Finite Group Databasebeta

← C2×#21448927 #29839688

Subgroups — C2×#21448927 #29839688

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#21448927C2116yesmaximal, direct product factor
3C2×#16839668C211yesmaximal, characteristic, complemented
4C2×#16839666C211yesmaximal, characteristic, complemented
5C2×#16839655C211yesmaximal, characteristic, complemented
6C2×#16839654C211yesmaximal, characteristic, complemented
7C2×#16839653C211yesmaximal, characteristic, complemented
8C2×#16839650C211yesmaximal, characteristic, complemented
9C2×#16839641C211yesmaximal, characteristic
10C2×#16839638C211yesmaximal, characteristic
11C2×C4×#11758198C211yesmaximal, characteristic, complemented
12C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
13C2×#16839609C211yesmaximal, characteristic, complemented
14C2×#16839608C211yesmaximal, characteristic, complemented
15C2×#16839607C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519763C4116yescomplemented
21C2×#14519763C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839668C2218yescomplemented
38#16839666C2218yescomplemented
39#16839655C2218yescomplemented
40#16839654C2218yescomplemented
41#16839653C2218yescomplemented
42#16839650C2218yescomplemented
43#16839641C2218yes—
44#16839638C2218yes—
45C4×#11758198C2218yescomplemented
46C4×C22⋊Dic61C2218yescomplemented
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
60C24×C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C4×C22⋊C4×C61C2218yescomplemented
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×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C22×C4×D61—24no—
85C22×C4×D61—24no—
86C22×C4×D61—42no—
87C22×C4×D61C2314yes—
88#14519763C2×C4164yescomplemented
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—42no—
92C2×#11758196C2314yes—
93C2×C22⋊Dic61—24no—
94C2×C22⋊Dic61—42no—
95C2×C22⋊Dic61C2×C418yescomplemented
96C2×C22⋊Dic61C2314yes—
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×Dic61C2×C418yescomplemented
114C2×C4×Dic61C2314yes—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129C25×C61C2311yescharacteristic
130C23×C4×C61—24no—
131C23×C4×C61—24no—
132C23×C4×C61—42no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2314yes—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—24no—
141C2×C22⋊C4×C61C2×C418yescomplemented
142C2×C22⋊C4×C61C2314yes—
143C2×C22⋊C4×C61C2314yes—
144C2×C42×C61—24no—
145C2×C42×C61—42no—
146C2×C42×C61C2314yes—
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—28no—
181C22×C4×C61—28no—
182C22×C4×C61—44no—
183C22×C4×C61—416no—
184C22×C4×C61C22×C414yes—
185C22×C4×C61C22×C414yes—
186C22×C4×C61#4114yes—
187C22×C4×C61#4114yes—
188C22×C4×C61#4114yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C2×C22⋊D61—416no—
196C2×C22⋊D61—44no—
197C2×C22⋊D61—44no—
198C2×C22⋊D61C22×C4116yes—
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—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C414yes—
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
235C22⋊C4×C61—28no—
236C22⋊C4×C61C22×C4116yescomplemented
237C42×C61—28no—
238C42×C61—44no—
239C22⋊Dic61—28no—
240C22⋊Dic61—44no—
241C22⋊Dic61C22×C4116yescomplemented
242#11758198—28no—
243#11758198—28no—
244#11758198—44no—
245#11758198C22×C4116yescomplemented
246#11758198C22×C4116yescomplemented
247C4⋊Dic61—44no—
248#11758196—44no—
249C4×Dic61—28no—
250C4×Dic61—28no—
251C4×Dic61—28no—
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—28no—
294C2×C4×C61—28no—
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—416no—
309C2×C4×C61—44no—
310C2×C4×C61C23×C414yes—
311C2×C4×C61C23×C414yes—
312C2×C4×C61C2×#4114yes—
313C2×C4×C61C2×#4114yes—
314C2×C4×C61C2×#4114yes—
315C22⋊D61—416no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—28no—
320C2×Dic61—22no—
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—22no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61C23×C414yes—
341C2×Dic61C23×C414yes—
342C2×Dic61C23×C414yes—
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—24no—
381C4×C61—24no—
382C4×C61—42no—
383Dic61—24no—
384Dic61—24no—
385Dic61—24no—
386Dic61—24no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C22×#124—611no—
391#2372—6116no—
392C2×#391—611no—
393C2×#391—611no—
394C2×#388—611no—
395C2×#388—611no—
396C2×#388—611no—
397C2×#388—611no—
398C2×#386—611no—
399C2×#386—611no—
400C2×C4×C22⋊C4—611no—
401C2×C4×C22⋊C4—611no—
402C2×C4×C22⋊C4—611no—
403C2×C4×C22⋊C4D6111yescharacteristic, complemented
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×C4C2×D6111yescharacteristic
420C2×#124—6116no—
421C2×#124—618no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
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⋊C4—611no—
432C22×C22⋊C4C2×D6111yescharacteristic
433C22×C22⋊C4C2×D6111yescharacteristic
434C22×C42—611no—
435C22×C42—611no—
436C22×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42C2×D6111yescharacteristic
440C22×C42C2×D6111yescharacteristic
441#391—618no—
442#391—618no—
443#388—618no—
444#388—618no—
445#388—618no—
446#388—618no—
447#386—618no—
