Finite Group Databasebeta

← #29723704

Subgroups — #29723704

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840083C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3#21448768C211yesmaximal, characteristic, complemented
4#21447347C211yesmaximal, characteristic, complemented
5#21447222C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446443C211yesmaximal, characteristic, complemented
9#21446443C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445850C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C61×#2408C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic, complemented
19#16840083—24no—
20C2×#14519710C2211yescharacteristic, complemented
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24#16839767—24no—
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic, complemented
35C2×C22⋊#92418C2211yescharacteristic, complemented
36#16839665—21no—
37#16839655—21no—
38#16839655—21no—
39#16839632C2211yescharacteristic, complemented
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic, complemented
42C4⋊C4×Dic61—21no—
43C4×C4⋊Dic61C2211yescharacteristic, complemented
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×#121×C61C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×#120×C61—21no—
54C2×C4×D4×C61C2211yescharacteristic
55C61×#394—21no—
56C61×#392—21no—
57C61×#390C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#379—21no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519736—22no—
69#14519736—22no—
70#14519736—41no—
71#14519736—41no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85#14519710—22no—
86#14519710—41no—
87#14519708—22no—
88#14519708—41no—
89#14519698—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95#14519698—41no—
96#14519698D414yescomplemented
97C22⋊#92418—22no—
98C22⋊#92418—22no—
99C22⋊#92418—41no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C25×C61—21no—
104C22×D4×C61—22no—
105C22×D4×C61—22no—
106C22×D4×C61—21no—
107C22×D4×C61—21no—
108C22×D4×C61—21no—
109C22×D4×C61—22no—
110C22×D4×C61—22no—
111C22×D4×C61—41no—
112C22×D4×C61—41no—
113C22×D4×C61D411yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—41no—
121#121×C61—41no—
122#120×C61—44no—
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C2×C4⋊C4×C61D411yescharacteristic
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×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138#95×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×D4×C61—28no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—44no—
164C2×D4×C61—44no—
165C2×D4×C61—41no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—44no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61C2×D412yes—
177C2×D4×C61#4112yes—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4112yes—
195C22×C4×C61#4112yes—
196C22×C4×C61C2411yescharacteristic
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—81no—
214C22⋊C4×C61—81no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—81no—
220C22⋊Dic61—81no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61—81no—
230C4⋊Dic61C2×D412yes—
231C4×Dic61—42no—
232C4×Dic61—42no—
233C4×Dic61—42no—
234#11758194—44no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C2×D412yes—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—48no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61—84no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61—84no—
281C23×C61#12312yes—
282C23×C61C22×D411yescharacteristic
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—44no—
288D4×C61—48no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—84no—
294D4×C61—84no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61#12312yes—
320C2×C4×C61AGL(1,ℤ/8)12yes—
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×Dic61—22no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339#92418—22no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#24890—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—816no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61C2×#12311yescharacteristic
374C22×C61D4211yescharacteristic
375C22×C61#54611yescharacteristic
376C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C61#57511yescharacteristic
378C22×C61#57611yescharacteristic
379C22×C61#57711yescharacteristic
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—81no—
385C4×C61—81no—
386C4×C61#52511yescharacteristic
387C4×C61#53811yescharacteristic
388C4×C61#54611yescharacteristic
389C4×C61#55111yescharacteristic
390Dic61—42no—
391Dic61—81no—
392Dic61—81no—
393Dic61—81no—
394C2×#482—611no—
395C2×#418—611no—
396#2408D6111yescharacteristic
397#2354—611no—
398#2093—611no—
399#2071—611no—
400#2034—611no—
401#2033—611no—
402#1926—611no—
403#1926—611no—
404#1875—611no—
405#1870—611no—
406#1854—611no—
407#1809—611no—
408#1786—611no—
409C2×C61—42no—
410C2×C61—81no—
411C2×C61—82no—
412C2×C61—82no—
413C2×C61#241811yescharacteristic
414C2×C61#309411yescharacteristic
415C2×C61#309611yescharacteristic
416C2×C61#326711yescharacteristic
