Finite Group Databasebeta

← C2×#21449341 #29848015

Subgroups — C2×#21449341 #29848015

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3#21449341C2116yesmaximal, direct product factor
4C2×#16839698C211yesmaximal, characteristic
5C2×#16839698C211yesmaximal, characteristic
6C2×#16839695C211yesmaximal, characteristic, complemented
7C2×#16839694C211yesmaximal, characteristic, complemented
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839659C211yesmaximal, characteristic, complemented
10C2×#16839655C211yesmaximal, characteristic
11C2×#16839649C211yesmaximal, characteristic, complemented
12C2×#16839646C211yesmaximal, characteristic, complemented
13C2×#16839631C211yesmaximal, characteristic, complemented
14C2×#16839620C211yesmaximal, characteristic
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic
16C2×C61×#388C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519754—28no—
20C2×#14519754C2218yes—
21C2×C4×Dic122—28no—
22C2×C4×Dic122C2218yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
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
41#16839698C2218yes—
42#16839698C2218yes—
43#16839695C2218yescomplemented
44#16839694C2218yescomplemented
45#16839666C2218yescomplemented
46#16839659C2218yescomplemented
47#16839655C2218yes—
48#16839649C2218yescomplemented
49#16839646C2218yescomplemented
50#16839631C2218yescomplemented
51#16839620C2218yes—
52C22⋊C4×Dic61C2218yes—
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C61×#388C2218yes—
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C22×Dic122—24no—
70C22×Dic122—24no—
71C22×Dic122D418yes—
72C22×Dic122C2314yes—
73C23×Dic61—24no—
74C23×Dic61—24no—
75C23×Dic61—24no—
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2314yes—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85#14519754—232no—
86C4×Dic122—232no—
87C2×C4⋊Dic61—24no—
88C2×C4⋊Dic61—24no—
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61—42no—
91C2×C4⋊Dic61C2314yes—
92C2×C4⋊Dic61C2314yes—
93C2×C4⋊Dic61C2314yes—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—24no—
102C2×#11758196—42no—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×C22⋊Dic61—24no—
112C2×C22⋊Dic61—24no—
113C2×C22⋊Dic61—42no—
114C2×C22⋊Dic61C2314yes—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C25×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2314yes—
140C2×C22⋊C4×C61—24no—
141C2×C22⋊C4×C61—42no—
142C2×C22⋊C4×C61Q818yescomplemented
143C2×C22⋊C4×C61C2314yes—
144C2×C22⋊C4×C61C2314yes—
145C2×C22⋊C4×C61C2314yes—
146C2×C42×C61—24no—
147C2×C42×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61C2×Q814yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C22×C4×C61—22no—
160C22×C4×C61—22no—
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×C61C2×D414yes—
175C22×C4×C61C2×Q814yes—
176C22×C4×C61C2×Q814yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×Dic61—22no—
184C22×Dic61—22no—
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—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—28no—
203C22×Dic61—28no—
204C22×Dic61—28no—
205C22×Dic61—416no—
206C22×Dic61C2×D414yes—
207C22×Dic61C2×D414yes—
208C22×Dic61#4114yes—
209C22×Dic61#4114yes—
210C22×Dic61#4114yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C2×Dic122—232no—
220C2×Dic122—28no—
221C2×Dic122—28no—
222C2×Dic122C2×D4116yes—
223C4⋊C4×C61—44no—
224C22⋊C4×C61—28no—
225C22⋊C4×C61—44no—
226C22⋊C4×C61C2×Q8116yescomplemented
227C42×C61—28no—
228C22⋊Dic61—28no—
229C22⋊Dic61—28no—
230C22⋊Dic61—44no—
231C4⋊Dic61—28no—
232C4⋊Dic61—28no—
233C4⋊Dic61—44no—
234C4⋊Dic61—44no—
235#11758196—28no—
236#11758196—28no—
237#11758196—28no—
238#11758196—28no—
239#11758196—28no—
240#11758196—28no—
241#11758196—28no—
242#11758196—44no—
243C4×Dic61—28no—
244C4×Dic61—28no—
245C4×Dic61—28no—
246C23×C61—28no—
247C23×C61—28no—
248C23×C61—28no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—44no—
256C23×C61—44no—
257C23×C61—44no—
258C23×C61—44no—
259C23×C61C22×D412yes—
260C23×C61C22×Q814yes—
261C23×C61C22×Q812yes—
262C23×C61C2×#4112yes—
