Finite Group Databasebeta

← #29840960

Subgroups — #29840960

Order 15616.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2C2×#16840242C211yesmaximal, characteristic
3C2×#16840230C211yesmaximal, characteristic
4#21448736C212yesmaximal, complemented
5#21448731C212yesmaximal, complemented
6#21448727C212yesmaximal, complemented
7#21448725C214yesmaximal, complemented
8#21448719C212yesmaximal, complemented
9#21448717C214yesmaximal, complemented
10#21448441C212yesmaximal, complemented
11#21448435C211yesmaximal, characteristic, complemented
12#21448434C212yesmaximal, complemented
13#21448303C211yesmaximal, characteristic, complemented
14#21448300C212yesmaximal, complemented
15C2×#16839658C211yesmaximal, characteristic, complemented
16#389×D61C212yesmaximal, complemented
17C61×#2317C211yesmaximal, characteristic, complemented
18C22×#11758222C2211yescharacteristic
19#16840243—28no—
20#16840242C4116yescomplemented
21#16840230—28no—
22C2×C4×Dic122C2212yes—
23C2×#14519742C2211yescharacteristic
24C2×#14519742C2212yes—
25C2×#14519742C2211yescharacteristic
26C2×C4×D244C2212yes—
27C2×#14519739C2211yescharacteristic
28C2×#14519739C2212yes—
29C2×#14519739C2211yescharacteristic
30C2×C4×C22⋊D61C2214yes—
31C2×#14519737C2212yes—
32C2×#14519737C2212yes—
33C2×#14519737C2214yes—
34C2×#14519736C2211yescharacteristic
35C2×#14519735C2212yes—
36C2×#14519735C2212yes—
37C2×#14519734C2212yes—
38C22×C4⋊Dic61C2211yescharacteristic
39C22×#11758196C2212yes—
40C2×C4⋊C4×D61C2212yes—
41C2×C4⋊C4×D61C2214yes—
42C2×C4⋊C4×D61C2212yes—
43C22×C4×Dic61C2211yescharacteristic
44C2×C42×D61C2212yes—
45#16839661C2211yescharacteristic
46#16839661C2211yescharacteristic
47#16839661C2211yescharacteristic
48#16839661C2211yescharacteristic
49#16839660C2212yes—
50#16839660C2212yes—
51#16839659C2214yes—
52#16839659C2214yes—
53#16839658C2212yes—
54#16839658C2212yes—
55#16839658C2212yes—
56#16839658C2212yes—
57#16839658C2212yes—
58#16839658C2212yes—
59#16839657C2214yes—
60#16839657C2214yes—
61#16839637C2212yes—
62#16839637C2212yes—
63#16839636C2214yes—
64#16839636C2214yes—
65#16839633C2214yes—
66#16839633C2214yes—
67#16839631C2214yes—
68#16839626C2214yes—
69#16839621C2214yes—
70#16839620C2214yes—
71#16839619C2214yes—
72C4⋊C4×Dic61C2214yes—
73C4×C4⋊Dic61C2212yes—
74C4×C4⋊Dic61C2212yes—
75#16839613C2214yes—
76C2×#14519684C2212yes—
77#95×D61C2214yes—
78C2×#117×C61C2211yescharacteristic
79C2×#117×C61C2211yescharacteristic
80C22×C4⋊C4×C61C2211yescharacteristic
81C61×#389C2212yes—
82C61×#389C2212yes—
83C61×#385C2214yes—
84C61×#384C2212yes—
85C61×#382C2212yes—
86C2×#11758222C2×C418yes—
87C2×#11758222D418yes—
88C2×#11758222Q818yes—
89C22×Dic122C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61C2312yes—
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94C23×Dic61C2312yes—
95C22×C4×D61C2312yes—
96C22×C4×D61C2312yes—
97C22×C4×D61C2314yes—
98C22×C4×D61C2314yes—
99C22×C4×D61C2312yes—
100C4×Dic122C2×C4116yescomplemented
101#14519742—24no—
102#14519742—24no—
103#14519742—28no—
104C4×D244C2×C4116yescomplemented
105#14519739—24no—
106#14519739—24no—
107#14519739—28no—
108C4×C22⋊D61—216no—
109#14519737—28no—
110#14519737—28no—
111#14519737C2×C4132yescomplemented
112#14519736—24no—
113#14519735—28no—
114#14519735C2×C4116yescomplemented
115#14519734—28no—
116C2×C4⋊Dic61C2×C418yescomplemented
117C2×C4⋊Dic61C2311yescharacteristic
118C2×C4⋊Dic61C2312yes—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2312yes—
121C2×C4⋊Dic61C2312yes—
122C2×C4⋊Dic61C2312yes—
123C2×C4⋊Dic61C2312yes—
124C2×C4⋊Dic61C2312yes—
125C2×#11758196—44no—
126C2×#11758196C2314yes—
127C2×#11758196C2314yes—
128C2×#11758196C2312yes—
129C2×#11758196C2312yes—
130C2×#11758196C2314yes—
131C2×#11758196C2314yes—
132C2×#11758196C2314yes—
133C2×#11758196C2314yes—
134C4⋊C4×D61—28no—
135C4⋊C4×D61—48no—
136C4⋊C4×D61C2×C4116yescomplemented
137C2×C22⋊Dic61C2312yes—
