Finite Group Databasebeta

← #29700316

Subgroups — #29700316

Order 15616.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×#16839862C211yesmaximal, characteristic, complemented
3C2×#16839756C211yesmaximal, characteristic, complemented
4#21448659C211yesmaximal, characteristic, complemented
5#21446694C211yesmaximal, characteristic, complemented
6#21446515C211yesmaximal, characteristic, complemented
7#21446439C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446086C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445652C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#2363C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22#16839905C418yescomplemented
23#16839862—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26#16839756—24no—
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839622C2211yescharacteristic
43#16839621—21no—
44#16839609—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C61×#390—21no—
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#388—21no—
58C61×#386—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200C2×C414yes—
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199C2×C414yes—
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122—41no—
88C4×Dic122—41no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100#14519710—22no—
101#14519708—41no—
102#14519700—22no—
103#14519700C2×C414yescomplemented
104#14519700D414yescomplemented
105#14519698—22no—
106#14519698—41no—
107#14519697—22no—
108#14519697—22no—
109#14519697C2×C414yescomplemented
110C22⋊#92418C2×C414yescomplemented
111#14519688—22no—
112#14519688—41no—
113#14519684—21no—
114C22×D4×C61—21no—
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118#121×C61—22no—
119#121×C61C2×C414yes—
120C4×D4×C61—22no—
121C4×D4×C61—41no—
122#117×C61—22no—
123#117×C61—41no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139#95×C61—21no—
140#95×C61—21no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C2×D4×C61—24no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—81no—
153C2×D4×C61—81no—
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—81no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—24no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179#11758222—28no—
180#11758222—44no—
181#11758222—44no—
182#11758222—44no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244C22×C412yes—
189C2×C4×D61—24no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122C22×C412yes—
196C2×Dic122C2×D412yes—
197C2×Dic122#4112yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—81no—
203C4⋊C4×C61C22×C412yes—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—41no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—42no—
217C42×C61—81no—
218C22⋊Dic61—81no—
219#11758200—28no—
220#11758199—44no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229#11758196—42no—
230#11758196—42no—
231C4×Dic61—42no—
232C4×Dic61—42no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—44no—
243C2×#92418C22×C412yes—
244C2×#92418C22×C412yes—
245C2×#92418C2×D412yes—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C4×D412yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
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—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×C61C4×D412yes—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322C4×D61—48no—
323Dic122—22no—
324Dic122—22no—
325Dic122—22no—
326Dic122C4×D414yes—
327#92418—22no—
328#92418—22no—
329#92418—22no—
330#92418—41no—
331#22857—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61#54611yescharacteristic
349C22×C61#57511yescharacteristic
350C22×C61#57511yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57711yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61C2×C4×D411yescharacteristic
369C4×C61#51811yescharacteristic
370C4×C61#54611yescharacteristic
371C4×C61#55111yescharacteristic
372Dic61—24no—
373Dic61—81no—
374Dic61—81no—
375C2×#449—611no—
376C2×#440—611no—
377C2×#416—611no—
378#2363D6111yescharacteristic, complemented
379#2341—611no—
380#1972—611no—
381#1936—611no—
382#1925—611no—
383#1893—611no—
384#1880—611no—
385#1879—611no—
386#1865—611no—
387#1854—611no—
388#1763—611no—
389#1752—611no—
390C2×C61—42no—
391C2×C61—82no—
392C2×C61#235811yescharacteristic
393C2×C61#294311yescharacteristic
394C2×C61#294611yescharacteristic
395C2×C61#326811yescharacteristic
396C2×C61#327111yescharacteristic
397C2×C61#330911yescharacteristic
398C2×C61#332111yescharacteristic
399D61—82no—
400C22×#41—611no—
401C22×SD16—611no—
402C22×D8—611no—
403C23×C8—611no—
404C2×#121C2×D6111yescharacteristic
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×D4C2×D6111yescharacteristic
408C2×#117C2×D6111yescharacteristic
409#449—618no—
410#440—1224no—
411C2×#107—611no—
412C2×#106—611no—
413#416—1224no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×C22⋊C8—611no—
423C2×#97—611no—
