Finite Group Databasebeta

← #29679939

Subgroups — #29679939

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2C2×#16839818C211yesmaximal, characteristic, complemented
3C2×#16839814C211yesmaximal, characteristic, complemented
4#21445889C212yesmaximal, complemented
5#21445799C211yesmaximal, characteristic, complemented
6#21445796C211yesmaximal, characteristic, complemented
7#21445796C211yesmaximal, characteristic, complemented
8#21445730C212yesmaximal
9#21445587C212yesmaximal, complemented
10#21445584C212yesmaximal, complemented
11C61×#1797C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C4×#11758222—24no—
14C4×#11758222—24no—
15C2×C4×Dic122C411yescharacteristic
16C2×C4×Dic122C411yescharacteristic
17C2×C4×D244C411yescharacteristic
18C2×C4×D244C411yescharacteristic
19C2×C4×C22⋊D61C411yescharacteristic
20C2×C4×C22⋊D61C411yescharacteristic
21C2×C4×C22⋊D61C411yescharacteristic
22C2×C4×C22⋊D61C411yescharacteristic
23C2×#14519736C2211yescharacteristic
24C2×#14519734C2211yescharacteristic
25C2×#14519734C2211yescharacteristic
26C2×C42×D61C2211yescharacteristic
27C2×C42×D61C2211yescharacteristic
28#16839818—24no—
29#16839814—24no—
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2212yes—
33C2×#14519689C2212yes—
34C2×#14519689C2212yes—
35C2×#14519689C2212yes—
36C2×#14519689C2212yes—
37C2×#14519687C2212yes—
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C22×C42×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2212yes—
46C61×#336C2212yes—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C22×Dic122C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2312yes—
64C22×#92418C2312yes—
65C4×Dic122—24no—
66C4×Dic122—24no—
67C4×D244—24no—
68C4×D244—24no—
69C4×C22⋊D61—24no—
70C4×C22⋊D61—24no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—24no—
73#14519736—22no—
74#14519736—22no—
75#14519734—22no—
76#14519734—22no—
77#14519734—22no—
78#14519734—22no—
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C42×D61—22no—
98C42×D61—22no—
99C42×D61D414yes—
100C42×D61D414yes—
101C4⋊#92418—22no—
102C4⋊#92418—22no—
103C22⋊#92418—24no—
104#14519689—24no—
105#14519689—24no—
106#14519689—24no—
107#14519689—24no—
108#14519687—24no—
109C8×Dic61—24no—
110C23×C4×C61C2×C411yescharacteristic
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C22×C8×C61C2312yes—
114C22×C8×C61C2312yes—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61C2×C411yescharacteristic
118C2×C42×C61C2×C411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—22no—
122C4⋊C8×C61—22no—
123C22⋊C8×C61—24no—
124C24×C61C22×C411yescharacteristic
125C23×D61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61#4112yes—
143C22×C4×C61#4112yes—
144C22×C4×C61C2411yescharacteristic
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157#11758222—28no—
158#11758222—28no—
159#11758222—28no—
160#11758222—28no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61C22⋊C414yes—
183C2×C4×D61C22⋊C414yes—
184C2×C4×D61C2×D412yes—
185C2×C4×D61C2×D412yes—
186C2×C4×D61#4112yes—
187C2×C4×D61#4112yes—
188C2×Dic122—22no—
189C2×Dic122—22no—
190C2×Dic122—22no—
191C2×C8×C61—22no—
192C2×C8×C61—22no—
193C2×C8×C61—22no—
194C2×C8×C61—22no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C42×C61—22no—
198C42×C61—22no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61C2×D412yes—
202C42×C61C2×D412yes—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61C22⋊C414yes—
220C4×Dic61C22⋊C414yes—
221C4×Dic61C2×D412yes—
222C4×Dic61C2×D412yes—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—22no—
228C2×#92418—22no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61#11712yes—
