Finite Group Databasebeta

← #29601960

Subgroups — #29601960

Order 15616.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839650C212yesmaximal
2C2×#16839631C211yesmaximal, characteristic, complemented
3C2×#16839622C211yesmaximal, characteristic
4C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic
6#21444074C212yesmaximal, complemented
7#21444062C212yesmaximal
8#21444050C212yesmaximal, complemented
9#21444048C211yesmaximal, characteristic, complemented
10#21444048C211yesmaximal, characteristic, complemented
11C2×C61×#380C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758196C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839650—28no—
23#16839631—24no—
24#16839622—24no—
25C4⋊C4×Dic61—24no—
26C4×C22⋊Dic61C418yescomplemented
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C24×C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2212yes—
39C61×#380—24no—
40C2×#95×C61C2212yes—
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2311yescharacteristic
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61D414yes—
53C2×#11758196—24no—
54C2×#11758196—24no—
55C2×#11758196—24no—
56C2×#11758196—24no—
57C2×#11758196—42no—
58C2×#11758196—42no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—42no—
64C2×C22⋊Dic61C2×C414yes—
65C2×C22⋊Dic61C2×C414yes—
66C2×C22⋊Dic61D414yes—
67C2×C22⋊Dic61Q814yes—
68C2×C4×Dic61—22no—
69C2×C4×Dic61—22no—
70C2×C4×Dic61—22no—
71C2×C4×Dic61—22no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—42no—
75C2×C4×Dic61C2×C414yes—
76C2×C4×Dic61C2×C414yes—
77#14519684—24no—
78#14519684—24no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82#14519684—42no—
83#14519684C2×C414yes—
84#14519684C2×C414yes—
85C25×C61C2311yescharacteristic
86C23×C4×C61—22no—
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—22no—
91C23×C4×C61—22no—
92C23×C4×C61C2×C414yes—
93C23×C4×C61C2312yes—
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61D414yes—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—42no—
106#95×C61—24no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61C22×C412yes—
120C24×C61C2×D412yes—
121C24×C61C2×Q812yes—
122C24×C61C2411yescharacteristic
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—28no—
136C22×C4×C61—28no—
137C22×C4×C61—28no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—44no—
146C22×C4×C61—44no—
147C22×C4×C61—44no—
148C22×C4×C61—44no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D414yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61#4112yes—
155C22×C4×C61#4112yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61C22×C412yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C2×D414yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61C2×Q812yes—
197C22×Dic61C2×Q812yes—
198C22×Dic61#4112yes—
199C22×Dic61#4112yes—
200C4⋊C4×C61—28no—
201C4⋊C4×C61—44no—
202C22⋊C4×C61—48no—
203C22⋊Dic61—28no—
204C22⋊Dic61—48no—
205C22⋊Dic61C4⋊C4116yescomplemented
206C4⋊Dic61—28no—
207C4⋊Dic61—44no—
208#11758196—48no—
209#11758196—48no—
210C4×Dic61—28no—
211C4×Dic61—28no—
212C4×Dic61—48no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C2×C4⋊C414yes—
248C23×C61C23×C411yescharacteristic
249C23×C61C22×D411yescharacteristic
250C23×C61C22×D411yescharacteristic
251C23×C61C22×D411yescharacteristic
252C23×C61C22×Q811yescharacteristic
253C23×C61C2×#4111yescharacteristic
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61H(5,𝔽2)11yescharacteristic
260C23×C61H(5,𝔽2)11yescharacteristic
261C23×C612−1+411yescharacteristic
262C23×C612−1+411yescharacteristic
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—24no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—416no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61#11714yes—
286C2×C4×C61C4×D414yes—
287C2×C4×C61C4×D414yes—
288C2×C4×C61#12114yes—
289C2×C4×C61#12314yes—
290C2×C4×C61#12414yes—
291C2×C4×C61#12614yes—
292C2×Dic61—22no—
293C2×Dic61—22no—
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—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—42no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61C2×C4⋊C414yes—