448#386—618no—
449C4×C22⋊C4—618no—
450C4×C22⋊C4—618no—
451C4×C22⋊C4—618no—
452C4×C22⋊C4C2×D6118yescomplemented
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—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—614no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—2442no—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6114yes—
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499#124—6164no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—2442no—
503C2×C4⋊C4—2442no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—618no—
506C2×C22⋊C4—614no—
507C2×C22⋊C4—618no—
508C2×C22⋊C4—618no—
509C2×C22⋊C4—614no—
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⋊C4—2442no—
521C2×C22⋊C4C4×D6118yescomplemented
522C2×C22⋊C4C22×D6114yes—
523C2×C22⋊C4C22×D6114yes—
524C2×C42—24no—
525C2×C42—42no—
526C2×C42—618no—
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×C42C22×D6114yes—
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—28no—
589C22×C4—28no—
590C22×C4—44no—
591C22×C4—416no—
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—1222no—
605C22×C4—1222no—
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×C4C2×C4×D6114yes—
625C22×C4C2×C4×D6114yes—
626C22×C4#1175822214yes—
627C22×C4#1175822214yes—
628C22×C4#1175822414yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6112yes—
634C22×C4C23×D6112yes—
635C4⋊C4—2444no—
636C4⋊C4—2444no—
637C22⋊C4—28no—
638C22⋊C4—6116no—
639C22⋊C4—6116no—
640C22⋊C4—6116no—
641C22⋊C4—1228no—
642C22⋊C4—1228no—
643C22⋊C4—1228no—
644C22⋊C4—2444no—
645C22⋊C4—2444no—
646C22⋊C4C2×C4×D61116yescomplemented
647C42—28no—
648C42—44no—
649C42—6116no—
650C42—1228no—
651C42—1228no—
652C42—1228no—
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—
684C23C2×#1175822412yes—
685C23C2×#1175822212yes—
686C23C2×#1175822212yes—
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—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—614no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—614no—
716C2×C4—1228no—
717C2×C4—1228no—
718C2×C4—1228no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1228no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—24416no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4C22×C4×D6114yes—
742C2×C4C22×C4×D6114yes—
743C2×C4C2×#1175822414yes—
744C2×C4C2×#1175822214yes—
745C2×C4C2×#1175822214yes—
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—
763C22C4×#1175822214yes—
764C22#1684023414yes—
765C22#1684043814yes—
766C22#1684044114yes—
767C22#1684047514yes—
768C22#1684047714yes—
769C22C23×C4×D6111yescharacteristic
770C22C2×#41×D6111yescharacteristic
771C22C22×#1175822411yescharacteristic
772C22C22×#1175822211yescharacteristic
773C22C22×#1175822211yescharacteristic
774C22C2×#1451982211yescharacteristic
775C22C2×#1451982311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—24no—
781C4—42no—
782C4—1224no—
783C4—1224no—
784C4—1224no—
785C4—1224no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C2—44no—
790C2—2444no—
791C2#2144892718yesdirect product factor
792C2C2×C4×#1175822411yescharacteristic
793C2C2×C4×#1175822211yescharacteristic
794C2C2×#1684023411yescharacteristic
795C2C2×#1684043811yescharacteristic
796C2C2×#1684044111yescharacteristic
797C2C2×#1684047511yescharacteristic
798C2C2×#1684047711yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2372
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21448927C2direct (N × H)
3. C2×#16839668C2semidirect
4. C2×#16839666C2semidirect
5. C2×#16839655C2semidirect
6. C2×#16839654C2semidirect
7. C2×#16839653C2semidirect
8. C2×#16839650C2semidirect
11. C2×C4×#11758198C2semidirect
12. C2×C4×C22⋊Dic61C2semidirect
13. C2×#16839609C2semidirect
14. C2×#16839608C2semidirect
15. C2×#16839607C2semidirect
16. C2×C4×C22⋊C4×C61C2semidirect
20. C2×#14519763C4semidirect
37. #16839668C22semidirect
38. #16839666C22semidirect
39. #16839655C22semidirect
40. #16839654C22semidirect
41. #16839653C22semidirect
42. #16839650C22semidirect
45. C4×#11758198C22semidirect
46. C4×C22⋊Dic61C22semidirect
47. #16839609C22semidirect
48. #16839608C22semidirect
49. #16839607C22semidirect
65. C4×C22⋊C4×C61C22semidirect
71. C22×Dic122C2×C4semidirect
88. #14519763C2×C4semidirect
95. C2×C22⋊Dic61C2×C4semidirect
102. C2×#11758198C2×C4semidirect
103. C2×#11758198C2×C4semidirect
113. C2×C4×Dic61C2×C4semidirect
141. C2×C22⋊C4×C61C2×C4semidirect
234. C2×Dic122C22×C4semidirect
236. C22⋊C4×C61C22×C4semidirect
241. C22⋊Dic61C22×C4semidirect
245. #11758198C22×C4semidirect
246. #11758198C22×C4semidirect
253. C4×Dic61C22×C4semidirect
403. C2×C4×C22⋊C4D61semidirect
407. C2×C61#2372semidirect
452. C4×C22⋊C4C2×D61semidirect
467. C61C2×#2372semidirect
521. C2×C22⋊C4C4×D61semidirect
646. C22⋊C4C2×C4×D61semidirect
791. C2#21448927direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
#214489272
C2×#168396682
C2×#168396662
C2×#168396552
C2×#168396542
C2×#168396532
C2×#168396502
C2×#168396412
C2×#168396382
C2×C4×#117581982
C2×C4×C22⋊Dic612
C2×#168396092
C2×#168396082
C2×#168396072
C2×C4×C22⋊C4×C612
C2×#237261