Finite Group Databasebeta

← #29609372

Subgroups — #29609372

Order 15616.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839670C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic, complemented
3C2×#16839653C211yesmaximal, characteristic, complemented
4C2×#16839650C211yesmaximal, characteristic, complemented
5C2×#16839642C211yesmaximal, characteristic, complemented
6C2×#16839639C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444052C211yesmaximal, characteristic, complemented
13#21444051C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839670C418yescomplemented
33#16839662—24no—
34#16839653—24no—
35#16839650—24no—
36#16839642—24no—
37#16839639—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C23×D4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C61×#390—24no—
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61—41no—
66C22×C22⋊D61—41no—
67C22×C22⋊D61—41no—
68C22×C22⋊D61—41no—
69C22×C22⋊D61—41no—
70C22×C22⋊D61—41no—
71C22×C22⋊D61C2×C414yes—
72C22×C22⋊D61C2×C414yescomplemented
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—22no—
76C23×Dic61—41no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—41no—
92C2×#11758196—41no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61—41no—
106C2×C22⋊Dic61C2×C414yes—
107C2×C22⋊Dic61C2×C414yescomplemented
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198C2×C414yescomplemented
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—41no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135#14519684C2×C414yescomplemented
136#14519684D414yescomplemented
137#14519684D414yescomplemented
138C25×C61C2311yescharacteristic
139C25×C61C2311yescharacteristic
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—41no—
145C22×D4×C61—41no—
146C22×D4×C61C2×C414yes—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61—22no—
154C2×C4⋊C4×C61—41no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—41no—
161C2×C22⋊C4×C61—41no—
162C2×C22⋊C4×C61—41no—
163C2×C22⋊C4×C61—41no—
164C2×C22⋊C4×C61—41no—
165C2×C22⋊C4×C61—41no—
166C2×C22⋊C4×C61D414yescomplemented
167C2×C42×C61—22no—
168C2×C42×C61—22no—
169C2×C42×C61—41no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61C22×C412yes—
197C24×C61C22×C412yes—
198C24×C61C2×D412yes—
199C24×C61#4112yes—
200C24×C61C2411yescharacteristic
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61C22×C412yes—
216C2×D4×C61—28no—
217C2×D4×C61—28no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61C22×C412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D412yes—
257C22×C4×C61#4112yes—
258C2×C22⋊D61—28no—
259C2×C22⋊D61—28no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—44no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61—44no—
266C2×C22⋊D61—44no—
267C2×C22⋊D61—44no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—44no—
314C22×Dic61—44no—
315C22×Dic61—44no—
316C22×Dic61—44no—
317C22×Dic61—44no—
318C22×Dic61—44no—
319C22×Dic61—44no—
320C22×Dic61C22×C412yes—
321C22×Dic61C22×C412yes—
322C22×Dic61C22×C412yes—
323C22×Dic61C2×D412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61#4112yes—
328C4⋊C4×C61—44no—
329C22⋊C4×C61—44no—
330C22⋊C4×C61—44no—
331C22⋊C4×C61—44no—
332C22⋊C4×C61—44no—
333C42×C61—44no—
334C22⋊Dic61—28no—
335C22⋊Dic61—44no—
336C22⋊Dic61—44no—
337C22⋊Dic61—44no—
338C22⋊Dic61—44no—
339#11758198—28no—
340#11758198—44no—
341#11758198—44no—
342#11758198—44no—
343#11758198—44no—
344#11758196—44no—
345#11758196—44no—
