Finite Group Databasebeta

← #29712192

Subgroups — #29712192

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4#21446970C211yesmaximal, characteristic, complemented
5#21446965C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446156C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446127C211yesmaximal, characteristic, complemented
13#21446112C211yesmaximal, characteristic, complemented
14#21445911C211yesmaximal, characteristic, complemented
15C61×#2407C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840458—24no—
20#16840458—24no—
21C2×#14519772—21no—
22C2×#14519769C2211yescharacteristic
23C2×#14519759—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519749—21no—
27C2×C4×D244C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519736C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31#16839907—24no—
32#16839758—24no—
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#394—21no—
57C61×#392—21no—
58C61×#391C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#386—21no—
61C61×#385—21no—
62C61×#380C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—41no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—41no—
74C22×#92418—22no—
75C22×#92418—41no—
76C22×#92418—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519772—28no—
82#14519769—22no—
83#14519769—22no—
84#14519759—28no—
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751D414yescomplemented
89#14519749—28no—
90C4×D244—22no—
91C4×D244—22no—
92#14519737—28no—
93#14519736—22no—
94#14519736D414yescomplemented
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108#14519701—22no—
109#14519701—22no—
110#14519701—22no—
111#14519698—22no—
112#14519698—22no—
113#14519698—22no—
114#14519697—41no—
115#14519697—41no—
116C22⋊#92418—22no—
117C22⋊#92418—41no—
118C22⋊#92418—41no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—41no—
124C2×#41×C61—41no—
125C22×Q8×C61C2311yescharacteristic
126C22×D4×C61—21no—
127C22×D4×C61—21no—
128C22×D4×C61D411yescharacteristic
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61—21no—
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—41no—
135#121×C61—22no—
136#121×C61—41no—
137C4×D4×C61—22no—
138C4×D4×C61—22no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61D411yescharacteristic
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C42×C61C2311yescharacteristic
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C23×D61—21no—
158#41×C61—28no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61#4112yes—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—41no—
176C2×D4×C61—42no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—81no—
182C2×D4×C61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—42no—
197C22×C4×C61—42no—
198C22×C4×C61—42no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61—81no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244C2×D412yes—
224C2×C4×D61—24no—
225C2×C4×D61—81no—
226C2×C4×D61—81no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—42no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—42no—
236C22⋊C4×C61—42no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—81no—
239C22⋊C4×C61—81no—
240C42×C61—21no—
241C42×C61—21no—
242C22⋊Dic61—24no—
243#11758201—44no—
244#11758199—44no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C2×D412yes—
253C4⋊Dic61C2×D412yes—
254C4⋊Dic61C2×D412yes—
255#11758196—24no—
256#11758196—24no—
257C4×Dic61—24no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—44no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—22no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61#12012yes—
291C23×C61#13512yes—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—41no—
303Q8×C61—41no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—44no—
307D4×C61—48no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—84no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—48no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61#12012yes—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C22⋊D61—48no—
348C22⋊D61—84no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—84no—
359D244—22no—
360D244—22no—
361D244—41no—
362D244—41no—
363C4×D61—84no—
364#92418—41no—
365#92418—41no—
366#92418—41no—
367#92418—41no—
368#23962—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C2×#12011yescharacteristic
391C22×C61#54611yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61C2×#13511yescharacteristic
394C22×C61#57511yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C4×C61—22no—
405C4×C61—41no—
406C4×C61—42no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—81no—
410C4×C61—81no—
411C4×C61#52511yescharacteristic
412C4×C61#53511yescharacteristic
413C4×C61#54611yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—42no—
416Dic61—42no—
417Dic61—42no—
418C2×#553—611no—
419C2×#449—611no—
420C2×#416—611no—
421#2407D6111yescharacteristic, complemented
422#2026—611no—
423#2025—611no—
424#2000—611no—
425#1999—611no—
426#1893—611no—
427#1879—611no—
428#1877—611no—
429#1874—611no—
430#1872—611no—
431#1869—611no—
432#1825—611no—
433C2×C61—42no—
434C2×C61—42no—
435C2×C61—82no—
436C2×C61#240411yescharacteristic
437C2×C61#300211yescharacteristic
438C2×C61#301211yescharacteristic
439C2×C61#329711yescharacteristic
440C2×C61#330111yescharacteristic
441C2×C61#330711yescharacteristic
442C2×C61#330911yescharacteristic
443D61—82no—
444C22×#41C2×D6111yescharacteristic
445C22×SD16—611no—
446C22×D8—611no—
447C23×C8—611no—
448#553—1224no—
449#553—1224no—
