Finite Group Databasebeta

← #30608686

Subgroups — #30608686

Order 15616.

1710 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C212yesmaximal
2#21461000C212yesmaximal
3#21460999C212yesmaximal, complemented
4#21460997C211yesmaximal, characteristic, complemented
5#21460995C211yesmaximal, characteristic, complemented
6#21460994C212yesmaximal, complemented
7#21460993C211yesmaximal, characteristic
8#21460993C211yesmaximal, characteristic
9C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
10C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
11C4×C22⋊C4×D61C211yesmaximal, characteristic
12C22×C4⋊#6923C2212yes—
13C22×C22⋊#6923C2212yes—
14C22×C22⋊#6923C2212yes—
15C22×C4×#6923C2212yes—
16C22×C4×#6923C2212yes—
17#16840712C4116yescomplemented
18C2×(C2×#6923)⋊C4C2211yescharacteristic
19C2×(C2×#6923)⋊C4C2211yescharacteristic
20C2×(C2×#6923)⋊C4C2211yescharacteristic
21C2×(C2×#6923)⋊C4C2211yescharacteristic
22C2×(C2×#6923)⋊C4C2212yes—
23C2×(C2×#6923)⋊C4C2212yes—
24C2×(C2×#6923)⋊C4C2212yes—
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2212yes—
27C2×(C2×#6923)⋊C4C2212yes—
28C2×(C2×#6923)⋊C4C2212yes—
29C23×C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61C2211yescharacteristic
32C2×C42×D61C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34C22⋊C4×Dic61C411yescharacteristic, complemented
35C22⋊C4×Dic61C411yescharacteristic, complemented
36C4×#11758198C411yescharacteristic, complemented
37C4×#11758198C411yescharacteristic, complemented
38C4×C22⋊Dic61C411yescharacteristic, complemented
39#16839609C411yescharacteristic, complemented
40#16839609C411yescharacteristic, complemented
41#95×D61C2211yescharacteristic
42#95×D61C2211yescharacteristic
43C4×C22⋊C4×C61C411yescharacteristic, complemented
44C23×#6923C2312yes—
45C23×#6923C2312yes—
46C23×#6923C2312yes—
47C23×#6923C2312yes—
48C2×C4⋊#6923—42no—
49C2×C4⋊#6923—42no—
50C2×C4⋊#6923C2×C418yescomplemented
51C2×C22⋊#6923—42no—
52C2×C22⋊#6923—42no—
53C2×C22⋊#6923—42no—
54C2×C22⋊#6923—42no—
55C2×C22⋊#6923C2×C418yes—
56C2×C22⋊#6923C2×C418yes—
57C2×C4×#6923—24no—
58C2×C4×#6923—42no—
59C2×C4×#6923—42no—
60C2×C4×#6923—42no—
61C2×C4×#6923—42no—
62C2×C4×#6923C2×C418yescomplemented
63(C2×#6923)⋊C4—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—24no—
68(C2×#6923)⋊C4—42no—
69(C2×#6923)⋊C4—42no—
70(C2×#6923)⋊C4—42no—
71(C2×#6923)⋊C4—42no—
72(C2×#6923)⋊C4C2×C418yescomplemented
73(C2×#6923)⋊C4C2×C418yescomplemented
74C24×D61C2311yescharacteristic
75C23×Dic61C2×C411yescharacteristic
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—42no—
79C22×C4×D61—42no—
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C22⋊C4×D61—24no—
95C22⋊C4×D61C2×C418yes—
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C42×D61—42no—
103C42×D61—42no—
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110C23×C4×C61C2×C411yescharacteristic
111C2×C22⋊C4×C61C2×C411yescharacteristic
112C2×C22⋊C4×C61C2×C411yescharacteristic
113C2×C42×C61C2×C411yescharacteristic
114C2×C42×C61C2×C411yescharacteristic
115#95×C61C2×C411yescharacteristic
116#95×C61C2×C411yescharacteristic
117C24×C61C22×C411yescharacteristic
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61C22×C411yescharacteristic
128C23×D61C22×C414yes—
129C23×D61C2411yescharacteristic
130C22×#6923—22no—
131C22×#6923—22no—
132C22×#6923—22no—
133C22×#6923—22no—
134C22×#6923—22no—
135C22×#6923—22no—
136C22×#6923—22no—
137C22×#6923—22no—
138C22×#6923—22no—
139C22×#6923—22no—
140C22×#6923—22no—
141C22×#6923—22no—
142C22×#6923—22no—
143C22×#6923—22no—
144C22×#6923—22no—