346C4×Dic61—44no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61C4×D414yes—
417C23×C61C23×C411yescharacteristic
418C23×C61C22×D411yescharacteristic
419C23×C61C22×D411yescharacteristic
420C23×C61C22×D411yescharacteristic
421C23×C61C2×#4111yescharacteristic
422C23×C61C2×#4111yescharacteristic
423C23×C61C2×#4111yescharacteristic
424C23×C61H(5,𝔽2)11yescharacteristic
425C23×C61H(5,𝔽2)11yescharacteristic
426C23×C61H(5,𝔽2)11yescharacteristic
427C23×C61H(5,𝔽2)11yescharacteristic
428C23×C61H(5,𝔽2)11yescharacteristic
429C23×C61H(5,𝔽2)11yescharacteristic
430C23×C61H(5,𝔽2)11yescharacteristic
431C23×C612−1+411yescharacteristic
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—22no—
435C22×D61—22no—
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—22no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467D4×C61—416no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61C4×D414yes—
503C22⋊D61—416no—
504C22⋊D61—416no—
505C2×Dic61—22no—
506C2×Dic61—22no—
507C2×Dic61—22no—
508C2×Dic61—22no—
509C2×Dic61—22no—
510C2×Dic61—22no—
511C2×Dic61—22no—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—22no—
515C2×Dic61—22no—
516C2×Dic61—22no—
517C2×Dic61—22no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—416no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61C4×D414yes—
555#14521—611nomaximal, Sylow
556C22×C61—24no—
557C22×C61—24no—
558C22×C61—24no—
559C22×C61—42no—
560C22×C61—42no—
561C22×C61—42no—
562C22×C61—42no—
563C22×C61—42no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—42no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—81no—
579C22×C61—81no—
580C22×C61—81no—
581C22×C61—81no—
582C22×C61—81no—
583C22×C61—81no—
584C22×C61—81no—
585C22×C61—81no—
586C22×C61C2×C4×D411yescharacteristic
587C22×C61C2×C4×D411yescharacteristic
588C22×C61C2×C4×D411yescharacteristic
589C22×C61#51811yescharacteristic
590C22×C61#51811yescharacteristic
591C22×C61#51811yescharacteristic
592C22×C61#52011yescharacteristic
593C22×C61#53411yescharacteristic
594C22×C61#53511yescharacteristic
595C22×C61#53511yescharacteristic
596C22×C61#53711yescharacteristic
597C22×C61#53711yescharacteristic
598C22×C61#53711yescharacteristic
599C22×C61#53811yescharacteristic
600C22×C61#53911yescharacteristic
601C22×C61#54011yescharacteristic
602C22×C61#54011yescharacteristic
603C22×C61#54211yescharacteristic
604C22×C61#54211yescharacteristic
605C22×C61D4211yescharacteristic
606C22×C61D4211yescharacteristic
607C22×C61D4211yescharacteristic
608C22×C61#54611yescharacteristic
609C22×C61#54611yescharacteristic
610C22×C61#54611yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#55011yescharacteristic
613C22×C61#55011yescharacteristic
614C22×C61#55111yescharacteristic
615C22×C61#55111yescharacteristic
616C22×C61#55911yescharacteristic
617C22×C61#56011yescharacteristic
618C22×C61#56011yescharacteristic
619C22×C61#56011yescharacteristic
620C22×C61H(3,𝔽4)11yescharacteristic
621C2×D61—42no—
622C2×D61—42no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—81no—
629C2×D61—81no—
630C2×D61—81no—
631C2×D61—81no—
632C2×D61—81no—
633C2×D61—81no—
634C2×D61—81no—
635C2×D61—81no—
636C4×C61—24no—
637C4×C61—42no—
638C4×C61—42no—
639C4×C61—42no—
640C4×C61—81no—
641Dic61—24no—
642Dic61—42no—
643Dic61—42no—
644Dic61—42no—
645Dic61—42no—
646Dic61—42no—
647Dic61—81no—
648C2×#392—611no—
649C2×#390—611no—
650C2×#390D6111yescharacteristic, complemented
651C2×#388—611no—
652C2×#388—611no—
653C2×#386—611no—
654C2×#386—611no—
655#1439—611no—