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C612−1+412yes—
267C23×C61C2511yescharacteristic
268C2×C4×C61—28no—
269C2×C4×C61—28no—
270C2×C4×C61—28no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
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—44no—
287C2×C4×C61—44no—
288C2×C4×C61—44no—
289C2×C4×C61C22×D414yes—
290C2×C4×C61C22×Q814yes—
291C2×C4×C61C22×Q814yes—
292C2×Dic61—28no—
293C2×Dic61—28no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
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—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—44no—
314C2×Dic61—44no—
315C2×Dic61—44no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61—416no—
319C2×Dic61#123116yes—
320C2×Dic61C22×D414yes—
321C2×Dic61C22×D414yes—
322C2×Dic61C2×#4114yes—
323C2×Dic61C2×#4114yes—
324C2×Dic61C2×#4114yes—
325Dic122—232no—
326C2×#2423—611nomaximal, Sylow
327C22×C61—24no—
328C22×C61—24no—
329C22×C61—24no—
330C22×C61—42no—
331C22×C61—416no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61C2×#12314yes—
336C22×C61#53314yes—
337C22×C61#54214yes—
338C22×C61D4×Q814yes—
339C22×C61#55014yes—
340C22×C61#55214yes—
341C22×C61#55414yes—
342C22×C61C23×D411yescharacteristic
343C22×C61C23×Q811yescharacteristic
344C22×C61C22×#4111yescharacteristic
345C22×C61C22×#4111yescharacteristic
346C22×C61C22×#4111yescharacteristic
347C22×C61C2×H(5,𝔽2)11yescharacteristic
348C22×C61C2×2−1+411yescharacteristic
349C4×C61—24no—
350C4×C61—24no—
351C4×C61—24no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355Dic61—24no—
356Dic61—24no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61C2×#12318yes—
363C22×C22⋊Q8—611no—
364C22×C4×Q8—611no—
365#2423—6116no—
366C2×#399—611no—
367C2×#399—611no—
368C2×#398—611no—
369C2×#398—611no—
370C2×#391—611no—
371C2×#389—611no—
372C2×#388—611no—
373C2×#388D6111yescharacteristic
374C2×#387—611no—
375C2×#387—611no—
376C2×#384—611no—
377C2×#380—611no—
378C2×C4×C22⋊C4—611no—
379C2×C61—44no—
380C2×C61#242318yescomplemented
381C2×C61C22×#12311yescharacteristic
382C2×C61C2×#53311yescharacteristic
383C2×C61C2×#54211yescharacteristic
384C2×C61C2×D4×Q811yescharacteristic
385C2×C61C2×#55011yescharacteristic
386C2×C61C2×#55211yescharacteristic
387C2×C61C2×#55411yescharacteristic
388C23×Q8—611no—
389C24×C4—611no—
390C2×C22⋊Q8—618no—
391C2×C22⋊Q8—1228no—
392C2×C4×Q8—618no—
393C2×C4×Q8—1228no—
394C22×C4⋊C4—611no—
395C22×C4⋊C4—611no—
396C22×C4⋊C4—611no—
397C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
407C22×C22⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C22⋊C4—611no—
410C22×C22⋊C4C2×D6111yescharacteristic
411C22×C22⋊C4C2×D6111yescharacteristic
412C22×C22⋊C4C2×D6111yescharacteristic
413C22×C42—611no—
414C22×C42—611no—
415C22×C42—611no—
416C22×C42C2×D6111yescharacteristic
417#399—618no—
418#399—618no—
419#398—618no—
420#398—618no—
421#391—618no—
422#389—618no—
423#388—618no—
424#388C2×D6118yes—
425#387—618no—
426#387—618no—
427#384—618no—
428#380—618no—
429C4×C22⋊C4—618no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95C2×D6111yescharacteristic
439C2×#95C2×D6111yescharacteristic
440C61C2×#242311yescharacteristic, complemented, Sylow
441C25C22×D6111yescharacteristic
442C22×Q8—618no—
443C22×Q8—614no—
444C22×Q8—1224no—
445C22×Q8—1224no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—614no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—1224no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C22⋊Q8—12232no—
465C4×Q8—12232no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—614no—
468C2×C4⋊C4—614no—
469C2×C4⋊C4—614no—
470C2×C4⋊C4—614no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—1224no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1224no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—2442no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4—2442no—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4Dic12218yescomplemented
501C2×C22⋊C4C22×D6114yes—
502C2×C22⋊C4C22×D6114yes—
503C2×C22⋊C4C22×D6114yes—
504C2×C42—24no—
