Finite Group Databasebeta

← #29603224

Subgroups — #29603224

Order 15616.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839661C211yesmaximal, characteristic, complemented
2C2×#16839637C211yesmaximal, characteristic
3C2×#16839637C211yesmaximal, characteristic
4C2×#16839622C211yesmaximal, characteristic
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic
6C22×#14519684C211yesmaximal, characteristic
7#21444084C211yesmaximal, characteristic, complemented
8#21444076C211yesmaximal, characteristic, complemented
9#21444072C211yesmaximal, characteristic, complemented
10#21444072C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444048C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic
15C2×C61×#385C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C24×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×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839661—24no—
29#16839637—24no—
30#16839637—24no—
31#16839622—24no—
32C22⋊C4×Dic61—24no—
33C2×#14519684—24no—
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
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C24×C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#385C418yescomplemented
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—22no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61—41no—
71C23×Dic61Q814yes—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61—41no—
96C2×C4⋊Dic61—41no—
97C2×C4⋊Dic61—41no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61D414yes—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61—41no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—41no—
124#14519684—41no—
125#14519684D414yes—
126C25×C61C2311yescharacteristic
127C23×C4×C61—22no—
128C23×C4×C61—22no—
129C23×C4×C61—22no—
130C23×C4×C61—22no—
131C23×C4×C61—41no—
132C23×C4×C61—41no—
133C23×C4×C61C2×C414yes—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—41no—
143C2×C4⋊C4×C61—41no—
144C2×C4⋊C4×C61C2×C414yescomplemented
145C2×C4⋊C4×C61C2×C414yescomplemented
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61C2×C414yes—
149C2×C22⋊C4×C61C2×C414yes—
150C2×C22⋊C4×C61D414yes—
151C2×C22⋊C4×C61Q814yes—
152#95×C61C2×C414yescomplemented
153#95×C61C2×C414yescomplemented
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61C22×C412yes—
163C24×C61C2×D412yes—
164C24×C61C2×D412yes—
165C24×C61C2×Q812yes—
166C24×C61C2×Q812yes—
167C24×C61#4112yes—
168C24×C61#4112yes—
169C24×C61C2411yescharacteristic
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—28no—
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×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—28no—
202C22×C4×C61—44no—
203C22×C4×C61—44no—
204C22×C4×C61—44no—
205C22×C4×C61—44no—
206C22×C4×C61—44no—
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C412yes—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×Q812yes—
217C22×C4×C61C2×Q812yes—
218C22×C4×C61#4112yes—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—28no—
224C22×Dic61—28no—
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—21no—
255C22×Dic61—28no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—44no—
271C22×Dic61—44no—
272C22×Dic61—44no—
273C22×Dic61—44no—
274C22×Dic61—44no—
275C22×Dic61—44no—
276C22×Dic61—44no—
277C22×Dic61—44no—
278C22×Dic61—44no—
279C22×Dic61—44no—
280C22×Dic61—44no—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×Q812yes—
286C22×Dic61C2×Q812yes—
287C22×Dic61#4112yes—
288C22×Dic61#4112yes—
289C4⋊C4×C61—28no—
290C4⋊C4×C61—44no—
291C22⋊C4×C61—28no—
292C22⋊C4×C61C4⋊C4116yescomplemented
293C22⋊Dic61—28no—
294C22⋊Dic61—44no—
295C4⋊Dic61—44no—
296C4⋊Dic61—44no—
297C4⋊Dic61—44no—
298C4⋊Dic61—44no—
299C4⋊Dic61—44no—
300C4⋊Dic61—44no—
301C4×Dic61—44no—
302C4×Dic61—44no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61C2×C4⋊C414yes—
332C23×C61C4×D414yes—
333C23×C61C4×Q814yes—
