Finite Group Databasebeta

← C2×#21462553 #30625377

Subgroups — C2×#21462553 #30625377

Order 15616.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519864C211yesmaximal, characteristic, complemented
2C22×D61⋊M16C211yesmaximal, characteristic, complemented
3#21462553C2116yesmaximal, direct product factor
4C2×#16840796C211yesmaximal, characteristic, complemented
5C2×#16840795C211yesmaximal, characteristic, complemented
6C2×#16840794C211yesmaximal, characteristic, complemented
7C2×#16840792C211yesmaximal, characteristic, complemented
8C2×#16840792C211yesmaximal, characteristic, complemented
9C2×#16840791C211yesmaximal, characteristic, complemented
10C2×#16840790C211yesmaximal, characteristic, complemented
11C2×#16840789C211yesmaximal, characteristic, complemented
12C2×#16840768C211yesmaximal, characteristic, complemented
13C2×#16840735C211yesmaximal, characteristic, complemented
14C22×#14519834C211yesmaximal, characteristic, complemented
15C2×#16840726C211yesmaximal, characteristic, complemented
16C2×#16840270C211yesmaximal, characteristic
17C2×#14519864—28no—
18C2×#14519864C2218yescomplemented
19C22×#11758213C2211yescharacteristic
20C22×#11758213C2211yescharacteristic
21C22×#11758213C2211yescharacteristic, complemented
22C2×D61⋊M16—28no—
23C2×D61⋊M16C2218yescomplemented
24C22×#11758217C2211yescharacteristic
25C22×#11758217C2211yescharacteristic
26C22×#11758217C2211yescharacteristic, complemented
27C22×D61⋊C8C2211yescharacteristic
28C22×D61⋊C8C2211yescharacteristic
29C22×D61⋊C8C2211yescharacteristic, complemented
30C23×#92420C2211yescharacteristic
31C23×#92420C2211yescharacteristic
32C23×#92420C2211yescharacteristic, complemented
33#16840796C2218yescomplemented
34#16840795C2218yescomplemented
35#16840794C2218yescomplemented
36#16840792C2218yescomplemented
37#16840792C2218yescomplemented
38#16840791C2218yescomplemented
39#16840790C2218yescomplemented
40#16840789C2218yescomplemented
41#16840768C2218yescomplemented
42C2×#14519844C2211yescharacteristic, complemented
43C2×#14519844C2211yescharacteristic, complemented
44C2×C4⋊#92420C2211yescharacteristic, complemented
45C2×C4⋊#92420C2211yescharacteristic, complemented
46#16840735C2218yescomplemented
47C2×#14519834C2211yescharacteristic
48C2×#14519834C2211yescharacteristic
49C2×#14519834C2211yescharacteristic
50C2×#14519834C2211yescharacteristic
51C2×#14519834C2218yescomplemented
52C2×#14519834C2211yescharacteristic, complemented
53C2×#14519834C2211yescharacteristic, complemented
54C2×C22⋊#92420C2211yescharacteristic, complemented
55C2×C22⋊#92420C2211yescharacteristic, complemented
56#16840726C2218yescomplemented
57C2×#14519832C2211yescharacteristic, complemented
58C2×#14519832C2211yescharacteristic, complemented
59C2×C4×#92420C2211yescharacteristic, complemented
60C2×C4×#92420C2211yescharacteristic, complemented
61C22×#11758224C2211yescharacteristic
62C23×C4×D61C2211yescharacteristic
63#16840270C418yes—
64#16840270C2218yes—
65C2×#14519760C411yescharacteristic
66C2×#14519755C411yescharacteristic