424C2×#97—611no—
425#390—21no—
426#390—611no—
427#390—611no—
428#390—1221no—
429#390—1221no—
430#390C2×D6111yescharacteristic
431#389C2×D6111yescharacteristic
432#388—21no—
433#386—21no—
434#380—611no—
435#380—1221no—
436C4×C4⋊C4C2×D6111yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—1221no—
439C4×C22⋊C4C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2285711yescharacteristic, complemented, Sylow
447C2×#41—614no—
448C2×#41—1222no—
449C2×#41—1222no—
450C2×#41—1222no—
451C2×#41—2441no—
452C2×#41—2441no—
453C22×Q8—611no—
454C22×D4—21no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×SD16—614no—
462C2×SD16—1222no—
463C2×SD16—1222no—
464C2×D8—614no—
465C2×D8—2441no—
466C2×D8—2441no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—2441no—
474#121—22no—
475#121C4×D6114yes—
476C4×Q8—1222no—
477C4×Q8—1222no—
478C4×Q8—2441no—
479C4×Q8—2441no—
480C4×D4—22no—
481C4×D4—41no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509C2×C42C22×D6111yescharacteristic
510#107—1222no—
511#106—2441no—
512#103—614no—
513#103—614no—
514#103—1222no—
515#102—614no—
516#102—1222no—
517#102—1222no—
518#102—1222no—
519#102—2441no—
520C22⋊C8—614no—
521#97—1222no—
522#97—2441no—
523#95—21no—
524#95—21no—
525#95—1221no—
526#95C22⋊D6111yescharacteristic
527#95C22⋊D6111yescharacteristic
528C24—21no—
529C24—1221no—
530C24C2×C22⋊D6111yescharacteristic
531#41—1228no—
532#41—2444no—
533#41—2444no—
534#41—2444no—
535C2×Q8—612no—
536C2×Q8—612no—
537C2×Q8—612no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—612no—
550C2×D4—1224no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—2442no—
557C2×D4—2442no—
558C2×D4C2×C4×D6112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—1221no—
570C22×C4—1224no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4C2×C4×D6112yes—
576C22×C4#1175822212yes—
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583SD16—1228no—
584D8—2444no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—2444no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—81no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4C2×C4×D6112yes—
610C4⋊C4D4×D6112yes—
611C22⋊C4—24no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
620C22⋊C4—4881no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—81no—
629C42—2442no—
630C42—2442no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—1222no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23C4×C22⋊D6112yes—
652C23C22×C22⋊D6111yescharacteristic
653Q8—614no—
654Q8—1222no—
655Q8—1222no—
656Q8—1222no—
657D4—22no—
658D4—22no—
659D4—41no—
660D4—41no—
661D4—84no—
662D4—1222no—
663D4—1222no—
664D4—2448no—
665D4—2441no—
666D4—2441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—84no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—2448no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4C4×C22⋊D6112yes—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822211yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982311yescharacteristic
712C8—1222no—
713C8—1222no—
714C8—1222no—
715C8—2441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22C2×C4×C22⋊D6111yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22#1684040011yescharacteristic
740C22#1684056011yescharacteristic
741C22#1684056011yescharacteristic
742C22#1684056511yescharacteristic
743C22#1684057311yescharacteristic
744C4—22no—
745C4—42no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—1224no—
753C4—4881no—
754C4—4881no—
755C4C4×D4×D6111yescharacteristic
756C4#1684023411yescharacteristic
757C4#1684040811yescharacteristic
758C4#1684044111yescharacteristic
759C2—42no—
760C2—82no—
761C2—4882no—
762C2#2144879611yescharacteristic
763C2#2145461711yescharacteristic
764C2#2145465111yescharacteristic
765C2#2145735511yescharacteristic
766C2#2145740011yescharacteristic
767C2#2145781911yescharacteristic
768C2#2145799911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2363C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
cosocleC22×C4×C61C24
hypercenter#2363D61
hypocenterC61#22857
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#16839862C2semidirect
3. C2×#16839756C2semidirect
4. #21448659C2semidirect
5. #21446694C2semidirect
6. #21446515C2semidirect
7. #21446439C2semidirect
8. #21446248C2semidirect
9. #21446177C2semidirect
10. #21446167C2semidirect
11. #21446086C2semidirect
12. #21446018C2semidirect
13. #21445652C2semidirect
14. #21445597C2semidirect
15. C61×#2363C2semidirect
22. #16839905C4semidirect
67. C2×#11758222C2×C4semidirect
103. #14519700C2×C4semidirect
104. #14519700D4semidirect
109. #14519697C2×C4semidirect
110. C22⋊#92418C2×C4semidirect
378. #2363D61semidirect
446. C61#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168398622
C2×#168397562
#214486592
#214466942
#214465152
#214464392
#214462482
#214461772
#214461672
#214460862
#214460182
#214456522
#214455972
C61×#23632
#2285761