Finite Group Databasebeta

← #29689837

Subgroups — #29689837

Order 15616.

1098 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
1C2×#16840354C211yesmaximal, characteristic
2#21448436C211yesmaximal, characteristic, complemented
3#21448421C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446276C212yesmaximal, complemented
7#21446274C212yesmaximal, complemented
8#21445807C211yesmaximal, characteristic, complemented
9#21445804C211yesmaximal, characteristic, complemented
10#21445804C211yesmaximal, characteristic, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12#16840354—22no—
13#16840354—22no—
14#16840354—22no—
15#16840354—22no—
16C2×#14519771C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519769C411yescharacteristic, complemented
19C2×#14519767C411yescharacteristic, complemented
20C2×#14519761C2211yescharacteristic
21C2×#14519760C411yescharacteristic, complemented
22C2×#14519759C411yescharacteristic, complemented
23C2×#14519758C2211yescharacteristic
24C2×#14519756C411yescharacteristic, complemented
25C2×#14519755C411yescharacteristic, complemented
26C2×#14519754C2211yescharacteristic
27C2×#14519749C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519733C2212yes—
30C22×#11758196C2211yescharacteristic
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839659—22no—
35#16839657—22no—
36#16839649—22no—
37#16839643—22no—
38#16839623C2212yes—
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839620C2212yes—
42C22⋊C4×Dic61C2212yes—
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2212yes—
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#342C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57#14519771—22no—
58#14519771—22no—
59#14519770—22no—
60#14519770—22no—
61#14519769—22no—
62#14519769—22no—
63#14519767—22no—
64#14519767—22no—
65#14519761—22no—
66#14519761—22no—
67#14519760—22no—
68#14519760—22no—
69#14519759—22no—
70#14519759—22no—
71#14519758—22no—
72#14519758—22no—
73#14519756—22no—
74#14519756—22no—
75#14519755—22no—
76#14519755—22no—
77#14519754—22no—
78#14519754—22no—
79#14519749—22no—
80#14519749—22no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85#14519733—42no—
86#14519733—42no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196D412yes—
105C2×#11758196D412yes—
106C2×#11758196D412yes—
107C2×#11758196D412yes—
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2311yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61C2×C411yescharacteristic
121#14519692—42no—
122#14519691—42no—
123#14519691—42no—
124#14519684—21no—
125#14519684—21no—
126#14519684—22no—
127#14519684—22no—
128#14519684—24no—
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C42×C61C2×C411yescharacteristic
144#99×C61—42no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C22×C411yescharacteristic
148C24×C61C2411yescharacteristic
149C23×D61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—81no—
161C22×C4×C61—81no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—81no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—81no—
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61C2×D412yes—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—81no—
200C2×Dic122—22no—
201C2×Dic122—81no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61—81no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊C4×C61—21no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—21no—
217C22⋊Dic61—21no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225#11758198—21no—
226#11758198—21no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61—22no—
233C4⋊Dic61—81no—
234C4⋊Dic61—81no—
235#11758196—21no—
236#11758196—21no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—44no—
243#11758196—82no—
244#11758196C22⋊C412yes—
245#11758196C22⋊C412yes—
246#11758196C22⋊C412yes—
247#11758196C22⋊C412yes—
248#11758196C22⋊C412yes—
249#11758196C22⋊C412yes—
250#11758196C22⋊C412yes—
251#11758196C22⋊C412yes—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C4×Dic61—44no—
255C4×Dic61—82no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61C23×C411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61H(5,𝔽2)11yescharacteristic
267C23×C61H(5,𝔽2)11yescharacteristic
268C23×C612−1+411yescharacteristic
269C23×C612−1+411yescharacteristic
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—41no—
274C22×D61—41no—
275D4×C61—41no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—81no—
299C2×C4×C61—81no—
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C22⋊D61—41no—
305C22⋊D61—41no—
306C22⋊D61—41no—
307C22⋊D61—41no—
308C22⋊D61—82no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61C2×C22⋊C412yes—
335C2×Dic61C2×C22⋊C412yes—
336C2×Dic61C2×C22⋊C412yes—
337C2×Dic61C2×C22⋊C412yes—
338C4×D61—81no—
339C4×D61—81no—
340Dic122—82no—
341#21877—611nomaximal, Sylow
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
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×C61C22×C22⋊C411yescharacteristic
358C22×C61#52011yescharacteristic
359C22×C61#52011yescharacteristic
360C22×C61#53511yescharacteristic
361C22×C61#53611yescharacteristic
362C22×C61#53711yescharacteristic
363C22×C61#53711yescharacteristic
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—81no—
368C2×D61—81no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—82no—
377C4×C61—82no—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—22no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—82no—
386Dic61—82no—
387C2×#539—611no—
388#2316—611no—
389#2313—611no—
390#1996—612no—
391#1964—612no—
392#1899—612no—
393#1899—612no—
394#1799—611no—