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61C2×C22⋊C412yes—
250C22×D61#11712yes—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—44no—
266C2×C4×C61—44no—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C2×C22⋊C412yes—
269C2×C4×C61#11712yes—
270C2×C4×C61#13112yes—
271C2×C4×C61#13112yes—
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C22⋊D61—28no—
279C22⋊D61—28no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61C2×C22⋊C412yes—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C2×C22⋊C412yes—
297C2×Dic61#11712yes—
298D244—28no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—28no—
308C4×D61—44no—
309C4×D61—44no—
310C4×D61—44no—
311Dic122—28no—
312C8×C61—42no—
313C8×C61—42no—
314#92418—42no—
315#92418—42no—
316#20721—611nomaximal, Sylow
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61C2×#11711yescharacteristic
326C22×C61C2×#11711yescharacteristic
327C22×C61C2×#13111yescharacteristic
328C22×C61C2×#13111yescharacteristic
329C22×C61#56811yescharacteristic
330C22×C61#56811yescharacteristic
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61#40814yes—
350C4×C61#52511yescharacteristic
351C4×C61#52511yescharacteristic
352C4×C61#52511yescharacteristic
353C4×C61#52511yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—41no—
359Dic61—41no—
360C2×C4×#41—611no—
361C2×#432—611no—
362C2×#431—611no—
363#1818—612no—
364#1797—611no—
365#1797—611no—
366#1797—611no—
367#1797D6111yescharacteristic, complemented
368#1780—612no—
369#1750—612no—
370#1750—612no—
371C2×C61—42no—
372C2×C61#228011yescharacteristic
373C2×C61C2×#40811yescharacteristic
374C2×C61#287911yescharacteristic
375C2×C61#292511yescharacteristic
376C2×C61#292511yescharacteristic
377C2×C61#292511yescharacteristic
378C2×C61#292511yescharacteristic
379D61—42no—
380D61—42no—
381C22×#41—611no—
382C4×#41—1224no—
383C4×#41—1224no—
384C2×C4×Q8—611no—
385C2×C4×Q8—611no—
386C2×C4×D4—611no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×C4×D4—611no—
392C2×#117—611no—
393C2×#117—611no—
394C2×#117—611no—
395C22×C42—611no—
396C22×C42—611no—
397C22×C42C2×D6111yescharacteristic
398#432—1224no—
399#431—1224no—
400C2×C4⋊C8—611no—
401C2×C4⋊C8—611no—
402C2×C4⋊C8C2×D6111yescharacteristic
403C2×C4⋊C8C2×D6111yescharacteristic
404C2×C22⋊C8—612no—
405C2×C22⋊C8—612no—
406C2×C22⋊C8—612no—
407C2×C22⋊C8—612no—
408C2×C22⋊C8—612no—
409C2×C22⋊C8C2×D6112yes—
410C2×#97—612no—
411C2×C4×C8—612no—
412#336—612no—
413#336—612no—
414#336—612no—
415#336C2×D6112yes—
416C61#2072111yescharacteristic, complemented, Sylow
417C2×#41—1222no—
418C2×#41—1222no—
419C2×#41—1222no—
420C2×#41—1222no—
421C2×#41—1222no—
422C2×#41—1222no—
423C22×Q8—611no—
424C22×D4—611no—
425C22×D4—611no—
426C22×D4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4C4×D6111yescharacteristic
434C23×C4C4×D6111yescharacteristic
435C23×C4C22×D6111yescharacteristic
436C22×C8—612no—
437C22×C8—612no—
438C22×C8C22×D6112yes—
439C22×C8C22×D6112yes—
440C4×Q8—1224no—
441C4×Q8—1224no—
442C4×D4—1224no—
443C4×D4—1224no—
444C4×D4—1224no—
445C4×D4—1224no—
446C4×D4—1224no—
447C4×D4—1224no—
448#117—1222no—
449#117—1222no—
450#117—1222no—
451#117—1222no—
452#117—1222no—
453#117—1222no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—614no—
472C2×C42—614no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—1222no—
477C2×C42—1222no—
478C2×C42C4×D6111yescharacteristic
479C2×C42C4×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481C2×C42C22×D6111yescharacteristic
482C4⋊C8—22no—
483C4⋊C8—22no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C22⋊C8—24no—
