Finite Group Databasebeta

← #29601449

Subgroups — #29601449

Order 15616.

1838 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839631C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic
3C2×C4⋊C4×Dic61C211yesmaximal, characteristic
4C2×C4×#11758196C211yesmaximal, characteristic
5C2×C4×C4⋊Dic61C211yesmaximal, characteristic
6C2×#16839613C212yesmaximal
7#21444054C212yesmaximal
8#21444050C212yesmaximal
9#21444048C211yesmaximal, characteristic
10#21444047C212yesmaximal
11C61×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758196C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×#11758196C2211yescharacteristic
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839631C418yescomplemented
24C4⋊C4×Dic61—24no—
25C4⋊C4×Dic61C418yescomplemented
26C4×#11758196C418yescomplemented
27C4×C4⋊Dic61—24no—
28#16839613—28no—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61C2×C414yes—
50C2×C4⋊Dic61C2×C414yes—
51C2×C4⋊Dic61D414yes—
52C2×C4⋊Dic61Q814yes—
53C2×#11758196—24no—
54C2×#11758196—22no—
55C2×#11758196—22no—
56C2×#11758196—24no—
57C2×#11758196—42no—
58C2×#11758196—42no—
59C2×#11758196C2×C414yes—
60C2×#11758196C2×C418yes—
61C2×#11758196C2×C418yes—
62C2×#11758196C2×C414yes—
63C2×#11758196D414yes—
64C2×#11758196Q814yes—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—24no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—24no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—42no—
74C2×C4×Dic61—42no—
75C2×C4×Dic61C2×C414yes—
76C2×C4×Dic61C2×C418yes—
77C2×C4×Dic61C2×C414yes—
78C2×C4×Dic61C2×C414yes—
79C2×C4×Dic61C2×C414yes—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—42no—
84#14519684C2×C414yes—
85#14519684C2×C414yes—
86#14519684C2×C418yes—
87C23×C4×C61C2312yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61C2×C414yes—
97C2×C4⋊C4×C61C2×C414yes—
98C2×C42×C61—22no—
99C2×C42×C61—22no—
100C2×C42×C61C2×C414yes—
101#95×C61—24no—
102#95×C61—42no—
103C24×C61C2411yescharacteristic
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C414yes—
128C22×C4×C61C22×C414yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C412yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×Q812yes—
136C22×C4×C61C2×Q812yes—
137C22×C4×C61#4112yes—
138C22×C4×C61#4112yes—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—22no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C414yes—
165C22×Dic61C22×C412yes—
166C22×Dic61C22×C412yes—
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C414yes—
170C22×Dic61C22×C412yes—
171C22×Dic61C22×C412yes—
172C22×Dic61C22×C412yes—
173C22×Dic61C2×D412yes—
174C22×Dic61C2×D414yes—
175C22×Dic61C2×D412yes—
176C22×Dic61C2×Q812yes—
177C22×Dic61C2×Q814yes—
178C22×Dic61C2×Q812yes—
179C22×Dic61#4112yes—
180C22×Dic61#4112yes—
181C4⋊C4×C61—28no—
182C4⋊C4×C61—28no—
183C42×C61—28no—
184C4⋊Dic61—28no—
185C4⋊Dic61C4⋊C4116yescomplemented
186#11758196—28no—
187#11758196—216no—
188#11758196—48no—
189#11758196C4⋊C4116yescomplemented
190C4×Dic61—28no—
191C4×Dic61—216no—
192C4×Dic61—48no—
193C4×Dic61—48no—
194C4×Dic61C42116yescomplemented
195C23×C61C23×C411yescharacteristic
196C23×C61C23×C411yescharacteristic
197C23×C61C23×C411yescharacteristic
198C23×C61C22×D411yescharacteristic
199C23×C61C22×D411yescharacteristic
200C23×C61C22×Q811yescharacteristic
201C23×C61C22×Q811yescharacteristic
202C23×C61C2×#4111yescharacteristic
203C23×C61C2×#4111yescharacteristic