395#1799—611no—
396#1799—611no—
397#1799D6111yescharacteristic, complemented
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—81no—
405C2×C61#231111yescharacteristic
406C2×C61#288311yescharacteristic
407C2×C61#288411yescharacteristic
408D61—81no—
409#539—1222no—
410#539—1222no—
411#539—1222no—
412#539—1222no—
413C2×#126—611no—
414C2×#126—611no—
415C2×#125—611no—
416C2×#125—611no—
417C2×#123—611no—
418C2×#123—611no—
419C2×#123—611no—
420C2×#123—611no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—611no—
423C2×C22⋊Q8—611no—
424C2×#121—611no—
425C2×C4×D4—611no—
426C2×C4×D4C2×D6111yescharacteristic
427C2×#117—612no—
428C22×C4⋊C4—611no—
429C2×#99—612no—
430C2×#99—612no—
431C2×#99—612no—
432C2×#99C2×D6112yes—
433#389—1222no—
434#389—1222no—
435#387—1222no—
436#387—1222no—
437#381—612no—
438#380—611no—
439#380—611no—
440#380—612no—
441#380C2×D6111yescharacteristic
442#380C2×D6111yescharacteristic
443C4×C22⋊C4—612no—
444#342—612no—
445#342—612no—
446#342—612no—
447#342C2×D6112yes—
448C61#2187711yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4C4×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458#126—1222no—
459#126—1222no—
460#126—1222no—
461#126—1222no—
462#125—1222no—
463#125—1222no—
464#125—1222no—
465#125—1222no—
466#123—1222no—
467#123—1222no—
468#123—1222no—
469#123—1222no—
470#123—1222no—
471#123—1222no—
472#123—1222no—
473#123—1222no—
474C22⋊Q8—1222no—
475C22⋊Q8—1222no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478C22⋊Q8—1222no—
479C22⋊Q8—1222no—
480#121—1222no—
481#121—1222no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—1221no—
487C4×D4—1221no—
488C4×D4—1221no—
489C4×D4—1221no—
490#117—2442no—
491#117—2442no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—612no—
499C2×C4⋊C4—612no—
500C2×C4⋊C4—612no—
501C2×C4⋊C4—612no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—612no—
525C2×C22⋊C4—612no—
526C2×C22⋊C4C4×D6111yescharacteristic
527C2×C22⋊C4C22×D6112yes—
528C2×C22⋊C4C22×D6112yes—
529C2×C22⋊C4C22×D6111yescharacteristic
530C2×C42—611no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42C4×D6111yescharacteristic
534#99—42no—
535#99—2442no—
536#99—2442no—
537#99—2442no—
538#95—21no—
539#95—21no—
540#95—1222no—
541#95—1222no—
542#95—1224no—
543#95—1221no—
544#95—1221no—
545C24—611no—
546C24C2×C4×D6111yescharacteristic
547C24C23×D6111yescharacteristic
548C2×Q8—1222no—
549C2×Q8—4881no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—1222no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—4881no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—4881no—
590C22×C4—4881no—
591C22×C4C2×C4×D6111yescharacteristic
592C22×C4C2×C4×D6111yescharacteristic
593C22×C4C2×C4×D6111yescharacteristic
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—81no—
603C4⋊C4—81no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1222no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—4882no—
623C4⋊C4—4881no—
624C4⋊C4—4881no—
625C4⋊C4—2444no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1221no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C42—21no—
649C42—21no—
650C42—1221no—
651C42—1221no—
652C42—4882no—
653C42—2444no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—2441no—
665C23—2441no—
666C23C22×C4×D6111yescharacteristic
667C23C2×D4×D6111yescharacteristic
668C23C2×D4×D6111yescharacteristic
669C23#1451982211yescharacteristic
670C23#1451982311yescharacteristic
671C23#1451982411yescharacteristic
672C23#1451982511yescharacteristic
673Q8—4882no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—4882no—
679D4—2441no—
680D4—2441no—
681D4—2441no—
682D4—2441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
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—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—4881no—
722C2×C4—4881no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4C22⋊C4×D6111yescharacteristic
736C2×C4C22⋊C4×D6111yescharacteristic
737C2×C4C22⋊C4×D6111yescharacteristic
738C2×C4C22⋊C4×D6111yescharacteristic
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—4881no—
755C22—4881no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22C2×C22⋊C4×D6111yescharacteristic
760C22#1684024211yescharacteristic
761C22#1684024311yescharacteristic
762C22#1684032811yescharacteristic
763C22#1684033511yescharacteristic
764C22#1684034111yescharacteristic
765C22#1684034211yescharacteristic
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—82no—
774C4—82no—
775C4—1222no—
776C4—1222no—
777C4—1222no—
778C4—1222no—
779C4—4882no—
780C4—4882no—
781C4—2441no—
782C4—2441no—
783C4—2441no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—81no—
791C2—4881no—
792C2#2144840811yescharacteristic
793C2#2145427711yescharacteristic
794C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#21877
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448436C2semidirect
3. #21448421C2semidirect
4. #21446802C2semidirect
6. #21446276C2semidirect
7. #21446274C2semidirect
8. #21445807C2semidirect
9. #21445804C2semidirect
10. #21445804C2semidirect
11. C61×#1799C2semidirect
16. C2×#14519771C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519769C4semidirect
19. C2×#14519767C4semidirect
21. C2×#14519760C4semidirect
22. C2×#14519759C4semidirect
24. C2×#14519756C4semidirect
25. C2×#14519755C4semidirect
397. #1799D61semidirect
448. C61#21877semidirect

Maximal subgroups

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

subgroupindex
C2×#168403542
#214484362
#214484212
#214468022
#214466532
#214462762
#214462742
#214458072
#214458042
C61×#17992
#2187761