67C2×#14519755C411yescharacteristic
68C2×#14519750C411yescharacteristic
69C2×#14519750C411yescharacteristic
70C2×#14519747C411yescharacteristic
71C2×#14519745C411yescharacteristic
72C2×#14519739C2211yescharacteristic
73C2×#14519739C2211yescharacteristic
74C2×#14519737C2211yescharacteristic
75C2×#14519737C2211yescharacteristic
76C2×#14519733C2211yescharacteristic
77C2×#123×C61C411yescharacteristic
78#14519864—232no—
79C2×#11758213—24no—
80C2×#11758213—24no—
81C2×#11758213—24no—
82C2×#11758213C2314yes—
83C2×#11758213C2314yes—
84C2×#11758213C2314yescomplemented
85D61⋊M16—232no—
86C2×#11758217—24no—
87C2×#11758217—24no—
88C2×#11758217D418yescomplemented
89C2×#11758217C2314yes—
90C2×#11758217C2314yes—
91C2×#11758217C2314yescomplemented
92C2×D61⋊C8—24no—
93C2×D61⋊C8—24no—
94C2×D61⋊C8—24no—
95C2×D61⋊C8C2314yes—
96C2×D61⋊C8C2314yes—
97C2×D61⋊C8C2314yescomplemented
98C22×#92420—24no—
99C22×#92420—24no—
100C22×#92420—24no—
101C22×#92420C2311yescharacteristic
102C22×#92420C2311yescharacteristic
103C22×#92420C2314yes—
104C22×#92420C2311yescharacteristic
105C22×#92420C2311yescharacteristic
106C22×#92420C2311yescharacteristic
107C22×#92420C2311yescharacteristic
108C22×#92420C2314yes—
109C22×#92420C2311yescharacteristic
110C22×#92420C2311yescharacteristic
111C22×#92420C2314yescomplemented
112#14519844C2314yescomplemented
113#14519844C2314yescomplemented
114C4⋊#92420C2314yescomplemented
115C4⋊#92420C2314yescomplemented
116#14519834C2314yes—
117#14519834C2314yes—
118#14519834C2314yes—
119#14519834C2314yes—
120#14519834C2314yescomplemented
121#14519834C2314yescomplemented
122C22⋊#92420C2314yescomplemented
123C22⋊#92420C2314yescomplemented
124#14519832C2314yescomplemented
125#14519832C2314yescomplemented
126C4×#92420C2314yescomplemented
127C4×#92420C2314yescomplemented
128C24×D61C2×C411yescharacteristic
129C2×#11758224—24no—
130C2×#11758224—24no—
131C2×#11758224C2×C414yes—
132C2×#11758224C2314yes—
133C22×Dic122C2×C411yescharacteristic
134C22×D244C2×C411yescharacteristic
135C22×D244C2×C411yescharacteristic
136C22×C22⋊D61C2×C411yescharacteristic
137C22×C22⋊D61C2×C411yescharacteristic
138C22×C22⋊D61C2×C411yescharacteristic
139C22×C22⋊D61C2×C411yescharacteristic
140C23×Dic61C2311yescharacteristic
141C23×Dic61C2311yescharacteristic
142C22×C4×D61—24no—
143C22×C4×D61—24no—
144C22×C4×D61C2×C411yescharacteristic
145C22×C4×D61C2×C411yescharacteristic
146C22×C4×D61C2×C414yes—
147C22×C4×D61C2311yescharacteristic
148C22×C4×D61C2311yescharacteristic
149C22×C4×D61C2311yescharacteristic
150C22×C4×D61C2314yes—
151#14519760C2×C418yes—
152#14519755C2×C418yes—
153#14519755C2×C418yes—
154#14519750C2×C418yes—
155#14519750C2×C418yes—
156#14519747C2×C418yes—
157#14519745C2×C418yes—
158#14519739C2×C414yes—
159#14519739C2×C414yes—
160#14519739C2314yes—
161#14519739C2314yes—
162#14519737C2×C414yes—
163#14519737C2×C414yes—
164#14519737C2314yes—
165#14519737C2314yes—
166#14519733C2×C414yes—
167#14519733C2314yes—
168C2×#11758196C2×C411yescharacteristic