138C2×#11758198C2312yes—
139C2×#11758198C2312yes—
140C2×#11758198C2314yes—
141C2×#11758198C2314yes—
142C2×C4×Dic61—24no—
143C2×C4×Dic61C2311yescharacteristic
144C2×C4×Dic61C2312yes—
145C2×C4×Dic61C2312yes—
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2314yes—
150C2×C4×Dic61C2312yes—
151C2×C4×Dic61C2314yes—
152C42×D61—28no—
153#14519684C2312yes—
154#14519684C2314yes—
155#14519684C2314yes—
156#14519684C2314yes—
157#14519684C2312yes—
158#14519684C2312yes—
159#14519684C2312yes—
160#14519684C2314yes—
161C23×C4×C61C2312yes—
162C23×C4×C61C2311yescharacteristic
163#117×C61—24no—
164#117×C61C2×C418yescomplemented
165C2×C4⋊C4×C61—24no—
166C2×C4⋊C4×C61C2312yes—
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C4⋊C4×C61C2312yes—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2314yes—
171C2×C4⋊C4×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61C2312yes—
175C2×C22⋊C4×C61C2312yes—
176C2×C42×C61C2312yes—
177C2×C42×C61C2312yes—
178#95×C61C2314yes—
179#95×C61C2314yes—
180C24×C61C2411yescharacteristic
181C23×D61C2412yes—
182C22×C4×C61—24no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C22×C414yes—
186C22×C4×C61C2×D414yes—
187C22×C4×C61C2×Q814yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2414yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61C22×C418yes—
196C2×C22⋊D61C2×D418yes—
197C2×C22⋊D61C2×Q818yes—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—42no—
203C22×Dic61—41no—
204C22×Dic61—41no—
205C22×Dic61—42no—
206C22×Dic61C22×C418yes—
207C22×Dic61C2412yes—
208C22×Dic61C2411yescharacteristic
209C22×Dic61C2411yescharacteristic
210C22×Dic61C2412yes—
211C22×Dic61C2414yes—
212C22×Dic61C2411yescharacteristic
213C22×Dic61C2411yescharacteristic
214C22×Dic61C2412yes—
215#11758222C4⋊C4164yescomplemented
216C2×D244C22×C414yes—
217C2×D244C2×D414yes—
218C2×D244C2×Q814yes—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—28no—
224C2×C4×D61—44no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61C22×C4116yes—
231C2×C4×D61C22×C418yes—
232C2×C4×D61C2×D418yes—
233C2×C4×D61C2×Q818yes—
234C2×Dic122C22×C414yes—
235C2×Dic122C2×D414yes—
236C2×Dic122C2×Q814yes—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—22no—
240C4⋊C4×C61—22no—
241C4⋊C4×C61—44no—
242C4⋊C4×C61—44no—
243C4⋊C4×C61C22×C414yes—
244C4⋊C4×C61C22×C414yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61C22×C418yes—
247C42×C61—24no—
248C42×C61C22×C418yes—
249C22⋊Dic61—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—28no—
253#11758198C22×C4116yes—
254C4⋊Dic61—22no—
255C4⋊Dic61—22no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—42no—
259C4⋊Dic61—42no—
260C4⋊Dic61C22×C418yes—
261C4⋊Dic61C22×C418yes—
262#11758196—28no—
263#11758196—24no—
264#11758196—24no—
265#11758196—28no—
266#11758196—44no—
267#11758196—44no—
268#11758196—44no—
269#11758196C22×C4116yes—
270C4×Dic61—22no—
271C4×Dic61—22no—
272C4×Dic61—22no—
273C4×Dic61—22no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61—24no—
277C4×Dic61—28no—
278C4×Dic61C22×C4116yes—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C23×C412yes—
284C23×C61C22×D412yes—
285C23×C61C22×Q812yes—
286C23×C61C2511yescharacteristic
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61C23×C414yes—
292C22×D61C22×D414yes—
293C22×D61C22×Q814yes—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
307C2×C4×C61—84no—
308C2×C4×C61C2×C4⋊C4116yescomplemented
309C2×C4×C61C23×C414yes—
310C2×C4×C61C23×C414yes—
311C2×C4×C61C23×C412yes—
312C2×C4×C61C23×C412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×Q812yes—
316C2×C4×C61C22×Q812yes—
317C22⋊D61C2×C4⋊C4132yescomplemented
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—22no—
336C2×Dic61—48no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61C23×C418yes—
340C2×Dic61C23×C414yes—
341C2×Dic61C22×D414yes—
342C2×Dic61C22×Q814yes—
343C2×Dic61H(5,𝔽2)12yes—
