Finite Group Databasebeta

← #30608741

Subgroups — #30608741

Order 15616.

1906 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
1C2×#16840712C212yesmaximal
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840698C211yesmaximal, characteristic, complemented
4#21461000C212yesmaximal
5#21460999C212yesmaximal, complemented
6#21460997C211yesmaximal, characteristic, complemented
7#21460995C211yesmaximal, characteristic, complemented
8#21460993C211yesmaximal, characteristic
9C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
10#95×#6923C212yesmaximal, complemented
11C4×C22⋊C4×D61C211yesmaximal, characteristic
12C22×C4⋊#6923C2212yes—
13C22×C22⋊#6923C2212yes—
14C22×C22⋊#6923C2212yes—
15C22×C4×#6923C2212yes—
16C22×C4×#6923C2212yes—
17C22×C4×#6923C2212yes—
18#16840712C4116yescomplemented
19C4×C22⋊#6923—24no—
20#16840698—24no—
21C2×(C2×#6923)⋊C4C2211yescharacteristic
22C2×(C2×#6923)⋊C4C2211yescharacteristic
23C2×(C2×#6923)⋊C4C2212yes—
24C2×(C2×#6923)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2212yes—
27C2×(C2×#6923)⋊C4C2212yes—
28C2×(C2×#6923)⋊C4C2212yes—
29C2×(C2×#6923)⋊C4C2212yes—
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C23×C4×D61C2211yescharacteristic
32C2×C22⋊C4×D61C2211yescharacteristic
33C2×C22⋊C4×D61C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35C2×C42×D61C2211yescharacteristic
36C22⋊C4×Dic61C411yescharacteristic, complemented
37C22⋊C4×Dic61C411yescharacteristic, complemented
38C4×#11758198C411yescharacteristic, complemented
39C4×#11758198C411yescharacteristic, complemented
40C4×C22⋊Dic61C411yescharacteristic, complemented
41#16839609C411yescharacteristic, complemented
42#16839609C411yescharacteristic, complemented
43#95×D61C2211yescharacteristic
44#95×D61C2211yescharacteristic
45C4×C22⋊C4×C61C411yescharacteristic, complemented
46C23×#6923C2312yes—
47C23×#6923C2312yes—
48C23×#6923C2312yes—
49C23×#6923C2312yes—
50C2×C4⋊#6923—42no—
51C2×C4⋊#6923—42no—
52C2×C4⋊#6923C2×C418yescomplemented
53C2×C22⋊#6923—24no—
54C2×C22⋊#6923—24no—
55C2×C22⋊#6923—42no—
56C2×C22⋊#6923—42no—
57C2×C22⋊#6923C2×C418yes—
58C2×C22⋊#6923C2×C418yes—
59C2×C4×#6923—24no—
60C2×C4×#6923—24no—
61C2×C4×#6923—24no—
62C2×C4×#6923—24no—
63C2×C4×#6923—24no—
64C2×C4×#6923—24no—
65C2×C4×#6923—42no—
66C2×C4×#6923—42no—
67C2×C4×#6923C2×C418yescomplemented
68(C2×#6923)⋊C4—24no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—24no—
72(C2×#6923)⋊C4—24no—
73(C2×#6923)⋊C4—22no—
74(C2×#6923)⋊C4—42no—
75(C2×#6923)⋊C4C2×C418yescomplemented
76(C2×#6923)⋊C4C2×C418yescomplemented
77(C2×#6923)⋊C4D414yes—
78C24×D61C2311yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C22×C4×D61—22no—
81C22×C4×D61—24no—
82C22×C4×D61—22no—
83C22×C4×D61—42no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C22⋊C4×D61—22no—
99C22⋊C4×D61—22no—
100C22⋊C4×D61C2×C418yes—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C42×D61—22no—
108C42×D61—22no—
109C42×D61—42no—
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116C23×C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C2×C42×C61C2×C411yescharacteristic
120C2×C42×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123C24×C61C22×C411yescharacteristic
124C23×D61—21no—
125C23×D61—22no—
126C23×D61—21no—
127C23×D61—22no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—22no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C414yes—
135C23×D61C2411yescharacteristic
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×#6923—22no—
155C22×#6923—22no—
156C22×#6923—22no—
157C22×#6923—22no—
158C22×#6923C22×C414yes—
159C22×#6923C22×C414yes—
