Finite Group Databasebeta

← C4×#16840753 #30614140

Subgroups — C4×#16840753 #30614140

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840753C212yesmaximal
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#21461591C212yesmaximal, complemented
5#21461589C212yesmaximal, complemented
6C4×#14519840C212yesmaximal, complemented
7C4×#14519839C212yesmaximal, complemented
8#21461508C212yesmaximal, complemented
9C4×#41×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2212yes—
11C22×C4⋊#6923C2212yes—
12C22×C4×#6923—21no—
13#16840753C4116yesdirect product factor
14C2×#14519840C2214yes—
15C2×#14519839C2214yes—
16C4×#11758213—21no—
17C4×#11758213—21no—
18C4×#11758217—21no—
19C4×#11758217—21no—
20#16840721C2212yes—
21C4×D61⋊C8C2212yes—
22C4×C4⋊#6923—21no—
23C4×C4⋊#6923—21no—
24C4×C4⋊#6923C2212yes—
25C4×C4⋊#6923C2212yes—
26C2×(C2×#6923)⋊C4—21no—
27#16840635C2214yes—
28#16840635C2214yes—
29C2×#41×D61C2211yescharacteristic
30#41×Dic61C411yescharacteristic, complemented
31C4×#11758226C411yescharacteristic, complemented
32C4×#11758226C411yescharacteristic, complemented
33C4×#11758222—21no—
34C4×#11758222C411yescharacteristic, complemented
35#16840230—21no—
36#16840230C411yescharacteristic, complemented
37C4×#11758224—21no—
38C4×#11758224—21no—
39C4×#11758224C411yescharacteristic, complemented
40C4×#11758224C411yescharacteristic, complemented
41C4×Q8×D61C2211yescharacteristic
42C4×Q8×D61C2211yescharacteristic
43C4×D4×D61—21no—
44C4×D4×D61—21no—
45C4×D4×D61C2211yescharacteristic
46C4×D4×D61C2211yescharacteristic
47#117×D61—21no—
48#117×D61C2211yescharacteristic
49C2×C42×D61—21no—
50C2×C42×D61C2211yescharacteristic
51C4×#41×C61C411yescharacteristic, complemented
52C23×#6923—22no—
53C2×#11758213—22no—
54D61⋊M16—24no—
55D61⋊M16C2×C418yescomplemented
56C2×#11758217—22no—
57C2×D61⋊C8C2314yes—
58C2×C4⋊#6923—22no—
59C2×C4⋊#6923—24no—
60C2×C4⋊#6923C2×C418yescomplemented
61C2×C4⋊#6923C2314yes—
62C2×C4×#6923—22no—
63C2×C4×#6923—22no—
64C2×C4×#6923—44no—
65#14519840C2×C4116yescomplemented
66#14519839C2×C4116yescomplemented
67#14519832—22no—
68#14519832—22no—
69C4×#92420—22no—
70C4×#92420—22no—
71(C2×#6923)⋊C4—22no—
72(C2×#6923)⋊C4—22no—
73C2×#11758226C2×C411yescharacteristic
74C2×#11758222—21no—
75C2×#11758222C2×C411yescharacteristic
76C2×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic
78#41×D61—24no—
79#41×D61C2×C418yes—
80C2×Q8×D61C2311yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2311yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89Q8×Dic61C2×C411yescharacteristic, complemented
90Q8×Dic61C2×C411yescharacteristic, complemented
91C4×Dic122—21no—
92C4×Dic122—21no—
93C4×Dic122C2×C411yescharacteristic, complemented
94C4×Dic122C2×C411yescharacteristic, complemented
95#14519742—21no—
96#14519742—21no—
97#14519742C2×C411yescharacteristic, complemented
98#14519742C2×C411yescharacteristic, complemented
99C4×D244—21no—
100C4×D244—21no—
101C4×D244C2×C411yescharacteristic, complemented
102C4×D244C2×C411yescharacteristic, complemented
103D4×Dic61—21no—
104D4×Dic61—21no—
105D4×Dic61C2×C411yescharacteristic, complemented
106D4×Dic61C2×C411yescharacteristic, complemented
107#14519739—21no—
108#14519739—21no—
109#14519739C2×C411yescharacteristic, complemented
110#14519739C2×C411yescharacteristic, complemented
111C4×C22⋊D61—21no—
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117#14519737—21no—
118#14519737—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519736—21no—
124#14519736C2×C411yescharacteristic
125#14519735—21no—
126#14519735—21no—
127#14519735C2×C411yescharacteristic
