Finite Group Databasebeta

← #29727398

Subgroups — #29727398

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839981C211yesmaximal, characteristic, complemented
2C2×#16839917C211yesmaximal, characteristic, complemented
3C2×#16839900C211yesmaximal, characteristic
4C2×C4×#11758202C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic122C211yesmaximal, characteristic, complemented
6#21447211C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446998C211yesmaximal, characteristic
9#21446913C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446177C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14#21446086C211yesmaximal, characteristic, complemented
15C61×#2426C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16839981—24no—
24#16839917—24no—
25#16839900—24no—
26C4×#11758202—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839666—21no—
44#16839666—21no—
45#16839622C2211yescharacteristic
46#16839620—21no—
47C22⋊C4×Dic61—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#394—21no—
58C61×#390—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—41no—
69C22×Dic122—41no—
70C22×Dic122C2311yescharacteristic
71C22×Dic122C2311yescharacteristic
72C23×Dic61—21no—
73C2×#11758202—22no—
74C2×#11758202—22no—
75C2×#11758202—22no—
76C2×#11758202—22no—
77C2×#11758202—41no—
78C2×#11758202D414yescomplemented
79C2×#11758200—22no—
80C2×#11758200—22no—
81C2×#11758200—22no—
82C2×#11758200—22no—
83C2×#11758200—22no—
84C2×#11758200—41no—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—41no—
92C4×Dic122—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100#14519710—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519700—22no—
106#14519700—22no—
107#14519700—22no—
108#14519700D414yes—
109#14519698—22no—
110#14519698—41no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#124×C61—22no—
124#124×C61—41no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127#121×C61—22no—
128#121×C61—41no—
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
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
146C2×C42×C61C2311yescharacteristic
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C2×D412yes—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
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×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C22×Dic61—21no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—24no—
197C2×Dic122—21no—
198C2×Dic122—44no—
199C2×Dic122—44no—
200C2×Dic122—44no—
201C2×Dic122—42no—
202C2×Dic122—42no—
203C2×Dic122—44no—
204C2×Dic122C2×D412yes—
205C2×Dic122C2×D412yes—
206C2×Dic122#4112yes—
207C2×Dic122#4112yes—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—81no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—42no—
228C22⋊Dic61—42no—
229#11758202—28no—
230#11758202—44no—
231#11758200—44no—
232#11758200—44no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—42no—
240C4×Dic61—42no—
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×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61#13512yes—
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272D4×C61—41no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276D4×C61—84no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
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—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61#13712yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—48no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324Dic122—22no—
325Dic122—22no—
326Dic122—22no—
327Dic122—22no—
328Dic122—22no—
329Dic122—48no—
330Dic122—41no—
331Dic122—41no—
332Dic122#12114yes—
333#92418—22no—
334#92418—22no—
335#92418—41no—
336#92418—41no—
337#25149—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61#52511yescharacteristic
353C22×C61D4211yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61C2×#13511yescharacteristic
356C22×C61C2×#13711yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57811yescharacteristic
359C4×C61—22no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—42no—
365C4×C61—41no—
366C4×C61—81no—
367C4×C61C2×#12111yescharacteristic
368C4×C61#53811yescharacteristic
369C4×C61#54611yescharacteristic
370C4×C61#54611yescharacteristic
371Dic61—24no—
372Dic61—42no—
373Dic61—81no—
374Dic61—81no—
375C2×#464—611no—
376C2×#451—611no—
377C2×#448—611no—
378C2×C4×Q16—611no—
379#2426D6111yescharacteristic
380Q8×C22⋊C4—611no—
381#2068—611no—
382#2035—611no—
383#2033—611no—
384#2015—611no—
385#1968—611no—
386#1923—611no—
387#1880—611no—
388#1878—611no—
389#1865—611no—
390C2×C61—42no—
391C2×C61—161no—
392C2×C61#242411yescharacteristic
393C2×C61#310811yescharacteristic
394C2×C61#312111yescharacteristic
395C2×C61#327011yescharacteristic
396C2×C61#327811yescharacteristic
397C2×C61#328211yescharacteristic
398C2×C61#328511yescharacteristic
399C23×Q8—611no—
400C22×Q16—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C2×#124C2×D6111yescharacteristic
405C2×C22⋊Q8C2×D6111yescharacteristic
406C2×#121C2×D6111yescharacteristic
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8C2×D6111yescharacteristic
