Finite Group Databasebeta

← #29695412

Subgroups — #29695412

Order 15616.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446244C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C23×#92418C2211yescharacteristic, complemented
19C22×C8×D61C2211yescharacteristic, complemented
20D4×C22⋊D61—24no—
21D4×C22⋊D61C418yescomplemented
22C2×#14519773C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519746—21no—
27C2×#14519745—21no—
28C2×D4×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737—21no—
31C22×C4⋊Dic61C2211yescharacteristic, complemented
32C2×C4⋊C4×D61C2211yescharacteristic, complemented
33#16839825—24no—
34C2×#14519706C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic, complemented
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519698—24no—
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519698C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44#102×D61—24no—
45C2×#14519689C2211yescharacteristic, complemented
46C2×C8×Dic61C2211yescharacteristic, complemented
47#16839659—21no—
48#16839636—21no—
49#16839634—21no—
50#16839631C2211yescharacteristic, complemented
51#16839619C2211yescharacteristic, complemented
52C4⋊C4×Dic61C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—28no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—44no—
73C22×C22⋊D61—44no—
74C22×C22⋊D61D411yescharacteristic
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yescomplemented
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418—22no—
86C22×#92418—22no—
87C22×#92418—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—41no—
93#14519773—22no—
94#14519773C2×C414yescomplemented
95#14519751—22no—
96#14519751C2×C414yescomplemented
97#14519749—28no—
98#14519748—22no—
99#14519748C2×C414yescomplemented
100#14519746—28no—
101#14519745—28no—
102D4×Dic61—22no—
103D4×Dic61C2×C414yescomplemented
104C4×C22⋊D61C2×C414yes—
105C4×C22⋊D61D414yes—
106#14519737—44no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—41no—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×#11758196D411yescharacteristic
117C4⋊C4×D61—22no—
118C4⋊C4×D61—41no—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×C22⋊Dic61D411yescharacteristic
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198D411yescharacteristic
125C2×C4×Dic61—21no—
126C2×C4×Dic61C2311yescharacteristic
127#14519706—22no—
128#14519699—22no—
129#14519699—41no—
130#14519698—22no—
131#14519698—22no—
132#14519698—22no—
133#14519698D414yescomplemented
134#14519697—22no—
135#14519697—41no—
136#14519689—22no—
137C8×Dic61—22no—
138#14519684—21no—
139#14519684—21no—
140C25×C61—21no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—21no—
144C22×D4×C61—22no—
145C22×D4×C61—41no—
146C22×D4×C61—41no—
147C22×D4×C61C2×C414yescomplemented
148C22×D4×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—41no—
159#102×C61—41no—
160C22⋊C8×C61—22no—
161#95×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—24no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—42no—
169C24×C61—81no—
170C24×C61—81no—
171C24×C61C2×D411yescharacteristic
172C23×D61—21no—
173C23×D61—24no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—42no—
178C23×D61—81no—
179C23×D61—81no—
180C23×D61C2×D411yescharacteristic
181C2×D4×C61—28no—
182C2×D4×C61—24no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61C22×C412yes—
197C2×D4×C61C22×C412yes—
198C2×D4×C61C2×D412yes—
199C2×D4×C61#4112yes—
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×C61C22×C412yes—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—432no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—81no—
225C2×C22⋊D61—81no—
226C2×C22⋊D61C22⋊C414yes—
227C2×C22⋊D61D814yes—
228C2×C22⋊D61SD1614yes—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—21no—
233C22×Dic61—42no—
234C22×Dic61—42no—
235C22×Dic61—42no—
236C22×Dic61—42no—
237C22×Dic61—81no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241D4×D61—28no—
242D4×D61—44no—
243D4×D61—44no—
244D4×D61—44no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244C22×C412yes—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—81no—