334C23×C61#12114yes—
335C23×C61C22⋊Q814yes—
336C23×C61#12514yes—
337C23×C61C4⋊Q814yes—
338C23×C61C23×C411yescharacteristic
339C23×C61C22×D411yescharacteristic
340C23×C61C22×D411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×Q811yescharacteristic
343C23×C61C22×Q811yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C612−1+411yescharacteristic
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—416no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61C2×C4⋊C414yes—
394C2×C4×C61C2×C4⋊C414yes—
395C2×C4×C61C4×D414yes—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—416no—
418C2×Dic61—416no—
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—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61C22⋊Q814yes—
454#14004—611nomaximal, Sylow
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—24no—
459C22×C61—24no—
460C22×C61—24no—
461C22×C61—24no—
462C22×C61—24no—
463C22×C61—24no—
464C22×C61—24no—
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—24no—
468C22×C61—24no—
469C22×C61#38918yescomplemented
470C22×C61C22×C4⋊C411yescharacteristic
471C22×C61C2×C4×D411yescharacteristic
472C22×C61C2×C4×D411yescharacteristic
473C22×C61C2×C4×Q811yescharacteristic
474C22×C61C4×#4111yescharacteristic
475C22×C61#51811yescharacteristic
476C22×C61#52011yescharacteristic
477C22×C61C2×#12111yescharacteristic
478C22×C61C2×C22⋊Q811yescharacteristic
479C22×C61C2×C22⋊Q811yescharacteristic
480C22×C61#52511yescharacteristic
481C22×C61C2×#12511yescharacteristic
482C22×C61#52911yescharacteristic
483C22×C61C2×C4⋊Q811yescharacteristic
484C22×C61#53311yescharacteristic
485C22×C61#53811yescharacteristic
486C22×C61#53911yescharacteristic
487C22×C61#54311yescharacteristic
488C22×C61#54411yescharacteristic
489C22×C61D4211yescharacteristic
490C22×C61D4211yescharacteristic
491C22×C61#54611yescharacteristic
492C22×C61#54611yescharacteristic
493C22×C61#54611yescharacteristic
494C22×C61#54611yescharacteristic
495C22×C61#54611yescharacteristic
496C22×C61#54711yescharacteristic
497C22×C61#54711yescharacteristic
498C22×C61D4×Q811yescharacteristic
499C22×C61#55111yescharacteristic
500C22×C61#55111yescharacteristic
501C22×C61#55211yescharacteristic
502C22×C61#55411yescharacteristic
503C22×C61#55411yescharacteristic
504C22×C61#55411yescharacteristic
505C4×C61—24no—
506C4×C61—24no—
507C4×C61—24no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61—42no—
511Dic61—24no—
512Dic61—42no—
513Dic61—42no—
514Dic61—42no—
515Dic61—42no—
516Dic61—42no—
517Dic61—81no—
518Dic61—81no—
519C2×#389—611no—
520C2×#385—611no—
521C2×#385—611no—
522C2×#385D6111yescharacteristic
523C2×#380—611no—
524C2×C4×C22⋊C4—611no—
525C22×#95—611no—
526#1444—611no—
527#1442—611no—
528#1441—611no—
529#1441—611no—
530#1436—611no—
531#1436—611no—
532C4⋊#95—611no—
533C22⋊#95—611no—
534C2×C61—28no—
535C2×C61C2×#38911yescharacteristic
536C2×C61C4×C22⋊Q811yescharacteristic
537C2×C61#232911yescharacteristic
538C2×C61D4×C4⋊C411yescharacteristic
539C2×C61#234911yescharacteristic
540C2×C61#235811yescharacteristic
541C2×C61#235911yescharacteristic
542C2×C61#242411yescharacteristic
543C2×C61#242511yescharacteristic
544C2×C61#243711yescharacteristic
545C2×C61#243811yescharacteristic
546C2×C61#244011yescharacteristic
547C2×C61#247311yescharacteristic
548C2×C61#250511yescharacteristic
549C2×C61#254911yescharacteristic
550C24×C4—611no—
551C24×C4—611no—
552C24×C4C2×D6111yescharacteristic
553C22×C4⋊C4—611no—
554C22×C4⋊C4—611no—
555C22×C4⋊C4—611no—
556C22×C4⋊C4—611no—
557C22×C4⋊C4—611no—
558C22×C4⋊C4—611no—
559C22×C4⋊C4C2×D6111yescharacteristic
560C22×C4⋊C4C2×D6111yescharacteristic
561C22×C22⋊C4—611no—
562C22×C22⋊C4—611no—
563C22×C22⋊C4C2×D6111yescharacteristic
564C22×C22⋊C4C2×D6111yescharacteristic
565C22×C42—611no—
566C22×C42—611no—
567#389—1224no—
568#385—1224no—
569#385—1224no—