169C2×#11758196C2×C411yescharacteristic
170C2×#11758196C2×C411yescharacteristic
171C2×#11758196C2×C411yescharacteristic
172C2×C22⋊Dic61C2×C411yescharacteristic
173C2×#11758198C2×C411yescharacteristic
174C2×#11758198C2×C411yescharacteristic
175C2×#11758198C2×C411yescharacteristic
176C2×#11758198C2×C411yescharacteristic
177C2×#11758198C2×C411yescharacteristic
178C2×#11758198C2×C411yescharacteristic
179C2×C4×Dic61C2311yescharacteristic
180C2×C4×Dic61C2311yescharacteristic
181C22×D4×C61C2×C411yescharacteristic
182C23×C4×C61C2×C411yescharacteristic
183#123×C61C2×C418yes—
184C2×C4⋊C4×C61C2×C411yescharacteristic
185C2×C4⋊C4×C61C2×C411yescharacteristic
186C2×C22⋊C4×C61C2×C411yescharacteristic
187C2×C22⋊C4×C61C2×C411yescharacteristic
188C2×C22⋊C4×C61C2×C411yescharacteristic
189C24×C61C22×C411yescharacteristic
190C24×C61C22×C411yescharacteristic
191C23×D61—24no—
192C23×D61—24no—
193C23×D61—42no—
194C23×D61C22×C411yescharacteristic
195C23×D61C22×C411yescharacteristic
196C23×D61C22×C414yes—
197C23×D61C22×C411yescharacteristic
198C2×D4×C61—24no—
199C2×D4×C61C22×C414yes—
200C22×C4×C61—24no—
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C414yes—
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61C22×C414yes—
212C2×C22⋊D61C22×C414yes—
213C2×C22⋊D61C22×C414yes—
214C2×C22⋊D61C22×C414yes—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C412yes—
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C412yes—
223C22×Dic61C2×D414yes—
224C22×Dic61#4114yes—
225C22×Dic61C2412yes—
226C22×Dic61C2411yescharacteristic
227C22×Dic61C2412yes—
228#11758224—216no—
229#11758224—28no—
230#11758224—28no—
231C2×D244—24no—
232C2×D244—42no—
233C2×D244C22×C414yes—
234C2×D244C22×C414yes—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—216no—
238C2×C4×D61—22no—
239C2×C4×D61—28no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—28no—
245C2×C4×D61—22no—
246C2×C4×D61C22×C412yes—
247C2×C4×D61C22×C412yes—
248C2×C4×D61C22×C414yes—
249C2×C4×D61C22×C414yes—
250C2×C4×D61C22×C412yes—
251C2×C4×D61C2412yes—
252C2×C4×D61C2412yes—
253C2×C4×D61C2412yes—
254C2×Dic122—24no—
255C2×Dic122C22×C414yes—
256#11758217—28no—
257#11758217—28no—
258#11758217C2×D4116yescomplemented
259C2×#92420—22no—
260C2×#92420—22no—
261C2×#92420—28no—
262C2×#92420—22no—
263C2×#92420—22no—
264C2×#92420—22no—
265C2×#92420—22no—
266C2×#92420—28no—
267C2×#92420—28no—
268C2×#92420C2×D414yes—
269C2×#92420C2×D414yes—
270C2×#92420C2412yes—
271C2×#92420C2412yes—
272C2×#92420C2412yes—
273C2×#92420C2412yes—
274C2×#92420C2412yes—
275C2×#92420C2412yes—
276C2×#92420C2412yes—
277C2×#92420C2412yes—
278#11758213—28no—
279#11758213—28no—
280#11758213—28no—
281D61⋊C8—28no—
282D61⋊C8—28no—
283D61⋊C8—28no—
284C4⋊C4×C61C22×C414yes—
285C4⋊C4×C61C22×C414yes—
286C22⋊C4×C61C22×C414yes—
287C22⋊C4×C61C22×C414yes—
288C22⋊C4×C61C22×C414yes—
289C22⋊Dic61C22×C414yes—
290#11758198C22×C414yes—
291#11758198C22×C414yes—
292#11758198C22×C414yes—
293#11758198C22×C414yes—
294#11758198C22×C414yes—
295#11758198C22×C414yes—
