—2441no—
489C4×D4—2441no—
490#117—41no—
491#117—41no—
492#117—2441no—
493#117—2441no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4D24411yescharacteristic
501C2×C4⋊C4D24411yescharacteristic
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4D24411yescharacteristic
517C2×C22⋊C4D24411yescharacteristic
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42C22×D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522#107—2441no—
523#106—2441no—
524#102—614no—
525#102—614no—
526#102—2441no—
527#102—2441no—
528#102—2441no—
529#102—2441no—
530#102—2441no—
531#102—2441no—
532C22⋊C8—22no—
533C22⋊C8C4×D6114yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—1224no—
540C24—1221no—
541C24—1221no—
542C24—1221no—
543C24—4881no—
544C24—4881no—
545C24—4881no—
546C24—4881no—
547C24—2442no—
548C24—2442no—
549C24C2×D24411yescharacteristic
550C2×D4—612no—
551C2×D4—612no—
552C2×D4—612no—
553C2×D4—1224no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1224no—
570C2×D4—4881no—
571C2×D4—4881no—
572C2×D4—2444no—
573C2×D4—2444no—
574C2×D4—2442no—
575C2×D4—2442no—
576C2×D4—2444no—
577C2×D4—2444no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—4881no—
589C22×C4—2442no—
590C22×C4C2×C4×D6112yes—
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4C2×D24411yescharacteristic
595C22×C4C2×D24411yescharacteristic
596C22×C4#1175822212yes—
597C22×C4C23×D6111yescharacteristic
598D8—2444no—
599D8—2444no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×C4×D6112yes—
611C2×C8C2×C4×D6112yes—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—612no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—4881no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—1224no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—4881no—
646C42—2442no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—4884no—
657C23—4884no—
658C23—4884no—
659C23—4884no—
660C23—4884no—
661C23—4884no—
662C23—2448no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23C4×D24412yes—
682C23C22×D24411yescharacteristic
683D4—1222no—
684D4—1222no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—1222no—
689D4—4884no—
690D4—2448no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695D4—2441no—
696D4—2441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
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—21no—
715C2×C4—1222no—
716C2×C4—4884no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
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×C4C4×D24412yes—
732C2×C4C22×C4×D6111yescharacteristic
733C2×C4C2×#1175822211yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982311yescharacteristic
737C2×C4#1451982311yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—48816no—
750C22—4881no—
751C22—4881no—
752C22—4881no—
753C22—4881no—
754C22—4881no—
755C22—4881no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22C2×C4×D24411yescharacteristic
772C22#1684032411yescharacteristic
773C22#1684033111yescharacteristic
774C22#1684056711yescharacteristic
775C22#1684056711yescharacteristic
776C22#1684056711yescharacteristic
777C22#1684057411yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—4881no—
784C4—4881no—
785C4—4881no—
786C4—4881no—
787C4—2442no—
788C4#1684023411yescharacteristic
789C4#1684023411yescharacteristic
790C4#1684034511yescharacteristic
791C4#1684034511yescharacteristic
792C2—42no—
793C2—4882no—
794C2—4882no—
795C2—4882no—
796C2#2144847911yescharacteristic
797C2#2145465311yescharacteristic
798C2#2145467211yescharacteristic
799C2#2145667311yescharacteristic
800C2#2145668411yescharacteristic
801C2#2145687111yescharacteristic
802C2#2145691511yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1750C2
socleC23×C61C22×D4
prime radicalC2×#16839898C2
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. #21448512C2semidirect
3. #21448399C2semidirect
4. #21446695C2semidirect
5. #21446685C2semidirect
6. #21446516C2semidirect
7. #21446502C2semidirect
8. #21446447C2semidirect
9. #21446440C2semidirect
10. #21446166C2semidirect
11. #21446166C2semidirect
12. #21446139C2semidirect
13. #21446020C2semidirect
14. #21445751C2semidirect
15. C61×#1750C2semidirect
20. C2×C4×D244C22semidirect
22. #16839898C4semidirect
23. C2×#14519711C22semidirect
24. C2×#14519709C22semidirect
31. C2×#14519699C22semidirect
32. C2×#14519699C22semidirect
37. #16839664C22semidirect
41. #16839660C22semidirect
48. C4×C4⋊Dic61C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
56. C2×#97×C61C22semidirect
57. C2×C4×C8×C61C22semidirect
58. C61×#336C22semidirect
59. C61×#336C22semidirect
67. C22×D244C2×C4semidirect
115. #14519699C2×C4semidirect
116. #14519699C2×C4semidirect
134. C22⋊C8×C61C2×C4semidirect
405. #1750D61semidirect
437. C2×#97C2×D61semidirect
438. C2×C4×C8C2×D61semidirect
459. #336C2×D61semidirect
460. #336C2×D61semidirect
461. C61#22056semidirect
533. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398982
#214485122
#214483992
#214466952
#214466852
#214465162
#214465022
#214464472
#214464402
#214461662
#214461392
#214460202
#214457512
C61×#17502
#2205661