Finite Group Databasebeta

← #29587196

Subgroups — #29587196

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519691C211yesmaximal, characteristic
2#21448394C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic
4C2×#16839529C211yesmaximal, characteristic, complemented
5C2×#16839528C211yesmaximal, characteristic, complemented
6#21444042C211yesmaximal, characteristic, complemented
7C2×C61×#385C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9C22×C22⋊Dic61C2211yescharacteristic
10C22×C22⋊Dic61C2211yescharacteristic
11C22×C22⋊Dic61C2211yescharacteristic
12C22×#11758198—21no—
13C2×#14519691—22no—
14C2×#14519691—22no—
15C2×#14519691C414yescomplemented
16#16839641—22no—
17#16839641—22no—
18#16839641—21no—
19#16839641—21no—
20#16839639—22no—
21#16839623—21no—
22#16839617—21no—
23C2×#14519684—21no—
24C2×#14519684—22no—
25#16839529—22no—
26#16839528—22no—
27C24×C4×C61C2211yescharacteristic
28C22×C4⋊C4×C61—21no—
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2211yescharacteristic
31C61×#385—22no—
32C61×#385—22no—
33C2×#95×C61—21no—
34C24×D61D411yescharacteristic
35C22×C22⋊D61—21no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61—21no—
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C22×C22⋊D61—21no—
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C22⋊D61—21no—
47C22×C22⋊D61C2×C412yes—
48C22×C22⋊D61Q812yes—
49C23×Dic61—21no—
50C23×Dic61—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D412yes—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—21no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61C2×C412yes—
70C2×C22⋊Dic61D412yes—
71C2×#11758198—24no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×#11758198—44no—
75#14519691—28no—
76#14519684—24no—
77#14519684—22no—
78#14519684—22no—
79#14519684—44no—
80C25×C61C2311yescharacteristic
81C23×C4×C61—21no—
82C23×C4×C61—21no—
83C23×C4×C61—21no—
84C23×C4×C61—21no—
85C23×C4×C61—21no—
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61—44no—
89C23×C4×C61D412yes—
90C23×C4×C61D411yescharacteristic
91C23×C4×C61D411yescharacteristic
92C2×C4⋊C4×C61—24no—
93C2×C4⋊C4×C61—44no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61C2×C412yes—
104C2×C22⋊C4×C61D412yes—
105C2×C22⋊C4×C61D412yes—
106#95×C61—24no—
107C24×C61—42no—
108C24×C61—42no—
109C24×C61C22×C411yescharacteristic
110C24×C61C2×D411yescharacteristic
111C24×C61C2×D411yescharacteristic
112C24×C61C2×D411yescharacteristic
113C24×C61C2×D411yescharacteristic
114C24×C61C2×D411yescharacteristic
115C24×C61C2×D411yescharacteristic
116C24×C61C2×D411yescharacteristic
117C24×C61C2×Q811yescharacteristic
118C24×C61#4111yescharacteristic
119C24×C61#4111yescharacteristic
120C24×C61#4111yescharacteristic
121C24×C61#4111yescharacteristic
122C24×C61#4111yescharacteristic
123C24×C61#4111yescharacteristic
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—42no—
131C23×D61—42no—
132C23×D61C4⋊C412yescomplemented
133C22×C4×C61—24no—
134C22×C4×C61—24no—
135C22×C4×C61—24no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—44no—
149C22×C4×C61—44no—
150C22×C4×C61—44no—
151C22×C4×C61—44no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C2×C22⋊D61—41no—
182C2×C22⋊D61—41no—
183C2×C22⋊D61—41no—
184C2×C22⋊D61—41no—
185C2×C22⋊D61—41no—
186C2×C22⋊D61—41no—
187C2×C22⋊D61—41no—
188C2×C22⋊D61—41no—
189C2×C22⋊D61—41no—
190C2×C22⋊D61—41no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C22×Dic61—41no—
209C22×Dic61—41no—
210C22×Dic61—41no—
211C22×Dic61—41no—
212C22×Dic61C4⋊C412yescomplemented