204C23×C61C2×#4111yescharacteristic
205C23×C61C2×#4111yescharacteristic
206C23×C61H(5,𝔽2)11yescharacteristic
207C23×C61H(5,𝔽2)11yescharacteristic
208C23×C612−1+411yescharacteristic
209C23×C612−1+411yescharacteristic
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—22no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C4214yes—
238C2×C4×C61C2×C4⋊C414yes—
239C2×C4×C61C2×C4⋊C414yes—
240C2×C4×C61#11714yes—
241C2×C4×C61C4×D414yes—
242C2×C4×C61C4×D414yes—
243C2×C4×C61C4×Q814yes—
244C2×C4×C61C4×Q814yes—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—24no—
257C2×Dic61—22no—
258C2×Dic61—24no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—22no—
269C2×Dic61—42no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61C2×C4214yes—
278C2×Dic61C2×C4214yes—
279C2×Dic61C2×C4⋊C414yes—
280C2×Dic61C2×C4⋊C418yes—
281C2×Dic61C2×C4⋊C414yes—
282C2×Dic61#11714yes—
283C2×Dic61C4×D414yes—
284C2×Dic61C4×D414yes—
285C2×Dic61C4×Q814yes—
286C2×Dic61C4×Q814yes—
287C4⋊C42—611nomaximal, Sylow
288C22×C61C22×C4211yescharacteristic
289C22×C61C22×C4⋊C411yescharacteristic
290C22×C61C22×C4⋊C411yescharacteristic
291C22×C61C2×#11711yescharacteristic
292C22×C61C2×#11711yescharacteristic
293C22×C61C2×C4×D411yescharacteristic
294C22×C61C2×C4×D411yescharacteristic
295C22×C61C2×C4×D411yescharacteristic
296C22×C61C2×C4×D411yescharacteristic
297C22×C61C2×C4×Q811yescharacteristic
298C22×C61C2×C4×Q811yescharacteristic
299C22×C61C2×C4×Q811yescharacteristic
300C22×C61C2×C4×Q811yescharacteristic
301C22×C61#51811yescharacteristic
302C22×C61#51911yescharacteristic
303C22×C61#52011yescharacteristic
304C22×C61#52011yescharacteristic
305C22×C61#52011yescharacteristic
306C22×C61#52011yescharacteristic
307C22×C61D4211yescharacteristic
308C22×C61#54711yescharacteristic
309C22×C61#54711yescharacteristic
310C22×C61D4×Q811yescharacteristic
311C22×C61D4×Q811yescharacteristic
312C22×C61#55011yescharacteristic
313C22×C61#55011yescharacteristic
314C22×C61#55411yescharacteristic
315C22×C61#55411yescharacteristic
316C22×C61#55511yescharacteristic
317C22×C61#55611yescharacteristic
318C22×C61#55611yescharacteristic
319C22×C61#55711yescharacteristic
320C22×C61#55711yescharacteristic
321C22×C61Q8211yescharacteristic
322C22×C61#55911yescharacteristic
323C4×C61—24no—
324C4×C61—42no—
325C4×C61—44no—
326C4×C61—44no—
327C4×C61C4×C4⋊C418yescomplemented
328Dic61—24no—
329Dic61—28no—
330Dic61—24no—
331Dic61—42no—
332Dic61—44no—
333Dic61C4×C4⋊C418yescomplemented
334C2×#384—611no—
335C2×C4×C4⋊C4—611no—
336C2×C4×C4⋊C4—611no—
337C2×C4×C4⋊C4—612no—
338C2×C4×C4⋊C4—611no—
339C2×C4×C4⋊C4—611no—
340#1436—612no—
341#1436—612no—
342C4⋊#95—612no—
343C4⋊#95—611no—
344C4⋊#95D6111yescharacteristic
345C2×C61C2×C4×C4⋊C411yescharacteristic
346C2×C61C2×C4×C4⋊C411yescharacteristic
347C2×C61#227411yescharacteristic
348C2×C61D4×C4⋊C411yescharacteristic
349C2×C61D4×C4⋊C411yescharacteristic
350C2×C61Q8×C4⋊C411yescharacteristic
351C2×C61Q8×C4⋊C411yescharacteristic
352C2×C61#235411yescharacteristic
353C2×C61#235411yescharacteristic
354C2×C61#235511yescharacteristic
355C2×C61#235511yescharacteristic
356C2×C61#236511yescharacteristic
357C2×C61#236511yescharacteristic
358C2×C61#236611yescharacteristic
359C2×C61#236911yescharacteristic
360C22×C4⋊C4—611no—
361C22×C4⋊C4—611no—
362C22×C4⋊C4—611no—
363C22×C4⋊C4—612no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—612no—
