Finite Group Databasebeta

← C2×#21448926 #29839687

Subgroups — C2×#21448926 #29839687

Order 15616.

3158 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2#21448926C2116yesmaximal, direct product factor
3C2×#16839667C211yesmaximal, characteristic, complemented
4C2×#16839666C211yesmaximal, characteristic, complemented
5C2×#16839656C211yesmaximal, characteristic, complemented
6C2×#16839652C211yesmaximal, characteristic, complemented
7C2×#16839651C211yesmaximal, characteristic, complemented
8C2×#16839639C211yesmaximal, characteristic
9C2×#16839638C211yesmaximal, characteristic
10C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
12C2×C4×#11758198C211yesmaximal, characteristic, complemented
13C2×#16839609C211yesmaximal, characteristic, complemented
14C2×#16839608C211yesmaximal, characteristic, complemented
15C2×#16839607C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519763C4116yescomplemented
22C2×#14519763C2218yes—
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839667C2218yescomplemented
38#16839666C2218yescomplemented
39#16839656C2218yescomplemented
40#16839652C2218yescomplemented
41#16839651C2218yescomplemented
42#16839639C2218yes—
43#16839638C2218yes—
44C22⋊C4×Dic61C2218yescomplemented
45C22⋊C4×Dic61C2218yescomplemented
46C4×#11758198C2218yescomplemented
47#16839609C2218yescomplemented
48#16839608C2218yescomplemented
49#16839607C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#388C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×Dic122—42no—
70C22×Dic122—42no—
71C22×Dic122C2×C418yescomplemented
72C22×Dic122C2314yes—
73C22×C22⋊D61—42no—
74C22×C22⋊D61—42no—
75C22×C22⋊D61C2×C418yes—
76C22×C22⋊D61C2314yes—
77C23×Dic61—24no—
78C23×Dic61—24no—
79C23×Dic61—42no—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2314yes—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—42no—
91C22×C4×D61C2314yes—
92#14519763C2×C4164yescomplemented
93C2×#11758196—42no—
94C2×#11758196C2314yes—
95C2×C22⋊Dic61—24no—
96C2×C22⋊Dic61C2×C418yescomplemented
97C2×C22⋊Dic61C2314yes—
98C2×C22⋊Dic61C2314yes—
99C2×#11758198—24no—
100C2×#11758198—24no—
101C2×#11758198—42no—
102C2×#11758198C2×C418yescomplemented
103C2×#11758198C2×C418yescomplemented
104C2×#11758198C2314yes—
105C2×#11758198C2314yes—
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×C4×Dic61—24no—
110C2×C4×Dic61—24no—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—42no—
113C2×C4×Dic61—42no—
114C2×C4×Dic61C2×C418yescomplemented
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
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×C61C2×C418yescomplemented
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×C61C22×C414yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61C22×C414yes—
166C23×D61C2412yes—
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×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61C22×C414yes—
183C22×C4×C61C22×C414yes—
184C22×C4×C61#4114yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C2×C22⋊D61—416no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—44no—
194C2×C22⋊D61C22×C4116yes—
195C22×Dic61—22no—
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×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—28no—
211C22×Dic61—28no—
212C22×Dic61—44no—
213C22×Dic61—416no—
214C22×Dic61C22×C414yes—
215C22×Dic61C22×C414yes—
216C22×Dic61C22×C414yes—
217C22×Dic61#4114yes—
218C22×Dic61#4114yes—