258C2×C4×D61C22×C412yes—
259C2×C4×D61C2×D412yes—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C22⋊C4×C61—42no—
271C22⋊Dic61—24no—
272C22⋊Dic61—24no—
273C22⋊Dic61C22⋊C414yes—
274#11758198—24no—
275#11758198—42no—
276#11758198C22⋊C414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—42no—
282C4⋊Dic61C22×C412yes—
283C4⋊Dic61C2×D412yescomplemented
284#11758196—42no—
285#11758196—42no—
286#11758196—81no—
287#11758196C22⋊C414yes—
288C4×Dic61—42no—
289C4×Dic61C22×C412yes—
290C4×Dic61C2×D412yes—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—44no—
297C2×#92418C2×D412yescomplemented
298C8×D61—44no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—48no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—48no—
319C23×C61—84no—
320C23×C61—84no—
321C23×C61—84no—
322C23×C61—84no—
323C23×C61—84no—
324C23×C61C2×C22⋊C412yes—
325C23×C61C2×D812yes—
326C23×C61C2×SD1612yes—
327C23×C61C22×D411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—22no—
333C22×D61—48no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—48no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61—84no—
345C22×D61—84no—
346C22×D61C2×C22⋊C412yes—
347C22×D61C2×D812yes—
348C22×D61C2×SD1612yes—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—48no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61C4×D414yescomplemented
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
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×C61C2×C22⋊C412yes—
371C2×C4×C61C23×C411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C2×#4111yescharacteristic
375C2×C4×C61H(5,𝔽2)11yescharacteristic
376C2×C4×C61H(5,𝔽2)11yescharacteristic
377C22⋊D61—48no—
378C22⋊D61—48no—
379C22⋊D61—48no—
380C22⋊D61—48no—
381C22⋊D61—84no—
382C22⋊D61#102116yescomplemented
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—48no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—84no—
398C2×Dic61C2×C22⋊C412yes—
399C2×Dic61C2×C22⋊C412yes—
400C2×Dic61C2×C22⋊C412yes—
401C2×Dic61C2×D812yes—
402C2×Dic61C2×SD1612yes—
403D244—22no—
404D244—22no—
405D244—41no—
406D244—41no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—84no—
412C8×C61—41no—
413C8×C61—41no—
414#92418—22no—
415#92418—41no—
416D4×#102—611nomaximal, Sylow
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—24no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—816no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61C2×#10214yescomplemented
439C22×C61C22×C22⋊C411yescharacteristic
440C22×C61D4211yescharacteristic
441C22×C61#54611yescharacteristic
442C22×C61C22×D811yescharacteristic
443C22×C61C22×SD1611yescharacteristic
444C22×C61#57611yescharacteristic
445C22×C61#57711yescharacteristic
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—22no—
450C2×D61—22no—
451C2×D61—22no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—816no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61C2×#10214yescomplemented
461C4×C61—22no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61C2×C4×D411yescharacteristic
465C4×C61#51811yescharacteristic
466C4×C61D4211yescharacteristic
467C4×C61#54611yescharacteristic
468Dic61—22no—
469Dic61—22no—
470Dic61—42no—
471Dic61—42no—
472Dic61—81no—
473Dic61C2×#10214yescomplemented
474C2×D42—611no—
475C2×C8×D4—611no—
476C22×#102—611no—
477C22×#102—611no—
478D4×C4⋊C4—611no—
479#1982—611no—
480#1957—611no—
481#1893—611no—
482#1893—611no—
483#1874—611no—
484#1874—611no—
485#1802—611no—
486#1786—611no—
487#1786D6111yescharacteristic, complemented
488C4×#102—611no—
489C2×C61—24no—
490C2×C61—44no—
491C2×C61—82no—
492C2×C61D4×C22⋊C411yescharacteristic
493C2×C61C22×#10211yescharacteristic
494C2×C61#289711yescharacteristic
495C2×C61D4×D811yescharacteristic
496C2×C61D4×SD1611yescharacteristic
497C2×C61#329411yescharacteristic
498C2×C61#329511yescharacteristic
499D61—24no—
500D61—82no—
501C23×D4—611no—
502C23×D4—1221no—
503C23×D4C2×D6111yescharacteristic
504C23×C8—611no—
505C23×C8—611no—
506D42—618no—
507D42—1224no—
508C2×#127—611no—
509C2×#121—611no—
510C2×#121—611no—
511C2×#121—1221no—
512C2×#120—1221no—
513C2×#120—1221no—
514C2×C4×D4—611no—
515C2×C4×D4—611no—