410#464—1224no—
411#451—1224no—
412#448—1224no—
413C4×Q16—1224no—
414C2×#107—611no—
415C2×#106—611no—
416C2×C4⋊C8—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C4×C8—611no—
428#396—21no—
429#394—21no—
430#391—611no—
431#391—611no—
432#391—1221no—
433#391—1221no—
434#390—21no—
435#390C2×D6111yescharacteristic
436#389C2×D6111yescharacteristic
437#388—21no—
438#380—611no—
439#380—1221no—
440C4×C22⋊C4—1221no—
441C4×C22⋊C4C2×D6111yescharacteristic
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2514911yescharacteristic, complemented, Sylow
447C22×Q8—611no—
448C22×Q8—611no—
449C22×Q8—1222no—
450C22×Q8—1222no—
451C22×Q8—1222no—
452C22×Q8—1222no—
453C22×Q8—1221no—
454C22×Q8—2441no—
455C22×Q8—2441no—
456C22×Q8C22×D6111yescharacteristic
457C22×D4—21no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×Q16—614no—
462C2×Q16—1222no—
463C2×Q16—1222no—
464C2×Q16—1222no—
465C2×Q16—1222no—
466C2×Q16—2441no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—2441no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477#124—22no—
478#124—41no—
479C22⋊Q8—22no—
480C22⋊Q8—41no—
481#121—22no—
482#121—41no—
483C4×Q8—22no—
484C4×Q8—41no—
485C4×Q8—1222no—
486C4×Q8—1222no—
487C4×Q8—2441no—
488C4×Q8—2441no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4C22⋊D6111yescharacteristic
506C2×C22⋊C4C22⋊D6111yescharacteristic
507C2×C42—21no—
508C2×C42—1221no—
509C2×C42—1221no—
510C2×C42C22×D6111yescharacteristic
511C2×C42C22×D6111yescharacteristic
512#107—1222no—
513#106—2441no—
514C4⋊C8—1222no—
515#103—614no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—1222no—
520#103—1222no—
521#102—1222no—
522#102—2441no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C4×C8—1222no—
526#95—21no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95C22⋊D6111yescharacteristic
533#95C22⋊D6111yescharacteristic
534C24—21no—
535C24C2×C22⋊D6111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—612no—
542C2×Q8—612no—
543C2×Q8—612no—
544C2×Q8—612no—
545C2×Q8—1224no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—2442no—
555C2×Q8—2442no—
556C2×Q8—2444no—
557C2×Q8—2444no—
558C2×Q8—2444no—
559C2×Q8—2444no—
560C2×Q8D4×D6112yes—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
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—1221no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592Q16—1228no—
593Q16—2444no—
594SD16—2444no—
595SD16—2444no—
596C2×C8—612no—
597C2×C8—612no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—81no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C4⋊C4D4×D6112yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—2442no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—2442no—
636C42—2442no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#1451979712yes—
651C23C22×C22⋊D6111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656Q8—614no—
657Q8—1222no—
658Q8—1222no—
659Q8—1222no—
660Q8—1222no—
661Q8—1222no—
662Q8—2448no—
663Q8—2441no—
664Q8—2441no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—84no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
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—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—2448no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4#1451980712yes—
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#1451982211yescharacteristic
716C2×C4#1451982211yescharacteristic
717C8—1222no—
718C8—1222no—
719C8—2441no—
720C8—2441no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22#1684026911yescharacteristic
736C22D4×C22⋊D6111yescharacteristic
737C22D4×C22⋊D6111yescharacteristic
738C22C2×#1451979711yescharacteristic
739C22C2×#1451980711yescharacteristic
740C22#1684057311yescharacteristic
741C22#1684057711yescharacteristic
742C4—22no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4—1224no—
751C4—4881no—
752C4—4881no—
753C4—2442no—
754C4#121×D6111yescharacteristic
755C4#1684034411yescharacteristic
756C4#1684040111yescharacteristic
757C4#1684040911yescharacteristic
758C2—42no—
759C2—161no—
760C2#2144935211yescharacteristic
761C2#2145589511yescharacteristic
762C2#2145604211yescharacteristic
763C2#2145738511yescharacteristic
764C2#2145748511yescharacteristic
765C2#2145752211yescharacteristic
766C2#2145755611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2426C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenter#2426D61
hypocenterC61#25149
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#16839981C2semidirect
2. C2×#16839917C2semidirect
4. C2×C4×#11758202C2semidirect
5. C22⋊C4×Dic122C2semidirect
6. #21447211C2semidirect
7. #21447012C2semidirect
9. #21446913C2semidirect
10. #21446672C2semidirect
11. #21446427C2semidirect
12. #21446177C2semidirect
13. #21446160C2semidirect
14. #21446086C2semidirect
78. C2×#11758202D4semidirect
446. C61#25149semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168399172
C2×#168399002
C2×C4×#117582022
C22⋊C4×Dic1222
#214472112
#214470122
#214469982
#214469132
#214466722
#214464272
#214461772
#214461602
#214460862
C61×#24262
#2514961