296#11758196C22×C414yes—
297#11758196C22×C414yes—
298#11758196C22×C414yes—
299#11758196C22×C414yes—
300C4×Dic61C22×C412yes—
301C4×Dic61C22×C412yes—
302C4×Dic61C2412yes—
303C4×Dic61C2412yes—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61C4×D414yes—
310C23×C61C23×C412yes—
311C23×C61C23×C412yes—
312C23×C61C23×C411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—28no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—28no—
323C22×D61—44no—
324C22×D61—416no—
325C22×D61#13114yescomplemented
326C22×D61C23×C412yes—
327C22×D61C23×C412yes—
328C22×D61C23×C412yes—
329D4×C61—28no—
330C2×C4×C61—22no—
331C2×C4×C61—28no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61C23×C412yes—
337C2×C4×C61C23×C412yes—
338C2×C4×C61C23×C412yes—
339C2×C4×C61C23×C412yes—
340C2×C4×C61C23×C412yes—
341C22⋊D61—28no—
342C22⋊D61—28no—
343C22⋊D61—28no—
344C22⋊D61—44no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—24no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61C4×D414yes—
352C2×Dic61C4×D418yes—
353C2×Dic61C23×C412yes—
354C2×Dic61C23×C412yes—
355C2×Dic61C23×C412yes—
356C2×Dic61C23×C411yescharacteristic
357C2×Dic61C23×C412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D414yes—
360C2×Dic61C2×#4112yes—
361C2×Dic61C2×#4114yes—
362C2×Dic61C2511yescharacteristic
363D244—28no—
364D244—44no—
365C4×D61—28no—
366C4×D61—28no—
367C4×D61—24no—
368C4×D61—24no—
369C4×D61—24no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376Dic122—28no—
377#92420—22no—
378#92420—22no—
379#92420—22no—
380#92420—22no—
381#92420—22no—
382#92420—22no—
383#92420C22×D414yes—
384#92420C22×D414yes—
385C2×#2933—611nomaximal, Sylow
386C22×C61—28no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—44no—
393C22×C61C2×C4×D414yes—
394C22×C61C2×C4×D412yes—
395C22×C61C2×#13112yes—
396C22×C61#56812yes—
397C22×C61C24×C411yescharacteristic
398C2×D61—22no—
399C2×D61—28no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—416no—
408C2×D61—44no—
409C2×D61—44no—
410C2×D61C2×#13114yescomplemented
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—22no—
416Dic61—22no—
417Dic61—22no—
418Dic61—22no—
419Dic61C2×C4×D414yes—
420Dic61C2×C4×D412yes—
421Dic61C23×D411yescharacteristic
422Dic61C22×#4111yescharacteristic
423C22×#131—611no—
424C23×M16—611no—
425C2×#525—611no—
426#2933—6116no—
427C2×#436—611no—
428C2×#436—611no—
429C2×#435—611no—
430C2×#435—611no—
431C2×#435—611no—
432C2×#435—611no—
433C2×C8×D4—611no—
434C2×C8×D4—611no—
435C2×#424—611no—
436C2×#408—611no—
437C22×C22⋊C8—611no—
438C2×#405—611no—
439C2×C61—24no—
440C2×C61—42no—
441C2×C61#293314yescomplemented
442C2×C61C22×C4×D411yescharacteristic
443C2×C61C22×#13111yescharacteristic
444C2×C61C2×#56811yescharacteristic
445D61—24no—
446D61—42no—
447D61—42no—
448C22×#41—611no—
449C24×C4—611no—
450C2×#131—618no—
451C2×#131—1228no—
452C22×M16—611no—
453C22×M16—611no—
454C22×M16—611no—
455C22×M16—611no—
456C22×M16—611no—
457C22×M16—611no—
458C22×M16—618no—
459C22×M16—1228no—
460C23×C8—611no—
461C23×C8—611no—
462C23×C8—611no—