213C4⋊C4×C61—48no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—41no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—41no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61C22⋊C414yescomplemented
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—41no—
227C22⋊Dic61—41no—
228C22⋊Dic61—41no—
229C22⋊Dic61—41no—
230C22⋊Dic61—41no—
231C22⋊Dic61—41no—
232C22⋊Dic61—41no—
233C22⋊Dic61—41no—
234#11758198—48no—
235#11758198—82no—
236#11758198—82no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—42no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—41no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C2×C4⋊C411yescharacteristic
261C23×C61#11711yescharacteristic
262C23×C61C4×D411yescharacteristic
263C23×C61C4×D411yescharacteristic
264C23×C61C4×D411yescharacteristic
265C23×C61C4×D411yescharacteristic
266C23×C61#12011yescharacteristic
267C23×C61#12011yescharacteristic
268C23×C61#12011yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61#12111yescharacteristic
271C23×C61#12111yescharacteristic
272C23×C61#12111yescharacteristic
273C23×C61#12111yescharacteristic
274C23×C61#12111yescharacteristic
275C23×C61#12111yescharacteristic
276C23×C61#12111yescharacteristic
277C23×C61C22⋊Q811yescharacteristic
278C23×C61C22⋊Q811yescharacteristic
279C23×C61C22⋊Q811yescharacteristic
280C23×C61C22⋊Q811yescharacteristic
281C23×C61C22⋊Q811yescharacteristic
282C23×C61C22⋊Q811yescharacteristic
283C23×C61#12311yescharacteristic
284C23×C61#12311yescharacteristic
285C23×C61#12311yescharacteristic
286C23×C61#12311yescharacteristic
287C23×C61#12311yescharacteristic
288C23×C61#12411yescharacteristic
289C23×C61#12411yescharacteristic
290C23×C61#12411yescharacteristic
291C23×C61#12611yescharacteristic
292C23×C61#12611yescharacteristic
293C23×C61#12711yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—44no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—82no—
308C22×D61—81no—
309C22×D61—81no—
310C22×D61—82no—
311C2×C4×C61—24no—
312C2×C4×C61—24no—
313C2×C4×C61—24no—
314C2×C4×C61—24no—
315C2×C4×C61—42no—
316C2×C4×C61—44no—
317C2×C4×C61—42no—
318C2×C4×C61—44no—
319C2×C4×C61—42no—
320C2×C4×C61—44no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—44no—
324C2×C4×C61—44no—
325C2×C4×C61—42no—
326C2×C4×C61—44no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—81no—
334C2×C4×C61—81no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C22⋊D61—42no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—42no—
351C2×Dic61—44no—
352C2×Dic61—42no—
353C2×Dic61—44no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—82no—
360C2×Dic61—81no—
361C2×Dic61—81no—
362C2×Dic61—82no—
363C2×Dic61—82no—
364C2×Dic61—82no—
365#11087—611nomaximal, Sylow
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61#38011yescharacteristic
407C22×C61#38511yescharacteristic
408C22×C61#38511yescharacteristic
409C22×C61#38611yescharacteristic
410C22×C61#38811yescharacteristic
411C22×C61#38811yescharacteristic
412C22×C61#39011yescharacteristic
413C22×C61#39211yescharacteristic
414C22×C61#39311yescharacteristic
415C22×C61#39411yescharacteristic
416C22×C61#39411yescharacteristic
417C22×C61#39611yescharacteristic
418C22×C61#39611yescharacteristic
419C22×C61#39711yescharacteristic
420C22×C61#39911yescharacteristic
421C22×C61B(4,𝔽2)12yes—
422C22×C61#45812yes—
423C2×D61—44no—
424C2×D61—44no—
425C2×D61—42no—
426C2×D61—82no—
427C2×D61—82no—
428C2×D61—81no—
429C2×D61—81no—
430C2×D61—82no—
431C2×D61—82no—
432C4×C61—44no—
433C4×C61—44no—
434C4×C61—81no—
435C4×C61—81no—
436Dic61—42no—
437Dic61—82no—
438Dic61—82no—
