Finite Group Databasebeta

← #29733101

Subgroups — #29733101

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840469C211yesmaximal, characteristic, complemented
2C2×#16840073C211yesmaximal, characteristic, complemented
3C2×#16840006C211yesmaximal, characteristic, complemented
4#21447147C211yesmaximal, characteristic, complemented
5#21447022C211yesmaximal, characteristic, complemented
6#21446955C211yesmaximal, characteristic, complemented
7#21446822C211yesmaximal, characteristic, complemented
8#21446177C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446072C211yesmaximal, characteristic, complemented
13#21446006C211yesmaximal, characteristic, complemented
14#21445540C211yesmaximal, characteristic, complemented
15C61×#2414C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840469—24no—
19#16840469—24no—
20C2×#14519777C2211yescharacteristic
21C2×#14519768—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519754—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×D4×Dic61—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30#16840073—24no—
31#16840006—24no—
32C2×#14519710C2211yescharacteristic
33C2×#14519710C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
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
52C2×#121×C61C2211yescharacteristic
53C2×#121×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#394—21no—
57C61×#392—21no—
58C61×#390—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C23×Dic61—21no—
66C23×Dic61—21no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519777—22no—
78#14519777—22no—
79#14519768—28no—
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756D414yescomplemented
84#14519754—28no—
85#14519754—28no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88D4×Dic61—28no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61D414yescomplemented
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C4×Dic61—21no—
105#14519710—22no—
106#14519710—22no—
107#14519710—22no—
108#14519700—22no—
109#14519700—22no—
110#14519700—41no—
111#14519698—22no—
112#14519698—22no—
113#14519698—22no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C22⋊#92418—41no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61D411yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#121×C61—22no—
124#121×C61—22no—
125#121×C61—22no—
126#121×C61—41no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129#117×C61—22no—
130#117×C61—41no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
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—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—81no—
164C2×D4×C61—81no—
165C2×D4×C61—81no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—24no—
191C22×Dic61—24no—
192C22×Dic61—81no—
193C22×Dic61—81no—
194C22×Dic61—81no—
195C22×Dic61—81no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—24no—
202C2×Dic122—81no—
203C2×Dic122—81no—
204C2×Dic122C2×D412yes—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—81no—
212C4⋊C4×C61#4112yes—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—81no—
220C22⋊C4×C61—81no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C22⋊Dic61—24no—
225C22⋊Dic61—24no—
226#11758200—44no—
227C4⋊Dic61—24no—
228C4⋊Dic61—24no—
229C4⋊Dic61—24no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C2×D412yes—
234C4⋊Dic61C2×D412yes—
235C4⋊Dic61C2×D412yes—
236#11758196—24no—
237#11758196—24no—
238#11758196—24no—
239C4×Dic61—24no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418#4112yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61#12012yes—
273C23×C61#13712yes—
274C23×C61C22×D411yescharacteristic
275D4×C61—28no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—84no—
281D4×C61—84no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
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×C61#12012yes—
310C2×C4×C61#13712yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C612−1+411yescharacteristic
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—84no—
330C2×Dic61—84no—
331Dic122—22no—
332Dic122—22no—
333Dic122—41no—
334Dic122—41no—
335Dic122—84no—
336#92418—22no—
337#92418—41no—
338#92418—41no—
339#92418—41no—
340#25559—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
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—41no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61C2×#12011yescharacteristic
363C22×C61#54611yescharacteristic
364C22×C61#54711yescharacteristic
365C22×C61C2×#13711yescharacteristic
366C22×C61C2×#13711yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57611yescharacteristic
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—81no—
375C4×C61—81no—
376C4×C61#53211yescharacteristic
377C4×C61#53711yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#54711yescharacteristic
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383Dic61—42no—
384C2×#554—611no—
385C2×#480—611no—
386C2×#468—611no—
387#2414D6111yescharacteristic
388#2057—611no—
389#2036—611no—
