Finite Group Databasebeta

← #29691213

Subgroups — #29691213

Order 15616.

1296 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839897C211yesmaximal, characteristic
2#21448327C211yesmaximal, characteristic, complemented
3#390×D61C211yesmaximal, characteristic, complemented
4#21446695C211yesmaximal, characteristic, complemented
5#21446694C211yesmaximal, characteristic, complemented
6#21446515C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446444C211yesmaximal, characteristic, complemented
9#21446168C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446135C211yesmaximal, characteristic, complemented
12#21446013C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C2×#14519739—21no—
21C2×#14519739C2211yescharacteristic, complemented
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24C2×C22⋊C4×D61—21no—
25C2×C42×D61C2211yescharacteristic
26#16839897C418yescomplemented
27C2×#14519709C2211yescharacteristic, complemented
28C2×#14519708C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic, complemented
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519688C2211yescharacteristic, complemented
38#16839665C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic, complemented
41#16839663C2211yescharacteristic
42#16839662—21no—
43#16839662—21no—
44#16839652—21no—
45#16839640—21no—
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic, complemented
48#16839609—21no—
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic, complemented
56C61×#390C2211yescharacteristic
57C61×#389C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244—21no—
62C22×D244C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61—41no—
70C2×D4×D61C2×C414yescomplemented
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C2×D488—41no—
77C2×D488—41no—
78C2×D488C2×C414yescomplemented
79C2×#11758199—41no—
80C2×#11758199—41no—
81C2×#11758199C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519752—22no—
85#14519752C2×C414yes—
86#14519739—41no—
87#14519739—41no—
88#14519739—44no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C4⋊C4×D61—41no—
93C4⋊C4×D61—41no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C22⋊C4×D61—44no—
106C22⋊C4×D61—44no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—41no—
112C42×D61—41no—
113#14519709—41no—
114#14519708—41no—
115#14519699—41no—
116#14519699—41no—
117#14519698—41no—
118#14519697—41no—
119#14519697—41no—
120#14519697C2×C414yescomplemented
121#14519689—22no—
122#14519689C2×C414yescomplemented
123#14519688—41no—
124#14519684—21no—
125#14519684—21no—
126C22×D4×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#102×C61—41no—
137#102×C61C2×C414yescomplemented
138#97×C61—41no—
139#95×C61—21no—
140C24×C61—21no—
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—24no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61C22×C412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—24no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171D4×D61—44no—
172D4×D61—44no—
173D4×D61—44no—
174D4×D61—44no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—24no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—42no—
187C2×D244—42no—
188C2×D244C22×C412yes—
189C2×D244C22×C412yes—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61—41no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61#4112yes—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61C22×C412yes—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C22×C412yes—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C42×C61—21no—
224C42×C61—21no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227#11758199—44no—
228#11758198—24no—
229#11758198—42no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241#11758196—42no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—41no—
245C4×Dic61—41no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C22×C412yes—
253D488—44no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61C22×D411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—48no—
269C22×D61—48no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—48no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61C4×D412yes—
288C22×D61AGL(1,ℤ/8)12yes—
289C22×D61AGL(1,ℤ/8)12yes—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—41no—