439Dic61—82no—
440C22×#99—611no—
441#2308—611no—
442C2×#386—611no—
443C2×#385D6111yescharacteristic, complemented
444C2×#342—611no—
445C2×#342—611no—
446C22⋊#95—611no—
447C2×C61—21no—
448C2×C61—21no—
449C2×C61—21no—
450C2×C61—21no—
451C2×C61—21no—
452C2×C61—21no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—21no—
456C2×C61—21no—
457C2×C61—21no—
458C2×C61—21no—
459C2×C61#143911yescharacteristic
460C2×C61#186712yes—
461C2×C61#202111yescharacteristic
462C2×C61#202211yescharacteristic
463C2×C61#204412yes—
464D61—82no—
465C23×D4—611no—
466C24×C4C2×D6111yescharacteristic
467C22×C4⋊C4—21no—
468C22×C22⋊C4—611no—
469C22×C22⋊C4—611no—
470C22×C22⋊C4—611no—
471C22×C22⋊C4—1221no—
472C22×C22⋊C4C2×D6111yescharacteristic
473C22×C22⋊C4C2×D6111yescharacteristic
474C2×#99—614no—
475C2×#99—1222no—
476C2×#99—1222no—
477#386—1222no—
478#386—1222no—
479#386—1221no—
480#386—1221no—
481#386—1222no—
482#385—22no—
483#385—22no—
484#381—1221no—
485#379—1221no—
486C2×#95—21no—
487C2×#95—1221no—
488C2×#95—1222no—
489#342—1222no—
490#342—1222no—
491C61#1108711yescharacteristic, complemented, Sylow
492C25—611no—
493C25C22×D6111yescharacteristic
494C22×D4—612no—
495C22×D4—612no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4—1221no—
501C22×D4—1221no—
502C22×D4—1221no—
503C22×D4—1221no—
504C22×D4—1221no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4—1221no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—44no—
516C23×C4—611no—
517C23×C4—612no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4C22⋊D6111yescharacteristic
521C23×C4C22⋊D6111yescharacteristic
522C23×C4C22⋊D6112yes—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—44no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—612no—
535C2×C22⋊C4—612no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1222no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—2444no—
556C2×C22⋊C4C4×D6112yes—
557C2×C22⋊C4D24412yes—
558C2×C22⋊C4C22⋊D6112yes—
559#99—1228no—
560#95—24no—
561#95—1224no—
562#95—1222no—
563#95—1222no—
564#95—2444no—
565C24—42no—
566C24—42no—
567C24—612no—
568C24—1221no—
569C24—1221no—
570C24—1221no—
571C24—1221no—
572C24—1221no—
573C24—1221no—
574C24—2442no—
575C24—2442no—
576C24C2×C4×D6111yescharacteristic
577C24C2×D24411yescharacteristic
578C24#1175822211yescharacteristic
579C24#1175822211yescharacteristic
580C24D4×D6111yescharacteristic
581C24D4×D6111yescharacteristic
582C24D4×D6111yescharacteristic
583C24#1175822411yescharacteristic
584C24Q8×D6111yescharacteristic
585C24#1175822611yescharacteristic
586C24#1175822611yescharacteristic
587C24#1175822611yescharacteristic
588C24C2×C22⋊D6111yescharacteristic
589C24C2×C22⋊D6111yescharacteristic
590C24C2×C22⋊D6111yescharacteristic
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4—2441no—
606C2×D4—2441no—
607C2×D4—2441no—
608C2×D4—2441no—
609C2×D4—2441no—
610C2×D4—2441no—
611C2×D4—2441no—
612C2×D4—2441no—
613C2×D4—2441no—
614C2×D4—2441no—
615C2×D4—2441no—
616C2×D4—2441no—
617C2×D4—2441no—
618C2×D4—2441no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—612no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2441no—
666C22×C4—2441no—
667C22×C4—2441no—
668C22×C4—2441no—
669C22×C4—2442no—
670C22×C4—2442no—
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—4882no—
684C22⋊C4—4882no—
685C22⋊C4—2448no—
686C22⋊C4—2441no—
687C22⋊C4—2441no—
688C22⋊C4—2441no—
689C22⋊C4—2441no—
690C22⋊C4—2441no—
691C22⋊C4—2441no—
692C22⋊C4—2441no—
693C22⋊C4—2441no—
694C22⋊C4#1175819814yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—4881no—
