Finite Group Databasebeta

← #102×C22⋊D61 #29695415

Subgroups — #102×C22⋊D61 #29695415

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×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446623C211yesmaximal, characteristic, complemented
7#21446247C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C22×#102×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic, complemented
19D4×C22⋊D61—24no—
20D4×C22⋊D61C418yescomplemented
21C2×#14519773C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic, complemented
33C2×#14519699C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic, complemented
41#102×D61—24no—
42C2×C22⋊#92418C2211yescharacteristic, complemented
43C2×#14519689C2211yescharacteristic, complemented
44C2×C8×Dic61C2211yescharacteristic, complemented
45#16839657—21no—
46#16839635—21no—
47#16839633—21no—
48#16839631C2211yescharacteristic, complemented
49#16839622C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic, complemented
58C22×C4⋊C4×C61C2211yescharacteristic, complemented
59C2×#102×C61—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C2×#102×C61C2211yescharacteristic, 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—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—22no—
87C2×C8×D61—22no—
88C2×C8×D61—41no—
89#14519773—22no—
90#14519773C2×C414yescomplemented
91#14519751—22no—
92#14519751C2×C414yescomplemented
93#14519749—28no—
94#14519748—22no—
95#14519748C2×C414yescomplemented
96#14519746—28no—
97#14519745—28no—
98D4×Dic61—22no—
99D4×Dic61C2×C414yescomplemented
100C4×C22⋊D61—44no—
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519706—22no—
122#14519699—22no—
123#14519699—41no—
124#14519698—22no—
125#14519698—22no—
126#14519698—41no—
127#14519698—41no—
128#14519697—22no—
129#14519697—41no—
130C22⋊#92418—22no—
131#14519689—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C25×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61—22no—
139C22×D4×C61—21no—
140C22×D4×C61—22no—
141C22×D4×C61—41no—
142C22×D4×C61—41no—
143C22×D4×C61C2×C414yescomplemented
144C22×D4×C61C2311yescharacteristic
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61—22no—
149C22×C8×C61—22no—
150C22×C8×C61—41no—
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153C2×C4⋊C4×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—41no—
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
158#102×C61—22no—
159#102×C61—22no—
160#102×C61—22no—
161#102×C61D414yescomplemented
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×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61—81no—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—432no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61—81no—
228C2×C22⋊D61—81no—
229C2×C22⋊D61C22⋊C414yes—
230C2×C22⋊D61D814yes—
231C2×C22⋊D61SD1614yes—
232C22×Dic61—21no—
233C22×Dic61—24no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—42no—
237C22×Dic61—42no—
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—44no—
266C2×C8×C61C2×D412yescomplemented
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—42no—
271C4⋊C4×C61C2×D412yescomplemented
272C22⋊Dic61—24no—
273C22⋊Dic61—24no—
274C22⋊Dic61—42no—
275C22⋊Dic61C22⋊C414yes—
276#11758198—24no—
277#11758198—42no—
278#11758198C22⋊C414yes—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C22×C412yes—
285#11758196—42no—
286#11758196—42no—
287#11758196—81no—
288#11758196C22⋊C414yes—
289C4×Dic61—42no—
290C4×Dic61C22×C412yes—
291C4×Dic61C2×D412yes—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
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—22no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—84no—
371C2×C4×C61C2×C22⋊C412yes—
372C2×C4×C61C23×C411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C2×#4111yescharacteristic
376C2×C4×C61H(5,𝔽2)11yescharacteristic
377C2×C4×C61H(5,𝔽2)11yescharacteristic
378C22⋊D61—48no—
379C22⋊D61—48no—
380C22⋊D61—48no—
381C22⋊D61—48no—
382C22⋊D61—84no—
383C22⋊D61#102116yesdirect product factor
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—22no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—48no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
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—22no—
413C8×C61—41no—
414#92418—41no—
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—42no—
463C4×C61—81no—
464C4×C61C2×C4×D411yescharacteristic
465C4×C61#51811yescharacteristic
466C4×C61D4211yescharacteristic
467C4×C61#54611yescharacteristic
468Dic61—22no—
469Dic61—22no—
470Dic61—42no—
471Dic61—81no—
472Dic61—81no—
473Dic61C2×#10214yescomplemented
474C2×D42—611no—
475C2×C8×D4—611no—
476C22×#102—611no—
477C22×#102D6111yescharacteristic, complemented
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#1786—611no—
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×C8C2×D6111yescharacteristic, complemented
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⋊C4C2×D6111yescharacteristic, complemented
519C8×D4—1224no—
520C2×C4⋊C8—611no—
521C2×#102—24no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—1224no—
531C2×#102C2×D6111yescharacteristic
532C2×#102C2×D6111yescharacteristic
