Finite Group Databasebeta

← #29713064

Subgroups — #29713064

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C2×#16840094C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21450123C211yesmaximal, characteristic
5#21447064C211yesmaximal, characteristic, complemented
6#21447063C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic, complemented
9#21446108C211yesmaximal, characteristic
10#21446088C211yesmaximal, characteristic, complemented
11#21446084C211yesmaximal, characteristic, complemented
12#21445755C211yesmaximal, characteristic, complemented
13#21445753C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#2035C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840425—24no—
20#16840425—24no—
21C2×#14519776—21no—
22C2×#14519775C2211yescharacteristic
23C2×#14519759—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519754—21no—
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C2×C4⋊C4×D61C2211yescharacteristic
31#16840094—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839696—21no—
47#16839690—21no—
48#16839661C2211yescharacteristic
49#16839658C2211yescharacteristic
50#16839624—21no—
51#16839622C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—22no—
69C22×Dic122—41no—
70C22×Dic122—41no—
71C22×Dic122C2311yescharacteristic
72C22×Dic122C2311yescharacteristic
73C2×Q8×D61—22no—
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—41no—
77C2×Q8×D61—41no—
78C2×Q8×D61D414yes—
79C22×C22⋊D61D411yescharacteristic
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—22no—
87C2×C8×D61—41no—
88C2×C8×D61—41no—
89#14519776—28no—
90#14519775—22no—
91#14519775—22no—
92#14519759—44no—
93#14519757—22no—
94#14519757D414yes—
95#14519755—28no—
96#14519754—28no—
97#14519742—22no—
98#14519742—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101#14519737—28no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519708—22no—
122#14519702—22no—
123#14519702—22no—
124#14519702—22no—
125#14519702—41no—
126#14519701—22no—
127#14519701—41no—
128#14519700—22no—
129#14519700—22no—
130#14519700—22no—
131#14519700—41no—
132C22⋊#92418—41no—
133#14519689—22no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×Q8×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—22no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150#106×C61—22no—
151#103×C61—22no—
152#103×C61—41no—
153C22⋊C8×C61—41no—
154#95×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C2×D412yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61SD1614yes—
178C22×Dic61—21no—
179C22×Dic61—24no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188Q8×D61—28no—
189Q8×D61—44no—
190Q8×D61—44no—
191Q8×D61—44no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—24no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61C2×D412yes—
203C2×C4×D61C2×D412yes—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—24no—
212C2×Dic122—21no—
213C2×Dic122—24no—
214C2×Dic122—44no—
215C2×Dic122—44no—
216C2×Dic122—44no—
217C2×Dic122—42no—
218C2×Dic122—42no—
219C2×Dic122—42no—
220C2×Dic122—42no—
221C2×Dic122—44no—
222C2×Dic122C2×D412yes—
223C2×Dic122C2×D412yes—
224C2×Dic122#4112yes—
225C2×Dic122#4112yes—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C2×D412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—42no—
241C22⋊Dic61—22no—
242C22⋊Dic61—42no—
243#11758198—24no—
244#11758198—22no—
245#11758198—42no—
246C4⋊Dic61—24no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—42no—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—22no—
256#11758196—42no—
257#11758196—42no—
258C4×Dic61—24no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C8×D61—44no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61C2×SD1612yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61#12012yes—
281C22×D61C2×SD1612yes—
282C22×D61#13712yes—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—41no—
286Q8×C61—41no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—41no—
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—41no—
305C2×C4×C61—41no—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C22⋊D61—28no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—48no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61#12012yes—
334C2×Dic61C2×SD1612yes—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—48no—
340C4×D61—84no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122—48no—
347Dic122—48no—
348Dic122—41no—
349Dic122—41no—
350Dic122#12314yescomplemented
351C8×C61—41no—
352C8×C61—41no—
353#92418—41no—
354#92418—41no—
355#24041—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61C2×#12011yescharacteristic
364C22×C61#54611yescharacteristic
365C22×C61#54611yescharacteristic
366C22×C61C22×SD1611yescharacteristic
367C22×C61C2×#13711yescharacteristic
368C22×C61#57811yescharacteristic
369C22×C61#57811yescharacteristic
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61#44814yes—
377C4×C61—41no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61C2×#12311yescharacteristic
383C4×C61#53411yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#54611yescharacteristic
386Dic61—24no—
387Dic61—22no—
388Dic61—22no—
389Dic61—42no—
390Dic61—41no—
391Dic61—81no—
392Dic61—81no—
393C2×D4×Q8—611no—
394C2×#483—611no—
395C22×#103—611no—
396#2486—611no—
397#2043—611no—
398#2043—611no—
399#2035—611no—
400#2035D6111yescharacteristic, complemented
401#1892—611no—
402#1869—611no—
403#1865—611no—
404#1865—611no—
405#1787—611no—
406#1787—611no—
407#1787—611no—
408C2×C61—42no—
409C2×C61#240511yescharacteristic
410C2×C61C2×#44811yescharacteristic
411C2×C61#301111yescharacteristic
412C2×C61#329811yescharacteristic
413C2×C61#329811yescharacteristic
414C2×C61#331211yescharacteristic
415C2×C61#331211yescharacteristic
416D61—24no—
417C23×Q8—611no—
418C23×Q8—611no—
419C23×C8—611no—
420D4×Q8—1224no—
421D4×Q8—1224no—
422C2×C4⋊Q8—611no—
423C2×C4⋊Q8—1221no—
424C2×#123—1221no—
