Finite Group Databasebeta

← #29601427

Subgroups — #29601427

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C2×#16839621C211yesmaximal, characteristic
3C2×C4×#11758196C211yesmaximal, characteristic, complemented
4C2×#16839613C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic
6C2×#16839609C211yesmaximal, characteristic
7C2×#16839609C211yesmaximal, characteristic
8#21444053C211yesmaximal, characteristic, complemented
9#21444053C211yesmaximal, characteristic, complemented
10#21444051C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic
14#21444040C211yesmaximal, characteristic
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C2×C4⋊C4×D61—24no—
25C2×C4⋊C4×D61—24no—
26C2×C4⋊C4×D61C418yescomplemented
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839621C418yescomplemented
37C4×#11758196—24no—
38#16839613—24no—
39C4×#11758198—24no—
40#16839609—24no—
41#16839609C418yescomplemented
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C414yes—
85C22×C4×D61C2×C414yes—
86C22×C4×D61C2×C414yes—
87C22×C4×D61C2×C414yes—
88C22×C4×D61C2×C414yes—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61C2×C414yes—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196C2×C414yes—
99C2×#11758196C2×C414yes—
100C2×#11758196C2×C414yescomplemented
101C2×#11758196C2×C414yescomplemented
102C2×#11758196D414yes—
103C2×#11758196D414yes—
104C4⋊C4×D61—232no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198C2×C414yes—
112C2×#11758198C2×C414yes—
113C2×#11758198C2×C414yes—
114C2×#11758198C2×C414yes—
115C2×#11758198D414yes—
116C2×#11758198Q814yes—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—41no—
128C2×C4×Dic61—41no—
129C2×C4×Dic61—41no—
130C2×C4×Dic61C2×C414yescomplemented
131C2×C4×Dic61C2×C414yescomplemented
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—41no—
139#14519684—41no—
140#14519684—41no—
141#14519684C2×C414yescomplemented
142#14519684C2×C414yescomplemented
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—22no—
152C2×C4⋊C4×C61C2×C414yes—
153C2×C42×C61—22no—
154C2×C42×C61—22no—
155C2×C42×C61—41no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61—41no—
159#95×C61C2×C414yescomplemented
160#95×C61C2×C414yescomplemented
161C24×C61C2411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61C22×C412yes—
171C23×D61C22×C412yes—
172C23×D61C22×C412yes—
173C23×D61C2×D412yes—
174C23×D61C2×Q812yes—
175C23×D61#4112yes—
176C23×D61#4112yes—
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—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—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C412yes—
214C22×C4×C61C22×C412yes—
215C22×C4×C61C22×C412yes—
216C22×C4×C61C22×C412yes—
217C22×C4×C61C22×C412yes—
218C22×C4×C61C22×C412yes—
219C22×C4×C61C22×C412yes—
220C22×C4×C61C22×C412yes—
221C22×C4×C61C22×C412yes—
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×Q812yes—
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×Dic61C22×C412yes—
259C22×Dic61C22×C412yes—
260C22×Dic61C22×C412yes—
261C22×Dic61C22×C412yes—
262C22×Dic61C22×C412yes—
263C22×Dic61C22×C412yes—
264C22×Dic61C22×C412yes—
265C22×Dic61C22×C412yes—
266C22×Dic61C22×C412yes—
267C22×Dic61C2×D412yes—
268C22×Dic61C2×D412yes—
269C22×Dic61C2×D412yes—
270C22×Dic61C2×D412yes—
271C22×Dic61C2×D412yes—
272C22×Dic61C2×Q812yes—
273C22×Dic61#4112yes—
274C22×Dic61#4112yes—
275C2×C4×D61—28no—
276C2×C4×D61—28no—
277C2×C4×D61—28no—
278C2×C4×D61—28no—
279C2×C4×D61—28no—