516C2×C4×D4—1221no—
517C22×C4⋊C4—611no—
518C22×C4⋊C4—611no—
519C8×D4—1224no—
520C2×C4⋊C8—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—1224no—
530C2×#102—1224no—
531C2×#102C2×D6111yescharacteristic
532C2×#102C2×D6111yescharacteristic
533C2×#102C2×D6111yescharacteristic, complemented
534C2×#102C2×D6111yescharacteristic, complemented
535C2×C22⋊C8—611no—
536C2×C22⋊C8C2×D6111yescharacteristic, complemented
537C2×C4×C8—611no—
538#389—1221no—
539#385—1221no—
540#385—1221no—
541#384—611no—
542#380—611no—
543#380C2×D6111yescharacteristic, complemented
544C4×C4⋊C4—611no—
545#340—611no—
546#340—611no—
547#340—611no—
548#340—611no—
549C61D4×#10211yescharacteristic, complemented, Sylow
550C25—21no—
551C25—1221no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—41no—
557C22×D4—41no—
558C22×D4—611no—
559C22×D4—614no—
560C22×D4—611no—
561C22×D4—1222no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4—1228no—
566C22×D4—1222no—
567C22×D4—1222no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4—2441no—
571C22×D4—2441no—
572C22×D4—2444no—
573C22×D4—2444no—
574C22×D4C4×D6114yescomplemented
575C22×D4C22×D6111yescharacteristic
576C22×D4C22×D6111yescharacteristic
577C23×C4—611no—
578C23×C4—1221no—
579C23×C4—1221no—
580C23×C4—1221no—
581C23×C4C22×D6111yescharacteristic
582C22×C8—611no—
583C22×C8—611no—
584C22×C8—1222no—
585C22×C8—1222no—
586C22×C8—1222no—
587C22×C8—1222no—
588C22×C8—2441no—
589C22×C8—2441no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592#127—614no—
593#127—1222no—
594#121—614no—
595#121—614no—
596#121—1228no—
597#121—1222no—
598#121—1222no—
599#120—1228no—
600#120—1228no—
601C4×D4—614no—
602C4×D4—614no—
603C4×D4—614no—
604C4×D4—1222no—
605C4×D4—2444no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C42—611no—
628C2×C42—1221no—
629C4⋊C8—1222no—
630#102—22no—
631#102—22no—
632#102—41no—
633#102—41no—
634#102—614no—
635#102—1222no—
636#102—1222no—
637#102—1222no—
638#102—1222no—
639#102—1222no—
640#102—2441no—
641#102—2441no—
642C22⋊C8—22no—
643C22⋊C8—1222no—
644C4×C8—1222no—
645#95—21no—
646#95—1221no—
647#95—1221no—
648C24—21no—
649C24—21no—
650C24—24no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—611no—
658C24—1224no—
659C24—1221no—
660C24—4881no—
661C24—4881no—
662C24—2442no—
663C24—2442no—
664C24—2442no—
665C24—2442no—
666C24D4×D6111yescharacteristic
667C2×D4—28no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—24no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—614no—
683C2×D4—614no—
684C2×D4—614no—
685C2×D4—612no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—1224no—
689C2×D4—1228no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—4881no—
698C2×D4—4881no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2444no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—24432no—
707C2×D4—2442no—
708C2×D4—2442no—
709C2×D4—2442no—
710C2×D4—2442no—
711C2×D4C2×C4×D6112yes—
712C2×D4C2×C4×D6112yes—
713C2×D4D4×D6112yes—
714C2×D4#1175822412yes—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—1224no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—4881no—
735C22×C4—4881no—
736C22×C4—2442no—
737C22×C4—2442no—
738C22×C4—2442no—
739C22×C4—2442no—
740C22×C4—2442no—
741C22×C4—2442no—
742C22×C4C2×C4×D6112yes—
743C22×C4D4×D6112yes—
744C22×C4D4×D6111yescharacteristic
745C22×C4C23×D6111yescharacteristic
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—612no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—2444no—
759C2×C8—2444no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—614no—
765C4⋊C4—612no—
766C4⋊C4—612no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—4881no—
772C4⋊C4—2442no—
773C4⋊C4—2442no—
774C4⋊C4—2442no—
775C22⋊C4—42no—
776C22⋊C4—614no—
777C22⋊C4—614no—
778C22⋊C4—1224no—
779C22⋊C4—1224no—
780C22⋊C4—1224no—
781C22⋊C4—2442no—
782C42—612no—
783C42—612no—
784C42—2442no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—48no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—48no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—612no—
811C23—612no—
812C23—612no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1222no—
