Finite Group Databasebeta

← #29608447

Subgroups — #29608447

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839661C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic
3C2×#16839637C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic
5#21444084C211yesmaximal, characteristic, complemented
6#21444076C211yesmaximal, characteristic, complemented
7#21444076C211yesmaximal, characteristic, complemented
8#21444072C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic
10#21444064C211yesmaximal, characteristic
11#21444053C211yesmaximal, characteristic, complemented
12#21444049C211yesmaximal, characteristic, complemented
13#21444049C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic
15C2×C61×#388C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839661—24no—
29#16839655—24no—
30#16839637—24no—
31#16839637—24no—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C22×C4⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C61×#388C418yescomplemented
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—41no—
60C23×Dic61—41no—
61C23×Dic61—41no—
62C23×Dic61—41no—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61—41no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61—41no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61—41no—
91C2×C4⋊Dic61D414yes—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61—41no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—41no—
104#14519684—22no—
105#14519684—22no—
106#14519684—22no—
107#14519684—22no—
108#14519684—22no—
109#14519684—22no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—41no—
114#14519684—41no—
115#14519684—41no—
116#14519684—41no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120C25×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61C2×C414yescomplemented
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61—41no—
134C2×C22⋊C4×C61C2×C414yes—
135C2×C22⋊C4×C61C2×C414yes—
136C2×C22⋊C4×C61C2×C414yes—
137C2×C22⋊C4×C61D414yes—
138C2×C22⋊C4×C61Q814yes—
139C2×C42×C61—41no—
140C2×C42×C61—41no—
141C2×C42×C61C2×C414yescomplemented
142#95×C61C2×C414yescomplemented
143#95×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C22×C412yes—
157C24×C61C2×D412yes—
158C24×C61C2×Q812yes—
159C24×C61C2411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C412yes—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C22×C412yes—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2×Q812yes—
200C22×C4×C61C2×Q812yes—
201C22×C4×C61#4112yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—44no—
255C22×Dic61—44no—
256C22×Dic61—44no—
257C22×Dic61—44no—
258C22×Dic61—44no—
259C22×Dic61—44no—
260C22×Dic61—44no—
261C22×Dic61C2×D412yes—
262C22×Dic61C2×D412yes—
263C22×Dic61#4112yes—
264C22×Dic61#4112yes—
265C4⋊C4×C61—28no—
266C22⋊C4×C61—28no—
267C22⋊C4×C61—44no—
268C22⋊C4×C61C4⋊C4116yescomplemented
269C42×C61—44no—
270C22⋊Dic61—44no—
271C22⋊Dic61—44no—
272C22⋊Dic61—44no—
273C4⋊Dic61—44no—
274C4⋊Dic61—44no—
275C4⋊Dic61—44no—
276C4⋊Dic61—44no—
277C4⋊Dic61—44no—
278C4⋊Dic61—44no—
279C4⋊Dic61—44no—
280C4×Dic61—44no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61C2×C4⋊C414yes—
316C23×C61C23×C411yescharacteristic
317C23×C61C22×D411yescharacteristic
318C23×C61C22×D411yescharacteristic
319C23×C61C22×Q811yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C612−1+411yescharacteristic
329C23×C612−1+411yescharacteristic
330C23×C612−1+411yescharacteristic
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61C2×C4⋊C414yes—
371C2×C4×C61C2×C4⋊C414yes—
372C2×C4×C61C4×D414yes—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—416no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430#14442—611nomaximal, Sylow
431C22×C61—24no—
432C22×C61—24no—
433C22×C61—24no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61C22×C4⋊C411yescharacteristic
447C22×C61C2×C4×D411yescharacteristic
448C22×C61C4×#4111yescharacteristic
449C22×C61#51811yescharacteristic
450C22×C61#52011yescharacteristic
451C22×C61#52011yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61#53411yescharacteristic
454C22×C61#53511yescharacteristic
455C22×C61#53611yescharacteristic
456C22×C61#53711yescharacteristic
457C22×C61#53811yescharacteristic
458C22×C61#53811yescharacteristic