280C2×C4×D61—28no—
281C2×C4×D61—28no—
282C2×C4×D61—28no—
283C2×C4×D61—28no—
284C2×C4×D61—28no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61C42116yescomplemented
296C4⋊C4×C61—28no—
297C42×C61—44no—
298#11758198—28no—
299#11758198—28no—
300#11758198—28no—
301#11758198C4⋊C4116yescomplemented
302C4⋊Dic61—28no—
303#11758196—28no—
304#11758196—28no—
305#11758196—28no—
306#11758196C22⋊C4116yescomplemented
307C4×Dic61—28no—
308C4×Dic61—28no—
309C4×Dic61—44no—
310C4×Dic61—44no—
311C4×Dic61—44no—
312C23×C61C23×C411yescharacteristic
313C23×C61C23×C411yescharacteristic
314C23×C61C23×C411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C23×C61C22×D411yescharacteristic
318C23×C61C22×Q811yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C612−1+411yescharacteristic
326C23×C612−1+411yescharacteristic
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61C2×C4214yes—
356C22×D61C2×C4⋊C414yes—
357C22×D61#11714yes—
358C22×D61C4×D414yes—
359C22×D61C4×D414yes—
360C22×D61C4×Q814yes—
361C22×D61C4×Q814yes—
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—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61C2×C4214yes—
409C2×C4×C61C2×C22⋊C414yes—
410C2×C4×C61C2×C4⋊C414yescomplemented
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
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×Dic61C2×C4214yes—
452C2×Dic61C2×C22⋊C414yes—
453C2×Dic61C2×C22⋊C414yes—
454C2×Dic61C2×C4⋊C414yescomplemented
455C2×Dic61#11714yes—
456C2×Dic61C4×D414yes—
457C2×Dic61C4×D414yes—
458C2×Dic61C4×D414yes—
459C2×Dic61C4×D414yes—
460C4×D61—232no—
461C4×D61—416no—
462C4×D61—416no—
463C22⋊C4×C4⋊C4—611nomaximal, Sylow
464C22×C61C22×C4211yescharacteristic
465C22×C61C22×C22⋊C411yescharacteristic
466C22×C61C22×C4⋊C411yescharacteristic
467C22×C61C2×#11711yescharacteristic
468C22×C61C2×#11711yescharacteristic
469C22×C61C2×C4×D411yescharacteristic
470C22×C61C2×C4×D411yescharacteristic
471C22×C61C2×C4×D411yescharacteristic
472C22×C61C2×C4×D411yescharacteristic
473C22×C61C2×C4×D411yescharacteristic
474C22×C61C2×C4×D411yescharacteristic
475C22×C61C2×C4×Q811yescharacteristic
476C22×C61C2×C4×Q811yescharacteristic
477C22×C61#51811yescharacteristic
478C22×C61#51911yescharacteristic
479C22×C61#52011yescharacteristic
480C22×C61#52011yescharacteristic
481C22×C61#52011yescharacteristic
482C22×C61#52011yescharacteristic
483C22×C61D4211yescharacteristic
484C22×C61D4211yescharacteristic
485C22×C61#54611yescharacteristic
486C22×C61#54611yescharacteristic
487C22×C61#54711yescharacteristic
488C22×C61#54711yescharacteristic
489C22×C61#54811yescharacteristic
490C22×C61#54811yescharacteristic
491C22×C61D4×Q811yescharacteristic
492C22×C61D4×Q811yescharacteristic
493C22×C61#55211yescharacteristic
494C22×C61#55211yescharacteristic
495C22×C61#55311yescharacteristic
496C22×C61#55311yescharacteristic
497C22×C61#55411yescharacteristic
498C22×C61#55411yescharacteristic
499C2×D61—24no—
500C2×D61—24no—
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—24no—
504C2×D61—24no—
505C2×D61—24no—
506C2×D61—24no—
507C2×D61—24no—
508C2×D61—24no—
509C2×D61—24no—
510C2×D61—24no—
511C2×D61—24no—
512C2×D61—24no—
513C2×D61C4×C4⋊C418yescomplemented
514C4×C61—24no—
515C4×C61—24no—
516C4×C61—24no—
517C4×C61—42no—
518C4×C61—42no—
519C4×C61—42no—
520C4×C61—42no—
521Dic61—24no—
522Dic61—24no—
523Dic61—42no—
524Dic61—42no—
525Dic61—42no—
526Dic61—42no—
527Dic61C4×C22⋊C418yescomplemented
528C23×C4⋊C4—611no—
