Finite Group Databasebeta

← #29695351

Subgroups — #29695351

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840413C211yesmaximal, characteristic
2C2×#16839735C212yesmaximal, complemented
3#21448688C211yesmaximal, characteristic, complemented
4#21446655C211yesmaximal, characteristic, complemented
5#21446654C211yesmaximal, characteristic, complemented
6#21446277C212yesmaximal, complemented
7#21446275C212yesmaximal, complemented
8#21445804C211yesmaximal, characteristic, complemented
9#21445736C212yesmaximal, complemented
10C4×#14519691C211yesmaximal, characteristic, complemented
11C61×#2344C211yesmaximal, characteristic, complemented
12C22×#11758222C2212yes—
13#16840413—21no—
14#16840413—22no—
15#16840413—21no—
16#16840413—21no—
17#16840413—22no—
18#16840413—21no—
19C2×#14519776C411yescharacteristic, complemented
20C2×#14519762C412yescomplemented
21C2×#14519760C2212yes—
22C2×#14519755C412yescomplemented
23C2×#14519752C411yescharacteristic, complemented
24C2×#14519751C2211yescharacteristic
25C2×#14519739C411yescharacteristic, complemented
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×#14519736C2212yes—
28C2×C4⋊C4×D61C411yescharacteristic, complemented
29#16839735—28no—
30C2×#14519691C2211yescharacteristic
31C2×#14519691C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34C2×#14519691C2212yes—
35C2×#14519691C2212yes—
36C2×#14519691C2211yescharacteristic
37#16839661—21no—
38#16839648—22no—
39#16839625C2212yes—
40#16839622C2211yescharacteristic
41C4⋊C4×Dic61—21no—
42C4×C22⋊Dic61C2211yescharacteristic
43#16839528C2211yescharacteristic
44#16839528C2212yes—
45#16839528C2211yescharacteristic
46C2×#117×C61C2212yes—
47C22×C4⋊C4×C61C2211yescharacteristic
48C61×#389—21no—
49C61×#387—22no—
50C61×#381C2212yes—
51C61×#380C2211yescharacteristic
52C4×C4⋊C4×C61—21no—
53C4×C22⋊C4×C61C2211yescharacteristic
54C2×#11758222—22no—
55C2×#11758222—22no—
56C2×#11758222—22no—
57C2×#11758222—22no—
58C2×#11758222—24no—
59C2×#11758222—24no—
60C2×#11758222—42no—
61C2×#11758222—42no—
62C22×Dic122C2×C412yes—
63C22×D244C2×C412yes—
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61C2312yes—
66C22×C22⋊D61C2311yescharacteristic
67C22×C4×D61C2×C412yes—
68C22×C4×D61C2×C412yes—
69C22×C4×D61C2×C411yescharacteristic
70#14519776—22no—
71#14519776—21no—
72#14519776—21no—
73#14519762—22no—
74#14519762—22no—
75#14519762—22no—
76#14519762—22no—
77#14519760—22no—
78#14519760—22no—
79#14519760—22no—
80#14519760—22no—
81#14519755—22no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519752—22no—
86#14519752—21no—
87#14519752—21no—
88#14519751—21no—
89#14519751—21no—
90#14519751—21no—
91#14519751—21no—
92#14519739—22no—
93#14519739—21no—
94#14519739—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98C4×C22⋊D61—21no—
99#14519736—24no—
100#14519736—42no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×#11758196C2×C412yes—
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C412yes—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C2×C22⋊Dic61C2312yes—
111C2×C22⋊Dic61C2311yescharacteristic
112C2×C22⋊Dic61C2311yescharacteristic
113C2×C22⋊Dic61C2311yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C412yes—
116C2×#11758198C2×C412yes—
117C2×#11758198C2×C412yes—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2×C411yescharacteristic
121#14519691—24no—
122#14519691—22no—
123#14519691—24no—
124#14519691—24no—
125#14519691—42no—
126#14519691—42no—
127#14519691D414yescomplemented
128#14519684—21no—
129#14519684—22no—
130#14519684—21no—
131#14519684—22no—
132C23×C4×C61C2312yes—
133C23×C4×C61C2311yescharacteristic
134#117×C61—24no—
135#117×C61—42no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—22no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C412yes—
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C4⋊C4×C61D412yes—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61D411yescharacteristic