128#14519735C2×C411yescharacteristic
129#14519734—21no—
130#14519734—21no—
131#14519734—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61—21no—
137C4⋊C4×D61C2311yescharacteristic
138C4⋊C4×D61C2311yescharacteristic
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C42×D61—21no—
149C42×D61—21no—
150C42×D61—21no—
151C42×D61—21no—
152C42×D61—21no—
153C42×D61—21no—
154C42×D61—21no—
155C42×D61C2×C411yescharacteristic
156C42×D61C2×C411yescharacteristic
157C42×D61D411yescharacteristic
158C42×D61D411yescharacteristic
159C42×D61D411yescharacteristic
160C42×D61D411yescharacteristic
161C42×D61C2311yescharacteristic
162C42×D61C2311yescharacteristic
163C2×#41×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic, complemented
165C4×Q8×C61C2×C411yescharacteristic, complemented
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61C2×C411yescharacteristic, complemented
169C4×D4×C61C2×C411yescharacteristic, complemented
170#117×C61—21no—
171#117×C61C2×C411yescharacteristic
172C2×C42×C61—21no—
173C2×C42×C61C2×C411yescharacteristic
174C23×D61—21no—
175C23×D61C2×D411yescharacteristic
176C22×#6923—28no—
177C22×#6923—24no—
178C22×#6923—44no—
179C22×#6923—44no—
180#41×C61—22no—
181#41×C61C4214yescomplemented
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C22⋊C411yescharacteristic
189C22×C4×C61C22⋊C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C22⋊C411yescharacteristic
198C22×Dic61C22⋊C411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200#11758226—22no—
201#11758226C4214yescomplemented
202Q8×D61—22no—
203Q8×D61C22×C414yes—
204#11758224—28no—
205#11758224—22no—
206#11758224C4214yescomplemented
207D4×D61—28no—
208D4×D61—22no—
209D4×D61C22×C414yes—
210#11758222—22no—
211#11758222—28no—
212#11758222C4214yescomplemented
213C2×D244—21no—
214C2×D244C22×C411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—28no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—42no—
228C2×C4×D61—44no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22⋊C411yescharacteristic
232C2×C4×D61C22⋊C411yescharacteristic
233C2×C4×D61C22⋊C411yescharacteristic
234C2×C4×D61C22⋊C411yescharacteristic
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C22×C414yes—
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61#4114yes—
244C2×C4×D61C2411yescharacteristic
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247#11758217—28no—
248C2×#92420—24no—
249C4⋊#6923—28no—
250C4⋊#6923—24no—
251C4⋊#6923C22×C418yes—
252C4×#6923—44no—
253C4×#6923—44no—
254#11758213—28no—
255D61⋊C8—24no—
256D61⋊C8C22×C418yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22×C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C42×C61—21no—
267C42×C61C22⋊C411yescharacteristic
268C42×C61C22⋊C411yescharacteristic
269C42×C61C22×C411yescharacteristic
270C42×C61C22×C411yescharacteristic
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61C22×C411yescharacteristic
283C4⋊Dic61C22×C411yescharacteristic
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290C4×Dic61—21no—
291C4×Dic61—21no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—21no—
297C4×Dic61—21no—
298C4×Dic61—21no—
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22⋊C411yescharacteristic
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22×C411yescharacteristic
306C4×Dic61C22×C411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C23×C61—21no—
312C23×C61C2×C22⋊C411yescharacteristic
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—22no—
316C22×D61—21no—
317C22×D61—24no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—42no—
321C22×D61C2×C22⋊C411yescharacteristic
