Finite Group Databasebeta

← C2×#21448494 #29838748

Subgroups — C2×#21448494 #29838748

Order 15616.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3C22×#14519733C211yesmaximal, characteristic
4#21448494C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839660C211yesmaximal, characteristic, complemented
7C2×#16839659C211yesmaximal, characteristic, complemented
8C2×#16839657C211yesmaximal, characteristic, complemented
9C2×#16839656C211yesmaximal, characteristic
10C2×#16839656C211yesmaximal, characteristic
11C2×#16839655C211yesmaximal, characteristic
12C2×#16839645C211yesmaximal, characteristic, complemented
13C2×#16839644C211yesmaximal, characteristic, complemented
14C2×#16839620C211yesmaximal, characteristic
15C2×C4×#11758196C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519754C4116yescomplemented
20C2×#14519754C2218yes—
21C2×#14519742—28no—
22C2×#14519742C2218yescomplemented
23C2×#14519733—28no—
24C2×#14519733C2218yes—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839666C2218yescomplemented
44#16839660C2218yescomplemented
45#16839659C2218yescomplemented
46#16839657C2218yescomplemented
47#16839656C2218yes—
48#16839656C2218yes—
49#16839655C2218yes—
50#16839645C2218yescomplemented
51#16839644C2218yescomplemented
52#16839620C2218yes—
53C4×#11758196C2218yescomplemented
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C61×#388C2218yes—
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122C2×C418yes—
73C22×Dic122C2314yes—
74C23×Dic61—24no—
75C23×Dic61—24no—
76C23×Dic61C2×C418yes—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86#14519754C2×C4164yescomplemented
87#14519742—232no—
88#14519733—232no—
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61C2×C418yes—
91C2×C4⋊Dic61C2314yes—
92C2×C4⋊Dic61C2314yes—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—42no—
99C2×#11758196C2×C418yes—
100C2×#11758196C2×C418yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×C22⋊Dic61—24no—
110C2×C22⋊Dic61—42no—
111C2×C22⋊Dic61C2×C418yes—
112C2×C22⋊Dic61C2314yes—
113C2×C22⋊Dic61C2314yes—
114C2×C22⋊Dic61C2314yes—
115C2×C4×Dic61—24no—
116C2×C4×Dic61—24no—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—42no—
119C2×C4×Dic61D418yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2314yes—
124C2×C4×Dic61C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133C25×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61C2314yes—
142C2×C22⋊C4×C61—24no—
143C2×C22⋊C4×C61—42no—
144C2×C22⋊C4×C61C2×C418yes—
145C2×C22⋊C4×C61C2314yes—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C42×C61—42no—
149C2×C42×C61C2314yes—
150#95×C61C2314yes—
151#95×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61C22×C414yes—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C22×C414yes—
178C22×C4×C61C2×D414yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—232no—
194C22×Dic61—28no—
195C22×Dic61—28no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61C22×C414yes—
206C22×Dic61C22×C4116yes—
207C22×Dic61C22×C414yes—
208C22×Dic61C22×C414yes—
209C22×Dic61C22×C414yes—
210C22×Dic61C2×D414yes—
211C22×Dic61C2×D414yes—
212C22×Dic61#4114yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C2×Dic122—232no—
222C2×Dic122—28no—
223C2×Dic122—28no—
224C2×Dic122C22×C4116yes—
225C4⋊C4×C61—28no—
226C22⋊C4×C61—28no—
227C22⋊C4×C61—44no—
228C22⋊C4×C61C22×C4116yes—
229C42×C61—44no—
230C22⋊Dic61—28no—
231C22⋊Dic61—44no—
232C22⋊Dic61C22×C4116yes—
233C4⋊Dic61—44no—
234C4⋊Dic61C22×C4116yes—
235#11758196—28no—
236#11758196—28no—
237#11758196—28no—
238#11758196—28no—
239#11758196—28no—
240#11758196—44no—
241#11758196C22×C4116yes—
242#11758196C22×C4116yes—
243C4×Dic61—28no—
244C4×Dic61—28no—
245C4×Dic61—28no—
246C4×Dic61—44no—
247C4×Dic61C2×D4116yes—
248C23×C61—28no—
249C23×C61—28no—
250C23×C61—28no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—44no—
258C23×C61—44no—
259C23×C61—44no—
260C23×C61—44no—
261C23×C61C23×C414yes—
262C23×C61C23×C412yes—
263C23×C61C22×D412yes—