332C2×Dic61C2×C4⋊C414yes—
333C2×Dic61#11714yes—
334#13876—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61C22×C4⋊C411yescharacteristic
351C22×C61C2×#11711yescharacteristic
352C22×C61C2×#11711yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×C4×D411yescharacteristic
355C22×C61#52011yescharacteristic
356C22×C61#52011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12311yescharacteristic
359C22×C61C2×#12411yescharacteristic
360C22×C61C2×#12611yescharacteristic
361C22×C61#53211yescharacteristic
362C22×C61#53211yescharacteristic
363C22×C61#53311yescharacteristic
364C22×C61#53311yescharacteristic
365C22×C61#54011yescharacteristic
366C22×C61#54111yescharacteristic
367C22×C61#54211yescharacteristic
368C22×C61#54211yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61D4211yescharacteristic
371C22×C61#54611yescharacteristic
372C22×C61#54711yescharacteristic
373C22×C61#54711yescharacteristic
374C22×C61#54711yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61D4×Q811yescharacteristic
377C22×C61D4×Q811yescharacteristic
378C22×C61#55011yescharacteristic
379C22×C61#55211yescharacteristic
380C22×C61#55311yescharacteristic
381C22×C61#55411yescharacteristic
382C22×C61#55411yescharacteristic
383C22×C61#55511yescharacteristic
384C22×C61#55611yescharacteristic
385C4×C61—44no—
386C4×C61—42no—
387C4×C61—82no—
388C4×C61#38818yescomplemented
389Dic61—24no—
390Dic61—24no—
391Dic61—24no—
392Dic61—42no—
393Dic61—44no—
394Dic61—82no—
395C2×#388—612no—
396C2×#384—611no—
397C2×#380—611no—
398C2×#380D6111yescharacteristic
399C2×C4×C4⋊C4—611no—
400C2×C4×C22⋊C4—611no—
401#1442—612no—
402#1439—612no—
403#1436—612no—
404C4⋊#95—611no—
405C4⋊#95—611no—
406C2×C61—44no—
407C2×C61#228511yescharacteristic
408C2×C61C2×#38811yescharacteristic
409C2×C61#231411yescharacteristic
410C2×C61D4×C4⋊C411yescharacteristic
411C2×C61D4×C4⋊C411yescharacteristic
412C2×C61#235211yescharacteristic
413C2×C61#235411yescharacteristic
414C2×C61#242211yescharacteristic
415C2×C61#242311yescharacteristic
416C2×C61#242811yescharacteristic
417C2×C61#242911yescharacteristic
418C2×C61#249111yescharacteristic
419C2×C61#249211yescharacteristic
420C2×C61#249611yescharacteristic
421C2×C61#249711yescharacteristic
422C24×C4C2×D6111yescharacteristic
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—612no—
426C22×C4⋊C4—612no—
427C22×C4⋊C4C2×D6111yescharacteristic
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4C2×D6112yes—
433C22×C42—611no—
434C22×C42—611no—
435C22×C42—612no—
436#388—1228no—
437#384—1224no—
438#380—24no—
439#380—1224no—
440C4×C4⋊C4—1224no—
441C4×C22⋊C4—618no—
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95C2×D6112yes—
451C61#1387611yescharacteristic, complemented, Sylow
452C25C22×D6111yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—612no—
463C23×C4—611no—
464C23×C4—612no—
465C23×C4C4×D6114yes—
466C23×C4C22×D6112yes—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6112yes—
469C23×C4C22×D6111yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1222no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—1224no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4C22⋊D6114yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—2442no—
500C2×C42—614no—
501C2×C42—614no—
502C2×C42—1222no—
503C2×C42—1222no—
504C2×C42—1222no—
505C2×C42—1222no—
506C2×C42—1224no—
507C2×C42—1224no—
508C2×C42—2442no—
509#95—24no—
510#95—614no—
511#95—614no—
512#95—1224no—
513#95—1224no—
514#95—1224no—
515#95—1224no—
516#95—1224no—
517#95—2442no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×C4×D6112yes—
531C24D4×D6112yes—
532C24Q8×D6112yes—
533C24C23×D6111yescharacteristic
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—614no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1222no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4C2×C4×D6112yes—
603C22×C4C2×C4×D6112yes—
604C22×C4#1175822212yes—