366C22×C4⋊C4C2×D6111yescharacteristic
367C22×C4⋊C4C2×D6111yescharacteristic
368C22×C42—611no—
369C22×C42—612no—
370C22×C42—611no—
371C22×C42—612no—
372C22×C42—612no—
373C22×C42C2×D6111yescharacteristic
374#384—618no—
375C4×C4⋊C4—618no—
376C4×C4⋊C4—618no—
377C4×C4⋊C4—1228no—
378C4×C4⋊C4—1224no—
379C4×C4⋊C4—1224no—
380C2×#95—611no—
381C2×#95—612no—
382C2×#95—611no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95—612no—
386C2×#95—612no—
387C2×#95C2×D6112yes—
388C2×#95C2×D6112yes—
389C61C4⋊C4211yescharacteristic, complemented, Sylow
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—612no—
393C23×C4—611no—
394C23×C4—612no—
395C23×C4—611no—
396C23×C4C22×D6112yes—
397C23×C4C22×D6111yescharacteristic
398C23×C4C22×D6112yes—
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—614no—
406C2×C4⋊C4—614no—
407C2×C4⋊C4—614no—
408C2×C4⋊C4—614no—
409C2×C4⋊C4—614no—
410C2×C4⋊C4—614no—
411C2×C4⋊C4—614no—
412C2×C4⋊C4—618no—
413C2×C4⋊C4—614no—
414C2×C4⋊C4—618no—
415C2×C4⋊C4—1224no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1224no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—2442no—
422C2×C4⋊C4—2442no—
423C2×C4⋊C4C4×D6114yes—
424C2×C4⋊C4C4×D6114yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—614no—
428C2×C42—614no—
429C2×C42—614no—
430C2×C42—618no—
431C2×C42—614no—
432C2×C42—1224no—
433C2×C42—1224no—
434C2×C42—1222no—
435C2×C42—1222no—
436C2×C42—1224no—
437C2×C42—1224no—
438C2×C42—1224no—
439C2×C42—1224no—
440C2×C42—2442no—
441C2×C42—2442no—
442C2×C42C4×D6114yes—
443#95—24no—
444#95—42no—
445#95—618no—
446#95—614no—
447#95—614no—
448#95—1224no—
449#95—1224no—
450#95—1224no—
451#95—2442no—
452C24C23×D6111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—614no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—614no—
489C22×C4—614no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—614no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1222no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1222no—
505C22×C4—1221no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1222no—
511C22×C4—1221no—
512C22×C4—1222no—
513C22×C4—1221no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1221no—
517C22×C4C2×C4×D6114yes—
518C22×C4C2×C4×D6112yes—
519C22×C4C2×C4×D6114yes—
520C22×C4C2×C4×D6112yes—
521C22×C4C2×C4×D6112yes—
522C22×C4C2×C4×D6112yes—
523C22×C4C2×C4×D6112yes—
524C22×C4D4×D6112yes—
525C22×C4D4×D6112yes—
526C22×C4#1175822412yes—
527C22×C4#1175822412yes—
528C22×C4Q8×D6112yes—
529C22×C4Q8×D6112yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—6116no—
533C4⋊C4—6116no—
534C4⋊C4—1228no—
535C4⋊C4—12216no—
536C4⋊C4—1228no—
537C4⋊C4—2448no—
538C42—28no—
539C42—6116no—
540C42—12216no—
541C42—1228no—
542C42—2448no—
543C42—2448no—
544C23C22×C4×D6111yescharacteristic
545C23C22×C4×D6111yescharacteristic
546C23C22×C4×D6111yescharacteristic
547C23C2×D4×D6111yescharacteristic
548C23C2×D4×D6111yescharacteristic
549C23C2×Q8×D6111yescharacteristic
550C23C2×Q8×D6111yescharacteristic
551C23#41×D6111yescharacteristic
552C23#41×D6111yescharacteristic
553C23C2×#1175822411yescharacteristic
554C23C2×#1175822411yescharacteristic
555C23#1451982211yescharacteristic
556C23#1451982311yescharacteristic
557C23#1451982411yescharacteristic
558C23#1451982511yescharacteristic
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—614no—
