Finite Group Databasebeta

← #29608030

Subgroups — #29608030

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×#16839655C211yesmaximal, characteristic
4C2×#16839622C211yesmaximal, characteristic
5#21444084C211yesmaximal, characteristic, complemented
6#21444076C211yesmaximal, characteristic, complemented
7#21444072C211yesmaximal, characteristic, complemented
8#21444072C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic
10#21444064C211yesmaximal, characteristic
11#21444053C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444048C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic
15C2×C61×#385C211yesmaximal, characteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839661—24no—
29#16839655—24no—
30#16839655—24no—
31#16839622—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
48C24×C4×C61C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C61×#385C418yescomplemented
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61—41no—
74C2×C4⋊Dic61—41no—
75C2×C4⋊Dic61—41no—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61—41no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61—41no—
81C2×C4⋊Dic61D414yes—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61—41no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—41no—
99C2×C4×Dic61—41no—
100#14519684—22no—
101#14519684—22no—
102#14519684—22no—
103#14519684—22no—
104#14519684—22no—
105#14519684—22no—
106#14519684—22no—
107#14519684—22no—
108#14519684—22no—
109#14519684—22no—
110#14519684—41no—
111#14519684—41no—
112#14519684—41no—
113#14519684—41no—
114#14519684—41no—
115#14519684—41no—
116C25×C61C2311yescharacteristic
117C23×C4×C61—22no—
118C23×C4×C61—22no—
119C23×C4×C61—41no—
120C23×C4×C61—41no—
121C23×C4×C61—41no—
122C23×C4×C61—41no—
123C23×C4×C61C2×C414yes—
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—41no—
133C2×C4⋊C4×C61—41no—
134C2×C4⋊C4×C61C2×C414yes—
135C2×C4⋊C4×C61C2×C414yes—
136C2×C22⋊C4×C61—41no—
137C2×C22⋊C4×C61—41no—
138C2×C22⋊C4×C61C2×C414yes—
139C2×C22⋊C4×C61C2×C414yes—
140C2×C22⋊C4×C61D414yes—
141C2×C22⋊C4×C61Q814yes—
142#95×C61C2×C414yes—
143#95×C61C2×C414yes—
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×C61—28no—
191C22×C4×C61—44no—
192C22×C4×C61—44no—
193C22×C4×C61—44no—
194C22×C4×C61—44no—
195C22×C4×C61—44no—
196C22×C4×C61—44no—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C22×C412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×Q812yes—
207C22×C4×C61C2×Q812yes—
208C22×C4×C61#4112yes—
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—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61C2×D412yes—
262C22×Dic61C2×D412yes—
263C22×Dic61#4112yes—
264C22×Dic61#4112yes—
265C4⋊C4×C61—28no—
266C4⋊C4×C61—44no—
267C22⋊C4×C61—44no—
268C22⋊C4×C61C4⋊C4116yescomplemented
269C22⋊Dic61—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—416no—
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×C61—41no—
371C2×C4×C61C2×C4⋊C414yes—
372C2×C4×C61C2×C4⋊C414yes—
373C2×C4×C61C4×D414yes—
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—22no—
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#14408—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#51811yescharacteristic
451C22×C61#51911yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61#53411yescharacteristic
454C22×C61#53511yescharacteristic
455C22×C61#53711yescharacteristic
456C22×C61#53711yescharacteristic
457C22×C61#53811yescharacteristic
458C22×C61#53811yescharacteristic
459C22×C61#53811yescharacteristic
460C22×C61#53911yescharacteristic
461C22×C61#54011yescharacteristic
462C22×C61#54211yescharacteristic
463C22×C61#54411yescharacteristic
464C22×C61#54411yescharacteristic
465C22×C61D4211yescharacteristic
466C22×C61#54611yescharacteristic
467C22×C61#54611yescharacteristic
468C22×C61#54711yescharacteristic
469C22×C61#54711yescharacteristic
470C22×C61#54811yescharacteristic
471C22×C61D4×Q811yescharacteristic
472C22×C61#55211yescharacteristic
473C22×C61#55411yescharacteristic
474C22×C61#55411yescharacteristic
475C22×C61#55411yescharacteristic
476C22×C61#55611yescharacteristic
477C22×C61#56211yescharacteristic
478C22×C61#56211yescharacteristic
479C22×C61#56311yescharacteristic
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×#388—611no—
498C2×#385D6111yescharacteristic
499C2×#380—611no—
500#1444—611no—
501#1442—611no—
502#1441—611no—
503#1441—611no—
504#1439—611no—
505#1439—611no—
506#1436—611no—
507#1436—611no—
508C4⋊#95—611no—
509C22⋊#95—611no—
510C2×C61—44no—
511C2×C61#231611yescharacteristic
512C2×C61#232111yescharacteristic
513C2×C61#233511yescharacteristic
514C2×C61D4×C4⋊C411yescharacteristic
515C2×C61#234911yescharacteristic
516C2×C61#236211yescharacteristic
517C2×C61#237811yescharacteristic
518C2×C61#267111yescharacteristic
519C2×C61#267611yescharacteristic
520C2×C61#269511yescharacteristic
521C2×C61#271511yescharacteristic
522C2×C61#272011yescharacteristic