390#2023—611no—
391#2000—611no—
392#1880—611no—
393#1874—611no—
394#1873—611no—
395#1870—611no—
396#1863—611no—
397#1852—611no—
398#1736—611no—
399C2×C61—42no—
400C2×C61—42no—
401C2×C61—161no—
402C2×C61#243011yescharacteristic
403C2×C61#300411yescharacteristic
404C2×C61#300811yescharacteristic
405C2×C61#331411yescharacteristic
406C2×C61#333311yescharacteristic
407C2×C61#334611yescharacteristic
408C2×C61#335711yescharacteristic
409C22×SD16—611no—
410C22×M16—611no—
411#554—1224no—
412#554—1224no—
413C2×C4⋊Q8—611no—
414C2×#125—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×#121C2×D6111yescharacteristic
420C2×#121C2×D6111yescharacteristic
421C2×C4×Q8—611no—
422C2×C4×D4—1221no—
423C2×C4×D4C2×D6111yescharacteristic
424C2×#117C2×D6111yescharacteristic
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427#480—1224no—
428#468—1224no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441#394—21no—
442#392—21no—
443#390—21no—
444#390C2×D6111yescharacteristic
445#389C2×D6111yescharacteristic
446#388—21no—
447#380C2×D6111yescharacteristic
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2555911yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C22⋊D6111yescharacteristic
462C22×D4C22×D6111yescharacteristic
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—2441no—
470C2×M16—1222no—
471C2×M16—1222no—
472C2×M16—2441no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477C4⋊Q8—1222no—
478C4⋊Q8—1222no—
479#125—1228no—
480C22⋊Q8—614no—
481C22⋊Q8—1228no—
482C22⋊Q8—1228no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490C4×Q8—1222no—
491C4×Q8—1222no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—1228no—
495#117—22no—
496#117—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22⋊D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4C22⋊D6111yescharacteristic
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C42—21no—
526C2×C42—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—1222no—
529#107—1222no—
530#107—1222no—
531#103—1222no—
532#103—1222no—
533#103—2441no—
534#102—1222no—
535#102—1222no—
536#102—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—21no—
541#95—21no—
542C24—21no—
543C24C2×C22⋊D6111yescharacteristic
544C24C2×C22⋊D6111yescharacteristic
545C2×Q8—612no—
546C2×Q8—1224no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—4881no—
553C2×Q8—4881no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—1224no—
583C22×C4—1224no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—4881no—
591C22×C4—4881no—
592C22×C4D4×D6112yes—
593C22×C4D4×D6112yes—
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599SD16—2444no—
600M16—2444no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—81no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4#1175822412yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—1224no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1451974512yes—
667C23#1451980712yes—
668C23C22×C22⋊D6111yescharacteristic
669Q8—1222no—
670Q8—1222no—
671Q8—4884no—
672Q8—2441no—
673Q8—2441no—
674D4—28no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—4884no—
713C2×C4—4884no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4#1451974512yes—
723C2×C4#1451980712yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982411yescharacteristic
730C8—1222no—
731C8—2441no—
732C8—2441no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#1451974511yescharacteristic
756C22#1684040611yescharacteristic
757C22#1684041111yescharacteristic
758C22C2×#1451980711yescharacteristic
759C22C2×#1451980711yescharacteristic
760C22#1684056511yescharacteristic
761C22#1684056511yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—2442no—
770C4—2442no—
771C4—2442no—
772C4—2442no—
773C4#1684030711yescharacteristic
774C4#1684033911yescharacteristic
775C4#1684040111yescharacteristic
776C4#1684041211yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2#2144942511yescharacteristic
781C2#2145505211yescharacteristic
782C2#2145508511yescharacteristic
783C2#2145790011yescharacteristic
784C2#2145815711yescharacteristic
785C2#2145830411yescharacteristic
786C2#2145843911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2414C2
socleC23×C61C22×D4
hypercenter#2414D61
hypocenterC61#25559
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. C2×#16840469C2semidirect
2. C2×#16840073C2semidirect
3. C2×#16840006C2semidirect
4. #21447147C2semidirect
5. #21447022C2semidirect
6. #21446955C2semidirect
7. #21446822C2semidirect
8. #21446177C2semidirect
9. #21446137C2semidirect
10. #21446131C2semidirect
11. #21446117C2semidirect
12. #21446072C2semidirect
13. #21446006C2semidirect
14. #21445540C2semidirect
83. #14519756D4semidirect
95. C2×C4⋊Dic61D4semidirect
456. C61#25559semidirect

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168400732
C2×#168400062
#214471472
#214470222
#214469552
#214468222
#214461772
#214461372
#214461312
#214461172
#214460722
#214460062
#214455402
C61×#24142
#2555961