264C23×C61C2×#4112yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C612−1+412yes—
267C23×C612−1+412yes—
268C23×C612−1+412yes—
269C23×C61C2511yescharacteristic
270C2×C4×C61—28no—
271C2×C4×C61—28no—
272C2×C4×C61—28no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—44no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61C23×C414yes—
292C2×C4×C61C23×C414yes—
293C2×C4×C61C22×D414yes—
294C2×Dic61—28no—
295C2×Dic61—28no—
296C2×Dic61—28no—
297C2×Dic61—28no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—232no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61—44no—
319C2×Dic61C4×D4116yes—
320C2×Dic61C23×C414yes—
321C2×Dic61C23×C414yes—
322C2×Dic61C23×C414yes—
323C2×Dic61C23×C414yes—
324C2×Dic61C22×D414yes—
325C2×Dic61C22×D414yes—
326C2×Dic61C2×#4114yes—
327Dic122—232no—
328C2×#2323—611nomaximal, Sylow
329C22×C61—24no—
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—416no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61C2×C4×D414yes—
338C22×C61#51914yes—
339C22×C61#52014yes—
340C22×C61#53614yes—
341C22×C61#53714yes—
342C22×C61#54114yes—
343C22×C61#54214yes—
344C22×C61C24×C411yescharacteristic
345C22×C61C23×D411yescharacteristic
346C22×C61C22×#4111yescharacteristic
347C22×C61C2×H(5,𝔽2)11yescharacteristic
348C22×C61C2×2−1+411yescharacteristic
349C22×C61C2×2−1+411yescharacteristic
350C22×C61C2×2−1+411yescharacteristic
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357Dic61—24no—
358Dic61—24no—
359Dic61—24no—
360Dic61—24no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61C2×C4×D418yes—
365C22×C22⋊Q8—611no—
366C22×C4×Q8—611no—
367C22×#117—611no—
368#2323—6116no—
369C2×#391—611no—
370C2×#389—611no—
371C2×#389—611no—
372C2×#389—611no—
373C2×#388—611no—
374C2×#388—611no—
375C2×#388—611no—
376C2×#388D6111yescharacteristic
377C2×#387—611no—
378C2×#387—611no—
379C2×#380—611no—
380C2×C4×C4⋊C4—611no—
381C2×C61—44no—
382C2×C61#232318yescomplemented
383C2×C61C22×C4×D411yescharacteristic
384C2×C61C2×#51911yescharacteristic
385C2×C61C2×#52011yescharacteristic
386C2×C61C2×#53611yescharacteristic
387C2×C61C2×#53711yescharacteristic
388C2×C61C2×#54111yescharacteristic
389C2×C61C2×#54211yescharacteristic
390C23×Q8—611no—
391C24×C4—611no—
392C2×C22⋊Q8—6116no—
393C2×C22⋊Q8—618no—
394C2×C4×Q8—618no—
395C2×C4×Q8—1228no—
396C2×#117—618no—
397C2×#117—1228no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4C2×D6111yescharacteristic
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4C2×D6111yescharacteristic
413C22×C22⋊C4C2×D6111yescharacteristic
414C22×C22⋊C4C2×D6111yescharacteristic
415C22×C42—611no—
416C22×C42—611no—
417C22×C42—611no—
418C22×C42—611no—
419C22×C42—611no—
420C22×C42C2×D6111yescharacteristic
421#391—618no—
422#389—618no—
423#389—618no—
424#389—618no—
425#388—618no—
426#388—618no—
427#388—618no—
428#388C2×D6118yes—
429#387—618no—
430#387—618no—
431#380—618no—
432C4×C4⋊C4—618no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95—611no—
439C2×#95—611no—
440C2×#95—611no—
441C2×#95C2×D6111yescharacteristic
442C2×#95C2×D6111yescharacteristic
443C61C2×#232311yescharacteristic, complemented, Sylow
444C25C22×D6111yescharacteristic
445C22×Q8—618no—
446C22×Q8—614no—
447C22×Q8—1224no—
448C22×Q8—1224no—
449C23×C4—611no—
450C23×C4—618no—
451C23×C4—614no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C22⋊Q8—6164no—
468C4×Q8—12232no—
469#117—12232no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—618no—
472C2×C4⋊C4—618no—
473C2×C4⋊C4—618no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1224no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4—2442no—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—618no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4C4×D6118yes—
501C2×C22⋊C4C22×D6114yes—
502C2×C22⋊C4C22×D6114yes—
503C2×C22⋊C4C22×D6114yes—
504C2×C42—42no—
505C2×C42—618no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—614no—
509C2×C42—614no—
510C2×C42—614no—
511C2×C42—1224no—
512C2×C42—1224no—