145C2×C4⋊C4×C61D412yes—
146C2×C4⋊C4×C61D411yescharacteristic
147C2×C22⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61C2312yes—
149C2×C22⋊C4×C61C2311yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61—22no—
152#95×C61—21no—
153#95×C61—22no—
154#95×C61—21no—
155#95×C61—22no—
156C24×C61C2411yescharacteristic
157C23×D61C22×C412yes—
158C23×D61C22×C411yescharacteristic
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—42no—
167C22×C4×C61C22×C412yes—
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C412yes—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61C2×D412yes—
190C2×C22⋊D61#4112yes—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61C22×C412yes—
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202#11758222—44no—
203#11758222—44no—
204#11758222—44no—
205#11758222—44no—
206C2×D244—24no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—42no—
212C2×D244—42no—
213C2×C4×D61—24no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—24no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—24no—
227C2×Dic122—42no—
228C4⋊C4×C61—44no—
229C4⋊C4×C61—42no—
230C4⋊C4×C61C22⋊C412yes—
231C4⋊C4×C61C22⋊C411yescharacteristic
232C4⋊C4×C61C22⋊C411yescharacteristic
233C4⋊C4×C61C22⋊C412yes—
234C4⋊C4×C61C22⋊C411yescharacteristic
235C4⋊C4×C61C22⋊C411yescharacteristic
236C4⋊C4×C61C22⋊C412yes—
237C4⋊C4×C61C22⋊C412yes—
238C4⋊C4×C61C22⋊C412yes—
239C4⋊C4×C61C22⋊C412yes—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61C2×D412yes—
246C42×C61—44no—
247C42×C61—42no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—22no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—22no—
255C22⋊Dic61C2×D412yes—
256#11758198—21no—
257#11758198—21no—
258#11758198—22no—
259#11758198—22no—
260#11758198—22no—
261#11758198—22no—
262#11758198—22no—
263#11758198—22no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—44no—
267C4⋊Dic61—42no—
268#11758196—22no—
269#11758196—22no—
270#11758196—21no—
271#11758196—21no—
272#11758196—22no—
273#11758196—22no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—44no—
277C4×Dic61—42no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61C23×C411yescharacteristic
281C23×C61C22×D411yescharacteristic
282C23×C61C22×D411yescharacteristic
283C23×C61C22×D411yescharacteristic
284C23×C61C2×#4111yescharacteristic
285C23×C61H(5,𝔽2)11yescharacteristic
286C23×C61H(5,𝔽2)11yescharacteristic
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61C4×D412yes—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—42no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—41no—
324C2×C4×C61C2×C22⋊C411yescharacteristic
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C412yes—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C2×C22⋊C412yes—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61C2×C22⋊C411yescharacteristic
332C22⋊D61—22no—
333C22⋊D61—22no—
334C22⋊D61—22no—
335C22⋊D61—22no—
336C22⋊D61—42no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—42no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—41no—
358C2×Dic61C4×D412yes—
359D244—44no—
360D244—44no—
361D244—42no—
362D244—42no—
363C4×D61—44no—
364C4×D61—44no—
365C4×D61—44no—
366C4×D61—44no—
367C4×D61—42no—
368C4×D61—42no—
369Dic122—44no—
370Dic122—44no—
371#22406—611nomaximal, Sylow
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61C2×C4×D411yescharacteristic
384C22×C61#51811yescharacteristic
385C22×C61D4211yescharacteristic
386C22×C61D4211yescharacteristic
387C22×C61#54611yescharacteristic
388C22×C61#54611yescharacteristic
389C2×D61—22no—
390C2×D61—42no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—82no—
398C2×D61—82no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—42no—
407C4×C61—82no—
408C4×C61—81no—
409C4×C61#41012yescomplemented
410Dic61—22no—
411Dic61—42no—
412Dic61—42no—
413Dic61—41no—
414Dic61—41no—
415Dic61—82no—
416Dic61—81no—
417C2×#547—611no—
418C2×#410—612no—