605C22×C4D4×D6112yes—
606C22×C4#1175822412yes—
607C22×C4#1175822412yes—
608C22×C4#1175822412yes—
609C22×C4C2×C22⋊D6114yes—
610C22×C4C2×C22⋊D6112yes—
611C4⋊C4—28no—
612C4⋊C4—44no—
613C4⋊C4—1228no—
614C4⋊C4—2448no—
615C4⋊C4—2448no—
616C4⋊C4—2444no—
617C22⋊C4—48no—
618C22⋊C4—6116no—
619C22⋊C4—1228no—
620C22⋊C4—2448no—
621C42—1228no—
622C42—1228no—
623C42—2448no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4⋊C4×D6114yes—
659C23C22×C4×D6111yescharacteristic
660C23C2×D4×D6111yescharacteristic
661C23C2×D4×D6111yescharacteristic
662C23C22×C22⋊D6111yescharacteristic
663C23C2×Q8×D6111yescharacteristic
664C23#41×D6111yescharacteristic
665C23#41×D6111yescharacteristic
666C23C2×#1175822411yescharacteristic
667C23C2×#1175822411yescharacteristic
668C23C2×#1175822411yescharacteristic
669C23C2×#1175822211yescharacteristic
670C23#1451982211yescharacteristic
671C23#1451982311yescharacteristic
672C23#1451982411yescharacteristic
673C23#1451982511yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—614no—
697C2×C4—614no—
698C2×C4—614no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2442no—
738C2×C4#1451973314yes—
739C2×C4#1451973714yes—
740C2×C4C4×C22⋊D6114yes—
741C2×C4#1451974814yes—
742C2×C4#1451975814yes—
743C2×C4#1451976314yes—
744C2×C4#1451977014yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×C4⋊C4×D6111yescharacteristic
761C22#117×D6111yescharacteristic
762C22C2×#1451973311yescharacteristic
763C22C2×#1451973711yescharacteristic
764C22C2×C4×C22⋊D6111yescharacteristic
765C22#1684024211yescharacteristic
766C22#1684024311yescharacteristic
767C22C2×#1451974811yescharacteristic
768C22C2×#1451975811yescharacteristic
769C22C2×#1451976311yescharacteristic
770C22C2×#1451977011yescharacteristic
771C22#1684030711yescharacteristic
772C22#1684030711yescharacteristic
773C22#1684031411yescharacteristic
774C22#1684031411yescharacteristic
775C22#1684036511yescharacteristic
776C22#1684037211yescharacteristic
777C22#1684037911yescharacteristic
778C22#1684038511yescharacteristic
779C22D4×C22⋊D6111yescharacteristic
780C22#1684039611yescharacteristic
781C22#1684040911yescharacteristic
782C22#1684041111yescharacteristic
783C22#1684041211yescharacteristic
784C22#1684041311yescharacteristic
785C22#1684042211yescharacteristic
786C22#1684042511yescharacteristic
787C22Q8×C22⋊D6111yescharacteristic
788C22#1684043111yescharacteristic
789C22#1684044611yescharacteristic
790C22#1684045911yescharacteristic
791C22#1684046711yescharacteristic
792C22#1684047011yescharacteristic
793C22#1684047511yescharacteristic
794C22#1684048011yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—1224no—
799C4—1224no—
800C4—1224no—
801C4—4882no—
802C4—2442no—
803C4—2444no—
804C4#1683965018yescomplemented
805C2—44no—
806C2#2144822111yescharacteristic
807C2C2×#1683965011yescharacteristic
808C2#2144842611yescharacteristic
809C2#2144871511yescharacteristic
810C2C4⋊C4×C22⋊D6111yescharacteristic
811C2#2144874111yescharacteristic
812C2#2144876911yescharacteristic
813C2#2144932911yescharacteristic
814C2#2144934011yescharacteristic
815C2#2144940311yescharacteristic
816C2#2144941411yescharacteristic
817C2#2145017811yescharacteristic
818C2#2145018911yescharacteristic
819C2#2145023711yescharacteristic
820C2#2145024811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#380C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#380D61
hypocenterC61#13876
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#16839631C2semidirect
4. C2×C4⋊C4×Dic61C2semidirect
6. #21444074C2semidirect
8. #21444050C2semidirect
9. #21444048C2semidirect
10. #21444048C2semidirect
26. C4×C22⋊Dic61C4semidirect
205. C22⋊Dic61C4⋊C4semidirect
388. C4×C61#388semidirect
451. C61#13876semidirect
804. C4#16839650semidirect

Maximal subgroups

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

subgroupindex
C2×#168396502
C2×#168396312
C2×#168396222
C2×C4⋊C4×Dic612
C2×C4×C22⋊Dic612
#214440742
#214440622
#214440502
#214440482
C2×C61×#3802
#1387661