523C2×C61#272911yescharacteristic
524C2×C61#276811yescharacteristic
525C2×C61#278811yescharacteristic
526C24×C4C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
534C22×C4⋊C4C2×D6111yescharacteristic
535C22×C22⋊C4—611no—
536C22×C22⋊C4—611no—
537C22×C22⋊C4—611no—
538C22×C22⋊C4—611no—
539C22×C22⋊C4C2×D6111yescharacteristic
540C22×C22⋊C4C2×D6111yescharacteristic
541C22×C42—611no—
542C22×C42—611no—
543#389—1224no—
544#388—1224no—
545#388—1224no—
546#385Dic6118yescomplemented
547#380—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#1440811yescharacteristic, complemented, Sylow
567C25C22×D6111yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4C2×Dic6114yes—
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—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—614no—
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—2441no—
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⋊C4C2×Dic6114yes—
612C2×C4⋊C4C2×Dic6114yes—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—1222no—
616C2×C22⋊C4—1222no—
617C2×C22⋊C4—1222no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—2441no—
624C2×C22⋊C4—2441no—
625C2×C22⋊C4—2441no—
626C2×C22⋊C4—2441no—
627C2×C22⋊C4Dic12214yes—
628C2×C22⋊C4D24414yes—
629C2×C22⋊C4C2×Dic6114yes—
630C2×C22⋊C4C2×Dic6114yes—
631C2×C42—1222no—
632C2×C42—1222no—
633C2×C42—1222no—
634C2×C42—1222no—
635C2×C42—2441no—
636C2×C42—2441no—
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—1222no—
647#95—2441no—
648#95—2441no—
649#95—2441no—
650#95—2441no—
651#95—2441no—
652#95—2441no—
653#95C2×Dic6114yes—
654#95C2×Dic6114yes—
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—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—612no—
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—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
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—44no—
778C4⋊C4—2444no—
779C4⋊C4—2444no—
780C4⋊C4—2444no—
781C4⋊C4—2444no—
782C4⋊C4—2444no—
783C4⋊C4—2444no—
784C22⋊C4—44no—
785C22⋊C4—2444no—
786C22⋊C4—2444no—
787C22⋊C4—2444no—
788C22⋊C4—2444no—
789C22⋊C4C4⋊Dic61116yescomplemented
790C42—2444no—
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#1451982211yescharacteristic
837C23#1451982211yescharacteristic
838C23#1451982311yescharacteristic
839C23#1451982411yescharacteristic
840C23#1451982511yescharacteristic
841C23#1451982511yescharacteristic
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—416no—
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—41no—
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—1222no—
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—2441no—
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#1684023711yescharacteristic
961C22#1684024011yescharacteristic
962C22#1684024511yescharacteristic
963C22#1684032211yescharacteristic
964C22#1684032711yescharacteristic
965C22#1684034311yescharacteristic
966C22#1684034311yescharacteristic
967C22#1684034711yescharacteristic
968C22#1684034711yescharacteristic
969C22#1684034811yescharacteristic
970C22#1684035511yescharacteristic
971C22#1684036411yescharacteristic
972C22#1684038011yescharacteristic
973C22#1684039311yescharacteristic
974C22#1684039311yescharacteristic
975C22D4×D24411yescharacteristic
976C22#1684040711yescharacteristic
977C22#1684040711yescharacteristic
978C22#1684041411yescharacteristic
979C22#1684041611yescharacteristic
980C22#1684042211yescharacteristic
981C22D4×Dic12211yescharacteristic
982C22#1684044611yescharacteristic
983C22#1684046911yescharacteristic
984C22#1684047111yescharacteristic
985C22#1684047111yescharacteristic
986C22#1684048311yescharacteristic
987C22#1684050811yescharacteristic
988C22#1684050811yescharacteristic
989C22#1684051311yescharacteristic
990C22#1684051311yescharacteristic
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#2144843711yescharacteristic
1007C2#2144848011yescharacteristic
1008C2#2144861311yescharacteristic
1009C2D4×C4⋊Dic6111yescharacteristic
1010C2#2144872911yescharacteristic
1011C2#2144885011yescharacteristic
1012C2#2144898511yescharacteristic
1013C2#2145205811yescharacteristic
1014C2#2145212311yescharacteristic
1015C2#2145235211yescharacteristic
1016C2#2145262811yescharacteristic
1017C2#2145270011yescharacteristic
1018C2#2145280511yescharacteristic
1019C2#2145329611yescharacteristic
1020C2#2145356911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61#14408
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
5. #21444084C2semidirect
6. #21444076C2semidirect
7. #21444072C2semidirect
8. #21444072C2semidirect
11. #21444053C2semidirect
12. #21444053C2semidirect
13. #21444048C2semidirect
53. C61×#385C4semidirect
268. C22⋊C4×C61C4⋊C4semidirect
546. #385Dic61semidirect
566. C61#14408semidirect
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×#168396222
#214440842
#214440762
#214440722
#214440642
#214440532
#214440482
#214440422
C2×C61×#3852
#1440861