533C2×#102C2×D6111yescharacteristic, complemented
534C2×#102C2×D6111yescharacteristic, complemented
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C4×C8—611no—
538#389—1221no—
539#385—1221no—
540#385—1221no—
541#384—611no—
542#380—611no—
543#380—611no—
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—21no—
578C23×C4—611no—
579C23×C4—1221no—
580C23×C4—1221no—
581C23×C4C22×D6111yescharacteristic
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—41no—
585C22×C8—611no—
586C22×C8—611no—
587C22×C8—1222no—
588C22×C8—1222no—
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—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—1221no—
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—22no—
633#102—1222no—
634#102—1222no—
635#102—1222no—
636#102—1222no—
637#102—2441no—
638#102—2441no—
639#102—2441no—
640#102—2441no—
641#102C22⋊D6114yesdirect product factor
642C22⋊C8—1222no—
643C22⋊C8—1222no—
644C4×C8—1222no—
645#95—1221no—
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×D4#1175822212yes—
714C2×D4C2×C22⋊D6112yes—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—81no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—1224no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—4881no—
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—44no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—2444no—
759C2×C8C2×C22⋊D6112yescomplemented
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—42no—
764C4⋊C4—614no—
765C4⋊C4—612no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—4881no—
772C4⋊C4—2442no—
773C4⋊C4—2442no—
774C4⋊C4C2×C22⋊D6112yescomplemented
775C22⋊C4—614no—
776C22⋊C4—614no—
777C22⋊C4—1224no—
778C22⋊C4—1224no—
779C22⋊C4—1224no—
780C22⋊C4—2442no—
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—
853D4C4×C22⋊D6114yescomplemented
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—84no—
867C2×C4—612no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—4884no—
882C2×C4—2448no—
883C2×C4—2441no—
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×C4C22×C22⋊D6111yescharacteristic
895C2×C4C2×#1175822211yescharacteristic
896C2×C4#1451982211yescharacteristic
897C2×C4#1451982211yescharacteristic
898C8—22no—
899C8—41no—
900C8—2441no—
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
940C22D4×C22⋊D6111yescharacteristic
941C22#1684040211yescharacteristic
942C22C2×D8×D6111yescharacteristic
943C22C2×SD16×D6111yescharacteristic
944C22#1684056311yescharacteristic
945C22#1684056811yescharacteristic
946C4—22no—
947C4—42no—
948C4—81no—
949C4—614no—
950C4—1222no—
951C4—1222no—
952C4—4881no—
953C4—4881no—
954C4—2442no—
955C4C2×C4×C22⋊D6111yescharacteristic
956C4#1684023511yescharacteristic
957C4D4×C22⋊D6111yescharacteristic
958C4#1684040211yescharacteristic
959C2—24no—
960C2—44no—
961C2—82no—
962C2—1224no—
963C2—4882no—
964C2C22⋊C4×C22⋊D6111yescharacteristic
965C2C2×#102×D6111yescharacteristic
966C2#2145434011yescharacteristic
967C2D8×C22⋊D6111yescharacteristic
968C2SD16×C22⋊D6111yescharacteristic
969C2#2145762811yescharacteristic
970C2#2145763911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61D4×#102
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. C2×#102×D61C2semidirect
4. C4⋊C4×C22⋊D61C2semidirect
5. #21446744C2semidirect
6. #21446623C2semidirect
7. #21446247C2semidirect
8. #21446244C2semidirect
9. #21446136C2semidirect
10. #21446133C2semidirect
11. #21445817C2semidirect
12. #21445750C2semidirect
13. #21445748C2semidirect
14. #102×Dic61C2semidirect
15. C22×#102×C61C2semidirect
18. C22×C8×D61C22semidirect
20. D4×C22⋊D61C4semidirect
30. C2×C4⋊C4×D61C22semidirect
32. C2×#14519706C22semidirect
33. C2×#14519699C22semidirect
34. C2×#14519699C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519697C22semidirect
40. C2×#14519697C22semidirect
42. C2×C22⋊#92418C22semidirect
43. C2×#14519689C22semidirect
44. C2×C8×Dic61C22semidirect
48. #16839631C22semidirect
49. #16839622C22semidirect
50. #16839619C22semidirect
51. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C23×C8×C61C22semidirect
58. C22×C4⋊C4×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×#102×C61C22semidirect
80. C2×D4×D61C2×C4semidirect
90. #14519773C2×C4semidirect
92. #14519751C2×C4semidirect
95. #14519748C2×C4semidirect
99. D4×Dic61C2×C4semidirect
143. C22×D4×C61C2×C4semidirect
161. #102×C61D4semidirect
266. C2×C8×C61C2×D4semidirect
271. C4⋊C4×C61C2×D4semidirect
357. D4×C61C4×D4semidirect
383. C22⋊D61#102direct (N × H)
438. C22×C61C2×#102semidirect
460. C2×D61C2×#102semidirect
473. Dic61C2×#102semidirect
477. C22×#102D61semidirect
505. C23×C8C2×D61semidirect
518. C22×C4⋊C4C2×D61semidirect
533. C2×#102C2×D61semidirect
534. C2×#102C2×D61semidirect
549. C61D4×#102semidirect
574. C22×D4C4×D61semidirect
641. #102C22⋊D61direct (N × H)
759. C2×C8C2×C22⋊D61semidirect
774. C4⋊C4C2×C22⋊D61semidirect
853. D4C4×C22⋊D61semidirect
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×C8×C22⋊D612
C2×#102×D612
C4⋊C4×C22⋊D612
#214467442
#214466232
#214462472
#214462442
#214461362
#214461332
#214458172
#214457502
#214457482
#102×Dic612
C22×#102×C612
D4×#10261