505C2×C42—614no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—1224no—
509C2×C42—1224no—
510C2×C42—1224no—
511C2×C42C22×D6114yes—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95C22×D6114yes—
521#95C22×D6114yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24C2×Dic12214yes—
529C24C23×D6112yes—
530C24C23×D6111yescharacteristic
531C2×Q8—6116no—
532C2×Q8—12232no—
533C2×Q8—1228no—
534C2×Q8—1228no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
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—614no—
551C22×C4—614no—
552C22×C4—614no—
553C22×C4—612no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—1228no—
564C22×C4—1228no—
565C22×C4—1228no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
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—24416no—
586C22×C4C2×Dic12214yes—
587C22×C4C2×Dic12214yes—
588C22×C4D4×D6114yes—
589C22×C4C23×D6112yes—
590C22×C4C23×D6112yes—
591C22×C4C23×D6112yes—
592C22×C4C23×D6112yes—
593C22×C4C23×D6112yes—
594C22×C4C23×D6112yes—
595C4⋊C4—44no—
596C4⋊C4—1228no—
597C4⋊C4—1228no—
598C4⋊C4—1228no—
599C4⋊C4—1228no—
600C4⋊C4—1228no—
601C4⋊C4—1228no—
602C4⋊C4—1228no—
603C4⋊C4—1228no—
604C4⋊C4—1228no—
605C4⋊C4—2444no—
606C4⋊C4—2444no—
607C4⋊C4—2444no—
608C22⋊C4—28no—
609C22⋊C4—44no—
610C22⋊C4—1228no—
611C22⋊C4—1228no—
612C22⋊C4—2444no—
613C22⋊C4C2×Dic122116yescomplemented
614C42—28no—
615C42—1228no—
616C42—1228no—
617C42—1228no—
618C23—28no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—28no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D6112yes—
632C23C22×Dic12214yes—
633C23C22×Dic12212yes—
634C23#41×D6112yes—
635C23#41×D6112yes—
636C23#41×D6112yes—
637C23#1451982212yes—
638C23#1451982412yes—
639C23C24×D6111yescharacteristic
640Q8—12232no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—6116no—
663C2×C4—614no—
664C2×C4—614no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—1228no—
669C2×C4—1228no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—24416no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4—2444no—
695C2×C4C2×D4×D6114yes—
696C2×C4C22×Dic12214yes—
697C2×C4C22×Dic12214yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22—42no—
706C22#123×D6114yes—
707C22#1684031514yes—
708C22#1684037614yes—
709C22D4×Dic12214yes—
710C22#1684043014yes—
711C22#1684044814yes—
712C22#1684047114yes—
713C22C22×D4×D6111yescharacteristic
714C22C23×Dic12211yescharacteristic
715C22C2×#41×D6111yescharacteristic
716C22C2×#41×D6111yescharacteristic
717C22C2×#41×D6111yescharacteristic
718C22C2×#1451982211yescharacteristic
719C22C2×#1451982411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—618no—
727C4—1224no—
728C4—1224no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C2—44no—
735C2#2144934118yesdirect product factor
736C2C2×#123×D6111yescharacteristic
737C2C2×#1684031511yescharacteristic
738C2C2×#1684037611yescharacteristic
739C2C2×D4×Dic12211yescharacteristic
740C2C2×#1684043011yescharacteristic
741C2C2×#1684044811yescharacteristic
742C2C2×#1684047111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61C2×#2423
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
3. #21449341C2direct (N × H)
6. C2×#16839695C2semidirect
7. C2×#16839694C2semidirect
8. C2×#16839666C2semidirect
9. C2×#16839659C2semidirect
11. C2×#16839649C2semidirect
12. C2×#16839646C2semidirect
13. C2×#16839631C2semidirect
22. C2×C4×Dic122C22semidirect
43. #16839695C22semidirect
44. #16839694C22semidirect
45. #16839666C22semidirect
46. #16839659C22semidirect
48. #16839649C22semidirect
49. #16839646C22semidirect
50. #16839631C22semidirect
142. C2×C22⋊C4×C61Q8semidirect
226. C22⋊C4×C61C2×Q8semidirect
380. C2×C61#2423semidirect
440. C61C2×#2423semidirect
500. C2×C22⋊C4Dic122semidirect
613. C22⋊C4C2×Dic122semidirect
735. C2#21449341direct (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×C4×Dic1222
#214493412
C2×#168396982
C2×#168396952
C2×#168396942
C2×#168396662
C2×#168396592
C2×#168396552
C2×#168396492
C2×#168396462
C2×#168396312
C2×#168396202
C2×C22⋊C4×Dic612
C2×C61×#3882
C2×#242361