513C2×C42—1224no—
514C2×C42—2442no—
515C2×C42C22×D6114yes—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—614no—
522#95—614no—
523#95—614no—
524#95C22×D6114yes—
525#95C22×D6114yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C4×D6114yes—
533C24C23×D6112yes—
534C24C23×D6111yescharacteristic
535C2×Q8—6116no—
536C2×Q8—1228no—
537C2×Q8—12232no—
538C2×Q8—1228no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—612no—
558C22×C4—614no—
559C22×C4—614no—
560C22×C4—614no—
561C22×C4—6116no—
562C22×C4—614no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—1228no—
571C22×C4—12232no—
572C22×C4—1228no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4C2×C4×D6114yes—
591C22×C4C2×C4×D6114yes—
592C22×C4D4×D6114yes—
593C22×C4C23×D6112yes—
594C22×C4C23×D6112yes—
595C22×C4C23×D6112yes—
596C22×C4C23×D6112yes—
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C4⋊C4—28no—
600C4⋊C4—6116no—
601C4⋊C4—6116no—
602C4⋊C4—6116no—
603C4⋊C4—1228no—
604C4⋊C4—1228no—
605C4⋊C4—1228no—
606C4⋊C4—1228no—
607C4⋊C4—1228no—
608C4⋊C4—2444no—
609C4⋊C4—2444no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—6116no—
613C22⋊C4—1228no—
614C22⋊C4—2444no—
615C22⋊C4C2×C4×D61116yes—
616C42—44no—
617C42—6116no—
618C42—1228no—
619C42—1228no—
620C42—1228no—
621C42—2444no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D6114yes—
636C23C22×C4×D6112yes—
637C23C2×D4×D6112yes—
638C23#41×D6112yes—
639C23#1451982212yes—
640C23#1451982412yes—
641C23#1451982412yes—
642C23#1451982412yes—
643C23C24×D6111yescharacteristic
644Q8—12232no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—6116no—
667C2×C4—614no—
668C2×C4—614no—
669C2×C4—614no—
670C2×C4—614no—
671C2×C4—614no—
672C2×C4—614no—
673C2×C4—614no—
674C2×C4—12232no—
675C2×C4—1228no—
676C2×C4—1228no—
677C2×C4—1228no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1228no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4—2444no—
699C2×C4C22×C4×D6114yes—
700C2×C4C22×C4×D6114yes—
701C2×C4C2×D4×D6114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—416no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C4×D4×D6114yes—
711C22#1684023914yes—
712C22#1684024114yes—
713C22#1684033214yes—
714C22#1684033914yes—
715C22#1684036914yes—
716C22#1684038014yes—
717C22C23×C4×D6111yescharacteristic
718C22C22×D4×D6111yescharacteristic
719C22C2×#41×D6111yescharacteristic
720C22C2×#1451982211yescharacteristic
721C22C2×#1451982411yescharacteristic
722C22C2×#1451982411yescharacteristic
723C22C2×#1451982411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—618no—
731C4—1224no—
732C4—1224no—
733C4—1224no—
734C4—1224no—
735C4—2442no—
736C4—2442no—
737C4—2442no—
738C2—44no—
739C2#2144849418yesdirect product factor
740C2C2×C4×D4×D6111yescharacteristic
741C2C2×#1684023911yescharacteristic
742C2C2×#1684024111yescharacteristic
743C2C2×#1684033211yescharacteristic
744C2C2×#1684033911yescharacteristic
745C2C2×#1684036911yescharacteristic
746C2C2×#1684038011yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×C61C23
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2323
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
4. #21448494C2direct (N × H)
5. C2×#16839666C2semidirect
6. C2×#16839660C2semidirect
7. C2×#16839659C2semidirect
8. C2×#16839657C2semidirect
12. C2×#16839645C2semidirect
13. C2×#16839644C2semidirect
15. C2×C4×#11758196C2semidirect
19. C2×#14519754C4semidirect
22. C2×#14519742C22semidirect
43. #16839666C22semidirect
44. #16839660C22semidirect
45. #16839659C22semidirect
46. #16839657C22semidirect
50. #16839645C22semidirect
51. #16839644C22semidirect
53. C4×#11758196C22semidirect
86. #14519754C2×C4semidirect
382. C2×C61#2323semidirect
443. C61C2×#2323semidirect
739. C2#21448494direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×#145197422
C22×#145197332
#214484942
C2×#168396662
C2×#168396602
C2×#168396592
C2×#168396572
C2×#168396562
C2×#168396552
C2×#168396452
C2×#168396442
C2×#168396202
C2×C4×#117581962
C2×C61×#3882
C2×#232361