Finite Group Databasebeta

← #29737067

Subgroups — #29737067

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic, complemented
2C22×#14519697C211yesmaximal, characteristic
3C22⋊C4×D244C211yesmaximal, characteristic
4#21447348C211yesmaximal, characteristic, complemented
5#21447204C211yesmaximal, characteristic, complemented
6#21447204C211yesmaximal, characteristic, complemented
7#21446952C211yesmaximal, characteristic, complemented
8#21446065C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446007C211yesmaximal, characteristic, complemented
11#21445999C211yesmaximal, characteristic, complemented
12#21445846C211yesmaximal, characteristic, complemented
13#21445816C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#2440C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C22⋊C4×D61—21no—
21#16840039—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519697—24no—
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839640—21no—
41#16839640—21no—
42#16839622C2211yescharacteristic
43#16839617—21no—
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C2×C4⋊Q8×C61C2211yescharacteristic, complemented
51C2×C22⋊Q8×C61—21no—
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#398—21no—
54C61×#395—21no—
55C61×#389C2211yescharacteristic, complemented
56C61×#389C2211yescharacteristic, complemented
57C61×#385—21no—
58C61×#384C2211yescharacteristic, complemented
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244Q814yescomplemented
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C4×D244—22no—
81C4×D244—22no—
82C4×D244—41no—
83C4×D244—41no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C22⋊C4×D61—44no—
94#14519710—22no—
95#14519710—22no—
96#14519710—41no—
97#14519710—41no—
98C4⋊#92418—22no—
99C4⋊#92418—41no—
100#14519697—22no—
101#14519697—22no—
102#14519697—22no—
103#14519697—22no—
104#14519697—22no—
105#14519697—41no—
106#14519697—41no—
107#14519697D414yes—
108C22⋊#92418—22no—
109#14519684—21no—
110C22×Q8×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61—41no—
115C22⋊Q8×C61—44no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—41no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—81no—
147C23×D61—81no—
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×Q8×C61—81no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—81no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×Q812yes—
168C22×C4×C61#4112yes—
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—28no—
180C2×D244—24no—
181C2×D244—21no—
182C2×D244—44no—
183C2×D244—44no—
184C2×D244—44no—
185C2×D244—42no—
186C2×D244—42no—
187C2×D244C2×D412yes—
188C2×D244C2×Q812yes—
189C2×D244C2×Q812yes—
190C2×D244#4112yes—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—81no—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61D814yes—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—21no—
218C22⋊Dic61—42no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—44no—
241C2×#92418C2×D412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61C22⋊Q812yes—
247C23×C61C2×D812yes—
248C23×C61#13712yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—48no—
255C22×D61—41no—
256C22×D61—41no—
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—48no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271Q8×C61—84no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—84no—
301C2×C4×C61C22⋊Q812yes—
302C2×C4×C61C2×D812yes—
303C2×C4×C61C2×D812yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×Q811yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316D244—22no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244—48no—
322D244—41no—
323D244—41no—
324D244C22⋊Q814yescomplemented
325C4×D61—84no—
326C4×D61—84no—
327#92418—22no—
328#92418—41no—
329#92418—41no—
330#92418—41no—
331#25950—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61#47414yescomplemented
339C22×C61C2×C22⋊Q811yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61C22×D811yescharacteristic
343C22×C61C2×#13711yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—24no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—816no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365C4×C61—42no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61—81no—
370C4×C61C2×C22⋊Q811yescharacteristic
371C4×C61#54311yescharacteristic
372C4×C61#54611yescharacteristic
373C4×C61#55111yescharacteristic
374Dic61—81no—
375Dic61—81no—
376C2×#474—611no—
377C22×#102—611no—
378#2440D6111yescharacteristic, complemented
379D4×C22⋊C4—611no—
380#2093—611no—
381#2067—611no—
382#2067—611no—
383#2023—611no—
384#1862—611no—
385#1862—611no—
386#1852—611no—
387#1850—611no—
388#1808—611no—
389#1802—611no—
390#1786—611no—
391C2×C61—24no—
392C2×C61#243711yescharacteristic
393C2×C61C2×#47411yescharacteristic
394C2×C61#308111yescharacteristic
395C2×C61#326611yescharacteristic
396C2×C61D4×D811yescharacteristic
397C2×C61#329411yescharacteristic
398C2×C61#331411yescharacteristic
399D61—44no—
400D61—82no—
401C23×D4—611no—
402C23×C8—611no—
403C2×C4⋊Q8C2×D6111yescharacteristic, complemented
404C2×C22⋊Q8—21no—
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408C22×C22⋊C4—1221no—
409#474—1224no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#107—611no—
413C2×#107—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—1224no—