160C22×#6923C22×C414yes—
161C22×#6923C22×C414yes—
162C22×#6923C2×D414yes—
163C22×#6923#4114yes—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—41no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—41no—
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—22no—
185C2×C4×D61—21no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
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—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—41no—
208C2×C4×D61—41no—
209C2×C4×D61C22×C414yes—
210C2×C4×D61C22×C414yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61#4114yes—
213C2×C4×D61#4112yes—
214C2×C4×D61#4112yes—
215C2×C4×D61#4112yes—
216C22⋊#6923—216no—
217C22⋊#6923—48no—
218C4⋊#6923—48no—
219C4×#6923—216no—
220C4×#6923—48no—
221C4×#6923—48no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61C4214yescomplemented
224C42×C61—22no—
225C42×C61—41no—
226C22⋊Dic61—22no—
227C22⋊Dic61C4214yescomplemented
228#11758198—22no—
229#11758198—22no—
230#11758198C4214yescomplemented
231#11758198C4214yescomplemented
232C4×Dic61—22no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—41no—
236C4×Dic61—41no—
237C4×Dic61—41no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61C2×C4212yes—
245C23×C61C23×C411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—42no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61C2×C4212yes—
269C22×D61C23×C412yes—
270C22×D61C22×D411yescharacteristic
271C22×D61C2×#4112yes—
272C22×D61C2×#4112yes—
273C22×D61C2×#4111yescharacteristic
274C22×D61C2×#4111yescharacteristic
275C22×D61C2×#4111yescharacteristic
276C22×D61H(5,𝔽2)11yescharacteristic
277C22×D61H(5,𝔽2)12yes—
278C22×D612−1+411yescharacteristic
279C2×#6923—24no—
280C2×#6923—24no—
281C2×#6923—24no—
282C2×#6923—24no—
283C2×#6923—24no—
284C2×#6923—24no—
285C2×#6923—24no—
286C2×#6923—24no—
287C2×#6923—24no—
288C2×#6923—24no—
289C2×#6923—24no—
290C2×#6923—24no—
291C2×#6923—24no—
292C2×#6923—24no—
293C2×#6923—24no—
294C2×#6923—42no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—42no—
298C2×#6923—42no—
299C2×#6923—42no—
300C2×#6923—42no—
301C2×#6923—42no—
302C2×#6923—42no—
303C2×#6923—42no—
304C2×#6923—42no—
305C2×#6923—42no—
306C2×#6923C4×D418yes—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—44no—
321C2×C4×C61C2×C4212yes—
322C2×C4×C61C2×C4212yes—
323C2×C4×C61#11712yes—
324C2×C4×C61#11712yes—
325C2×C4×C61C4×D412yes—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—44no—
340C2×Dic61C2×C4212yes—
341C2×Dic61C2×C4212yes—
342C2×Dic61#11712yes—
343C2×Dic61#11712yes—
344C2×Dic61C4×D412yes—
345C4×D61—24no—
346C4×D61—24no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—24no—
354C4×D61—24no—
355C4×D61—44no—
356C4×D61—44no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361#13816—611nomaximal, Sylow
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61C22×C4211yescharacteristic
370C22×C61C2×#11711yescharacteristic
371C22×C61C2×#11711yescharacteristic
372C22×C61C2×C4×D411yescharacteristic
373C22×C61C4×#4111yescharacteristic
374C22×C61#51811yescharacteristic
375C22×C61#52011yescharacteristic
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61C2×C4×D412yes—
388C2×D61C4×#4112yes—
389C2×D61C4×#4112yes—
390C2×D61C4×#4112yes—
391C2×D61#51812yes—
392C2×D61#52012yes—
393C2×D61#54612yes—
394C2×D61#54711yescharacteristic
395C2×D61#55011yescharacteristic
396C2×D61#55112yes—
397C2×D61#55112yes—
398C2×D61#55212yes—
399C2×D61#55312yes—
400C2×D61#55512yes—
401C2×D61#55511yescharacteristic
402C2×D61#55611yescharacteristic
403#6923—28no—
404#6923—44no—
405#6923—44no—
406#6923—44no—