145C22×#6923—22no—
146C22×#6923—22no—
147C22×#6923—22no—
148C22×#6923—22no—
149C22×#6923—22no—
150C22×#6923—22no—
151C22×#6923—22no—
152C22×#6923—22no—
153C22×#6923—22no—
154C22×#6923C22×C414yes—
155C22×#6923C22×C414yes—
156C22×#6923C22×C414yes—
157C22×#6923C22×C414yes—
158C22×C4×C61—22no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×Dic61—22no—
168C22×Dic61—41no—
169C22×Dic61—41no—
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—21no—
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—21no—
193C2×C4×D61—22no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—48no—
198C2×C4×D61—48no—
199C2×C4×D61—41no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61—41no—
203C2×C4×D61C22×C414yes—
204C2×C4×D61C22×C414yes—
205C2×C4×D61#4112yes—
206C2×C4×D61#4112yes—
207C2×C4×D61#4114yes—
208C22⋊#6923—48no—
209C22⋊#6923—48no—
210C4⋊#6923—48no—
211C4×#6923—48no—
212C4×#6923—48no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61C4214yescomplemented
215C42×C61—41no—
216C42×C61—41no—
217C22⋊Dic61—22no—
218C22⋊Dic61C4214yescomplemented
219#11758198—22no—
220#11758198—22no—
221#11758198C4214yescomplemented
222#11758198C4214yescomplemented
223C4×Dic61—41no—
224C4×Dic61—41no—
225C4×Dic61—41no—
226C4×Dic61—41no—
227C4×Dic61—41no—
228C4×Dic61—41no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61C2×C4212yes—
236C23×C61C23×C411yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—24no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—24no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—41no—
254C22×D61—42no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—42no—
259C22×D61C2×C4212yes—
260C22×D61C23×C412yes—
261C22×D61C2×#4111yescharacteristic
262C22×D61C2×#4111yescharacteristic
263C22×D61C2×#4112yes—
264C22×D61H(5,𝔽2)11yescharacteristic
265C22×D61H(5,𝔽2)11yescharacteristic
266C22×D61H(5,𝔽2)12yes—
267C22×D61H(5,𝔽2)12yes—
268C22×D612−1+411yescharacteristic
269C22×D612−1+411yescharacteristic
270C2×#6923—24no—
271C2×#6923—24no—
272C2×#6923—24no—
273C2×#6923—24no—
274C2×#6923—24no—
275C2×#6923—24no—
276C2×#6923—24no—
277C2×#6923—24no—
278C2×#6923—24no—
279C2×#6923—24no—
280C2×#6923—24no—
281C2×#6923—24no—
282C2×#6923—42no—
283C2×#6923—42no—
284C2×#6923—42no—
285C2×#6923—42no—
286C2×#6923—42no—
287C2×#6923—42no—
288C2×#6923—42no—
289C2×#6923—42no—
290C2×#6923—42no—
291C2×#6923—42no—
292C2×#6923—42no—
293C2×#6923—42no—
294C2×#6923—42no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—42no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—44no—
313C2×C4×C61C2×C4212yes—
314C2×C4×C61C2×C4212yes—
315C2×C4×C61#11712yes—
316C2×C4×C61#11712yes—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—44no—
332C2×Dic61C2×C4212yes—
333C2×Dic61C2×C4212yes—
334C2×Dic61#11712yes—
335C2×Dic61#11712yes—
336C4×D61—24no—
337C4×D61—24no—
338C4×D61—24no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—24no—
342C4×D61—24no—
343C4×D61—24no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—42no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61—42no—
350#13788—611nomaximal, Sylow
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C22×C4211yescharacteristic
359C22×C61C2×#11711yescharacteristic
360C22×C61C2×#11711yescharacteristic
361C22×C61#51811yescharacteristic
362C22×C61#51811yescharacteristic
363C22×C61#52011yescharacteristic
364C22×C61#52011yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61C4×#4112yes—
377C2×D61C4×#4112yes—
378C2×D61#51812yes—
379C2×D61#51812yes—
380C2×D61#52012yes—
381C2×D61#52012yes—
382C2×D61#53812yes—