529C2×#380—611no—
530C2×C4×C4⋊C4—611no—
531C2×C4×C4⋊C4—611no—
532C2×C4×C22⋊C4—611no—
533C2×C4×C22⋊C4—611no—
534C2×C4×C22⋊C4—611no—
535#1436—611no—
536#1436—611no—
537#1436—611no—
538#1436D6111yescharacteristic, complemented
539C4⋊#95—611no—
540C4⋊#95—611no—
541C22⋊#95—611no—
542C22⋊#95—611no—
543C2×C61C2×C4×C22⋊C411yescharacteristic
544C2×C61C2×C4×C4⋊C411yescharacteristic
545C2×C61#227411yescharacteristic
546C2×C61D4×C22⋊C411yescharacteristic
547C2×C61Q8×C22⋊C411yescharacteristic
548C2×C61#234411yescharacteristic
549C2×C61#234511yescharacteristic
550C2×C61D4×C4⋊C411yescharacteristic
551C2×C61D4×C4⋊C411yescharacteristic
552C2×C61#235211yescharacteristic
553C2×C61#235211yescharacteristic
554C2×C61#236011yescharacteristic
555C2×C61#236011yescharacteristic
556C2×C61#236111yescharacteristic
557C2×C61#236111yescharacteristic
558D61—28no—
559C24×C4—611no—
560C24×C4—611no—
561C24×C4—611no—
562C22×C4⋊C4—611no—
563C22×C4⋊C4—611no—
564C22×C4⋊C4—611no—
565C22×C4⋊C4—611no—
566C22×C4⋊C4—611no—
567C22×C4⋊C4—618no—
568C22×C4⋊C4—1224no—
569C22×C4⋊C4—1224no—
570C22×C4⋊C4C2×D6111yescharacteristic
571C22×C22⋊C4—611no—
572C22×C22⋊C4—611no—
573C22×C22⋊C4—611no—
574C22×C22⋊C4—611no—
575C22×C42—611no—
576C22×C42—611no—
577C22×C42—611no—
578C22×C42—611no—
579C22×C42—611no—
580C22×C42C2×D6111yescharacteristic
581#380—618no—
582C4×C4⋊C4—1224no—
583C4×C4⋊C4—1224no—
584C4×C22⋊C4—618no—
585C4×C22⋊C4—1224no—
586C4×C22⋊C4—1224no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—611no—
590C2×#95—611no—
591C2×#95—611no—
592C2×#95—611no—
593C2×#95—611no—
594C2×#95—611no—
595C2×#95—611no—
596C2×#95—611no—
597C2×#95—611no—
598C2×#95C2×D6111yescharacteristic
599C2×#95C2×D6111yescharacteristic
600C2×#95C2×D6111yescharacteristic
601C2×#95C2×D6111yescharacteristic
602C2×#95C2×D6111yescharacteristic
603C61C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
604C25—611no—
605C23×C4—611no—
606C23×C4—611no—
607C23×C4—611no—
608C23×C4—614no—
609C23×C4—614no—
610C23×C4—614no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C23×C4—611no—
615C23×C4—614no—
616C23×C4—614no—
617C23×C4—1222no—
618C23×C4—1222no—
619C23×C4—1222no—
620C23×C4—1222no—
621C23×C4—1222no—
622C23×C4—1222no—
623C23×C4—1222no—
624C23×C4—1222no—
625C23×C4—1222no—
626C23×C4—1222no—
627C23×C4—1222no—
628C23×C4—1222no—
629C23×C4—2441no—
630C23×C4—2441no—
631C23×C4—2441no—
632C23×C4—2441no—
633C23×C4C22×D6111yescharacteristic
634C23×C4C22×D6111yescharacteristic
635C23×C4C22×D6111yescharacteristic
636C23×C4C22×D6111yescharacteristic
637C23×C4C22×D6111yescharacteristic
638C23×C4C22×D6111yescharacteristic
639C23×C4C22×D6111yescharacteristic
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—614no—
643C2×C4⋊C4—614no—
644C2×C4⋊C4—614no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—614no—
647C2×C4⋊C4—614no—
648C2×C4⋊C4—614no—
649C2×C4⋊C4—12232no—
650C2×C4⋊C4—1222no—
651C2×C4⋊C4—1222no—
652C2×C4⋊C4—1222no—
653C2×C4⋊C4—1222no—
654C2×C4⋊C4—1222no—
655C2×C4⋊C4—1222no—
656C2×C4⋊C4—1222no—
657C2×C4⋊C4—1222no—
658C2×C4⋊C4C4×D6114yes—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—614no—
663C2×C22⋊C4—614no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4—1222no—
667C2×C22⋊C4—1222no—
668C2×C22⋊C4—1222no—
669C2×C22⋊C4—1222no—
670C2×C22⋊C4—1222no—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—41no—
674C2×C42—614no—
675C2×C42—614no—
676C2×C42—1222no—
677C2×C42—1222no—
678C2×C42—1222no—
679C2×C42—1222no—