407C4×C61—22no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—22no—
411C4×C61—22no—
412C4×C61—41no—
413Dic61—22no—
414Dic61—22no—
415Dic61—22no—
416Dic61—22no—
417Dic61—22no—
418Dic61—41no—
419C2×#388—612no—
420C2×C4×C22⋊C4—611no—
421C2×C4×C22⋊C4—611no—
422C2×#376—611no—
423#1437—612no—
424#1436—612no—
425C4⋊#95—611no—
426#1434—611no—
427C22⋊#95—611no—
428C4×#95—612no—
429C4×#95—611no—
430C2×C61—42no—
431C2×C61C4×#11711yescharacteristic
432C2×C61C42×D411yescharacteristic
433C2×C61#227511yescharacteristic
434C2×C61#234211yescharacteristic
435C2×C61#234611yescharacteristic
436C2×C61#235311yescharacteristic
437C2×C61#235411yescharacteristic
438D61—42no—
439D61#235912yes—
440D61#236312yes—
441D61#237212yes—
442D61#237312yes—
443C24×C4—611no—
444C22×C4⋊C4—612no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—612no—
447C22×C22⋊C4—612no—
448C22×C22⋊C4—611no—
449C22×C42—612no—
450C22×C42—611no—
451C22×C42—611no—
452C22×C42—612no—
453C22×C42—612no—
454#388—6116no—
455C4×C22⋊C4—611no—
456C4×C22⋊C4—611no—
457C4×C22⋊C4—611no—
458C4×C22⋊C4—611no—
459C4×C22⋊C4—611no—
460C4×C22⋊C4—611no—
461C4×C22⋊C4—611no—
462C4×C22⋊C4—1224no—
463C4×C22⋊C4#692311yescharacteristic, complemented
464#376—1224no—
465C2×#95—612no—
466C2×#95—612no—
467C2×#95—611no—
468C2×#95—611no—
469C2×#95—611no—
470C2×#95—611no—
471C2×#95—612no—
472C2×#95—612no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—612no—
476C2×#95—612no—
477C61#1381611yescharacteristic, complemented, Sylow
478C25—611no—
479C23×C4—612no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—612no—
486C23×C4—612no—
487C23×C4—612no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—1224no—
493C23×C4—1222no—
494C23×C4—1222no—
495C23×C4—2442no—
496C23×C4C2×#692311yescharacteristic
497C2×C4⋊C4—618no—
498C2×C4⋊C4—2442no—
499C2×C4⋊C4—2442no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—618no—
504C2×C22⋊C4—618no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—618no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—2442no—
514C2×C22⋊C4—2442no—
515C2×C22⋊C4C2×#692311yescharacteristic
516C2×C22⋊C4C2×#692311yescharacteristic
517C2×C42—618no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—1222no—
525C2×C42—1222no—
526C2×C42—1224no—
527C2×C42—1224no—
528C2×C42—1224no—
529C2×C42—1224no—
530C2×C42—1224no—
531C2×C42—1224no—
532C2×C42—2442no—
533C2×C42—2442no—
534C2×C42—2442no—
535C2×C42C2×#692311yescharacteristic
536C2×C42C2×#692311yescharacteristic
537#95—618no—
538#95—618no—
539#95—614no—
540#95—611no—
541#95—611no—
542#95—611no—
543#95—611no—
544#95—611no—
545#95—611no—
546#95—1224no—
547#95—1224no—
548#95—1222no—
549#95—1224no—
550#95—1222no—
551#95—1222no—
552#95—2442no—
553#95C2×#692311yescharacteristic
554#95C2×#692311yescharacteristic
555C24—611no—
556C24—614no—
557C24—611no—
558C24—1221no—
559C24—1221no—
560C24—1221no—
561C24—1222no—
562C24—1221no—
563C24—1222no—
564C24—1222no—
565C24—1221no—
566C24—1221no—
567C24C22×#692311yescharacteristic
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—614no—
572C22×C4—614no—
573C22×C4—614no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—614no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—614no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—614no—
587C22×C4—614no—
588C22×C4—614no—
589C22×C4—611no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—2441no—
638C22×C4—2441no—
639C22×C4—2448no—
640C22×C4—2448no—
641C22×C4—2441no—
642C22×C4C22×#692311yescharacteristic
643C22×C4C22×#692311yescharacteristic
644C22×C4C22×#692311yescharacteristic