570#385Dic6118yescomplemented
571#380—1224no—
572C4×C22⋊C4—1224no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C2×#95—611no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95—611no—
583C2×#95—611no—
584C2×#95—611no—
585C2×#95—611no—
586C2×#95—611no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—1224no—
590C2×#95C2×D6111yescharacteristic
591C2×#95C2×D6111yescharacteristic
592C61#1400411yescharacteristic, complemented, Sylow
593C25C22×D6111yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—611no—
606C23×C4—614no—
607C23×C4—611no—
608C23×C4—611no—
609C23×C4—1222no—
610C23×C4—1222no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—1222no—
614C23×C4—1222no—
615C23×C4—1222no—
616C23×C4—1222no—
617C23×C4—1222no—
618C23×C4—2441no—
619C23×C4—2441no—
620C23×C4—2441no—
621C23×C4—2441no—
622C23×C4C2×Dic6114yes—
623C23×C4C22×D6111yescharacteristic
624C23×C4C22×D6111yescharacteristic
625C23×C4C22×D6111yescharacteristic
626C23×C4C22×D6111yescharacteristic
627C23×C4C22×D6111yescharacteristic
628C23×C4C22×D6111yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—1222no—
634C2×C4⋊C4—1222no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4—1222no—
637C2×C4⋊C4—1222no—
638C2×C4⋊C4—1222no—
639C2×C4⋊C4—1222no—
640C2×C4⋊C4—1222no—
641C2×C4⋊C4—1222no—
642C2×C4⋊C4—1222no—
643C2×C4⋊C4—1222no—
644C2×C4⋊C4—1222no—
645C2×C4⋊C4—2441no—
646C2×C4⋊C4—2441no—
647C2×C4⋊C4—2441no—
648C2×C4⋊C4—2441no—
649C2×C4⋊C4—2441no—
650C2×C4⋊C4—2441no—
651C2×C4⋊C4C2×Dic6114yescomplemented
652C2×C4⋊C4C2×Dic6114yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—614no—
656C2×C22⋊C4—1222no—
657C2×C22⋊C4—1222no—
658C2×C22⋊C4—1222no—
659C2×C22⋊C4—1222no—
660C2×C22⋊C4—1222no—
661C2×C22⋊C4Dic12214yes—
662C2×C22⋊C4D24414yes—
663C2×C22⋊C4C2×Dic6114yes—
664C2×C22⋊C4C2×Dic6114yes—
665C2×C42—1222no—
666C2×C42—1222no—
667C2×C42—1222no—
668C2×C42—1222no—
669C2×C42—2441no—
670C2×C42—2441no—
671#95—614no—
672#95—1222no—
673#95—1222no—
674#95—1222no—
675#95—1222no—
676#95—1222no—
677#95—1222no—
678#95—1222no—
679#95—1222no—
680#95—1222no—
681#95—1222no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—2441no—
686#95—2441no—
687#95C2×Dic6114yescomplemented
688#95C2×Dic6114yescomplemented
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic12212yes—
698C24C2×D24412yes—
699C24D4×D6112yes—
700C24#1175822412yes—
701C24Q8×D6112yes—
702C24#1175822612yes—
703C24C22×Dic6112yes—
704C24C23×D6111yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—612no—
745C22×C4—612no—
746C22×C4—612no—
747C22×C4—612no—
748C22×C4—612no—
749C22×C4—612no—
750C22×C4—1228no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1228no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1228no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—2444no—
802C22×C4—2444no—
803C22×C4—2444no—
804C22×C4—2444no—
805C22×C4—2444no—
806C22×C4—2444no—
807C22×C4—2444no—
808C22×C4—2444no—
809C22×C4—2444no—
810C22×C4—2444no—
811C22×C4—2444no—
812C22×C4C2×Dic12212yes—
813C22×C4C2×Dic12212yes—
814C22×C4C2×D24412yes—
815C22×C4C2×D24412yes—
816C22×C4D4×D6112yes—
817C22×C4#1175822412yes—
818C22×C4C22×Dic6112yes—
819C22×C4C22×Dic6112yes—
820C22×C4C22×Dic6112yes—
821C22×C4C22×Dic6112yes—
822C22×C4C22×Dic6112yes—
823C22×C4C22×Dic6112yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—2444no—
827C4⋊C4—2444no—
828C4⋊C4—2444no—
829C4⋊C4—2444no—
830C4⋊C4—2444no—
831C4⋊C4—2444no—
832C22⋊C4—28no—
833C22⋊C4—1228no—
834C22⋊C4—2444no—
835C22⋊C4C4⋊Dic61116yescomplemented
836C42—2444no—
837C42—2444no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊Dic6114yes—
867C23D4×Dic6114yes—
868C23Q8×Dic6114yes—
869C23#1451975214yes—
870C23#1451975714yes—
871C23#1451976814yes—
872C23#1451977614yes—
873C23C23×Dic6111yescharacteristic
874C23C2×D4×D6111yescharacteristic
875C23C2×D4×D6111yescharacteristic