487C22⋊C8—1224no—
488C22⋊C8—1224no—
489C22⋊C8—1224no—
490C22⋊C8—1224no—
491C22⋊C8—1224no—
492#97—1224no—
493C4×C8—1224no—
494C24—611no—
495C24—611no—
496C24C2×C4×D6111yescharacteristic
497#41—1228no—
498#41—1228no—
499#41—1228no—
500#41—1228no—
501C2×Q8—1222no—
502C2×Q8—1222no—
503C2×Q8—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—614no—
532C22×C4—614no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—2441no—
550C22×C4—2441no—
551C22×C4—2441no—
552C22×C4—2441no—
553C22×C4C2×C4×D6111yescharacteristic
554C22×C4C2×C4×D6111yescharacteristic
555C22×C4C2×C4×D6111yescharacteristic
556C22×C4C2×C4×D6111yescharacteristic
557C22×C4C2×C4×D6111yescharacteristic
558C22×C4#1175822412yes—
559C22×C4#1175822612yes—
560C22×C4C23×D6111yescharacteristic
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—1222no—
568C2×C8—1222no—
569C2×C8—1222no—
570C2×C8—1222no—
571C2×C8—1222no—
572C2×C8—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1222no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C42—21no—
586C42—21no—
587C42—22no—
588C42—22no—
589C42—612no—
590C42—612no—
591C42—614no—
592C42—614no—
593C42—1221no—
594C42—1221no—
595C42—1222no—
596C42—1222no—
597C42D4×D6112yes—
598C42D4×D6112yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—612no—
606C23—612no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23#1451973512yes—
620C23C22×C4×D6111yescharacteristic
621Q8—1228no—
622D4—1228no—
623D4—1228no—
624D4—1228no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—612no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1228no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4C22⋊C4×D6112yes—
672C2×C4C22⋊C4×D6112yes—
673C2×C4#1451973512yes—
674C2×C4#1451978312yes—
675C2×C4#1451978512yes—
676C2×C4C2×D4×D6111yescharacteristic
677C2×C4C2×D4×D6111yescharacteristic
678C2×C4#41×D6111yescharacteristic
679C2×C4#41×D6111yescharacteristic
680C2×C4C2×#1175822411yescharacteristic
681C2×C4C2×#1175822611yescharacteristic
682C8—42no—
683C8—42no—
684C8—2442no—
685C8—2442no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—1222no—
694C22—1222no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22C2×C22⋊C4×D6111yescharacteristic
708C22#117×D6111yescharacteristic
709C22C2×#1451973511yescharacteristic
710C22C2×#1451978311yescharacteristic
711C22C2×#1451978511yescharacteristic
712C22#1684052811yescharacteristic
713C22#1684052811yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—1222no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—2441no—
723C4—2441no—
724C4#1683972714yes—
725C4#1684027211yescharacteristic
726C4#1684027211yescharacteristic
727C4#1684027511yescharacteristic
728C4#1684027511yescharacteristic
729C2—42no—
730C2—2442no—
731C2—2442no—
732C2#2144820111yescharacteristic
733C2C2×#1683972711yescharacteristic
734C2#2145426211yescharacteristic
735C2#2145448011yescharacteristic
736C2#2145448411yescharacteristic
737C2#2145448611yescharacteristic
738C2#2145448711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1797C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1797D61
hypocenterC61#20721
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#16839818C2semidirect
3. C2×#16839814C2semidirect
4. #21445889C2semidirect
5. #21445799C2semidirect
6. #21445796C2semidirect
7. #21445796C2semidirect
9. #21445587C2semidirect
10. #21445584C2semidirect
11. C61×#1797C2semidirect
367. #1797D61semidirect
416. C61#20721semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168398182
C2×#168398142
#214458892
#214457992
#214457962
#214457302
#214455872
#214455842
C61×#17972
#2072161