656#1439—611no—
657#1439—611no—
658#1438—611no—
659#1438—611no—
660#1436—611no—
661#1436—611no—
662C22⋊#95—611no—
663C2×C61—44no—
664C2×C61—82no—
665C2×C61#232411yescharacteristic
666C2×C61#232411yescharacteristic
667C2×C61#232511yescharacteristic
668C2×C61#235811yescharacteristic
669C2×C61#235811yescharacteristic
670C2×C61#236611yescharacteristic
671C2×C61#237511yescharacteristic
672C2×C61#267011yescharacteristic
673C2×C61#267311yescharacteristic
674C2×C61#267311yescharacteristic
675C2×C61#267511yescharacteristic
676C2×C61#270511yescharacteristic
677C2×C61#270511yescharacteristic
678C2×C61#271211yescharacteristic
679C2×C61#275211yescharacteristic
680D61—82no—
681C23×D4—611no—
682C23×D4—611no—
683C23×D4C2×D6111yescharacteristic
684C24×C4—611no—
685C22×C4⋊C4—611no—
686C22×C4⋊C4—611no—
687C22×C4⋊C4C2×D6111yescharacteristic
688C22×C22⋊C4—611no—
689C22×C22⋊C4—611no—
690C22×C22⋊C4—611no—
691C22×C22⋊C4—611no—
692C22×C22⋊C4—611no—
693C22×C22⋊C4—611no—
694C22×C22⋊C4—611no—
695C22×C22⋊C4—611no—
696C22×C22⋊C4—611no—
697C22×C22⋊C4—611no—
698C22×C22⋊C4C2×D6111yescharacteristic
699C22×C22⋊C4C2×D6111yescharacteristic
700C22×C22⋊C4C2×D6111yescharacteristic
701C22×C22⋊C4C2×D6111yescharacteristic
702C22×C42—611no—
703C22×C42C2×D6111yescharacteristic
704#392—618no—
705#390—24no—
706#390—1224no—
707#388—1224no—
708#388—1224no—
709#386—1224no—
710#386—1224no—
711C2×#95—611no—
712C2×#95—611no—
713C2×#95—611no—
714C2×#95—611no—
715C2×#95—611no—
716C2×#95—611no—
717C2×#95—611no—
718C2×#95—611no—
719C2×#95—611no—
720C2×#95—611no—
721C2×#95—611no—
722C2×#95—611no—
723C61#1452111yescharacteristic, complemented, Sylow
724C25—611no—
725C25C22×D6111yescharacteristic
726C25C22×D6111yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—614no—
734C22×D4—614no—
735C22×D4—1222no—
736C22×D4—1222no—
737C22×D4—1222no—
738C22×D4—1222no—
739C22×D4—2441no—
740C22×D4—2441no—
741C22×D4—2441no—
742C22×D4—2441no—
743C22×D4—2441no—
744C22×D4—2441no—
745C22×D4—2441no—
746C22×D4—2441no—
747C22×D4C4×D6114yes—
748C23×C4—611no—
749C23×C4—611no—
750C23×C4—611no—
751C23×C4—611no—
752C23×C4—611no—
753C23×C4—611no—
754C23×C4—611no—
755C23×C4—1222no—
756C23×C4—1222no—
757C23×C4—1222no—
758C23×C4—2441no—
759C23×C4—2441no—
760C23×C4—2441no—
761C23×C4—2441no—
762C23×C4C22×D6111yescharacteristic
763C23×C4C22×D6111yescharacteristic
764C23×C4C22×D6111yescharacteristic
765C23×C4C22×D6111yescharacteristic
766C23×C4C22×D6111yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—1222no—
771C2×C4⋊C4—1222no—
772C2×C4⋊C4—1222no—
773C2×C4⋊C4—1222no—
774C2×C4⋊C4—2441no—
775C2×C4⋊C4—2441no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—614no—
788C2×C22⋊C4—614no—
789C2×C22⋊C4—614no—
790C2×C22⋊C4—1222no—
791C2×C22⋊C4—1222no—
792C2×C22⋊C4—1222no—
793C2×C22⋊C4—1222no—
794C2×C22⋊C4—1222no—
795C2×C22⋊C4—1222no—
796C2×C22⋊C4—1222no—
797C2×C22⋊C4—1222no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—1222no—
800C2×C22⋊C4—1222no—
801C2×C22⋊C4—1222no—
802C2×C22⋊C4—1222no—
803C2×C22⋊C4—1222no—
804C2×C22⋊C4—1222no—
805C2×C22⋊C4—2441no—
806C2×C22⋊C4—2441no—
807C2×C22⋊C4—2441no—
808C2×C22⋊C4—2441no—
809C2×C22⋊C4—2441no—
810C2×C22⋊C4—2441no—
811C2×C22⋊C4—2441no—
812C2×C22⋊C4—2441no—
813C2×C22⋊C4—2441no—
814C2×C22⋊C4—2441no—
815C2×C22⋊C4—2441no—
816C2×C22⋊C4—2441no—
817C2×C22⋊C4C22⋊D6114yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—41no—
821C2×C42—1222no—
822C2×C42—1222no—
823C2×C42—2441no—
824#95—614no—
825#95—614no—
826#95—614no—
827#95—1222no—