680C2×C42—1222no—
681C2×C42—1222no—
682C2×C42—1222no—
683C2×C42—1222no—
684C2×C42—1222no—
685C2×C42—1222no—
686C2×C42—2441no—
687C2×C42—2441no—
688C2×C42—2441no—
689#95—22no—
690#95—22no—
691#95—41no—
692#95—614no—
693#95—614no—
694#95—1222no—
695#95—1222no—
696#95—1222no—
697#95—1222no—
698#95—1222no—
699#95—1222no—
700#95—2441no—
701#95—2441no—
702#95—2441no—
703#95C4×D6114yescomplemented
704#95C4×D6114yescomplemented
705C24—612no—
706C24—612no—
707C24—612no—
708C24—612no—
709C24—612no—
710C24—612no—
711C24—612no—
712C24—1221no—
713C24—1221no—
714C24—1221no—
715C24—1221no—
716C24—1221no—
717C24—1221no—
718C24—1221no—
719C24—1221no—
720C24C23×D6111yescharacteristic
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—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—612no—
758C22×C4—612no—
759C22×C4—612no—
760C22×C4—612no—
761C22×C4—612no—
762C22×C4—612no—
763C22×C4—612no—
764C22×C4—612no—
765C22×C4—612no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—612no—
770C22×C4—6116no—
771C22×C4—612no—
772C22×C4—612no—
773C22×C4—612no—
774C22×C4—612no—
775C22×C4—1228no—
776C22×C4—1228no—
777C22×C4—1228no—
778C22×C4—1228no—
779C22×C4—1228no—
780C22×C4—1228no—
781C22×C4—1228no—
782C22×C4—1228no—
783C22×C4—1228no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
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—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1228no—
817C22×C4—2444no—
818C22×C4—2444no—
819C22×C4—2444no—
820C22×C4—2444no—
821C22×C4—2444no—
822C22×C4—2444no—
823C22×C4—2444no—
824C22×C4—2444no—
825C22×C4—2444no—
826C22×C4—2444no—
827C22×C4C2×C4×D6112yes—
828C22×C4C2×C4×D6112yes—
829C22×C4C2×C4×D6112yes—
830C22×C4C2×C4×D6112yes—
831C22×C4C2×C4×D6112yes—
832C22×C4C2×C4×D6112yes—
833C22×C4C2×C4×D6112yes—
834C22×C4C2×C4×D6112yes—
835C22×C4C2×C4×D6112yes—
836C22×C4D4×D6112yes—
837C22×C4D4×D6112yes—
838C22×C4D4×D6112yes—
839C22×C4Q8×D6112yes—
840C4⋊C4—28no—
841C4⋊C4—6116no—
842C4⋊C4—1228no—
843C4⋊C4—1228no—
844C4⋊C4—1228no—
845C4⋊C4—1228no—
846C22⋊C4—6116no—
847C22⋊C4—1228no—
848C22⋊C4—1228no—
849C22⋊C4—1228no—
850C42—44no—
851C42—1228no—
852C42—1228no—
853C42—2444no—
854C42—2444no—
855C42—2444no—
856C23—614no—
857C23—614no—
858C23—614no—
859C23—614no—
860C23—614no—
861C23—614no—
862C23—614no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—1222no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—1222no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23C22×C4×D6111yescharacteristic
892C23C22×C4×D6111yescharacteristic
893C23C22×C4×D6111yescharacteristic
894C23C2×D4×D6111yescharacteristic
895C23C2×D4×D6111yescharacteristic
896C23C2×D4×D6111yescharacteristic
897C23C2×Q8×D6111yescharacteristic
898C23#41×D6111yescharacteristic
899C23#41×D6111yescharacteristic
900C23#41×D6111yescharacteristic
901C23#41×D6111yescharacteristic
902C23#1451982211yescharacteristic
903C23#1451982311yescharacteristic
904C23#1451982411yescharacteristic
905C23#1451982511yescharacteristic
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—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—614no—
953C2×C4—614no—
954C2×C4—614no—
955C2×C4—614no—
956C2×C4—614no—
957C2×C4—614no—
958C2×C4—614no—
959C2×C4—614no—
960C2×C4—614no—
961C2×C4—12232no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—24416no—
987C2×C4—24416no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4C42×D6114yes—
1005C2×C4C22⋊C4×D6114yes—
1006C2×C4C4⋊C4×D6114yescomplemented