293D4×C61—41no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C22⋊D61—48no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61C4×D412yes—
330C2×Dic61AGL(1,ℤ/8)12yes—
331D244—22no—
332D244—22no—
333D244—22no—
334D244—22no—
335D244—48no—
336D244—41no—
337D244—41no—
338D244—41no—
339D244—41no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—84no—
347C4×D61—84no—
348C8×C61—22no—
349C8×C61—41no—
350#92418—22no—
351#92418—41no—
352#22046—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61C2×C4×D411yescharacteristic
361C22×C61#53411yescharacteristic
362C22×C61#53511yescharacteristic
363C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C61#57511yescharacteristic
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—816no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61#44214yes—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—42no—
392C4×C61—81no—
393C4×C61—81no—
394C4×C61#51811yescharacteristic
395C4×C61#51811yescharacteristic
396C4×C61#53811yescharacteristic
397C4×C61#53811yescharacteristic
398Dic61—22no—
399Dic61—22no—
400Dic61—41no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C4×#121—611no—
405C2×#390—611no—
406#1972—611no—
407#1972—611no—
408#1936—611no—
409#1936D6111yescharacteristic, complemented
410#1926—611no—
411#1926—611no—
412#1879—611no—
413#1879—611no—
414#1874—611no—
415#1853—611no—
416#1786—611no—
417#1749—611no—
418C2×C61—82no—
419C2×C61#232111yescharacteristic
420C2×C61C2×#44211yescharacteristic
421C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C61#319211yescharacteristic
423C2×C61#319411yescharacteristic
424C2×C61#321311yescharacteristic
425C2×C61#321711yescharacteristic
426D61—24no—
427D61—82no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8—611no—
432C2×#121—611no—
433C2×C4×D4—611no—
434C2×C4×D4—1221no—
435C22×C4⋊C4—611no—
436C22×C22⋊C4—1221no—
437C22×C22⋊C4—1221no—
438C22×C42—611no—
439#447—618no—
440C2×#106—611no—
441C2×#106—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449C2×#102C2×D6111yescharacteristic
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×#97—611no—
453C2×#97C2×D6111yescharacteristic, complemented
454#390—611no—
455#390—611no—
456#390—611no—
457#390—611no—
458#390—1221no—
459#390—1221no—
460#390C2×D6111yescharacteristic
461#389C2×D6111yescharacteristic, complemented
462#388—1221no—
463#386—1221no—
464#380—611no—
465C4×C4⋊C4—611no—
466C4×C22⋊C4—1221no—
467#340—611no—
468#340—611no—
469#340C2×D6111yescharacteristic, complemented
470#340C2×D6111yescharacteristic, complemented
471#336—611no—
472#336—611no—
473C61#2204611yescharacteristic, complemented, Sylow
474C25—1221no—
475C22×D4—614no—
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—1221no—
479C22×D4—1222no—
480C22×D4—1221no—
481C22×D4—2441no—
482C22×D4—2441no—
483C22×D4—2441no—
484C22×D4—2441no—
485C22×D4C22×D6111yescharacteristic
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C2×D8—614no—
492C2×D8—614no—
493C2×D8—2441no—
494C2×D8—2441no—
495C2×D8—2441no—
496C2×D8—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501#121—614no—
502#121—1222no—
503C4×D4—2441no—
504C4×D4—2441no—
505C4×D4—2444no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—2441no—
511C2×C4⋊C4—2441no—
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—2444no—
529C2×C22⋊C4—2444no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—1221no—
534C2×C42—2441no—
535C2×C42—2441no—
536C2×C42C22×D6111yescharacteristic
537#106—2441no—
538#106—2441no—
539#102—41no—
540#102—614no—
541#102—2441no—
542#102—2441no—
543#102—2441no—
544#102—2441no—
545#102—2441no—
546#102C4×D6114yescomplemented
547C22⋊C8—614no—
548C22⋊C8—1222no—
549#97—41no—
550#97—2441no—
551#95—21no—
552#95—1221no—
553#95—1221no—
554C24—21no—
555C24—611no—
556C24—1224no—
557C24—1221no—
558C24—1221no—
559C24—2442no—
560C24—2442no—
561C24—2442no—
562C24—2442no—
563C24—2442no—
564C24—2442no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—612no—
571C2×D4—612no—
572C2×D4—1224no—
573C2×D4—1224no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—2442no—
585C2×D4—2442no—
586C2×D4—2444no—
587C2×D4—2444no—
588C2×D4—2444no—
589C2×D4—2444no—
590C2×D4—2442no—
591C2×D4—2442no—