876C23C22×D24411yescharacteristic
877C23C2×Q8×D6111yescharacteristic
878C23C22×Dic12211yescharacteristic
879C23#41×D6111yescharacteristic
880C23#41×D6111yescharacteristic
881C23C2×#1175822411yescharacteristic
882C23C2×#1175822411yescharacteristic
883C23C2×#1175822611yescharacteristic
884C23#1451982211yescharacteristic
885C23#1451982211yescharacteristic
886C23#1451982311yescharacteristic
887C23#1451982411yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—614no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—24416no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2441no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2441no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4—24416no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4C2×C4⋊Dic6114yes—
987C2×C4C2×C4⋊Dic6114yes—
988C2×C4D4×Dic6114yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1683966118yescomplemented
1004C22C22×C4⋊Dic6111yescharacteristic
1005C22C2×D4×Dic6111yescharacteristic
1006C22C2×D4×Dic6111yescharacteristic
1007C22C2×Q8×Dic6111yescharacteristic
1008C22#41×Dic6111yescharacteristic
1009C22#1684023711yescharacteristic
1010C22#1684024511yescharacteristic
1011C22C2×#1451975211yescharacteristic
1012C22C22⋊Q8×D6111yescharacteristic
1013C22C2×#1451975711yescharacteristic
1014C22#1684027511yescharacteristic
1015C22C2×#1451976811yescharacteristic
1016C22#1684029811yescharacteristic
1017C22C2×#1451977611yescharacteristic
1018C22#1684031411yescharacteristic
1019C22#1684035211yescharacteristic
1020C22#1684036111yescharacteristic
1021C22#1684038711yescharacteristic
1022C22#1684039111yescharacteristic
1023C22#1684039411yescharacteristic
1024C22D4×D24411yescharacteristic
1025C22#1684039911yescharacteristic
1026C22#1684039911yescharacteristic
1027C22#1684040411yescharacteristic
1028C22#1684040711yescharacteristic
1029C22#1684040711yescharacteristic
1030C22#1684041011yescharacteristic
1031C22#1684041611yescharacteristic
1032C22D4×Dic12211yescharacteristic
1033C22#1684043511yescharacteristic
1034C22#1684044311yescharacteristic
1035C22#1684044911yescharacteristic
1036C22#1684046911yescharacteristic
1037C22#1684047111yescharacteristic
1038C22#1684047111yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—1224no—
1046C4—4881no—
1047C4—4881no—
1048C4—2442no—
1049C4—2442no—
1050C4—2442no—
1051C4—2442no—
1052C4—2442no—
1053C2—28no—
1054C2C2×#1683966111yescharacteristic
1055C2C22⋊Q8×Dic6111yescharacteristic
1056C2#2144855411yescharacteristic
1057C2D4×C4⋊Dic6111yescharacteristic
1058C2#2144872911yescharacteristic
1059C2#2144880311yescharacteristic
1060C2#2144881511yescharacteristic
1061C2#2144935311yescharacteristic
1062C2#2144936811yescharacteristic
1063C2#2144948311yescharacteristic
1064C2#2144949311yescharacteristic
1065C2#2144952011yescharacteristic
1066C2#2144996711yescharacteristic
1067C2#2145032411yescharacteristic
1068C2#2145083211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61#14004
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16839661C2semidirect
7. #21444084C2semidirect
8. #21444076C2semidirect
9. #21444072C2semidirect
10. #21444072C2semidirect
11. #21444053C2semidirect
12. #21444053C2semidirect
13. #21444048C2semidirect
55. C61×#385C4semidirect
144. C2×C4⋊C4×C61C2×C4semidirect
145. C2×C4⋊C4×C61C2×C4semidirect
152. #95×C61C2×C4semidirect
153. #95×C61C2×C4semidirect
292. C22⋊C4×C61C4⋊C4semidirect
469. C22×C61#389semidirect
570. #385Dic61semidirect
592. C61#14004semidirect
651. C2×C4⋊C4C2×Dic61semidirect
652. C2×C4⋊C4C2×Dic61semidirect
687. #95C2×Dic61semidirect
688. #95C2×Dic61semidirect
835. C22⋊C4C4⋊Dic61semidirect
1003. C22#16839661semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×#168396372
C2×#168396222
C2×C22⋊C4×Dic612
C22×#145196842
#214440842
#214440762
#214440722
#214440532
#214440482
#214440412
C2×C61×#3852
#1400461