219C22×Dic61#4114yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—28no—
228C2×C4×D61—28no—
229C2×C4×D61—44no—
230C2×C4×D61—416no—
231C2×Dic122—416no—
232C2×Dic122—44no—
233C2×Dic122—44no—
234C2×Dic122C22×C4116yescomplemented
235C4⋊C4×C61—44no—
236C22⋊C4×C61—28no—
237C22⋊C4×C61—44no—
238C22⋊C4×C61C22×C4116yescomplemented
239C42×C61—28no—
240C22⋊Dic61—28no—
241C22⋊Dic61C22×C4116yescomplemented
242#11758198—28no—
243#11758198—28no—
244#11758198—44no—
245#11758198C22×C4116yescomplemented
246#11758198C22×C4116yescomplemented
247#11758196—44no—
248C4×Dic61—28no—
249C4×Dic61—28no—
250C4×Dic61—28no—
251C4×Dic61—44no—
252C4×Dic61—44no—
253C4×Dic61C22×C4116yescomplemented
254C23×C61—28no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61C23×C414yes—
268C23×C61C23×C412yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C61H(5,𝔽2)12yes—
274C23×C61H(5,𝔽2)12yes—
275C23×C61C2511yescharacteristic
276C22×D61—28no—
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61C23×C414yes—
290C2×C4×C61—28no—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
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—44no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61C23×C414yes—
312C2×C4×C61C23×C414yes—
313C2×C4×C61C2×#4114yes—
314C22⋊D61—416no—
315C2×Dic61—28no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—28no—
320C2×Dic61—28no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—416no—
337C2×Dic61—44no—
338C2×Dic61C23×C414yes—
339C2×Dic61C23×C414yes—
340C2×Dic61C23×C414yes—
341C2×Dic61C2×#4114yes—
342C2×Dic61C2×#4114yes—
343C2×Dic61C2×#4114yes—
344C4×D61—416no—
345Dic122—416no—
346C2×#2372—611nomaximal, Sylow
347C22×C61—24no—
348C22×C61—24no—
349C22×C61—24no—
350C22×C61—416no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61C4×#4114yes—
356C22×C61C4×#4114yes—
357C22×C61#51814yes—
358C22×C61#55114yes—
359C22×C61#55114yes—
360C22×C61#55514yes—
361C22×C61#55514yes—
362C22×C61C24×C411yescharacteristic
363C22×C61C22×#4111yescharacteristic
364C22×C61C22×#4111yescharacteristic
365C22×C61C22×#4111yescharacteristic
366C22×C61C22×#4111yescharacteristic
367C22×C61C2×H(5,𝔽2)11yescharacteristic
368C22×C61C2×H(5,𝔽2)11yescharacteristic
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—416no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—24no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383Dic61—24no—
384Dic61—24no—
385Dic61—24no—
386Dic61—24no—
387Dic61—24no—
388Dic61—24no—
389Dic61—42no—
390C22×#124—611no—
391#2372—6116no—
392C2×#391—611no—
393C2×#391—611no—
394C2×#388—611no—
395C2×#388—611no—
396C2×#388—611no—
397C2×#388D6111yescharacteristic, complemented
398C2×#386—611no—
399C2×#386—611no—
400C2×C4×C22⋊C4—611no—
401C2×C4×C22⋊C4—611no—
402C2×C4×C22⋊C4—611no—
403C2×C4×C22⋊C4—611no—
404C2×#376—611no—
405C2×#376—611no—
406C2×C61—44no—
407C2×C61#237218yescomplemented
408C2×C61C2×C4×#4111yescharacteristic
409C2×C61C2×C4×#4111yescharacteristic
410C2×C61C2×#51811yescharacteristic
411C2×C61C2×#55111yescharacteristic
412C2×C61C2×#55111yescharacteristic
413C2×C61C2×#55511yescharacteristic
414C2×C61C2×#55511yescharacteristic
415D61—44no—
416C23×Q8—611no—
417C23×D4—611no—
418C24×C4—611no—
419C24×C4—611no—
420C2×#124—6116no—
421C2×#124—618no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4C2×D6111yescharacteristic
424C22×C22⋊C4—611no—
425C22×C22⋊C4—611no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—611no—