645C22×C4C22×#692311yescharacteristic
646C22×C4C22×#692311yescharacteristic
647C22×C4C22×#692311yescharacteristic
648C4⋊C4—2448no—
649C22⋊C4—22no—
650C22⋊C4—614no—
651C22⋊C4—614no—
652C22⋊C4—614no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—12216no—
656C22⋊C4—1222no—
657C22⋊C4—2448no—
658C22⋊C4C4×#692314yescomplemented
659C42—22no—
660C42—41no—
661C42—1222no—
662C42—1222no—
663C42—12216no—
664C42—1222no—
665C42—2441no—
666C42—2441no—
667C42—2441no—
668C42—2448no—
669C42—2448no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—612no—
677C23—612no—
678C23—611no—
679C23—611no—
680C23—611no—
681C23—611no—
682C23—612no—
683C23—612no—
684C23—611no—
685C23—611no—
686C23—612no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—1224no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23C2×C4×#692312yes—
710C23C23×#692311yescharacteristic
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—44no—
725C2×C4—618no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1224no—
758C2×C4—1224no—
759C2×C4—1224no—
760C2×C4—1224no—
761C2×C4—1224no—
762C2×C4—1224no—
763C2×C4—1224no—
764C2×C4—1224no—
765C2×C4—1224no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2444no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4C2×C4×#692312yes—
789C2×C4C2×C4×#692312yes—
790C2×C4#1451985612yes—
791C2×C4#1451985612yes—
792C2×C4D4×#692312yes—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—612no—
801C22—612no—
802C22—612no—
803C22—612no—
804C22—612no—
805C22—612no—
806C22—611no—
807C22—611no—
808C22—611no—
809C22—611no—
810C22—612no—
811C22—612no—
812C22—612no—
813C22—612no—
814C22—612no—
815C22—612no—
816C22—1222no—
817C22—1222no—
818C22—1222no—
819C22—2444no—
820C22—2444no—
821C22—2444no—
822C22—2444no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22C22×C4×#692311yescharacteristic
828C22C2×#1451985611yescharacteristic
829C22C2×#1451985611yescharacteristic
830C22C2×D4×#692311yescharacteristic
831C22#41×#692311yescharacteristic
832C22#1684082911yescharacteristic
833C22#1684083111yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—41no—
840C4—1228no—
841C4—1222no—
842C4—1222no—
843C4—1222no—
844C4—1222no—
845C4—1222no—
846C4—2444no—
847C4—2444no—
848C4—2444no—
849C4—2441no—
850C2—42no—
851C2—612no—
852C2—612no—
853C2—612no—
854C2—612no—
855C2—2442no—
856C2C4×#1451985611yescharacteristic
857C2C4×D4×#692311yescharacteristic
858C2#2146225811yescharacteristic
859C2#2146232511yescharacteristic
860C2#2146232911yescharacteristic
861C2#2146233611yescharacteristic
862C2#2146233711yescharacteristic
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#13816
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840698C2semidirect
5. #21460999C2semidirect
6. #21460997C2semidirect
7. #21460995C2semidirect
9. C4×(C2×#6923)⋊C4C2semidirect
10. #95×#6923C2semidirect
18. #16840712C4semidirect
36. C22⋊C4×Dic61C4semidirect
37. C22⋊C4×Dic61C4semidirect
38. C4×#11758198C4semidirect
39. C4×#11758198C4semidirect
40. C4×C22⋊Dic61C4semidirect
41. #16839609C4semidirect
42. #16839609C4semidirect
45. C4×C22⋊C4×C61C4semidirect
52. C2×C4⋊#6923C2×C4semidirect
67. C2×C4×#6923C2×C4semidirect
75. (C2×#6923)⋊C4C2×C4semidirect
76. (C2×#6923)⋊C4C2×C4semidirect
223. C22⋊C4×C61C42semidirect
227. C22⋊Dic61C42semidirect
230. #11758198C42semidirect
231. #11758198C42semidirect
463. C4×C22⋊C4#6923semidirect
477. C61#13816semidirect
658. 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
C2×C4×C22⋊#69232
C2×#168406982
#214610002
#214609992
#214609972
#214609952
#214609932
C4×(C2×#6923)⋊C42
#95×#69232
C4×C22⋊C4×D612
#1381661