322C22×D61C4×D414yes—
323C22×D61C22×D411yescharacteristic
324C2×#6923—28no—
325C2×#6923—416no—
326C2×#6923—44no—
327C2×#6923—44no—
328Q8×C61—21no—
329Q8×C61C2×C4212yescomplemented
330D4×C61—24no—
331D4×C61—21no—
332D4×C61C2×C4212yescomplemented
333C2×C4×C61—21no—
334C2×C4×C61—24no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—41no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61C2×C4212yes—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61#11712yes—
348C2×C4×C61C23×C411yescharacteristic
349C22⋊D61—24no—
350C22⋊D61—24no—
351C22⋊D61—24no—
352C2×Dic61—21no—
353C2×Dic61—24no—
354C2×Dic61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C4×D414yes—
366C2×Dic61C22×D411yescharacteristic
367D244—24no—
368D244—21no—
369D244C2×C4212yescomplemented
370C4×D61—24no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—42no—
382C4×D61—42no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—42no—
386C4×D61—42no—
387C4×D61—42no—
388C4×D61C2×C4212yes—
389C4×D61#11712yes—
390C4×D61C4×D414yes—
391C4×D61C4×D414yes—
392C4×D61AGL(1,ℤ/8)12yes—
393C4×D61#13712yes—
394C4×D61C23×C412yes—
395C4×D61C2×#4112yes—
396Dic122—21no—
397Dic122—24no—
398Dic122C2×C4212yescomplemented
399#92420—28no—
400C4×#417—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—22no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61C4×C22⋊C412yes—
407C22×C61C22×C22⋊C411yescharacteristic
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—22no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—44no—
416C2×D61—44no—
417C2×D61C4×C22⋊C412yes—
418C2×D61C2×C4×D412yes—
419C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
420C2×D61C2×#13711yescharacteristic
421C2×D61#57512yes—
422#6923—48no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—22no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61C4×C22⋊C412yes—
430C4×C61#41712yescomplemented
431C4×C61C22×C4211yescharacteristic
432C4×C61C2×#11711yescharacteristic
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—22no—
437Dic61—41no—
438Dic61—41no—
439Dic61C4×C22⋊C412yes—
440Dic61#41712yescomplemented
441Dic61C2×C4×D412yes—
442C2×C4×#41—611no—
443C2×#417—612no—
444C2×C4×M16—611no—
445C2×C4×C4⋊C4—611no—
446#1763—612no—
447#1762—612no—
448C4×#103—612no—
449C4×#102—612no—
450#1736—612no—
451C2×C61—22no—
452C2×C61—42no—
453C2×C61C2×C4×C22⋊C411yescharacteristic
454C2×C61C2×#41711yescharacteristic
455C2×C61#289611yescharacteristic
456D61—22no—
457D61—42no—
458D61C4×AGL(1,ℤ/8)12yes—
459D61C4×#13712yes—
460C22×#41—611no—
461C22×M16—612no—
462C4×#41—611no—
463C4×#41—611no—
464C4×#41—611no—
465C4×#41—611no—
466C4×#41—611no—
467C4×#41—611no—
468C4×#41—611no—
469C4×#41—1221no—
470C4×#41—1221no—
471C4×#41—1221no—
472C4×#41—1221no—
473C4×#41#692311yescharacteristic, complemented
474C2×C4×Q8—611no—
475C2×C4×Q8—611no—
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4—1221no—
479C2×C4×D4—1221no—
480C2×#117—611no—
481C2×#117—1221no—
482C22×C4⋊C4—612no—
483C22×C42—611no—
484C22×C42—1221no—
485C22×C42—1221no—
486#417—6116no—
487C2×#103—614no—
488C2×#102—614no—
489C4×M16—1221no—
490C4×M16—1221no—
491C4×M16—1221no—
492C4×M16—1221no—
493C2×#97—612no—
494C2×C4×C8—612no—
495C4×C4⋊C4—612no—
496C4×C4⋊C4—612no—
497C4×C4⋊C4—1221no—
498C4×C4⋊C4—1221no—
499C2×#95—1221no—
500#340—614no—
501#340—614no—
502C61C4×#41711yescharacteristic, complemented, Sylow
503C2×#41—618no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—1221no—
508C2×#41—1221no—
509C2×#41—1224no—
510C2×#41C2×#692311yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—1221no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4—1222no—