828#95—1222no—
829#95—1222no—
830#95—1222no—
831#95—2441no—
832#95—2441no—
833#95—2441no—
834#95—2441no—
835#95—2441no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—612no—
863C24—1221no—
864C24—1221no—
865C24—1221no—
866C24—1221no—
867C24—1221no—
868C24—1221no—
869C24—1221no—
870C24—1221no—
871C24—1221no—
872C24—1221no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24C2×C4×D6112yes—
878C24C2×C4×D6112yes—
879C24#1175822212yes—
880C24C2×C22⋊D6112yes—
881C24C23×D6111yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—1228no—
890C2×D4—1228no—
891C2×D4—2444no—
892C2×D4—2444no—
893C2×D4—2444no—
894C2×D4—2444no—
895C2×D4—2444no—
896C2×D4—2444no—
897C2×D4—2444no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4—2444no—
901C2×D4—2444no—
902C2×D4—2444no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—612no—
933C22×C4—612no—
934C22×C4—612no—
935C22×C4—612no—
936C22×C4—612no—
937C22×C4—612no—
938C22×C4—612no—
939C22×C4—612no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—2444no—
982C22×C4—2444no—
983C22×C4—2444no—
984C22×C4—2444no—
985C22×C4—2444no—
986C22×C4—2444no—
987C22×C4—2444no—
988C22×C4C2×C4×D6112yes—
989C22×C4D4×D6112yes—
990C22×C4D4×D6112yes—
991C22×C4#1175822412yes—
992C22×C4C2×C22⋊D6112yes—
993C22×C4C2×C22⋊D6112yes—
994C4⋊C4—44no—
995C4⋊C4—2444no—
996C4⋊C4—2444no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—1228no—
1002C22⋊C4—1228no—
1003C22⋊C4—2444no—
1004C22⋊C4—2444no—
1005C22⋊C4—2444no—
1006C22⋊C4—2444no—
1007C22⋊C4—2444no—
1008C22⋊C4—2444no—
1009C22⋊C4—2444no—
1010C22⋊C4—2444no—
1011C42—44no—
1012C42—2444no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—1222no—
1083C23—1222no—
1084C23—1222no—
1085C23—1222no—
1086C23—1222no—
1087C23—1222no—
1088C23—1222no—
1089C23—2441no—
1090C23—2441no—
1091C23—2441no—
1092C23—2441no—
1093C23—2441no—
1094C23—2441no—
1095C23—2441no—
1096C23—2441no—
1097C23—2441no—
1098C23—2441no—
1099C23—2441no—
1100C23—2441no—
1101C23—2441no—
1102C23—2441no—
1103C23—2441no—
1104C23—2441no—
1105C23—2441no—
1106C23—2441no—
1107C23—2441no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23C4×C22⋊D6114yes—
1118C23C22×C4×D6111yescharacteristic
1119C23C2×D4×D6111yescharacteristic
1120C23C2×D4×D6111yescharacteristic
1121C23C22×C22⋊D6111yescharacteristic
1122C23#41×D6111yescharacteristic
1123C23C2×#1175822411yescharacteristic
1124C23C2×#1175822211yescharacteristic
1125C23#1451982211yescharacteristic
1126C23#1451982211yescharacteristic
1127C23#1451982211yescharacteristic
1128C23#1451982211yescharacteristic
1129C23#1451982211yescharacteristic
1130C23#1451982311yescharacteristic
1131C23#1451982311yescharacteristic
1132C23#1451982411yescharacteristic
1133D4—416no—
1134D4—24416no—
1135D4—24416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—614no—
1171C2×C4—1222no—
1172C2×C4—1222no—
1173C2×C4—1222no—
1174C2×C4—1222no—
1175C2×C4—1222no—
1176C2×C4—1222no—
1177C2×C4—1222no—
1178C2×C4—1222no—
1179C2×C4—1222no—
1180C2×C4—1222no—
1181C2×C4—1222no—
1182C2×C4—1222no—
1183C2×C4—1222no—
1184C2×C4—1222no—
1185C2×C4—1222no—
1186C2×C4—1222no—
1187C2×C4—1222no—
1188C2×C4—1222no—
1189C2×C4—1222no—
1190C2×C4—1222no—
1191C2×C4—1222no—
1192C2×C4—2441no—
1193C2×C4—2441no—
1194C2×C4—2441no—
1195C2×C4—2441no—
1196C2×C4—2441no—
1197C2×C4—2441no—
1198C2×C4—2441no—
1199C2×C4—24416no—
1200C2×C4—2441no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4—2441no—
1205C2×C4—2441no—
1206C2×C4—2441no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2441no—