463C23×C8—611no—
464C23×C8—611no—
465C23×C8—611no—
466#525—618no—
467#525—618no—
468C2×#123—611no—
469C2×#123#692311yescharacteristic
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—611no—
472C2×#121—611no—
473C2×#121—611no—
474C2×#120—611no—
475C2×#120—611no—
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4—611no—
479C2×C4×D4—611no—
480C2×#117—611no—
481#436—618no—
482#436—618no—
483#435—618no—
484#435—618no—
485#435—618no—
486#435—618no—
487C8×D4—618no—
488C8×D4—618no—
489#424—618no—
490C2×C4⋊C8—611no—
491C2×C4⋊C8—611no—
492C2×C4⋊C8—611no—
493C2×C4⋊C8—611no—
494#408—618no—
495C2×C22⋊C8—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8—611no—
499C2×C22⋊C8—611no—
500C2×C22⋊C8—611no—
501C2×C22⋊C8—618no—
502C2×C22⋊C8—611no—
503C2×C22⋊C8—611no—
504#405—618no—
505C2×#97—611no—
506C2×#97—611no—
507C2×C4×C8—611no—
508C2×C4×C8—611no—
509C61C2×#293311yescharacteristic, complemented, Sylow
510C25—611no—
511C2×#41—614no—
512C2×#41—614no—
513C2×#41—1224no—
514C2×#41—1224no—
515C22×Q8—611no—
516C22×D4—611no—
517C22×D4—611no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—611no—
522C22×D4C2×#692311yescharacteristic
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—611no—
530C23×C4—614no—
531C23×C4—614no—
532C23×C4—1224no—
533C23×C4—1224no—
534C23×C4C2×#692311yescharacteristic
535#131—12232no—
536C2×M16—618no—
537C2×M16—614no—
538C2×M16—614no—
539C2×M16—614no—
540C2×M16—614no—
541C2×M16—614no—
542C2×M16—614no—
543C2×M16—1224no—
544C2×M16—1224no—
545C2×M16—1224no—
546C2×M16—1224no—
547C2×M16—12232no—
548C2×M16—1224no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—611no—
555C22×C8—614no—
556C22×C8—611no—
557C22×C8—611no—
558C22×C8—614no—
559C22×C8—614no—
560C22×C8—614no—
561C22×C8—614no—
562C22×C8—614no—
563C22×C8—1224no—
564C22×C8—1224no—
565C22×C8—1224no—
566C22×C8—1224no—
567C22×C8—1224no—
568C22×C8—1224no—
569#123—618no—
570#123C2×#692318yes—
571C22⋊Q8—618no—
572C22⋊Q8—618no—
573#121—618no—
574#121—618no—
575#120—618no—
576#120—618no—
577C4×D4—614no—
578C4×D4—614no—
579C4×D4—614no—
580C4×D4—614no—
581C4×D4—614no—
582C4×D4—614no—
583C4×D4—614no—
584C4×D4—614no—
585#117—614no—
586#117—614no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4C2×#692311yescharacteristic
592C2×C4⋊C4C2×#692311yescharacteristic
593C2×C22⋊C4—611no—
594C2×C22⋊C4—611no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—611no—
597C2×C22⋊C4—611no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4C2×#692311yescharacteristic
601C2×C22⋊C4C2×#692311yescharacteristic
602C2×C22⋊C4C2×#692311yescharacteristic
603C2×C42—611no—
604C2×C42—611no—
605C4⋊C8—614no—
606C4⋊C8—614no—
607C4⋊C8—614no—
608C4⋊C8—614no—
609C22⋊C8—614no—
610C22⋊C8—614no—
611C22⋊C8—614no—
612C22⋊C8—614no—
613C22⋊C8—614no—
614C22⋊C8—614no—
615C22⋊C8—614no—
616C22⋊C8—614no—
617#97—614no—
618#97—614no—
619C4×C8—614no—
620C4×C8—614no—
621C24—611no—
622C24—611no—
623C24—611no—
624C24—614no—
625C24—1224no—
626C24—1224no—
627C24—2442no—
628C24C22×#692311yescharacteristic