587C2×C4—614no—
588C2×C4—614no—
589C2×C4—614no—
590C2×C4—614no—
591C2×C4—614no—
592C2×C4—614no—
593C2×C4—614no—
594C2×C4—614no—
595C2×C4—618no—
596C2×C4—1224no—
597C2×C4—1222no—
598C2×C4—1224no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1224no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1224no—
610C2×C4—1222no—
611C2×C4—1224no—
612C2×C4—1222no—
613C2×C4—1224no—
614C2×C4—1222no—
615C2×C4—1224no—
616C2×C4—1222no—
617C2×C4—1224no—
618C2×C4—1224no—
619C2×C4—1222no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4C42×D6114yes—
629C2×C4C4⋊C4×D6114yes—
630C2×C4C4⋊C4×D6114yes—
631C2×C4#1451973314yes—
632C2×C4#1451973714yes—
633C2×C4#1451973714yes—
634C2×C4#1451974214yes—
635C2×C4#1451974214yes—
636C22C2×C42×D6111yescharacteristic
637C22C2×C4⋊C4×D6111yescharacteristic
638C22C2×C4⋊C4×D6111yescharacteristic
639C22#117×D6111yescharacteristic
640C22C2×#1451973311yescharacteristic
641C22C4×D4×D6111yescharacteristic
642C22C4×D4×D6111yescharacteristic
643C22C2×#1451973711yescharacteristic
644C22C2×#1451973711yescharacteristic
645C22C4×Q8×D6111yescharacteristic
646C22C4×Q8×D6111yescharacteristic
647C22C2×#1451974211yescharacteristic
648C22C2×#1451974211yescharacteristic
649C22#1684023411yescharacteristic
650C22#1684023811yescharacteristic
651C22#1684024111yescharacteristic
652C22#1684024211yescharacteristic
653C22#1684024311yescharacteristic
654C22#1684024411yescharacteristic
655C22#1684039611yescharacteristic
656C22#1684041211yescharacteristic
657C22#1684041411yescharacteristic
658C22#1684042511yescharacteristic
659C22#1684042711yescharacteristic
660C22#1684043011yescharacteristic
661C22#1684043211yescharacteristic
662C22#1684046811yescharacteristic
663C22#1684047011yescharacteristic
664C22#1684047611yescharacteristic
665C22#1684048111yescharacteristic
666C22#1684048311yescharacteristic
667C22#1684048711yescharacteristic
668C22#1684048911yescharacteristic
669C22#1684049211yescharacteristic
670C22#1684049411yescharacteristic
671C4—24no—
672C4—42no—
673C4—44no—
674C4—44no—
675C4—618no—
676C4—1224no—
677C4—1228no—
678C4—1224no—
679C4—2442no—
680C4—2444no—
681C4#1683961318yescomplemented
682C2C4×C4⋊C4×D6111yescharacteristic
683C2C2×#1683961311yescharacteristic
684C2#2144817311yescharacteristic
685C2#2144871511yescharacteristic
686C2#2144872011yescharacteristic
687C2#2144873111yescharacteristic
688C2#2144873311yescharacteristic
689C2#2144876311yescharacteristic
690C2#2144876711yescharacteristic
691C2#2144877111yescharacteristic
692C2#2144877511yescharacteristic
693C2#2144887211yescharacteristic
694C2#2144887611yescharacteristic
695C2#2144888011yescharacteristic
696C2#2144890511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C4⋊#95C2
socle, prime radical, cosocleC24×C61C24
hypercenterC4⋊#95D61
hypocenterC61C4⋊C42
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
23. #16839631C4semidirect
25. C4⋊C4×Dic61C4semidirect
26. C4×#11758196C4semidirect
185. C4⋊Dic61C4⋊C4semidirect
189. #11758196C4⋊C4semidirect
194. C4×Dic61C42semidirect
327. C4×C61C4×C4⋊C4semidirect
333. Dic61C4×C4⋊C4semidirect
389. C61C4⋊C42semidirect
681. C4#16839613semidirect

Maximal subgroups

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

subgroupindex
C2×#168396312
C2×C4⋊C4×Dic612
C2×C4×#117581962
C2×C4×C4⋊Dic612
C2×#168396132
#214440542
#214440502
#214440482
#214440472
C61×C4⋊#952
C4⋊C4261