428C22×C22⋊C4—611no—
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4C2×D6111yescharacteristic
432C22×C22⋊C4C2×D6111yescharacteristic
433C22×C22⋊C4C2×D6111yescharacteristic
434C22×C42—611no—
435C22×C42—611no—
436C22×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42—611no—
440C22×C42C2×D6111yescharacteristic
441#391—618no—
442#391—618no—
443#388—618no—
444#388—618no—
445#388—618no—
446#388C2×D6118yescomplemented
447#386—618no—
448#386—618no—
449C4×C22⋊C4—618no—
450C4×C22⋊C4—618no—
451C4×C22⋊C4—618no—
452C4×C22⋊C4—618no—
453#376—618no—
454#376—618no—
455C2×#95—611no—
456C2×#95—611no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95C2×D6111yescharacteristic
466C2×#95C2×D6111yescharacteristic
467C61C2×#237211yescharacteristic, complemented, Sylow
468C25—611no—
469C25C22×D6111yescharacteristic
470C22×Q8—618no—
471C22×Q8—614no—
472C22×Q8—2442no—
473C22×Q8—2442no—
474C22×D4—618no—
475C22×D4—614no—
476C22×D4—2442no—
477C22×D4—2442no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—614no—
486C23×C4—614no—
487C23×C4—1224no—
488C23×C4—1224no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—2442no—
492C23×C4—2442no—
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499#124—6164no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—2442no—
503C2×C4⋊C4C22×D6114yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—618no—
507C2×C22⋊C4—614no—
508C2×C22⋊C4—618no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4—614no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—2442no—
520C2×C22⋊C4C4×D6118yescomplemented
521C2×C22⋊C4C22×D6114yes—
522C2×C22⋊C4C22×D6114yes—
523C2×C22⋊C4C22×D6114yes—
524C2×C42—24no—
525C2×C42—618no—
526C2×C42—614no—
527C2×C42—614no—
528C2×C42—614no—
529C2×C42—614no—
530C2×C42—614no—
531C2×C42—614no—
532C2×C42—1224no—
533C2×C42—1224no—
534C2×C42—1224no—
535C2×C42—2442no—
536C2×C42—2442no—
537C2×C42C22×D6114yes—
538#95—614no—
539#95—614no—
540#95—614no—
541#95—614no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95C22×D6114yes—
549#95C22×D6114yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—614no—
557C24—612no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24C2×C4×D6114yes—
565C24C23×D6112yes—
566C24C23×D6111yescharacteristic
567C2×Q8—6116no—
568C2×Q8—24416no—
569C2×Q8—2444no—
570C2×Q8—2444no—
571C2×D4—6116no—
572C2×D4—24416no—
573C2×D4—2444no—
574C2×D4—2444no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—614no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—614no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—1228no—
604C22×C4—1228no—
605C22×C4—1228no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1228no—
622C22×C4—2444no—
623C22×C4—24416no—
624C22×C4—2444no—
625C22×C4—24416no—
626C22×C4C2×C4×D6114yes—
627C22×C4C2×C4×D6114yes—
628C22×C4#1175822414yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6112yes—
634C22×C4C23×D6112yes—
635C4⋊C4—44no—
636C4⋊C4—2444no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—6116no—
640C22⋊C4—6116no—
641C22⋊C4—6116no—
642C22⋊C4—1228no—
643C22⋊C4—1228no—
644C22⋊C4—1228no—
645C22⋊C4—2444no—
646C22⋊C4C2×C4×D61116yescomplemented
647C42—28no—
648C42—6116no—
649C42—1228no—
650C42—1228no—
651C42—1228no—
652C42—2444no—
653C42—2444no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—614no—
668C23—1228no—
669C23—1228no—
670C23—1228no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—2444no—