521C2×M16—618no—
522C2×M16—1222no—
523C2×M16—1224no—
524C2×M16—1222no—
525C22×C8—614no—
526C4×Q8—611no—
527C4×Q8—611no—
528C4×Q8—611no—
529C4×Q8—611no—
530C4×Q8—611no—
531C4×Q8—611no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8—1221no—
535C4×Q8—1221no—
536C4×Q8C2×#692311yescharacteristic, complemented
537C4×Q8C2×#692311yescharacteristic, complemented
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—611no—
541C4×D4—611no—
542C4×D4—611no—
543C4×D4—611no—
544C4×D4—611no—
545C4×D4—611no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4—1221no—
554C4×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4C2×#692311yescharacteristic, complemented
565C4×D4C2×#692311yescharacteristic, complemented
566#117—21no—
567#117—611no—
568#117—611no—
569#117—611no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117—1221no—
575#117—1221no—
576#117—1221no—
577#117—1221no—
578#117—1221no—
579#117C2×#692311yescharacteristic
580C2×C4⋊C4—618no—
581C2×C4⋊C4—614no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4—1224no—
587C2×C4⋊C4—1222no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—21no—
592C2×C42—611no—
593C2×C42—611no—
594C2×C42—611no—
595C2×C42—611no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—1221no—
604C2×C42—1221no—
605C2×C42—1221no—
606C2×C42—1221no—
607C2×C42—1221no—
608C2×C42—1221no—
609C2×C42—1221no—
610C2×C42—1221no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—2444no—
616C2×C42C2×#692311yescharacteristic
617#103—6116no—
618#102—6116no—
619#97—1222no—
620#97—1222no—
621C4×C8—1222no—
622C4×C8—1222no—
623#95—1222no—
624#95—1222no—
625C24—611no—
626C24—1221no—
627#41—22no—
628#41—614no—
629#41—614no—
630#41—614no—
631#41—1228no—
632#41—1228no—
633#41—1222no—
634#41—1222no—
635#41—1222no—
636#41C4×#692314yescomplemented
637C2×Q8—614no—
638C2×Q8—611no—
639C2×Q8—1221no—
640C2×Q8—1222no—
641C2×Q8C22×#692311yescharacteristic
642C2×D4—21no—
643C2×D4—614no—
644C2×D4—611no—
645C2×D4—1221no—
646C2×D4—1222no—
647C2×D4—1221no—
648C2×D4—1228no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4C22×#692311yescharacteristic
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—611no—
656C22×C4—614no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—614no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—1221no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1228no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1224no—
686C22×C4—1228no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4—2444no—
693C22×C4—2444no—
694C22×C4—2444no—
695C22×C4C22⋊#692311yescharacteristic
696C22×C4C22⋊#692311yescharacteristic
697C22×C4C22×#692311yescharacteristic
698M16—1228no—
699M16—1228no—
700C2×C8—618no—
701C2×C8—1224no—
702C2×C8—1224no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—618no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1224no—
715C4⋊C4—1228no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4C22×#692311yescharacteristic
719C4⋊C4C22×#692311yescharacteristic
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42—1221no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42—2444no—
757C42—2444no—
758C42C22⋊#692311yescharacteristic
759C42C22⋊#692311yescharacteristic
760C42C22×#692311yescharacteristic
761C42C22×#692311yescharacteristic
762C23—21no—
763C23—611no—
764C23—611no—
765C23—614no—
766C23—1221no—
767C23—1221no—
768C23—1222no—
769C23—1224no—
770C23—1221no—
771C23—2441no—
772C23—2441no—
773C23—2442no—
774C23C2×C22⋊#692311yescharacteristic
775Q8—21no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8C2×C4×#692312yescomplemented
