Finite Group Databasebeta

← #29695826

Subgroups — #29695826

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic
2C2×#16839867C211yesmaximal, characteristic, complemented
3C2×#16839854C211yesmaximal, characteristic, complemented
4#21448657C211yesmaximal, characteristic
5#21448653C211yesmaximal, characteristic, complemented
6#21446703C211yesmaximal, characteristic, complemented
7#21446670C211yesmaximal, characteristic, complemented
8#21446175C211yesmaximal, characteristic, complemented
9#21446173C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21445851C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic
13#21445752C211yesmaximal, characteristic, complemented
14#21445601C211yesmaximal, characteristic, complemented
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519809—24no—
19C2×#14519809—24no—
20C2×#14519809C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519742C2211yescharacteristic
28#16839867—24no—
29#16839854—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519688C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839669C2211yescharacteristic
42#16839666—21no—
43#16839666—21no—
44#16839664—21no—
45#16839664C2211yescharacteristic
46#16839663—21no—
47#16839663C2211yescharacteristic
48#16839621—21no—
49#16839619—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52C4×#11758198—21no—
53C4×#11758198C2211yescharacteristic
54#16839609—21no—
55#16839525C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×Q16×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#391C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yes—
70C22×Dic122—21no—
71C22×Dic122C2311yescharacteristic
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61—22no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61C2×C414yes—
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83#14519809—232no—
84C2×#11758202C2×C414yes—
85C2×#11758202D414yes—
86C2×#11758202D414yes—
87C2×#11758190—22no—
88C2×#11758190—22no—
89C2×#11758190C2×C414yes—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201C2×C414yes—
93C2×#11758189—22no—
94C2×#11758189—22no—
95C2×#11758189C2×C414yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98Q8×Dic61—22no—
99Q8×Dic61—41no—
100C4×Dic122—22no—
101C4×Dic122—41no—
102#14519742—22no—
103#14519742—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×#11758198D411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519710—22no—
122#14519708—22no—
123#14519702—22no—
124#14519701—22no—
125#14519701—41no—
126#14519700—22no—
127#14519699—41no—
128#14519697—41no—
129#14519689—22no—
130#14519688—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684D411yescharacteristic
137#14519684D411yescharacteristic
138C22×Q8×C61C2311yescharacteristic
139C22×Q8×C61C2311yescharacteristic
140C2×Q16×C61—22no—
141C2×Q16×C61—22no—
142C2×Q16×C61C2×C414yes—
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C4×Q8×C61—22no—
146C4×Q8×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#103×C61—22no—
153#103×C61—41no—
154#95×C61—21no—
155#95×C61—21no—
156C23×D61—21no—
157C23×D61C2×D411yescharacteristic
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
167C2×Q8×C61C22×C412yes—
168C2×Q8×C61C2×D412yes—
169C2×Q8×C61C2×D412yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758226—28no—
184#11758226—44no—
185#11758226—44no—
186#11758226—44no—
187Q8×D61—28no—
188Q8×D61—44no—
189Q8×D61—44no—
190Q8×D61—44no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—24no—
196C2×D244—21no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61C22×C412yes—
211C2×C4×D61#4112yes—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—24no—
216C2×Dic122—42no—
217C2×Dic122—42no—
218C2×Dic122C22×C412yes—
219C2×Dic122C2×D412yes—
220C2×Dic122C2×D412yes—
221Q16×C61—28no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C412yes—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—42no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—42no—
236#11758202C22⋊C4116yescomplemented
237#11758201—28no—
238#11758198—22no—
239#11758198—41no—
240#11758198—42no—
241#11758198—42no—
242#11758198—42no—
243#11758198—81no—
244#11758198—81no—
245#11758198—81no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—42no—
251#11758196—42no—
252#11758196—42no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—42no—