721C23—4881no—
722C23—4882no—
723C23—4882no—
724C23—2442no—
725C23—2442no—
726C23—2444no—
727C23—2444no—
728C23—2441no—
729C23—2442no—
730C23—2442no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23C2×#1175819811yescharacteristic
735C23C4⋊C4×D6111yescharacteristic
736C23#1451973511yescharacteristic
737C23C4×C22⋊D6111yescharacteristic
738C23C4×C22⋊D6111yescharacteristic
739C23#1451973911yescharacteristic
740C23#1451973911yescharacteristic
741C23#1451974511yescharacteristic
742C23#1451974511yescharacteristic
743C23#1451974611yescharacteristic
744C23#1451974811yescharacteristic
745C23#1451974911yescharacteristic
746C23#1451974911yescharacteristic
747C23#1451975111yescharacteristic
748C23#1451975111yescharacteristic
749C23#1451975211yescharacteristic
750C23#1451975211yescharacteristic
751C23#1451975211yescharacteristic
752C23#1451975311yescharacteristic
753C23#1451975311yescharacteristic
754C23#1451975311yescharacteristic
755C23#1451975511yescharacteristic
756C23#1451975511yescharacteristic
757C23#1451975711yescharacteristic
758C23#1451976011yescharacteristic
759C23#1451976211yescharacteristic
760C23#1451976211yescharacteristic
761C23#1451976211yescharacteristic
762C23#1451976211yescharacteristic
763C23#1451976611yescharacteristic
764C23#1451976611yescharacteristic
765C23#1451976611yescharacteristic
766C23#1451977211yescharacteristic
767C23#1451977211yescharacteristic
768C23#1451977311yescharacteristic
769D4—2442no—
770D4—2442no—
771D4—2442no—
772D4—2442no—
773D4—2442no—
774D4—2442no—
775D4—2442no—
776D4—2442no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—4881no—
805C2×C4—4881no—
806C2×C4—4882no—
807C2×C4—4882no—
808C2×C4—4882no—
809C2×C4—4882no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2444no—
813C2×C4—2444no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—4882no—
864C22—4882no—
865C22—4882no—
866C22—4881no—
867C22—4881no—
868C22—4882no—
869C22—2444no—
870C22—2444no—
871C22—2442no—
872C22#1683961911yescharacteristic
873C22#1683963311yescharacteristic
874C22#1683963311yescharacteristic
875C22#1683964111yescharacteristic
876C22#1683965211yescharacteristic
877C22#1683965211yescharacteristic
878C22#1683966311yescharacteristic
879C22#1683967011yescharacteristic
880C22#1683967311yescharacteristic
881C22#1683967911yescharacteristic
882C22#1683967911yescharacteristic
883C22#1683968411yescharacteristic
884C22#1683968411yescharacteristic
885C22#1683968811yescharacteristic
886C22#1683969711yescharacteristic
887C22#1683994812yes—
888C22#1683995112yes—
889C4—44no—
890C4—44no—
891C4—81no—
892C4—81no—
893C4—4882no—
894C4—4882no—
895C4—4882no—
896C4—2442no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—4882no—
910C2#2144406111yescharacteristic
911C2#2144609812yes—
912C2#2144694211yescharacteristic
913C2#2144694711yescharacteristic
914C2#2144707012yes—
subgroupG/H
centerC23#14519745
commutatorC24×C61C22×C4
FrattiniC25C22×D61
FittingC2×C61×#385C2
socleC23×C61#120
prime radicalC23×C22⋊D61C22
cosocleC25×C61C23
hypercenterC2×#385D61
hypocenterC61#11087
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16839529C2semidirect
5. C2×#16839528C2semidirect
6. #21444042C2semidirect
7. C2×C61×#385C2semidirect
15. C2×#14519691C4semidirect
132. C23×D61C4⋊C4semidirect
212. C22×Dic61C4⋊C4semidirect
221. C22⋊C4×C61C22⋊C4semidirect
443. C2×#385D61semidirect
491. C61#11087semidirect
694. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145196912
#214483942
C2×#168396412
C2×#168395292
C2×#168395282
#214440422
C2×C61×#3852
#1108761