629C24C22×#692311yescharacteristic
630#41—1228no—
631#41—12216no—
632#41—1228no—
633C2×Q8—614no—
634C2×Q8—1224no—
635C2×D4—24no—
636C2×D4—614no—
637C2×D4—614no—
638C2×D4—614no—
639C2×D4—614no—
640C2×D4—614no—
641C2×D4—614no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4C22×#692314yes—
649C22×C4—24no—
650C22×C4—614no—
651C22×C4—614no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—614no—
668C22×C4—614no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1228no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—12216no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1228no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4C22×#692314yes—
683C22×C4C22×#692311yescharacteristic
684C22×C4C22×#692311yescharacteristic
685C22×C4C22×#692311yescharacteristic
686C22×C4C22×#692311yescharacteristic
687C22×C4C22×#692311yescharacteristic
688M16—6116no—
689M16—1228no—
690M16—1228no—
691M16—1228no—
692M16—1228no—
693M16—1228no—
694C2×C8—612no—
695C2×C8—612no—
696C2×C8—614no—
697C2×C8—614no—
698C2×C8—612no—
699C2×C8—612no—
700C2×C8—612no—
701C2×C8—612no—
702C2×C8—612no—
703C2×C8—612no—
704C2×C8—1228no—
705C2×C8—1228no—
706C2×C8—1228no—
707C2×C8—1228no—
708C2×C8—1222no—
709C2×C8—1222no—
710C2×C8—1222no—
711C2×C8—1222no—
712C2×C8—1228no—
713C2×C8—1222no—
714C2×C8—1222no—
715C2×C8—1228no—
716C4⋊C4—614no—
717C4⋊C4—614no—
718C4⋊C4—614no—
719C4⋊C4—614no—
720C4⋊C4C22×#692314yes—
721C4⋊C4C22×#692314yes—
722C22⋊C4—614no—
723C22⋊C4—614no—
724C22⋊C4—614no—
725C22⋊C4—614no—
726C22⋊C4—614no—
727C22⋊C4—614no—
728C22⋊C4—614no—
729C22⋊C4C22×#692314yes—
730C22⋊C4C22×#692314yes—
731C22⋊C4C22×#692314yes—
732C42—612no—
733C42—612no—
734C42—612no—
735C42—612no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—614no—
742C23—612no—
743C23—612no—
744C23—612no—
745C23—1228no—
746C23—1222no—
747C23—1222no—
748C23—1228no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1222no—
754C23—1222no—
755C23—2444no—
756C23—24416no—
757C23D4×#692314yes—
758C23C23×#692312yes—
759C23C23×#692312yes—
760C23C23×#692311yescharacteristic
761Q8—1228no—
762D4—28no—
763D4—1228no—
764D4—1228no—
765D4—1228no—
766D4—1228no—
767D4—2444no—
768D4—2444no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—614no—
776C2×C4—618no—
777C2×C4—612no—
778C2×C4—614no—
779C2×C4—612no—
780C2×C4—614no—
781C2×C4—611no—
782C2×C4—612no—
783C2×C4—611no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1224no—
791C2×C4—1224no—
792C2×C4—1228no—
793C2×C4—1228no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1224no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1224no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4C23×#692312yes—
805C2×C4C23×#692312yes—
806C2×C4C23×#692312yes—
807C2×C4C23×#692312yes—
808C2×C4C23×#692312yes—
809C8—614no—
810C8—614no—
811C8—1222no—
812C8—1222no—
813C8—1222no—
814C8—1222no—
815C8—1222no—
816C8—1222no—
817C22—22no—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—614no—
825C22—1222no—
826C22—1228no—
827C22—1222no—
828C22—1222no—
829C22—1222no—