592C2×D4C2×C4×D6112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—611no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—2441no—
611C22×C4—2441no—
612C22×C4—2441no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4C23×D6111yescharacteristic
622D8—2444no—
623D8—2444no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—612no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8C2×C4×D6112yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—42no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—2442no—
647C4⋊C4C2×C4×D6112yes—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—1224no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C42—21no—
662C42—21no—
663C42—1221no—
664C42—1221no—
665C42—2441no—
666C42—2441no—
667C42—2442no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—612no—
676C23—612no—
677C23—612no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1222no—
683C23—1222no—
684C23—4884no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—2448no—
689C23—2448no—
690C23—2448no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C2×D4×D6111yescharacteristic
704D4—22no—
705D4—22no—
706D4—41no—
707D4—41no—
708D4—1222no—
709D4—1222no—
710D4—1222no—
711D4—1222no—
712D4—2448no—
713D4—2448no—
714D4—2441no—
715D4—2441no—
716D4—2441no—
717D4—2441no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—612no—
734C2×C4—612no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—2444no—
749C2×C4—2444no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#1451982211yescharacteristic
759C2×C4#1451982311yescharacteristic
760C2×C4#1451982311yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—41no—
764C8—1222no—
765C8—2441no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—614no—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—48816no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—4881no—
787C22—4881no—
788C22—4881no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C4×D4×D6111yescharacteristic
796C22#1684032011yescharacteristic
797C22#1684033011yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22AGL(1,ℤ/8)×D6111yescharacteristic
800C22AGL(1,ℤ/8)×D6111yescharacteristic
801C22#1684056111yescharacteristic
802C4—42no—
803C4—41no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—1222no—
808C4—1222no—
809C4—4881no—
810C4—4881no—
811C4—2441no—
812C4#1684023411yescharacteristic
813C4#1684023611yescharacteristic
814C4#1684034811yescharacteristic
815C4#1684035111yescharacteristic
816C2—82no—
817C2—1224no—
818C2—4882no—
819C2—4882no—
820C2#2144847211yescharacteristic
821C2#442×D6111yescharacteristic
822C2#2145462411yescharacteristic
823C2#2145661511yescharacteristic
824C2#2145663411yescharacteristic
825C2#2145680711yescharacteristic
826C2#2145683811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
cosocleC22×C4×C61C24
hypercenter#1936D61
hypocenterC61#22046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #21448327C2semidirect
3. #390×D61C2semidirect
4. #21446695C2semidirect
5. #21446694C2semidirect
6. #21446515C2semidirect
7. #21446448C2semidirect
8. #21446444C2semidirect
9. #21446168C2semidirect
10. #21446164C2semidirect
11. #21446135C2semidirect
12. #21446013C2semidirect
13. #21445748C2semidirect
14. #21445582C2semidirect
15. C61×#1936C2semidirect
21. C2×#14519739C22semidirect
26. #16839897C4semidirect
27. C2×#14519709C22semidirect
28. C2×#14519708C22semidirect
30. C2×#14519699C22semidirect
34. C2×#14519697C22semidirect
37. C2×#14519688C22semidirect
40. #16839664C22semidirect
47. C4⋊C4×Dic61C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
55. C2×#97×C61C22semidirect
57. C61×#389C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
70. C2×D4×D61C2×C4semidirect
78. C2×D488C2×C4semidirect
81. C2×#11758199C2×C4semidirect
120. #14519697C2×C4semidirect
122. #14519689C2×C4semidirect
137. #102×C61C2×C4semidirect
409. #1936D61semidirect
453. C2×#97C2×D61semidirect
461. #389C2×D61semidirect
469. #340C2×D61semidirect
470. #340C2×D61semidirect
473. C61#22046semidirect
546. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398972
#214483272
#390×D612
#214466952
#214466942
#214465152
#214464482
#214464442
#214461682
#214461642
#214461352
#214460132
#214457482
#214455822
C61×#19362
#2204661