459C22×C61#53911yescharacteristic
460C22×C61#53911yescharacteristic
461C22×C61#54111yescharacteristic
462C22×C61#54211yescharacteristic
463C22×C61#54411yescharacteristic
464C22×C61#54411yescharacteristic
465C22×C61D4211yescharacteristic
466C22×C61#54611yescharacteristic
467C22×C61#54611yescharacteristic
468C22×C61#54611yescharacteristic
469C22×C61#54711yescharacteristic
470C22×C61#54811yescharacteristic
471C22×C61D4×Q811yescharacteristic
472C22×C61#55411yescharacteristic
473C22×C61#55411yescharacteristic
474C22×C61#55411yescharacteristic
475C22×C61#55611yescharacteristic
476C22×C61#55911yescharacteristic
477C22×C61#56011yescharacteristic
478C22×C61#56211yescharacteristic
479C22×C61#56211yescharacteristic
480C22×C61#56311yescharacteristic
481C4×C61—24no—
482C4×C61—24no—
483C4×C61—24no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61—42no—
487Dic61—42no—
488Dic61—42no—
489Dic61—42no—
490Dic61—42no—
491Dic61—81no—
492Dic61—81no—
493Dic61—81no—
494Dic61—81no—
495C2×#389—611no—
496C2×#388—611no—
497C2×#388D6111yescharacteristic
498C2×#385—611no—
499C2×#385—611no—
500#1444—611no—
501#1442—611no—
502#1442—611no—
503#1441—611no—
504#1439—611no—
505#1439—611no—
506#1436—611no—
507C4⋊#95—611no—
508C4⋊#95—611no—
509C22⋊#95—611no—
510C2×C61—44no—
511C2×C61#231711yescharacteristic
512C2×C61#232511yescharacteristic
513C2×C61#233411yescharacteristic
514C2×C61D4×C4⋊C411yescharacteristic
515C2×C61#234911yescharacteristic
516C2×C61#236711yescharacteristic
517C2×C61#237611yescharacteristic
518C2×C61#267811yescharacteristic
519C2×C61#268111yescharacteristic
520C2×C61#268911yescharacteristic
521C2×C61#270411yescharacteristic
522C2×C61#271011yescharacteristic
523C2×C61#272911yescharacteristic
524C2×C61#278811yescharacteristic
525C2×C61#280711yescharacteristic
526C24×C4—611no—
527C22×C4⋊C4—611no—
528C22×C4⋊C4—611no—
529C22×C4⋊C4—611no—
530C22×C4⋊C4—611no—
531C22×C4⋊C4—611no—
532C22×C4⋊C4—611no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4C2×D6111yescharacteristic
535C22×C22⋊C4—611no—
536C22×C22⋊C4—611no—
537C22×C22⋊C4—611no—
538C22×C22⋊C4C2×D6111yescharacteristic
539C22×C22⋊C4C2×D6111yescharacteristic
540C22×C22⋊C4C2×D6111yescharacteristic
541C22×C42—611no—
542C22×C42C2×D6111yescharacteristic
543#389—1224no—
544#388—1224no—
545#388Dic6118yescomplemented
546#385—1224no—
547#385—1224no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95C2×D6111yescharacteristic
565C2×#95C2×D6111yescharacteristic
566C61#1444211yescharacteristic, complemented, Sylow
567C25C22×D6111yescharacteristic
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—1222no—
577C23×C4—1222no—
578C23×C4—1222no—
579C23×C4—2441no—
580C23×C4—2441no—
581C23×C4—2441no—
582C23×C4—2441no—
583C23×C4C22×D6111yescharacteristic
584C23×C4C22×D6111yescharacteristic
585C23×C4C22×D6111yescharacteristic
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588C23×C4C22×D6111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—614no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—2441no—
603C2×C4⋊C4—2441no—
604C2×C4⋊C4—2441no—
605C2×C4⋊C4—2441no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4—2441no—
608C2×C4⋊C4—2441no—
609C2×C4⋊C4—2441no—
610C2×C4⋊C4—2441no—
611C2×C4⋊C4—2441no—
612C2×C4⋊C4C2×Dic6114yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—1222no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—2441no—
623C2×C22⋊C4—2441no—
624C2×C22⋊C4—2441no—
625C2×C22⋊C4—2441no—
626C2×C22⋊C4Dic12214yes—
627C2×C22⋊C4D24414yes—
628C2×C22⋊C4C2×Dic6114yes—
629C2×C22⋊C4C2×Dic6114yes—
630C2×C22⋊C4C2×Dic6114yes—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—1222no—
634C2×C42—1222no—
635C2×C42—2441no—
636C2×C42C2×Dic6114yescomplemented
637#95—1222no—
638#95—1222no—
639#95—1222no—
640#95—1222no—
641#95—1222no—
642#95—1222no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—2441no—
647#95—2441no—
648#95—2441no—
649#95—2441no—
650#95—2441no—
651#95—2441no—
652#95—2441no—
653#95C2×Dic6114yescomplemented
654#95C2×Dic6114yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic12212yes—
668C24C2×D24412yes—
669C24C22×Dic6112yes—
670C24C23×D6111yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—2444no—
758C22×C4—2444no—
759C22×C4—2444no—