425C2×C22⋊Q8—611no—
426C2×C22⋊Q8—1221no—
427C2×C22⋊Q8—1221no—
428C2×C22⋊Q8C2×D6111yescharacteristic
429C2×C4×Q8—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432C22×C4⋊C4—611no—
433#483—1224no—
434C2×#106—611no—
435C2×#106C2×D6111yescharacteristic
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103—1224no—
447C2×#103C2×D6111yescharacteristic
448C2×#103C2×D6111yescharacteristic
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8C2×D6111yescharacteristic
452#398—1221no—
453#397—1221no—
454#389—611no—
455#389—611no—
456#381—1221no—
457#380—611no—
458#380—611no—
459#380C2×D6111yescharacteristic
460#340—611no—
461#340C2×D6111yescharacteristic
462#336—611no—
463#336—611no—
464C61#2404111yescharacteristic, complemented, Sylow
465C22×Q8—614no—
466C22×Q8—611no—
467C22×Q8—611no—
468C22×Q8—1221no—
469C22×Q8—1222no—
470C22×Q8—1222no—
471C22×Q8—1222no—
472C22×Q8—1222no—
473C22×Q8—1222no—
474C22×Q8—1221no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—2441no—
478C22×Q8—2441no—
479C22×Q8—2441no—
480C22×Q8—2441no—
481C22×Q8C22×D6111yescharacteristic
482C22×D4—611no—
483C23×C4—611no—
484C23×C4—1221no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4C22×D6111yescharacteristic
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—1222no—
491C22×C8—2441no—
492C22×C8—2441no—
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C4⋊Q8—1228no—
496C4⋊Q8—1222no—
497C4⋊Q8—1222no—
498#123—2444no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—614no—
502C22⋊Q8—1228no—
503C22⋊Q8—1222no—
504C22⋊Q8—1228no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×D4—1228no—
508C4×D4—1222no—
509C4×D4—1222no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C42—611no—
534C2×C42—1221no—
535#106—22no—
536#106—1222no—
537#103—22no—
538#103—41no—
539#103—1222no—
540#103—1222no—
541#103—1222no—
542#103—1222no—
543#103—1222no—
544#103—1222no—
545#103—1222no—
546#103—2441no—
547#103—2441no—
548#103—2441no—
549C22⋊C8—41no—
550C22⋊C8—1222no—
551C22⋊C8—2441no—
552#95—21no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556#95—1221no—
557C24—611no—
558C24D4×D6111yescharacteristic
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—612no—
565C2×Q8—612no—
566C2×Q8—612no—
567C2×Q8—612no—
568C2×Q8—1224no—
569C2×Q8—1224no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1228no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—2442no—
580C2×Q8—2442no—
581C2×Q8—2442no—
582C2×Q8—2442no—
583C2×Q8—2444no—
584C2×Q8—2444no—
585C2×Q8—2444no—
586C2×Q8—2444no—
587C2×Q8—2444no—
588C2×Q8—2444no—
589C2×Q8—2444no—
590C2×Q8D4×D6112yes—
591C2×D4—614no—
592C2×D4—1222no—
593C2×D4—1222no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—611no—
609C22×C4—1224no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1224no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4D4×D6111yescharacteristic
627C22×C4C23×D6111yescharacteristic
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—2444no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—1222no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C4⋊C4—2442no—
659C4⋊C4D4×D6112yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—1222no—
663C22⋊C4—1224no—
664C22⋊C4—1222no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C42—1224no—
668C42—1221no—
669C42—1221no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—612no—
677C23—612no—
678C23—612no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23SD16×D6112yes—
684C23C2×D4×D6111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—614no—
690Q8—1222no—
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695Q8—2448no—
696Q8—2448no—
697Q8—2441no—
698Q8—2441no—
699D4—1228no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
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—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—1221no—
722C2×C4—1222no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—4884no—
737C2×C4—2448no—
738C2×C4—2448no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#41×D6111yescharacteristic
750C2×C4#41×D6111yescharacteristic
751C2×C4#1451982211yescharacteristic
752C2×C4#1451982311yescharacteristic
753C8—41no—
754C8—41no—
755C8—2441no—
756C8—2441no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—614no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22#120×D6111yescharacteristic
772C22#1684040111yescharacteristic
773C22#1684040411yescharacteristic
774C22C2×SD16×D6111yescharacteristic
775C22#137×D6111yescharacteristic
776C22#1684057611yescharacteristic
777C22#1684057811yescharacteristic
778C4—42no—
779C4—41no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—1222no—
784C4—1222no—
785C4—1224no—
786C4—4881no—
787C4—4881no—
788C4—2441no—
789C4—2442no—
790C4#123×D6111yescharacteristic
791C4#1684032011yescharacteristic
792C4#1684040511yescharacteristic
793C4#1684040911yescharacteristic
794C2—42no—
795C2—1224no—
796C2#2144914111yescharacteristic
797C2#448×D6111yescharacteristic
798C2#2145511111yescharacteristic
799C2#2145767911yescharacteristic
800C2#2145768211yescharacteristic
801C2#2145786511yescharacteristic
802C2#2145787311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2035C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2035D61
hypocenterC61#24041
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#16840094C2semidirect
3. C2×#103×D61C2semidirect
5. #21447064C2semidirect
6. #21447063C2semidirect
7. #21447012C2semidirect
8. #21446241C2semidirect
10. #21446088C2semidirect
11. #21446084C2semidirect
12. #21445755C2semidirect
13. #21445753C2semidirect
14. #21445752C2semidirect
15. C61×#2035C2semidirect
350. Dic122#123semidirect
400. #2035D61semidirect
464. C61#24041semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168400942
C2×#103×D612
#214501232
#214470642
#214470632
#214470122
#214462412
#214461082
#214460882
#214460842
#214457552
#214457532
#214457522
C61×#20352
#2404161