383C2×D61#53812yes—
384C2×D61#53812yes—
385C2×D61#53912yes—
386C2×D61#54011yescharacteristic
387C2×D61#54012yes—
388C2×D61#54111yescharacteristic
389C2×D61#54212yes—
390C2×D61#54211yescharacteristic
391C2×D61#54211yescharacteristic
392#6923—44no—
393#6923—44no—
394#6923—44no—
395#6923—44no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—41no—
407Dic61—41no—
408C2×#388—612no—
409C2×C4×C22⋊C4—611no—
410#1437—612no—
411#1436—612no—
412C4⋊#95—611no—
413#1434—612no—
414#1434—611no—
415C22⋊#95—611no—
416C22⋊#95—611no—
417C4×#95—611no—
418C4×#95—611no—
419C2×C61—42no—
420C2×C61C4×#11711yescharacteristic
421C2×C61#227511yescharacteristic
422C2×C61#227511yescharacteristic
423C2×C61#231211yescharacteristic
424C2×C61#231411yescharacteristic
425C2×C61#231811yescharacteristic
426C2×C61#231911yescharacteristic
427D61—42no—
428D61#233312yes—
429D61#233412yes—
430D61#233512yes—
431D61#233712yes—
432C24×C4—611no—
433C22×C4⋊C4—612no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4—611no—
438C22×C42—612no—
439C22×C42—611no—
440C22×C42—611no—
441C22×C42—612no—
442#388—6116no—
443C4×C22⋊C4—611no—
444C4×C22⋊C4—611no—
445C4×C22⋊C4—611no—
446C4×C22⋊C4—611no—
447C4×C22⋊C4—611no—
448C4×C22⋊C4—611no—
449C4×C22⋊C4—611no—
450C4×C22⋊C4#692311yescharacteristic, complemented
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—611no—
454C2×#95—611no—
455C2×#95—611no—
456C2×#95—611no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—612no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C61#1378811yescharacteristic, complemented, Sylow
465C25—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—612no—
471C23×C4—612no—
472C23×C4—612no—
473C23×C4—612no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—1222no—
480C23×C4—1222no—
481C23×C4—2442no—
482C23×C4—2442no—
483C23×C4C2×#692311yescharacteristic
484C2×C4⋊C4—618no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4—2442no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—618no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—618no—
495C2×C22⋊C4—618no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—2442no—
498C2×C22⋊C4—2442no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4—2442no—
501C2×C22⋊C4C2×#692311yescharacteristic
502C2×C22⋊C4C2×#692311yescharacteristic
503C2×C42—618no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—1224no—
511C2×C42—2442no—
512C2×C42—2442no—
513C2×C42—2442no—
514C2×C42—2442no—
515C2×C42—2442no—
516C2×C42—2442no—
517C2×C42C2×#692311yescharacteristic
518C2×C42C2×#692311yescharacteristic
519#95—618no—
520#95—618no—
521#95—611no—
522#95—611no—
523#95—611no—
524#95—611no—
525#95—611no—
526#95—611no—
527#95—1222no—
528#95—1222no—
529#95—1222no—
530#95—1222no—
531#95—1224no—
532#95—2442no—
533#95—2442no—
534#95—2442no—
535#95—2442no—
536#95C2×#692311yescharacteristic
537#95C2×#692311yescharacteristic
538C24—611no—
539C24—614no—
540C24—611no—
541C24—1222no—
542C24—1221no—
543C24—1221no—
544C24—1222no—
545C24—1222no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24C22×#692311yescharacteristic
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—614no—
559C22×C4—614no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—614no—
565C22×C4—614no—
566C22×C4—614no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2441no—
616C22×C4—2441no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4—2448no—
620C22×C4—2448no—
621C22×C4—2441no—
622C22×C4—2441no—
623C22×C4C22×#692311yescharacteristic
624C22×C4C22×#692311yescharacteristic
625C22×C4C22×#692311yescharacteristic