1210C2×C4—2441no—
1211C2×C4—2441no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4#1451973714yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—4881no—
1252C22—4881no—
1253C22—4881no—
1254C22—4881no—
1255C22—4881no—
1256C22—4881no—
1257C22—4881no—
1258C22—4881no—
1259C22—2442no—
1260C22—2442no—
1261C22—2442no—
1262C22—2442no—
1263C22—2442no—
1264C22—2442no—
1265C22—2442no—
1266C22C4×D4×D6111yescharacteristic
1267C22C2×#1451973711yescharacteristic
1268C22C2×C4×C22⋊D6111yescharacteristic
1269C22#1684023411yescharacteristic
1270C22#1684023411yescharacteristic
1271C22#1684023511yescharacteristic
1272C22#1684024111yescharacteristic
1273C22#1684032111yescharacteristic
1274C22#1684032511yescharacteristic
1275C22#1684032811yescharacteristic
1276C22#1684033911yescharacteristic
1277C22#1684034011yescharacteristic
1278C22#1684034111yescharacteristic
1279C22#1684034511yescharacteristic
1280C22#1684035411yescharacteristic
1281C22#1684036211yescharacteristic
1282C22#1684036611yescharacteristic
1283C22#1684037611yescharacteristic
1284C22#1684038111yescharacteristic
1285C22D4×C22⋊D6111yescharacteristic
1286C22D4×C22⋊D6111yescharacteristic
1287C22#1684039611yescharacteristic
1288C22#1684040011yescharacteristic
1289C22#1684040211yescharacteristic
1290C22#1684040611yescharacteristic
1291C22#1684040811yescharacteristic
1292C22#1684043011yescharacteristic
1293C22#1684043211yescharacteristic
1294C22#1684043811yescharacteristic
1295C22#1684044111yescharacteristic
1296C22#1684049411yescharacteristic
1297C22#1684049911yescharacteristic
1298C22#1684050011yescharacteristic
1299C22#1684050011yescharacteristic
1300C22#1684050411yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—1224no—
1307C4—4881no—
1308C4—2442no—
1309C4—2442no—
1310C4—2442no—
1311C4—2442no—
1312C4—2442no—
1313C2—44no—
1314C2—82no—
1315C2—4882no—
1316C2#2144850511yescharacteristic
1317C2#2144851511yescharacteristic
1318C2#2144851711yescharacteristic
1319C2#2144879611yescharacteristic
1320C2#2144879811yescharacteristic
1321C2#2144888011yescharacteristic
1322C2#2144895611yescharacteristic
1323C2#2145204211yescharacteristic
1324C2#2145207911yescharacteristic
1325C2#2145208111yescharacteristic
1326C2#2145210911yescharacteristic
1327C2#2145248711yescharacteristic
1328C2#2145249511yescharacteristic
1329C2#2145258511yescharacteristic
1330C2#2145308111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#390C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC2×#390D61
hypocenterC61#14521
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16839662C2semidirect
3. C2×#16839653C2semidirect
4. C2×#16839650C2semidirect
5. C2×#16839642C2semidirect
6. C2×#16839639C2semidirect
7. #21444062C2semidirect
8. #21444062C2semidirect
9. #21444061C2semidirect
10. #21444058C2semidirect
11. #21444058C2semidirect
12. #21444052C2semidirect
13. #21444051C2semidirect
14. #21444041C2semidirect
15. C2×C61×#390C2semidirect
32. #16839670C4semidirect
72. C22×C22⋊D61C2×C4semidirect
107. C2×C22⋊Dic61C2×C4semidirect
122. C2×#11758198C2×C4semidirect
135. #14519684C2×C4semidirect
136. #14519684D4semidirect
137. #14519684D4semidirect
166. C2×C22⋊C4×C61D4semidirect
650. C2×#390D61semidirect
723. C61#14521semidirect
817. C2×C22⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396622
C2×#168396532
C2×#168396502
C2×#168396422
C2×#168396392
#214440622
#214440612
#214440582
#214440522
#214440512
#214440412
C2×C61×#3902
#1452161