780D4—24no—
781D4—21no—
782D4—612no—
783D4—1224no—
784D4—1224no—
785D4—1224no—
786D4—1224no—
787D4—1221no—
788D4C2×C4×#692312yescomplemented
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—614no—
801C2×C4—612no—
802C2×C4—612no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—612no—
807C2×C4—614no—
808C2×C4—614no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—1222no—
813C2×C4—1224no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1222no—
820C2×C4—1224no—
821C2×C4—1221no—
822C2×C4—1222no—
823C2×C4—1224no—
824C2×C4—1228no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4—2441no—
837C2×C4—2442no—
838C2×C4—2444no—
839C2×C4—2444no—
840C2×C4—24416no—
841C2×C4—2442no—
842C2×C4C2×C4×#692312yes—
843C2×C4C2×C22⋊#692311yescharacteristic
844C2×C4C2×C22⋊#692311yescharacteristic
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4#1451985612yes—
849C2×C4C23×#692311yescharacteristic
850C8—1228no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—611no—
857C22—611no—
858C22—612no—
859C22—612no—
860C22—612no—
861C22—1224no—
862C22—1224no—
863C22—1221no—
864C22—1221no—
865C22—1222no—
866C22—2444no—
867C22—2444no—
868C22—2441no—
869C22—2441no—
870C22C4×C22⋊#692312yes—
871C22C22×C22⋊#692311yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—612no—
879C4—612no—
880C4—612no—
881C4—1221no—
882C4—1221no—
883C4—1221no—
884C4—1222no—
885C4—2448no—
886C4—2441no—
887C4—2441no—
888C4C4×C22⋊#692312yes—
889C4#1684075312yesdirect product factor
890C4C22×C4×#692311yescharacteristic
891C4C2×#1451985611yescharacteristic
892C2—22no—
893C2—42no—
894C2—612no—
895C2—612no—
896C2—1222no—
897C2—2442no—
898C2C2×C4×C22⋊#692311yescharacteristic
899C2C2×#1684075311yescharacteristic
900C2#2146243911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61C4×#417
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C4×D61⋊M16C2semidirect
3. C2×C4×C4⋊#6923C2semidirect
4. #21461591C2semidirect
5. #21461589C2semidirect
6. C4×#14519840C2semidirect
7. C4×#14519839C2semidirect
8. #21461508C2semidirect
13. #16840753C4direct (N × H)
30. #41×Dic61C4semidirect
31. C4×#11758226C4semidirect
32. C4×#11758226C4semidirect
34. C4×#11758222C4semidirect
36. #16840230C4semidirect
39. C4×#11758224C4semidirect
40. C4×#11758224C4semidirect
51. C4×#41×C61C4semidirect
55. D61⋊M16C2×C4semidirect
60. C2×C4⋊#6923C2×C4semidirect
65. #14519840C2×C4semidirect
66. #14519839C2×C4semidirect
89. Q8×Dic61C2×C4semidirect
90. Q8×Dic61C2×C4semidirect
93. C4×Dic122C2×C4semidirect
94. C4×Dic122C2×C4semidirect
97. #14519742C2×C4semidirect
98. #14519742C2×C4semidirect
101. C4×D244C2×C4semidirect
102. C4×D244C2×C4semidirect
105. D4×Dic61C2×C4semidirect
106. D4×Dic61C2×C4semidirect
109. #14519739C2×C4semidirect
110. #14519739C2×C4semidirect
164. C4×Q8×C61C2×C4semidirect
165. C4×Q8×C61C2×C4semidirect
168. C4×D4×C61C2×C4semidirect
169. C4×D4×C61C2×C4semidirect
181. #41×C61C42semidirect
201. #11758226C42semidirect
206. #11758224C42semidirect
212. #11758222C42semidirect
329. Q8×C61C2×C42semidirect
332. D4×C61C2×C42semidirect
369. D244C2×C42semidirect
398. Dic122C2×C42semidirect
430. C4×C61#417semidirect
440. Dic61#417semidirect
473. C4×#41#6923semidirect
502. C61C4×#417semidirect
536. C4×Q8C2×#6923semidirect
537. C4×Q8C2×#6923semidirect
564. C4×D4C2×#6923semidirect
565. C4×D4C2×#6923semidirect
636. #41C4×#6923semidirect
779. Q8C2×C4×#6923semidirect
788. D4C2×C4×#6923semidirect
889. C4#16840753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407532
C4×D61⋊M162
C2×C4×C4⋊#69232
#214615912
#214615892
C4×#145198402
C4×#145198392
#214615082
C4×#41×D612
C4×#41761