818C23—4884no—
819C23—4884no—
820C23—4884no—
821C23—4884no—
822C23—4884no—
823C23—2448no—
824C23—2448no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23C22⋊C4×D6112yes—
832C23D8×D6112yes—
833C23SD16×D6112yes—
834C23C2×D4×D6111yescharacteristic
835D4—22no—
836D4—22no—
837D4—22no—
838D4—22no—
839D4—22no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—6116no—
844D4—1222no—
845D4—1222no—
846D4—4884no—
847D4—2448no—
848D4—2448no—
849D4—2448no—
850D4—2448no—
851D4—2441no—
852D4—2441no—
853D4#1451973714yescomplemented
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—612no—
867C2×C4—612no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—4884no—
882C2×C4—4884no—
883C2×C4—2448no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4C22⋊C4×D6112yes—
892C2×C4C22×C4×D6111yescharacteristic
893C2×C4C2×D4×D6111yescharacteristic
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4C2×#1175822411yescharacteristic
896C2×C4#1451982211yescharacteristic
897C2×C4#1451982211yescharacteristic
898C8—41no—
899C8—41no—
900C8—1222no—
901C8—2441no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—24no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—614no—
924C22—1222no—
925C22—1222no—
926C22—1222no—
927C22—1222no—
928C22—1222no—
929C22—1222no—
930C22—48816no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—4881no—
935C22—2442no—
936C22—2442no—
937C22—2442no—
938C22#102×D6114yescomplemented
939C22C2×C22⋊C4×D6111yescharacteristic
940C22#1684039411yescharacteristic
941C22#1684039911yescharacteristic
942C22C2×D8×D6111yescharacteristic
943C22C2×SD16×D6111yescharacteristic
944C22#1684056611yescharacteristic
945C22#1684057211yescharacteristic
946C4—22no—
947C4—81no—
948C4—81no—
949C4—614no—
950C4—1222no—
951C4—1222no—
952C4—4881no—
953C4—2442no—
954C4—2442no—
955C4C2×#1451973711yescharacteristic
956C4#1684023511yescharacteristic
957C4#1684039411yescharacteristic
958C4#1684039911yescharacteristic
959C2—24no—
960C2—44no—
961C2—82no—
962C2—1224no—
963C2—4882no—
964C2#2144863511yescharacteristic
965C2C2×#102×D6111yescharacteristic
966C2#2145434411yescharacteristic
967C2#2145748911yescharacteristic
968C2#2145751311yescharacteristic
969C2#2145762511yescharacteristic
970C2#2145763611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61D4×#102
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. C22×#14519698C2semidirect
4. C2×#102×D61C2semidirect
5. #21448715C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446245C2semidirect
9. #21446244C2semidirect
10. #21446134C2semidirect
11. #21446133C2semidirect
12. #21445817C2semidirect
13. #21445748C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1786C2semidirect
18. C23×#92418C22semidirect
19. C22×C8×D61C22semidirect
21. D4×C22⋊D61C4semidirect
31. C22×C4⋊Dic61C22semidirect
32. C2×C4⋊C4×D61C22semidirect
34. C2×#14519706C22semidirect
35. C2×#14519699C22semidirect
36. C2×#14519699C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519698C22semidirect
42. C2×#14519697C22semidirect
43. C2×#14519697C22semidirect
45. C2×#14519689C22semidirect
46. C2×C8×Dic61C22semidirect
50. #16839631C22semidirect
51. #16839619C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
80. C2×D4×D61C2×C4semidirect
94. #14519773C2×C4semidirect
96. #14519751C2×C4semidirect
99. #14519748C2×C4semidirect
103. D4×Dic61C2×C4semidirect
133. #14519698D4semidirect
147. C22×D4×C61C2×C4semidirect
283. C4⋊Dic61C2×D4semidirect
297. C2×#92418C2×D4semidirect
357. D4×C61C4×D4semidirect
382. C22⋊D61#102semidirect
438. C22×C61C2×#102semidirect
460. C2×D61C2×#102semidirect
473. Dic61C2×#102semidirect
487. #1786D61semidirect
533. C2×#102C2×D61semidirect
534. C2×#102C2×D61semidirect
536. C2×C22⋊C8C2×D61semidirect
543. #380C2×D61semidirect
549. C61D4×#102semidirect
574. C22×D4C4×D61semidirect
853. D4#14519737semidirect
938. C22#102×D61semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D612
C2×#168398252
C22×#145196982
C2×#102×D612
#214487152
#214467442
#214466232
#214462452
#214462442
#214461342
#214461332
#214458172
#214457482
#102×Dic612
C61×#17862
D4×#10261