1007C22—618no—
1008C22—1224no—
1009C22—1224no—
1010C22—1224no—
1011C22—1224no—
1012C22—1224no—
1013C22—1224no—
1014C22—1224no—
1015C22—1224no—
1016C22—1224no—
1017C22—1224no—
1018C22—1224no—
1019C22—1224no—
1020C22—1224no—
1021C22—1224no—
1022C22C2×C42×D6111yescharacteristic
1023C22C2×C22⋊C4×D6111yescharacteristic
1024C22C2×C4⋊C4×D6111yescharacteristic
1025C22#117×D6111yescharacteristic
1026C22#117×D6111yescharacteristic
1027C22C4×D4×D6111yescharacteristic
1028C22C4×D4×D6111yescharacteristic
1029C22C4×D4×D6111yescharacteristic
1030C22C4×D4×D6111yescharacteristic
1031C22C4×D4×D6111yescharacteristic
1032C22C4×D4×D6111yescharacteristic
1033C22C4×Q8×D6111yescharacteristic
1034C22C4×Q8×D6111yescharacteristic
1035C22#1684023411yescharacteristic
1036C22#1684023811yescharacteristic
1037C22#1684024111yescharacteristic
1038C22#1684024211yescharacteristic
1039C22#1684024311yescharacteristic
1040C22#1684024411yescharacteristic
1041C22#1684039411yescharacteristic
1042C22#1684039611yescharacteristic
1043C22#1684040111yescharacteristic
1044C22#1684040411yescharacteristic
1045C22#1684041011yescharacteristic
1046C22#1684041411yescharacteristic
1047C22#1684042011yescharacteristic
1048C22#1684042211yescharacteristic
1049C22#1684042511yescharacteristic
1050C22#1684042711yescharacteristic
1051C22#1684044411yescharacteristic
1052C22#1684044811yescharacteristic
1053C22#1684045711yescharacteristic
1054C22#1684046311yescharacteristic
1055C22#1684046611yescharacteristic
1056C22#1684046811yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—42no—
1064C4—618no—
1065C4—1224no—
1066C4—1224no—
1067C4—2442no—
1068C4—2442no—
1069C4—2442no—
1070C4—2442no—
1071C2—1228no—
1072C2C4×C22⋊C4×D6111yescharacteristic
1073C2C4×C4⋊C4×D6111yescharacteristic
1074C2#2144817311yescharacteristic
1075C2#2144863711yescharacteristic
1076C2#2144865311yescharacteristic
1077C2#2144868511yescharacteristic
1078C2#2144869311yescharacteristic
1079C2#2144871711yescharacteristic
1080C2#2144872011yescharacteristic
1081C2#2144874311yescharacteristic
1082C2#2144874711yescharacteristic
1083C2#2144882111yescharacteristic
1084C2#2144882711yescharacteristic
1085C2#2144883211yescharacteristic
1086C2#2144883811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1436D61
hypocenterC61C22⋊C4×C4⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758196C2semidirect
4. C2×#16839613C2semidirect
8. #21444053C2semidirect
9. #21444053C2semidirect
10. #21444051C2semidirect
11. #21444047C2semidirect
12. #21444047C2semidirect
15. C61×#1436C2semidirect
26. C2×C4⋊C4×D61C4semidirect
36. #16839621C4semidirect
41. #16839609C4semidirect
100. C2×#11758196C2×C4semidirect
101. C2×#11758196C2×C4semidirect
130. C2×C4×Dic61C2×C4semidirect
131. C2×C4×Dic61C2×C4semidirect
141. #14519684C2×C4semidirect
142. #14519684C2×C4semidirect
159. #95×C61C2×C4semidirect
160. #95×C61C2×C4semidirect
295. C2×C4×D61C42semidirect
301. #11758198C4⋊C4semidirect
306. #11758196C22⋊C4semidirect
410. C2×C4×C61C2×C4⋊C4semidirect
454. C2×Dic61C2×C4⋊C4semidirect
513. C2×D61C4×C4⋊C4semidirect
527. Dic61C4×C22⋊C4semidirect
538. #1436D61semidirect
603. C61C22⋊C4×C4⋊C4semidirect
703. #95C4×D61semidirect
704. #95C4×D61semidirect
1006. C2×C4C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
C2×#168396212
C2×C4×#117581962
C2×#168396132
C2×C4×#117581982
C2×#168396092
#214440532
#214440512
#214440472
#214440402
C61×#14362
C22⋊C4×C4⋊C461