678C23—2444no—
679C23—2444no—
680C23—2444no—
681C23C22×C4×D6114yes—
682C23C22×C4×D6112yes—
683C23#41×D6112yes—
684C23#41×D6112yes—
685C23#41×D6112yes—
686C23C2×#1175822412yes—
687C23#1451982212yes—
688C23#1451982312yes—
689C23C24×D6111yescharacteristic
690Q8—24416no—
691D4—24416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—614no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—1228no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1228no—
735C2×C4—1228no—
736C2×C4—1228no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—24416no—
741C2×C4—24416no—
742C2×C4—2444no—
743C2×C4C22×C4×D6114yes—
744C2×C4C22×C4×D6114yes—
745C2×C4C2×#1175822414yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—1224no—
755C22—1224no—
756C22—1224no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—24416no—
762C22C4×#1175822414yes—
763C22#1684023014yes—
764C22#1684023414yes—
765C22#1684043514yes—
766C22#1684043714yes—
767C22#1684047414yes—
768C22#1684047614yes—
769C22C23×C4×D6111yescharacteristic
770C22C2×#41×D6111yescharacteristic
771C22C2×#41×D6111yescharacteristic
772C22C2×#41×D6111yescharacteristic
773C22C22×#1175822411yescharacteristic
774C22C2×#1451982211yescharacteristic
775C22C2×#1451982311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—1224no—
783C4—1224no—
784C4—1224no—
785C4—1224no—
786C4—1224no—
787C4—1224no—
788C4—2442no—
789C2—44no—
790C2—2444no—
791C2#2144892618yesdirect product factor
792C2C2×C4×#1175822411yescharacteristic
793C2C2×#1684023011yescharacteristic
794C2C2×#1684023411yescharacteristic
795C2C2×#1684043511yescharacteristic
796C2C2×#1684043711yescharacteristic
797C2C2×#1684047411yescharacteristic
798C2C2×#1684047611yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2372
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448926C2direct (N × H)
3. C2×#16839667C2semidirect
4. C2×#16839666C2semidirect
5. C2×#16839656C2semidirect
6. C2×#16839652C2semidirect
7. C2×#16839651C2semidirect
10. C2×C22⋊C4×Dic61C2semidirect
11. C2×C22⋊C4×Dic61C2semidirect
12. C2×C4×#11758198C2semidirect
13. C2×#16839609C2semidirect
14. C2×#16839608C2semidirect
15. C2×#16839607C2semidirect
16. C2×C61×#388C2semidirect
21. C2×#14519763C4semidirect
37. #16839667C22semidirect
38. #16839666C22semidirect
39. #16839656C22semidirect
40. #16839652C22semidirect
41. #16839651C22semidirect
44. C22⋊C4×Dic61C22semidirect
45. C22⋊C4×Dic61C22semidirect
46. C4×#11758198C22semidirect
47. #16839609C22semidirect
48. #16839608C22semidirect
49. #16839607C22semidirect
65. C61×#388C22semidirect
71. C22×Dic122C2×C4semidirect
92. #14519763C2×C4semidirect
96. C2×C22⋊Dic61C2×C4semidirect
102. C2×#11758198C2×C4semidirect
103. C2×#11758198C2×C4semidirect
114. C2×C4×Dic61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
234. C2×Dic122C22×C4semidirect
238. C22⋊C4×C61C22×C4semidirect
241. C22⋊Dic61C22×C4semidirect
245. #11758198C22×C4semidirect
246. #11758198C22×C4semidirect
253. C4×Dic61C22×C4semidirect
397. C2×#388D61semidirect
407. C2×C61#2372semidirect
446. #388C2×D61semidirect
467. C61C2×#2372semidirect
520. C2×C22⋊C4C4×D61semidirect
646. C22⋊C4C2×C4×D61semidirect
791. C2#21448926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
#214489262
C2×#168396672
C2×#168396662
C2×#168396562
C2×#168396522
C2×#168396512
C2×#168396392
C2×#168396382
C2×C22⋊C4×Dic612
C2×C4×#117581982
C2×#168396092
C2×#168396082
C2×#168396072
C2×C61×#3882
C2×#237261