256C4×Dic61—42no—
257C4×Dic61—42no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418C22×C412yes—
262C2×#92418C2×D412yes—
263C2×#92418C2×D412yes—
264#11758190—28no—
265#11758189—28no—
266C23×C61C22×D411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61C4×D412yes—
281Q8×C61—22no—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61C2×C22⋊C414yes—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
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×C61C23×C411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—22no—
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×Dic61#13712yescomplemented
331D244—22no—
332D244—22no—
333D244—48no—
334D244—41no—
335D244—41no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—48no—
341C4×D61—48no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—48no—
346Dic122C2×C22⋊C414yes—
347C8×C61—22no—
348C8×C61—41no—
349#92418—41no—
350#92418C2×C22⋊C414yes—
351#22445—611nomaximal, Sylow
352C22×C61C2×C4×D411yescharacteristic
353C22×C61D4211yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61C2×#13711yescharacteristic
356C22×C61#57511yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57811yescharacteristic
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C4×C61—24no—
374C4×C61—42no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61C22×C22⋊C411yescharacteristic
380C4×C61#51811yescharacteristic
381C4×C61#54611yescharacteristic
382C4×C61#54611yescharacteristic
383Dic61—24no—
384Dic61—22no—
385Dic61—22no—
386Dic61—41no—
387Dic61—81no—
388Dic61—81no—
389C22×#137—611no—
390C2×#441—611no—
391C2×C4×Q16—611no—
392#2341—611no—
393Q8×C22⋊C4—611no—
394#1973—611no—
395#1968—611no—
396#1880—611no—
397#1880—611no—
398#1878—611no—
399#1878D6111yescharacteristic, complemented
400#1809—611no—
401#1788—611no—
402#1787—611no—
403#1753—611no—
404C2×C61D4×C22⋊C411yescharacteristic
405C2×C61C4×#13711yescharacteristic
406C2×C61#294711yescharacteristic
407C2×C61#327011yescharacteristic
408C2×C61#327111yescharacteristic
409C2×C61#327711yescharacteristic
410C2×C61#327811yescharacteristic
411D61—42no—
412D61—82no—
413C22×#41—611no—
414C23×Q8—611no—
415C2×#137—618no—
416C2×#137—1224no—
417C2×#137—1224no—
418C22×Q16—611no—
419C22×Q16C2×D6111yescharacteristic
420C22×SD16—611no—
421C22×SD16—611no—
422C22×M16—611no—
423C2×C4×Q8—611no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8C2×D6111yescharacteristic
427#441—1224no—
428C4×Q16—1224no—
429C2×#107—611no—
430C2×#106—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103C2×D6111yescharacteristic
436C2×#103C2×D6111yescharacteristic
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×#97—611no—
441C2×C4×C8—611no—
442#391—611no—
443#391—1221no—
444#391—1221no—
445#391C2×D6111yescharacteristic
446#390—611no—
447#390—611no—
448#390—1221no—
449#390—1221no—
450#380—611no—
451#380—611no—
452#380—1221no—
453#380—1221no—
454C4×C22⋊C4—611no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4—1221no—
457#340—611no—
458#340C2×D6111yescharacteristic
459#336—611no—
460#336C2×D6111yescharacteristic
461C61#2244511yescharacteristic, complemented, Sylow
462C2×#41—614no—
463C2×#41—1222no—
464C2×#41—1222no—
465C2×#41—1222no—
466C2×#41—2441no—
467C2×#41—2441no—
468C22×Q8—614no—
469C22×Q8—611no—
470C22×Q8—1221no—
471C22×Q8—1222no—
472C22×Q8—1222no—
473C22×Q8—1222no—
474C22×Q8—2441no—
475C22×Q8—2441no—
476C22×Q8C22×D6111yescharacteristic
477C22×Q8C22×D6111yescharacteristic
478C22×D4—611no—
479C22×D4—1221no—
480C23×C4—611no—
481C23×C4—1221no—
482C23×C4—1221no—
483#137—12232no—
484C2×Q16—22no—
485C2×Q16—22no—
486C2×Q16—614no—
487C2×Q16—614no—
488C2×Q16—614no—
489C2×Q16C4×D6114yes—
490C2×SD16—614no—
491C2×SD16—614no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×M16—614no—
497C2×M16—1222no—
498C2×M16—1222no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8C22×D6111yescharacteristic
502C22×C8C22×D6111yescharacteristic
503C4×Q8—22no—
504C4×Q8—41no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—1222no—
508C4×Q8—2441no—
509C4×Q8—2441no—
510C4×Q8—2441no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
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×C42—21no—
528C2×C42—611no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42C22×D6111yescharacteristic
533#107—1222no—