425C2×C22⋊C8—611no—
426#398—21no—
427#395—21no—
428#390—611no—
429#390—611no—
430#389C2×D6111yescharacteristic, complemented
431#389C2×D6111yescharacteristic, complemented
432#386—1221no—
433#386—1221no—
434#385—21no—
435#384C2×D6111yescharacteristic, complemented
436#380—611no—
437#380C2×D6111yescharacteristic
438#379—1221no—
439C4×C22⋊C4C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2595011yescharacteristic, complemented, Sylow
447C25—1221no—
448C22×Q8—21no—
449C22×D4—614no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1221no—
456C22×D4—2441no—
457C22×D4—2441no—
458C23×C4—21no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—2441no—
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—44no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2441no—
475C4×D4—2441no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—2444no—
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C22⋊C4C22⋊D6111yescharacteristic
501C2×C42C22×D6111yescharacteristic
502C2×C42C22×D6111yescharacteristic
503#107—1222no—
504#107—1222no—
505#107—2441no—
506#107—2441no—
507C4⋊C8—1222no—
508C4⋊C8—2441no—
509#102—614no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—2441no—
516#102—2441no—
517C22⋊C8—1222no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—1221no—
522#95C22⋊D6111yescharacteristic
523#95C22⋊D6111yescharacteristic
524C24—1221no—
525C24—1224no—
526C24—1221no—
527C24—4881no—
528C24—4881no—
529C24—2442no—
530C24—2442no—
531C24—2442no—
532C24—2442no—
533C24C2×C22⋊D6111yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—612no—
538C2×D4—612no—
539C2×D4—612no—
540C2×D4—612no—
541C2×D4—1228no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1224no—
551C2×D4—2444no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2442no—
555C2×D4—2442no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4Q8×D6112yes—
576C22×C4#1175822612yes—
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583C2×C8—612no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—2444no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4D4×D6112yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—4881no—
617C22⋊C4—4881no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4#1175819914yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—4884no—
637C23—4884no—
638C23—4884no—
639C23—4884no—
640C23—4884no—
641C23—2448no—
642C23—2441no—
643C23—2448no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23#1451975312yes—
654C23C2×#1175819912yes—
655C23#1451980812yes—
656C23C22×C22⋊D6111yescharacteristic
657Q8—84no—
658D4—614no—
659D4—1222no—
660D4—1222no—
661D4—1222no—
662D4—1222no—
663D4—1222no—
664D4—2448no—
665D4—2441no—
666D4—2441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—4884no—
697C2×C4—4884no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4#1451975312yes—
705C2×C4C2×#1175819912yes—
706C2×C4C2×#1175819912yes—
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4C2×Q8×D6111yescharacteristic
709C2×C4#41×D6111yescharacteristic
710C2×C4C2×#1175822611yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982311yescharacteristic
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—1224no—
724C22—48816no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1684003914yescomplemented
739C22C2×#1451975311yescharacteristic
740C22D4×C22⋊D6111yescharacteristic
741C22#1684040011yescharacteristic
742C22C22×#1175819911yescharacteristic
743C22C2×#1451980811yescharacteristic
744C22#1684056511yescharacteristic
745C22#1684057011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—4881no—
756C4—4881no—
757C4C22⋊Q8×D6111yescharacteristic
758C4#1684038711yescharacteristic
759C4#1684040311yescharacteristic
760C4#1684043911yescharacteristic
761C2—24no—
762C2—4882no—
763C2—2444no—
764C2#2144948211yescharacteristic
765C2C2×#1684003911yescharacteristic
766C2#2145564411yescharacteristic
767C2#2145733011yescharacteristic
768C2D4×#1175819911yescharacteristic
769C2#2145762611yescharacteristic
770C2#2145789411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2440C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2440D61
hypocenterC61#25950
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#16840039C2semidirect
4. #21447348C2semidirect
5. #21447204C2semidirect
6. #21447204C2semidirect
7. #21446952C2semidirect
8. #21446065C2semidirect
9. #21446065C2semidirect
10. #21446007C2semidirect
11. #21445999C2semidirect
12. #21445846C2semidirect
13. #21445816C2semidirect
15. C61×#2440C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519710C22semidirect
25. C2×#14519710C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×C4⋊#92418C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
50. C2×C4⋊Q8×C61C22semidirect
55. C61×#389C22semidirect
56. C61×#389C22semidirect
58. C61×#384C22semidirect
68. C22×D244Q8semidirect
324. D244C22⋊Q8semidirect
338. C22×C61#474semidirect
378. #2440D61semidirect
403. C2×C4⋊Q8C2×D61semidirect
430. #389C2×D61semidirect
431. #389C2×D61semidirect
435. #384C2×D61semidirect
446. C61#25950semidirect
738. C22#16840039semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
C22×#145196972
C22⋊C4×D2442
#214473482
#214472042
#214469522
#214460652
#214460072
#214459992
#214458462
#214458162
#214457492
C61×#24402
#2595061