626C22×C4C22×#692311yescharacteristic
627C22×C4C22×#692311yescharacteristic
628C22×C4C22×#692311yescharacteristic
629C4⋊C4—2448no—
630C22⋊C4—22no—
631C22⋊C4—614no—
632C22⋊C4—614no—
633C22⋊C4—614no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—2448no—
638C22⋊C4—2448no—
639C22⋊C4C4×#692314yescomplemented
640C42—41no—
641C42—41no—
642C42—2441no—
643C42—2441no—
644C42—2441no—
645C42—2441no—
646C42—2441no—
647C42—2441no—
648C42—2448no—
649C42—2448no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—612no—
657C23—611no—
658C23—611no—
659C23—612no—
660C23—612no—
661C23—612no—
662C23—611no—
663C23—611no—
664C23—611no—
665C23—611no—
666C23—612no—
667C23—1224no—
668C23—1224no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—2442no—
680C23—2442no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2442no—
686C23—2442no—
687C23—2442no—
688C23—2442no—
689C23C2×C4×#692312yes—
690C23C23×#692311yescharacteristic
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—44no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—1224no—
716C2×C4—1224no—
717C2×C4—1224no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2444no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4C2×C4×#692312yes—
768C2×C4C2×C4×#692312yes—
769C2×C4#1451985612yes—
770C2×C4#1451985612yes—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—612no—
779C22—612no—
780C22—611no—
781C22—611no—
782C22—611no—
783C22—611no—
784C22—612no—
785C22—612no—
786C22—612no—
787C22—612no—
788C22—612no—
789C22—612no—
790C22—612no—
791C22—612no—
792C22—612no—
793C22—612no—
794C22—1222no—
795C22—1222no—
796C22—1222no—
797C22—2444no—
798C22—2444no—
799C22—2444no—
800C22—2444no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22C22×C4×#692311yescharacteristic
806C22C2×#1451985611yescharacteristic
807C22C2×#1451985611yescharacteristic
808C22#1684082911yescharacteristic
809C22#1684082911yescharacteristic
810C22#1684083111yescharacteristic
811C22#1684083111yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—1222no—
819C4—1222no—
820C4—1222no—
821C4—1222no—
822C4—2444no—
823C4—2444no—
824C4—2444no—
825C4—2444no—
826C4—2441no—
827C4—2441no—
828C2—42no—
829C2—612no—
830C2—612no—
831C2—612no—
832C2—612no—
833C2—2442no—
834C2C4×#1451985611yescharacteristic
835C2#2146225811yescharacteristic
836C2#2146225811yescharacteristic
837C2#2146229511yescharacteristic
838C2#2146229711yescharacteristic
839C2#2146230111yescharacteristic
840C2#2146230211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC4×C22⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC4×C22⋊C4#6923
hypocenterC61#13788
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460999C2semidirect
4. #21460997C2semidirect
5. #21460995C2semidirect
6. #21460994C2semidirect
9. C4×(C2×#6923)⋊C4C2semidirect
10. C4×(C2×#6923)⋊C4C2semidirect
17. #16840712C4semidirect
34. C22⋊C4×Dic61C4semidirect
35. C22⋊C4×Dic61C4semidirect
36. C4×#11758198C4semidirect
37. C4×#11758198C4semidirect
38. C4×C22⋊Dic61C4semidirect
39. #16839609C4semidirect
40. #16839609C4semidirect
43. C4×C22⋊C4×C61C4semidirect
50. C2×C4⋊#6923C2×C4semidirect
62. C2×C4×#6923C2×C4semidirect
72. (C2×#6923)⋊C4C2×C4semidirect
73. (C2×#6923)⋊C4C2×C4semidirect
214. C22⋊C4×C61C42semidirect
218. C22⋊Dic61C42semidirect
221. #11758198C42semidirect
222. #11758198C42semidirect
450. C4×C22⋊C4#6923semidirect
464. C61#13788semidirect
639. C22⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
#214610002
#214609992
#214609972
#214609952
#214609942
#214609932
C4×(C2×#6923)⋊C42
C4×C22⋊C4×D612
#1378861