419#2344—611no—
420#2344D6111yescharacteristic, complemented
421#1964—611no—
422#1964—611no—
423#1899—612no—
424#1899—612no—
425#1799—611no—
426#1782—612no—
427C4×#99—611no—
428C2×C61—21no—
429C2×C61—21no—
430C2×C61—21no—
431C2×C61—21no—
432C2×C61—21no—
433C2×C61—21no—
434C2×C61D4×C22⋊C411yescharacteristic
435C2×C61C2×#41011yescharacteristic
436C2×C61#288411yescharacteristic
437D61—42no—
438D61—82no—
439C22×#41—612no—
440#547—1221no—
441#547—1222no—
442#547—1221no—
443#547—1221no—
444#547—1222no—
445#547—1221no—
446C2×C4⋊Q8—611no—
447C2×#123—612no—
448C2×#123—612no—
449C2×C22⋊Q8—612no—
450C2×#121—611no—
451C2×#121—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×#117—612no—
455C2×#117C2×D6112yes—
456C22×C4⋊C4—611no—
457C22×C4⋊C4C2×D6111yescharacteristic
458#410—1228no—
459C2×#99—611no—
460C2×#99—612no—
461C2×#99—612no—
462C2×#99—612no—
463C2×#99—611no—
464C2×#99—612no—
465C2×#99—612no—
466#389—21no—
467#389—1221no—
468#387—22no—
469#387—1222no—
470#381—612no—
471#381C2×D6112yes—
472#380—611no—
473#380C2×D6111yescharacteristic
474C4×C4⋊C4—21no—
475C4×C4⋊C4—1221no—
476C4×C22⋊C4—611no—
477C4×C22⋊C4C2×D6111yescharacteristic
478#342—612no—
479#342—611no—
480#342—611no—
481C61#2240611yescharacteristic, complemented, Sylow
482C2×#41—1224no—
483C2×#41—1224no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2442no—
489C2×#41—2442no—
490C22×Q8—612no—
491C22×D4—611no—
492C22×D4—612no—
493C22×D4—612no—
494C22×D4—611no—
495C23×C4—612no—
496C23×C4—612no—
497C23×C4—611no—
498C23×C4C22×D6112yes—
499C23×C4C22×D6111yescharacteristic
500C4⋊Q8—1222no—
501C4⋊Q8—1221no—
502C4⋊Q8—1221no—
503#123—1222no—
504#123—1222no—
505#123—1222no—
506#123—1222no—
507#123—1222no—
508#123—1222no—
509#123—1222no—
510#123—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1222no—
515#121—1221no—
516#121—1221no—
517#121—1221no—
518#121—1221no—
519#121—1222no—
520#121—1221no—
521#121—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1222no—
527C4×D4—1221no—
528C4×D4—1221no—
529#117—24no—
530#117—42no—
531#117—1224no—
532#117—2442no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—612no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—612no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C4×D6111yescharacteristic
545C2×C4⋊C4C4×D6111yescharacteristic
546C2×C4⋊C4C4×D6112yes—
547C2×C4⋊C4D24411yescharacteristic
548C2×C4⋊C4D24412yes—
549C2×C4⋊C4D24411yescharacteristic
550C2×C4⋊C4C22⋊D6111yescharacteristic
551C2×C4⋊C4C22⋊D6112yes—
552C2×C4⋊C4C22⋊D6111yescharacteristic
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—612no—
558C2×C22⋊C4—612no—
559C2×C22⋊C4—612no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4C22×D6112yes—
562C2×C22⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4C22×D6111yescharacteristic
564C2×C42—22no—
565C2×C42—21no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569#99—614no—
570#99—1224no—
571#99—1222no—
572#99—1224no—
573#99—1224no—
574#99—2442no—
575#99—2442no—
576#95—21no—
577#95—22no—
578#95—21no—
579#95—22no—
580#95—1221no—
581#95—1222no—
582#95—1221no—
583#95—1222no—
584C24—611no—
585C24—612no—
586C24C23×D6111yescharacteristic
587#41—2444no—
588#41—2444no—
589#41—2444no—
590#41—2444no—
591#41—2444no—
592#41—2444no—
593#41—2444no—
594#41—2444no—
595C2×Q8—1224no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—2442no—
599C2×D4—612no—
600C2×D4—612no—
601C2×D4—1224no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—2442no—
617C2×D4—2442no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—42no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1221no—
640C22×C4—1222no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4C2×C4×D6111yescharacteristic
645C22×C4C2×C4×D6112yes—
646C22×C4C2×C4×D6112yes—
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×D24412yes—
649C22×C4C2×D24412yes—
650C22×C4C2×D24411yescharacteristic
651C22×C4C2×D24411yescharacteristic
