Finite Group Databasebeta

← #29586774

Subgroups — #29586774

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic
3#21448407C211yesmaximal, characteristic
4C2×#16839669C211yesmaximal, characteristic, complemented
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839521C211yesmaximal, characteristic, complemented
7C2×C61×#419C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C2×#14519808—22no—
10C2×#14519808—22no—
11C2×#14519808—22no—
12C2×#14519808—22no—
13C2×#14519808—22no—
14C2×#14519808C414yescomplemented
15C22×#11758202—21no—
16C22×#11758201—21no—
17C22×#11758194C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C2×#14519703—22no—
21C2×#14519703—22no—
22C2×#14519703—22no—
23#16839669—22no—
24#16839669—22no—
25#16839668—21no—
26#16839664—21no—
27#16839639—22no—
28#16839619—22no—
29C2×#14519684—22no—
30#16839530—22no—
31#16839521—22no—
32C23×Q8×C61C2211yescharacteristic
33C22×M16×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C61×#419—22no—
36C61×#419—22no—
37C2×#103×C61—22no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222C2×C412yes—
49C2×#11758222D412yes—
50C22×Dic122D411yescharacteristic
51C22×D244D411yescharacteristic
52C22×C22⋊D61—21no—
53C23×Dic61—21no—
54C23×Dic61D412yes—
55C22×C4×D61—21no—
56#14519808—28no—
57#14519808—28no—
58#14519808—28no—
59#14519808—28no—
60C2×#11758202—24no—
61C2×#11758202—24no—
62C2×#11758202—24no—
63C2×#11758201—24no—
64C2×#11758201—24no—
65C2×#11758201—24no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194C2×C412yes—
70C2×#11758194D412yes—
71C2×#11758194D412yes—
72C22×#92418—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×#11758198—24no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61D412yes—
86#14519703—28no—
87#14519684—28no—
88#14519684—24no—
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61—21no—
96C22×Q8×C61—21no—
97C22×Q8×C61—21no—
98C22×Q8×C61—21no—
99C22×Q8×C61—21no—
100C22×Q8×C61C2×C412yes—
101C22×Q8×C61D412yes—
102C22×Q8×C61D412yes—
103C23×C4×C61—21no—
104C23×C4×C61C2311yescharacteristic
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61D412yes—
111C22×C8×C61—21no—
112#117×C61—21no—
113#117×C61—21no—
114#117×C61—21no—
115#117×C61—21no—
116C2×C4⋊C4×C61D412yes—
117C2×C22⋊C4×C61—21no—
118C2×C42×C61—21no—
119#103×C61—28no—
120C24×C61C2×D411yescharacteristic
121C23×D61—21no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61—22no—
129C2×Q8×C61—22no—
130C2×Q8×C61—22no—
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61—22no—
135C2×Q8×C61—22no—
136C2×Q8×C61—22no—
137C2×Q8×C61—41no—
138C2×Q8×C61—41no—
139C2×Q8×C61—41no—
140C2×Q8×C61—41no—
141C2×Q8×C61—41no—
142C2×Q8×C61—41no—
143C2×Q8×C61—41no—
144C2×Q8×C61—41no—
145C2×Q8×C61—41no—
146C2×Q8×C61—41no—
147C2×Q8×C61—41no—
148C2×Q8×C61—41no—
149C2×Q8×C61C22⋊C414yescomplemented
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C22×C4×C61—41no—
157C22×C4×C61—41no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61#4111yescharacteristic
171C22×C4×C61#4111yescharacteristic
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—41no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—41no—
178C22×Dic61—24no—
179C22×Dic61—21no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—42no—
185C22×Dic61—41no—
186C22×Dic61—41no—
187C22×Dic61—44no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C22⋊C412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—41no—
213C2×C4×D61—41no—
214C2×C4×D61—41no—
215C2×C4×D61—41no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122C22⋊C412yes—
222M16×C61—22no—
223M16×C61—22no—
224M16×C61—41no—
225M16×C61—41no—
226C2×C8×C61—22no—
227C2×C8×C61—41no—
228C2×C8×C61—41no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C22⋊C4×C61—41no—
232C22⋊C4×C61—41no—
233C42×C61—41no—
234C42×C61—41no—
235#11758202—216no—
236#11758201—216no—
237#11758198—84no—
238C4⋊Dic61—41no—
239C4⋊Dic61—41no—
240C4⋊Dic61—41no—
241C4⋊Dic61—41no—
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61—41no—
245C4×Dic61—41no—
246#11758194—22no—
247#11758194—22no—
248#11758194—22no—
249#11758194C22⋊C414yescomplemented
250C2×#92418—22no—
251C2×#92418—22no—
252C2×#92418—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61C4×D411yescharacteristic
256C23×C61#12011yescharacteristic
257C23×C61#12011yescharacteristic
258C23×C61#12111yescharacteristic
259C23×C61#12111yescharacteristic
260C23×C61#12111yescharacteristic
261C23×C61#12711yescharacteristic
262C22×D61—22no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—42no—
266C22×D61—42no—
267Q8×C61—24no—
268Q8×C61—24no—
269Q8×C61—42no—