534#106—1222no—
535#103—22no—
536#103—41no—
537#103—1222no—
538#103—1222no—
539#103—1222no—
540#103—2441no—
541#102—2441no—
542#102—2441no—
543C22⋊C8—1222no—
544#97—1222no—
545C4×C8—1222no—
546#95—21no—
547#95—21no—
548#95—611no—
549#95—611no—
550#95—1221no—
551#95—1221no—
552#95—1221no—
553#95—1221no—
554C24—611no—
555C24—1221no—
556#41—1228no—
557#41—2444no—
558#41—2444no—
559#41—2444no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—612no—
569C2×Q8—612no—
570C2×Q8—612no—
571C2×Q8—1224no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1228no—
576C2×Q8—2442no—
577C2×Q8—2442no—
578C2×Q8—2444no—
579C2×Q8—2444no—
580C2×Q8—2444no—
581C2×Q8C2×C4×D6112yes—
582C2×Q8C2×C4×D6112yes—
583C2×Q8D4×D6112yes—
584C2×Q8D4×D6112yes—
585C2×D4—612no—
586C2×D4—1224no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—2442no—
593C2×D4—2442no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—611no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4D4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6111yescharacteristic
619Q16—28no—
620Q16—6116no—
621SD16—1228no—
622SD16—1228no—
623M16—1228no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—612no—
630C2×C8—612no—
631C2×C8—612no—
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—42no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—2442no—
646C4⋊C4—2442no—
647C4⋊C4—2442no—
648C22⋊C4—1222no—
649C22⋊C4—4881no—
650C22⋊C4—4881no—
651C22⋊C4—4881no—
652C22⋊C4—2441no—
653C22⋊C4—2442no—
654C22⋊C4—2442no—
655C22⋊C4—2442no—
656C42—21no—
657C42—21no—
658C42—42no—
659C42—1221no—
660C42—1221no—
661C42—2442no—
662C42—2442no—
663C42—2442no—
664C23—612no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1222no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23C2×D4×D6111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—614no—
687Q8—1222no—
688Q8—1222no—
689Q8—1222no—
690Q8—2448no—
691Q8C22⋊C4×D6114yes—
692D4—1222no—
693D4—1222no—
694D4—2448no—
695D4—2441no—
696D4—2441no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—612no—
716C2×C4—612no—
717C2×C4—1222no—
718C2×C4—1221no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1222no—
723C2×C4—1221no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—2448no—
732C2×C4—2448no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4C22×C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C2×C4#41×D6111yescharacteristic
743C2×C4#1451982211yescharacteristic
744C2×C4#1451982311yescharacteristic
745C8—22no—
746C8—41no—
747C8—614no—
748C8—2441no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—4881no—
753C22—4881no—
754C22—4881no—
755C22—4881no—
756C22—2442no—
757C22—2442no—
758C22—2442no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22C4×D4×D6111yescharacteristic
764C22#1684039411yescharacteristic
765C22#1684039611yescharacteristic
766C22#137×D6111yescharacteristic
767C22#1684056111yescharacteristic
768C22#1684056911yescharacteristic
769C22#1684057511yescharacteristic
770C4—24no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4—1222no—
777C4—1224no—
778C4—1222no—
779C4—4881no—
780C4—4881no—
781C4—2441no—
782C4C2×C22⋊C4×D6111yescharacteristic
783C4#1684023411yescharacteristic
784C4#1684040111yescharacteristic
785C4#1684040411yescharacteristic
786C2—4882no—
787C2—2442no—
788C2#2144863711yescharacteristic
789C2#2145463511yescharacteristic
790C2#2145465711yescharacteristic
791C2#2145739511yescharacteristic
792C2#2145741011yescharacteristic
793C2#2145747611yescharacteristic
794C2#2145747811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1878D61
hypocenterC61#22445
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#16839867C2semidirect
3. C2×#16839854C2semidirect
5. #21448653C2semidirect
6. #21446703C2semidirect
7. #21446670C2semidirect
8. #21446175C2semidirect
9. #21446173C2semidirect
10. #21446162C2semidirect
11. #21445851C2semidirect
13. #21445752C2semidirect
14. #21445601C2semidirect
15. C61×#1878C2semidirect
20. C2×#14519809C4semidirect
236. #11758202C22⋊C4semidirect
330. C2×Dic61#137semidirect
399. #1878D61semidirect
461. C61#22445semidirect

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×#168398672
C2×#168398542
#214486572
#214486532
#214467032
#214466702
#214461752
#214461732
#214461622
#214458512
#214457582
#214457522
#214456012
C61×#18782
#2244561