830C22—1222no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—24416no—
835C22—2444no—
836C22—2444no—
837C22C2×D4×#692314yes—
838C22C2×D4×#692312yes—
839C22D61⋊#13112yes—
840C22#1684084112yes—
841C22C24×#692311yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—612no—
848C4—614no—
849C4—611no—
850C4—611no—
851C4—1222no—
852C4—1222no—
853C4—1222no—
854C2—24no—
855C2—42no—
856C2—1224no—
857C2—2442no—
858C2—2442no—
859C2#2146255314yesdirect product factor
860C2C22×D4×#692311yescharacteristic
861C2C2×D61⋊#13111yescharacteristic
862C2C2×#1684084111yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#123×C61C4
socleC23×C61C23×C4
prime radicalC2×#16840270C2
cosocleC2×Dic61C25
hypercenterC2×#123#6923
hypocenterC61C2×#2933
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#14519864C2semidirect
2. C22×D61⋊M16C2semidirect
3. #21462553C2direct (N × H)
4. C2×#16840796C2semidirect
5. C2×#16840795C2semidirect
6. C2×#16840794C2semidirect
7. C2×#16840792C2semidirect
8. C2×#16840792C2semidirect
9. C2×#16840791C2semidirect
10. C2×#16840790C2semidirect
11. C2×#16840789C2semidirect
12. C2×#16840768C2semidirect
13. C2×#16840735C2semidirect
14. C22×#14519834C2semidirect
15. C2×#16840726C2semidirect
18. C2×#14519864C22semidirect
21. C22×#11758213C22semidirect
23. C2×D61⋊M16C22semidirect
26. C22×#11758217C22semidirect
29. C22×D61⋊C8C22semidirect
32. C23×#92420C22semidirect
33. #16840796C22semidirect
34. #16840795C22semidirect
35. #16840794C22semidirect
36. #16840792C22semidirect
37. #16840792C22semidirect
38. #16840791C22semidirect
39. #16840790C22semidirect
40. #16840789C22semidirect
41. #16840768C22semidirect
42. C2×#14519844C22semidirect
43. C2×#14519844C22semidirect
44. C2×C4⋊#92420C22semidirect
45. C2×C4⋊#92420C22semidirect
46. #16840735C22semidirect
51. C2×#14519834C22semidirect
52. C2×#14519834C22semidirect
53. C2×#14519834C22semidirect
54. C2×C22⋊#92420C22semidirect
55. C2×C22⋊#92420C22semidirect
56. #16840726C22semidirect
57. C2×#14519832C22semidirect
58. C2×#14519832C22semidirect
59. C2×C4×#92420C22semidirect
60. C2×C4×#92420C22semidirect
84. C2×#11758213C23semidirect
88. C2×#11758217D4semidirect
91. C2×#11758217C23semidirect
97. C2×D61⋊C8C23semidirect
111. C22×#92420C23semidirect
112. #14519844C23semidirect
113. #14519844C23semidirect
114. C4⋊#92420C23semidirect
115. C4⋊#92420C23semidirect
120. #14519834C23semidirect
121. #14519834C23semidirect
122. C22⋊#92420C23semidirect
123. C22⋊#92420C23semidirect
124. #14519832C23semidirect
125. #14519832C23semidirect
126. C4×#92420C23semidirect
127. C4×#92420C23semidirect
258. #11758217C2×D4semidirect
325. C22×D61#131semidirect
410. C2×D61C2×#131semidirect
441. C2×C61#2933semidirect
509. C61C2×#2933semidirect
859. C2#21462553direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198642
C22×D61⋊M162
#214625532
C2×#168407962
C2×#168407952
C2×#168407942
C2×#168407922
C2×#168407912
C2×#168407902
C2×#168407892
C2×#168407682
C2×#168407352
C22×#145198342
C2×#168407262
C2×#168402702
C2×#293361