270Q8×C61—42no—
271Q8×C61—42no—
272Q8×C61—42no—
273Q8×C61—42no—
274Q8×C61—42no—
275C2×C4×C61—24no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61C2×C22⋊C411yescharacteristic
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C4×D411yescharacteristic
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61#12011yescharacteristic
292C2×C4×C61#12011yescharacteristic
293C2×C4×C61#12011yescharacteristic
294C2×C4×C61#12011yescharacteristic
295C2×C4×C61#12011yescharacteristic
296C2×C4×C61#12011yescharacteristic
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12311yescharacteristic
307C2×C4×C61#12311yescharacteristic
308C2×C4×C61#12311yescharacteristic
309C2×C4×C61#12311yescharacteristic
310C2×C4×C61#12411yescharacteristic
311C2×C4×C61#12411yescharacteristic
312C2×C4×C61#12711yescharacteristic
313C22⋊D61—42no—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C22⋊D61—42no—
317C2×Dic61—24no—
318C2×Dic61—22no—
319C2×Dic61—44no—
320C2×Dic61—42no—
321C2×Dic61—44no—
322C2×Dic61—42no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—44no—
326C2×Dic61—42no—
327C2×Dic61—44no—
328C2×Dic61—82no—
329D244—22no—
330D244—22no—
331D244—41no—
332D244—41no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—42no—
336C4×D61—42no—
337Dic122—22no—
338Dic122—22no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—42no—
342#92418—24no—
343#11017—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61#38611yescharacteristic
353C22×C61#38611yescharacteristic
354C22×C61#39011yescharacteristic
355C22×C61#39211yescharacteristic
356C22×C61#39211yescharacteristic
357C22×C61#39211yescharacteristic
358C22×C61#39411yescharacteristic
359C22×C61#45512yes—
360C22×C61#45612yes—
361C2×D61—44no—
362C2×D61—42no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—82no—
366C4×C61—44no—
367C4×C61—82no—
368C4×C61#37911yescharacteristic
369C4×C61#38611yescharacteristic
370C4×C61#38611yescharacteristic
371C4×C61#39011yescharacteristic
372C4×C61#39211yescharacteristic
373C4×C61#39411yescharacteristic
374C4×C61#39411yescharacteristic
375C4×C61#39411yescharacteristic
376Dic61—44no—
377Dic61—42no—
378Dic61—82no—
379C22×#137—611no—
380C22×#104—611no—
381C2×#419D6111yescharacteristic, complemented
382#2311—611no—
383C2×#391—611no—
384C2×#343—611no—
385C2×#339—611no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61#143811yescharacteristic
391C2×C61#188212yes—
392C2×C61#200411yescharacteristic
393C2×C61#200511yescharacteristic
394C2×C61#200712yes—
395D61—82no—
396C22×#41—611no—
397C23×Q8C2×D6111yescharacteristic
398C2×#137—614no—
399C2×#137—1222no—
400C2×#137—1222no—
401C2×#137—1222no—
402C2×#137—1222no—
403C2×#137—1222no—
404C22×Q16—1221no—
405C22×SD16—1221no—
406C22×M16—611no—
407C22×M16C2×D6111yescharacteristic
408C2×#117C2×D6111yescharacteristic
409C22×C4⋊C4—611no—
410C22×C42—611no—
411C2×#104—1222no—
412C2×#104—1222no—
413C2×#104—1222no—
414#419—22no—
415#419—22no—
416C2×#103—22no—
417#391—1221no—
418#391—1222no—
419#391—1222no—
420#390—1221no—
421#386—1222no—
422#380—1222no—
423C2×#95—1222no—
424#343—1222no—
425#339—1222no—
426C61#1101711yescharacteristic, complemented, Sylow
427C2×#41—612no—
428C2×#41—612no—
429C2×#41—1221no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C2×#41—1221no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8—611no—
451C22×Q8C4×D6112yes—
452C22×Q8D24412yes—
453C22×Q8C22⋊D6112yes—
454C22×D4—611no—
455C22×D4—1221no—
456C23×C4—21no—
457C23×C4—612no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461#137—1228no—
462#137—1228no—
463#137—1228no—
464#137—1228no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×Q16—1224no—
468C2×SD16—1224no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—612no—
477C2×M16—612no—
478C2×M16—612no—
479C2×M16—1221no—
480C2×M16—1221no—
481C2×M16—1221no—
482C2×M16C22⋊D6112yes—
483C22×C8—21no—
484C22×C8—1221no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4C22⋊D6112yes—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1224no—
498C2×C42—21no—
499C2×C42—612no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505#104—1228no—
506#103—28no—
507#95—1228no—
508#95—1224no—
509C24—1221no—
510C24D4×D6111yescharacteristic
511#41—1222no—
512#41—1222no—
513#41—1222no—
514#41—1222no—
515#41—1222no—
516#41—1222no—
517#41—1222no—
518#41—1222no—
519#41—2441no—
520#41—2441no—
521#41—2441no—
522#41—2441no—
523#41—2441no—
524#41—2441no—
525#41—2441no—
526#41—2441no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—612no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8#1175819814yescomplemented