652C22×C4C2×C22⋊D6112yes—
653C22×C4C2×C22⋊D6112yes—
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C2×C22⋊D6111yescharacteristic
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—2444no—
667C4⋊C4—2442no—
668C4⋊C4#1175819812yes—
669C4⋊C4#1175819811yescharacteristic
670C4⋊C4#1175819811yescharacteristic
671C4⋊C4#1175819812yes—
672C4⋊C4#1175819811yescharacteristic
673C4⋊C4#1175819811yescharacteristic
674C4⋊C4#1175819812yes—
675C4⋊C4#1175819812yes—
676C4⋊C4#1175819812yes—
677C4⋊C4#1175819812yes—
678C22⋊C4—21no—
679C22⋊C4—22no—
680C22⋊C4—21no—
681C22⋊C4—22no—
682C22⋊C4—21no—
683C22⋊C4—612no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1222no—
699C22⋊C4D4×D6112yes—
700C42—44no—
701C42—42no—
702C42—1221no—
703C42—1221no—
704C42—2444no—
705C42—2442no—
706C23—41no—
707C23—41no—
708C23—612no—
709C23—1221no—
710C23—1221no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—2442no—
715C23—2442no—
716C23—2441no—
717C23—2441no—
718C23C22×C4×D6111yescharacteristic
719C23C2×D4×D6111yescharacteristic
720C23C22×C22⋊D6111yescharacteristic
721C23C22×D24411yescharacteristic
722C23#41×D6111yescharacteristic
723C23#1451982211yescharacteristic
724C23#1451982311yescharacteristic
725Q8—2444no—
726Q8—2444no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—2444no—
732D4—2444no—
733D4—2442no—
734D4—2442no—
735D4—2442no—
736D4—2442no—
737D4—2442no—
738D4—2442no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—612no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—2444no—
776C2×C4—2444no—
777C2×C4—2444no—
778C2×C4—2444no—
779C2×C4—2442no—
780C2×C4—2441no—
781C2×C4—2442no—
782C2×C4—2441no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2442no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4C2×#1175819811yescharacteristic
792C2×C4C2×#1175819811yescharacteristic
793C2×C4C2×#1175819811yescharacteristic
794C2×C4C2×#1175819812yes—
795C2×C4C2×#1175819812yes—
796C2×C4C2×#1175819812yes—
797C2×C4C2×#1175819812yes—
798C2×C4C2×#1175819811yescharacteristic
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—1222no—
810C22—4882no—
811C22—4882no—
812C22—2442no—
813C22—2442no—
814C22—2442no—
815C22—2442no—
816C22—2442no—
817C22—2441no—
818C22—2441no—
819C22C22×#1175819811yescharacteristic
820C22C4×D4×D6111yescharacteristic
821C22#1684023411yescharacteristic
822C22D4×C22⋊D6111yescharacteristic
823C22D4×D24411yescharacteristic
824C22#1684040011yescharacteristic
825C22#1684040711yescharacteristic
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—42no—
834C4—82no—
835C4—81no—
836C4—1222no—
837C4—4882no—
838C4—4881no—
839C4—2442no—
840C4—2442no—
841C4—2441no—
842C4—2441no—
843C4#1683973512yescomplemented
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—21no—
850C2—4882no—
851C2—2442no—
852C2D4×#1175819811yescharacteristic
853C2C2×#1683973511yescharacteristic
854C2#2145428211yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2344C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840413C2
cosocleC24×C61C24
hypercenter#2344D61
hypocenterC61#22406
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. C2×#16839735C2semidirect
3. #21448688C2semidirect
4. #21446655C2semidirect
5. #21446654C2semidirect
6. #21446277C2semidirect
7. #21446275C2semidirect
8. #21445804C2semidirect
9. #21445736C2semidirect
10. C4×#14519691C2semidirect
11. C61×#2344C2semidirect
19. C2×#14519776C4semidirect
20. C2×#14519762C4semidirect
22. C2×#14519755C4semidirect
23. C2×#14519752C4semidirect
25. C2×#14519739C4semidirect
28. C2×C4⋊C4×D61C4semidirect
127. #14519691D4semidirect
409. C4×C61#410semidirect
420. #2344D61semidirect
481. C61#22406semidirect
843. C4#16839735semidirect

Maximal subgroups

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

subgroupindex
C2×#168404132
C2×#168397352
#214486882
#214466552
#214466542
#214462772
#214462752
#214458042
#214457362
C4×#145196912
C61×#23442
#2240661