450C2×#126—1221no—
451C2×#125—611no—
452C2×#123—1221no—
453C2×C22⋊Q8C2×D6111yescharacteristic
454C2×#121—611no—
455C2×#121—611no—
456C2×#121—1221no—
457C2×#121C2×D6111yescharacteristic
458C2×C4×D4—611no—
459C2×C4×D4—1221no—
460C2×C4×D4C2×D6111yescharacteristic
461C2×#117—611no—
462C22×C4⋊C4—611no—
463#449—1224no—
464#416—1224no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475C2×C22⋊C8—611no—
476#394—21no—
477#392—21no—
478#391C2×D6111yescharacteristic
479#390C2×D6111yescharacteristic
480#386—21no—
481#385—21no—
482#380C2×D6111yescharacteristic
483#340—611no—
484#340—611no—
485#340—611no—
486#340—611no—
487#340—611no—
488#340—611no—
489#336—611no—
490#336—611no—
491C61#2396211yescharacteristic, complemented, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C22×D6111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4—1221no—
504C22×D4C22⋊D6111yescharacteristic
505C22×D4C22×D6111yescharacteristic
506C23×C4—21no—
507C23×C4—1221no—
508C23×C4—1221no—
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C2×SD16—1222no—
512C2×SD16—1222no—
513C2×SD16—2441no—
514C2×D8—1222no—
515C2×D8—1222no—
516C2×D8—2441no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1222no—
522C22×C8—2441no—
523C22×C8—2441no—
524#126—1228no—
525#125—1222no—
526#125—1222no—
527#123—1228no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—41no—
532#121—614no—
533#121—1222no—
534#121—1222no—
535#121—1228no—
536#121—1222no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—1228no—
542#117—614no—
543#117—1222no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22⋊D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4C22⋊D6111yescharacteristic
566C2×C22⋊C4C22⋊D6111yescharacteristic
567C2×C42—1221no—
568C2×C42C22×D6111yescharacteristic
569#103—1222no—
570#103—1222no—
571#103—1222no—
572#102—1222no—
573#102—1222no—
574#102—1222no—
575#102—2441no—
576#102—2441no—
577C22⋊C8—1222no—
578C22⋊C8—2441no—
579C22⋊C8—2441no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—1221no—
585C24C2×C22⋊D6111yescharacteristic
586C24C2×C22⋊D6111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#1175822412yes—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—612no—
612C2×D4—1224no—
613C2×D4—1224no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—4881no—
620C2×D4—4881no—
621C2×D4—2442no—
622C2×D4—2442no—
623C2×D4#1175822412yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4881no—
646C22×C4—4881no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4D4×D6112yes—
650C22×C4D4×D6112yes—
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656SD16—2444no—
657D8—2444no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—2444no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—42no—
677C4⋊C4—612no—
678C4⋊C4—612no—
679C4⋊C4—612no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1224no—
696C22⋊C4—1224no—
697C42—21no—
698C42—21no—
699C42—1224no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—1222no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23#1451974512yes—
727C23#1451979712yes—
728C23C22×C22⋊D6111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—44no—
736D4—48no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—1222no—
741D4—1222no—
742D4—4884no—
743D4—2448no—
744D4—2441no—
745D4—2441no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—48no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—4884no—
779C2×C4—4884no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4#1451974512yes—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4C2×D4×D6111yescharacteristic
789C2×C4C2×#1175822411yescharacteristic
790C2×C4C2×#1175822411yescharacteristic
791C2×C4#1451982211yescharacteristic
792C2×C4#1451982211yescharacteristic
793C8—2441no—
794C8—2441no—
795C8—2441no—
796C8—2441no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—4881no—
819C22—4881no—
820C22—4881no—
821C22—4881no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22C2×#1451974511yescharacteristic
826C22#1684040611yescharacteristic
827C22#1684040611yescharacteristic
828C22C2×#1451979711yescharacteristic
829C22#1684056011yescharacteristic
830C22#1684056511yescharacteristic
831C22#1684057011yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—2442no—
840C4—2442no—
841C4—2442no—
842C4#1684026811yescharacteristic
843C4#1684032711yescharacteristic
844C4#1684039911yescharacteristic
845C4#1684039911yescharacteristic
846C2—42no—
847C2—42no—
848C2—82no—
849C2—4882no—
850C2#2144913511yescharacteristic
851C2#2145503511yescharacteristic
852C2#2145512011yescharacteristic
853C2#2145766911yescharacteristic
854C2#2145772111yescharacteristic
855C2#2145779511yescharacteristic
856C2#2145782511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2407C2
socleC23×C61C22×D4
hypercenter#2407D61
hypocenterC61#23962
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839758C2semidirect
4. #21446970C2semidirect
5. #21446965C2semidirect
6. #21446820C2semidirect
7. #21446815C2semidirect
8. #21446245C2semidirect
9. #21446170C2semidirect
10. #21446156C2semidirect
11. #21446137C2semidirect
12. #21446127C2semidirect
13. #21446112C2semidirect
14. #21445911C2semidirect
15. C61×#2407C2semidirect
88. #14519751D4semidirect
94. #14519736D4semidirect
421. #2407D61semidirect
491. C61#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168399072
C2×#168397582
#214469702
#214469652
#214468202
#214468152
#214462452
#214461702
#214461562
#214461372
#214461272
#214461122
#214459112
C61×#24072
#2396261