561C2×D4—612no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—1224no—
582C22×C4—1221no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—2444no—
590C22×C4—2442no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4#1175822211yescharacteristic
600C22×C4#1175822211yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4D4×D6111yescharacteristic
603C22×C4D4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4D4×D6111yescharacteristic
606C22×C4#1175822411yescharacteristic
607C22×C4#1175822411yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611Q16—12216no—
612SD16—12216no—
613M16—22no—
614M16—22no—
615M16—41no—
616M16—41no—
617M16—614no—
618M16—1222no—
619M16—1222no—
620M16—1222no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—1222no—
625C2×C8—1222no—
626C2×C8—1222no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—2441no—
630C4⋊C4—2441no—
631C4⋊C4—2441no—
632C4⋊C4—2441no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—4884no—
636C42—41no—
637C42—41no—
638C42—1222no—
639C42—1222no—
640C42—2441no—
641C42—2441no—
642C23—22no—
643C23—22no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2441no—
648C23—2441no—
649C23#1451973711yescharacteristic
650C23#1451974511yescharacteristic
651C23#1451974711yescharacteristic
652C23#1451974911yescharacteristic
653C23#1451975011yescharacteristic
654C23#1451975011yescharacteristic
655C23#1451977311yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—1222no—
665Q8—1222no—
666Q8—2441no—
667Q8—2441no—
668D4—1222no—
669D4—1222no—
670D4—2442no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674D4—2441no—
675D4—2441no—
676C2×C4—24no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—1224no—
687C2×C4—1222no—
688C2×C4—4882no—
689C2×C4—2444no—
690C2×C4—2444no—
691C2×C4—2442no—
692C2×C4—2444no—
693C2×C4—2442no—
694C2×C4—2444no—
695C2×C4—2441no—
696C2×C4—2442no—
697C2×C4—2441no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4C22⋊C4×D6111yescharacteristic
703C2×C4C22⋊C4×D6111yescharacteristic
704C2×C4C2×#1175819811yescharacteristic
705C2×C4#1451973711yescharacteristic
706C2×C4C4×C22⋊D6111yescharacteristic
707C2×C4C4×C22⋊D6111yescharacteristic
708C2×C4#1451974511yescharacteristic
709C2×C4#1451974511yescharacteristic
710C2×C4#1451974511yescharacteristic
711C2×C4#1451974611yescharacteristic
712C2×C4#1451974711yescharacteristic
713C2×C4#1451974711yescharacteristic
714C2×C4#1451974811yescharacteristic
715C2×C4#1451974811yescharacteristic
716C2×C4#1451974911yescharacteristic
717C2×C4#1451974911yescharacteristic
718C2×C4#1451974911yescharacteristic
719C2×C4#1451975011yescharacteristic
720C2×C4#1451975011yescharacteristic
721C2×C4#1451975111yescharacteristic
722C2×C4#1451975111yescharacteristic
723C2×C4#1451975911yescharacteristic
724C2×C4#1451975911yescharacteristic
725C2×C4#1451976011yescharacteristic
726C2×C4#1451976111yescharacteristic
727C2×C4#1451976311yescharacteristic
728C2×C4#1451976311yescharacteristic
729C2×C4#1451977311yescharacteristic
730C8—42no—
731C8—1224no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—4881no—
741C22—4881no—
742C22—4882no—
743C22—2444no—
744C22—2442no—
745C22#1683963811yescharacteristic
746C22#1683963911yescharacteristic
747C22#1683966211yescharacteristic
748C22#1683967011yescharacteristic
749C22#1683967111yescharacteristic
750C22#1683967111yescharacteristic
751C22#1683967711yescharacteristic
752C22#1683993812yes—
753C22#1683994312yes—
754C4—44no—
755C4—82no—
756C4—4882no—
757C4—2444no—
758C4—2442no—
759C4#1683961711yescharacteristic
760C4#1683963811yescharacteristic
761C4#1683964111yescharacteristic
762C4#1683966211yescharacteristic
763C4#1683967011yescharacteristic
764C4#1683967711yescharacteristic
765C4#1683967811yescharacteristic
766C4#1683967811yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—4882no—
772C2#2144405811yescharacteristic
773C2#2144618512yes—
774C2#2144684911yescharacteristic
775C2#2144685611yescharacteristic
776C2#2144686412yes—
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#419C2
socleC23×C61#120
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#419D61
hypocenterC61#11017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
4. C2×#16839669C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839521C2semidirect
7. C2×C61×#419C2semidirect
14. C2×#14519808C4semidirect
149. C2×Q8×C61C22⋊C4semidirect
249. #11758194C22⋊C4semidirect
381. C2×#419D61semidirect
426. C61#11017semidirect
560. C2×Q8#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145197032
#214484072
C2×#168396692
C2×#168395302
C2×#168395212
C2×C61×#4192
#1101761