417C2×C61#327411yescharacteristic
418C2×C61#331911yescharacteristic
419C2×C61#332411yescharacteristic
420C23×D4C2×D6111yescharacteristic
421C22×M16—611no—
422C2×#121C2×D6111yescharacteristic
423C2×#121C2×D6111yescharacteristic
424C2×#120—21no—
425C2×C4×D4C2×D6111yescharacteristic
426C2×#117—611no—
427C2×#117—611no—
428#482—1224no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#106—611no—
432C2×#106—611no—
433#418—1224no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445#394—21no—
446#392—21no—
447#390—1221no—
448#390C2×D6111yescharacteristic
449#390C2×D6111yescharacteristic
450#388—1221no—
451#388—1221no—
452#384—611no—
453#380—611no—
454#380—611no—
455#380C2×D6111yescharacteristic
456#379—21no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—1221no—
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#336—611no—
464#336—611no—
465C61#2489011yescharacteristic, complemented, Sylow
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C22⋊D6111yescharacteristic
477C22×D4C22×D6111yescharacteristic
478C22×D4C22×D6111yescharacteristic
479C23×C4C22×D6111yescharacteristic
480C23×C4C22×D6111yescharacteristic
481C2×M16—1222no—
482C2×M16—1222no—
483C2×M16—2441no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—1222no—
496#117—1222no—
497#117—2441no—
498#117—2441no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22⋊D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4C22⋊D6111yescharacteristic
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42C22×D6111yescharacteristic
525#107—1222no—
526#107—2441no—
527#106—1222no—
528#106—2441no—
529#102—614no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—1222no—
534#102—1222no—
535#102—2441no—
536#102—2441no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—21no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×C22⋊D6111yescharacteristic
554C24C2×C22⋊D6111yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4D4×D6112yes—
582C2×D4#1175822412yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4#1175822412yes—
600C22×C4#1175822412yes—
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606M16—2444no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—612no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—4881no—
633C4⋊C4—2442no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—4881no—
644C22⋊C4—4881no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—21no—
648C42—21no—
649C42—2442no—
650C42—2442no—
651C42—2442no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—22no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#1451975812yes—
687C23C22×C22⋊D6111yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—1222no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4#1451975812yes—
737C2×C4#1451980312yes—
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4C2×#1175822411yescharacteristic
740C2×C4C2×#1175822411yescharacteristic
741C2×C4C2×#1175822411yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C8—1222no—
745C8—2441no—
746C8—2441no—
747C8—2441no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#1451975811yescharacteristic
778C22D4×C22⋊D6111yescharacteristic
779C22#1684040611yescharacteristic
780C22C2×#1451980311yescharacteristic
781C22#1684056011yescharacteristic
782C22#1684056511yescharacteristic
783C22#1684057311yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—4881no—
791C4—4881no—
792C4—4881no—
793C4—2442no—
794C4#1684026811yescharacteristic
795C4#1684034711yescharacteristic
796C4#1684039911yescharacteristic
797C4#1684044311yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2#2144927711yescharacteristic
803C2#2145575511yescharacteristic
804C2#2145577111yescharacteristic
805C2#2145734011yescharacteristic
806C2#2145743511yescharacteristic
807C2#2145797511yescharacteristic
808C2#2145805011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2408C2
socleC23×C61C22×D4
hypercenter#2408D61
hypocenterC61#24890
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#16840083C2semidirect
2. C2×#16839767C2semidirect
3. #21448768C2semidirect
4. #21447347C2semidirect
5. #21447222C2semidirect
6. #21447005C2semidirect
7. #21446998C2semidirect
8. #21446443C2semidirect
9. #21446443C2semidirect
10. #21446142C2semidirect
11. #21446117C2semidirect
12. #21446016C2semidirect
13. #21445850C2semidirect
14. #21445750C2semidirect
18. C2×#14519736C22semidirect
20. C2×#14519710C22semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519708C22semidirect
34. C2×C22⋊#92418C22semidirect
35. C2×C22⋊#92418C22semidirect
39. #16839632C22semidirect
41. #16839622C22semidirect
43. C4×C4⋊Dic61C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
96. #14519698D4semidirect
465. C61#24890semidirect

Maximal subgroups

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

subgroupindex
C2×#168400832
C2×#168397672
#214487682
#214473472
#214472222
#214470052
#214469982
#214464432
#214461422
#214461172
#214460162
#214458502
#214457502
C61×#24082
#2489061