760C22×C4—2444no—
761C22×C4—2444no—
762C22×C4—2444no—
763C22×C4—2444no—
764C22×C4C2×Dic12212yes—
765C22×C4C2×Dic12212yes—
766C22×C4C2×D24412yes—
767C22×C4C2×D24412yes—
768C22×C4D4×D6112yes—
769C22×C4#1175822412yes—
770C22×C4C22×Dic6112yes—
771C22×C4C22×Dic6112yes—
772C22×C4C22×Dic6112yes—
773C22×C4C22×Dic6112yes—
774C22×C4C22×Dic6112yes—
775C22×C4C22×Dic6112yes—
776C4⋊C4—28no—
777C4⋊C4—2444no—
778C4⋊C4—2444no—
779C4⋊C4—2444no—
780C4⋊C4—2444no—
781C4⋊C4—2444no—
782C4⋊C4—2444no—
783C4⋊C4—2444no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—2444no—
787C22⋊C4—2444no—
788C22⋊C4—2444no—
789C22⋊C4C4⋊Dic61116yescomplemented
790C42—44no—
791C42—2444no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic6114yes—
827C23C23×Dic6111yescharacteristic
828C23C2×D4×D6111yescharacteristic
829C23C22×D24411yescharacteristic
830C23C22×Dic12211yescharacteristic
831C23#41×D6111yescharacteristic
832C23#41×D6111yescharacteristic
833C23C2×#1175822411yescharacteristic
834C23#1451982211yescharacteristic
835C23#1451982211yescharacteristic
836C23#1451982311yescharacteristic
837C23#1451982311yescharacteristic
838C23#1451982311yescharacteristic
839C23#1451982411yescharacteristic
840C23#1451982411yescharacteristic
841C23#1451982411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—24416no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C2×C4⋊Dic6114yes—
939C2×C4C2×C4⋊Dic6114yes—
940C2×C4D4×Dic6114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic6111yescharacteristic
957C22C2×D4×Dic6111yescharacteristic
958C22#41×Dic6111yescharacteristic
959C22#1684023711yescharacteristic
960C22#1684024511yescharacteristic
961C22#1684024511yescharacteristic
962C22#1684024511yescharacteristic
963C22#1684032011yescharacteristic
964C22#1684033111yescharacteristic
965C22#1684033811yescharacteristic
966C22#1684033911yescharacteristic
967C22#1684034911yescharacteristic
968C22#1684035111yescharacteristic
969C22#1684035311yescharacteristic
970C22#1684035711yescharacteristic
971C22#1684036911yescharacteristic
972C22#1684037811yescharacteristic
973C22#1684039011yescharacteristic
974C22#1684039011yescharacteristic
975C22D4×D24411yescharacteristic
976C22#1684040511yescharacteristic
977C22#1684040711yescharacteristic
978C22#1684040711yescharacteristic
979C22#1684041611yescharacteristic
980C22#1684042011yescharacteristic
981C22D4×Dic12211yescharacteristic
982C22#1684046911yescharacteristic
983C22#1684047111yescharacteristic
984C22#1684047111yescharacteristic
985C22#1684048111yescharacteristic
986C22#1684049411yescharacteristic
987C22#1684050211yescharacteristic
988C22#1684050911yescharacteristic
989C22#1684050911yescharacteristic
990C22#1684051511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—4881no—
998C4—4881no—
999C4—4881no—
1000C4—4881no—
1001C4—2442no—
1002C4—2442no—
1003C4—2442no—
1004C4—2442no—
1005C2—44no—
1006C2#2144844211yescharacteristic
1007C2#2144852411yescharacteristic
1008C2#2144859811yescharacteristic
1009C2D4×C4⋊Dic6111yescharacteristic
1010C2#2144872911yescharacteristic
1011C2#2144889411yescharacteristic
1012C2#2144896711yescharacteristic
1013C2#2145214211yescharacteristic
1014C2#2145216911yescharacteristic
1015C2#2145226811yescharacteristic
1016C2#2145247411yescharacteristic
1017C2#2145255911yescharacteristic
1018C2#2145279811yescharacteristic
1019C2#2145356211yescharacteristic
1020C2#2145378611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#14442
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16839661C2semidirect
5. #21444084C2semidirect
6. #21444076C2semidirect
7. #21444076C2semidirect
8. #21444072C2semidirect
11. #21444053C2semidirect
12. #21444049C2semidirect
13. #21444049C2semidirect
53. C61×#388C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C42×C61C2×C4semidirect
142. #95×C61C2×C4semidirect
143. #95×C61C2×C4semidirect
268. C22⋊C4×C61C4⋊C4semidirect
545. #388Dic61semidirect
566. C61#14442semidirect
612. C2×C4⋊C4C2×Dic61semidirect
636. C2×C42C2×Dic61semidirect
653. #95C2×Dic61semidirect
654. #95C2×Dic61semidirect
789. C22⋊C4C4⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×#168396552
C2×#168396372
#214440842
#214440762
#214440722
#214440642
#214440532
#214440492
#214440412
C2×C61×#3882
#1444261