344C2×Dic612−1+412yes—
345D244C2×C4⋊C4116yescomplemented
346C4×D61—416no—
347C4×D61—48no—
348C4×D61—48no—
349C4×D61—88no—
350C4×D61C2×C4⋊C4132yescomplemented
351Dic122C2×C4⋊C4116yescomplemented
352#34250—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61C22×C4⋊C414yes—
360C22×C61C24×C411yescharacteristic
361C22×C61C23×D411yescharacteristic
362C22×C61C23×Q811yescharacteristic
363C22×C61C2×H(5,𝔽2)11yescharacteristic
364C22×C61C2×2−1+411yescharacteristic
365C22×C61#58511yescharacteristic
366C22×C61#58511yescharacteristic
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61C22×C4⋊C418yes—
374C4×C61—24no—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61—44no—
378C4×C61—42no—
379C4×C61C22×C4⋊C414yes—
380C4×C61C22×C4⋊C414yes—
381Dic61—28no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—41no—
386Dic61—42no—
387Dic61—41no—
388Dic61C22×C4⋊C418yes—
389C2×#520—611no—
390C2×#520—611no—
391C2×C4×#41—611no—
392#2351—612no—
393Q8×C4⋊C4—612no—
394#2349—614no—
395#2349—612no—
396D4×C4⋊C4—614no—
397D4×C4⋊C4—612no—
398#2317—612no—
399#2317D6111yescharacteristic, complemented
400#2316—612no—
401#2316—611no—
402#2296—612no—
403#2296—611no—
404C2×#389—612no—
405C2×#389—611no—
406C2×C61—24no—
407C2×C61C23×C4⋊C411yescharacteristic
408C2×C61C4×H(5,𝔽2)11yescharacteristic
409C2×C61C4×2−1+411yescharacteristic
410C2×C61#348811yescharacteristic
411C2×C61#348911yescharacteristic
412C2×C61#350311yescharacteristic
413C2×C61#350411yescharacteristic
414D61—28no—
415C22×#41—611no—
416#520—6116no—
417#520—1228no—
418C4×#41—1228no—
419C2×C4×Q8—611no—
420C2×C4×Q8—612no—
421C2×C4×Q8—611no—
422C2×C4×Q8—612no—
423C2×C4×D4—614no—
424C2×C4×D4—611no—
425C2×C4×D4—612no—
426C2×C4×D4—611no—
427C2×C4×D4—614no—
428C2×C4×D4—612no—
429C2×C4×D4—612no—
430C2×C4×D4—612no—
431C2×#117—611no—
432C2×#117—612no—
433C2×#117—612no—
434C2×#117—612no—
435C2×#117C2×D6111yescharacteristic
436C2×#117C2×D6111yescharacteristic
437C22×C4⋊C4—611no—
438C22×C4⋊C4—612no—
439C22×C4⋊C4—612no—
440C22×C4⋊C4—612no—
441C22×C4⋊C4—614no—
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C42—611no—
444C22×C42—612no—
445#389—611no—
446#389—612no—
447#389—614no—
448#389—612no—
449#389—612no—
450#389—611no—
451#389—612no—
452#389—614no—
453#389—612no—
454#389—612no—
455#389—611no—
456#389—611no—
457#389—612no—
458#389—612no—
459#389—614no—
460#389—614no—
461#389C2×D6112yes—
462#389C2×D6112yes—
463#385—614no—
464#385—614no—
465#385—612no—
466#385—612no—
467#385—614no—
468#385—614no—
469#385C2×D6114yes—
470#384—614no—
471#384C2×D6112yes—
472#382—614no—
473#382C2×D6112yes—
474#380—614no—
475#380—614no—
476#380—614no—
477C4×C4⋊C4—614no—
478C4×C4⋊C4—612no—
479C4×C4⋊C4—612no—
480C4×C4⋊C4—614no—
481C2×#95—612no—
482C2×#95—614no—
483C61#3425011yescharacteristic, complemented, Sylow
484C2×#41—618no—
485C2×#41—618no—
486C2×#41—618no—
487C22×Q8—611no—
488C22×D4—612no—
489C22×D4—611no—
490C23×C4—612no—
491C23×C4—612no—
492C23×C4—614no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—612no—
496C23×C4—612no—
497C23×C4—614no—
498C23×C4C22×D6112yes—
499C23×C4C22×D6111yescharacteristic
500C4×Q8—6116no—
501C4×Q8—1224no—
502C4×Q8—1224no—
503C4×Q8—1228no—
504C4×D4—6132no—
505C4×D4—6116no—
506C4×D4—1228no—
507C4×D4—1228no—
508C4×D4—1224no—
509C4×D4—1224no—
510C4×D4—1228no—
511C4×D4—12216no—
512#117—24no—
513#117—6116no—
514#117—1228no—
515#117—1228no—
516#117—1224no—
517#117C4×D6118yescomplemented
518C2×C4⋊C4—24no—
519C2×C4⋊C4—618no—
520C2×C4⋊C4—612no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—612no—
523C2×C4⋊C4—6116no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—612no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—612no—
530C2×C4⋊C4—612no—
531C2×C4⋊C4—612no—
532C2×C4⋊C4—614no—
533C2×C4⋊C4—614no—
534C2×C4⋊C4—614no—
535C2×C4⋊C4—612no—
536C2×C4⋊C4—612no—
537C2×C4⋊C4—1228no—
538C2×C4⋊C4—2448no—
539C2×C4⋊C4—2444no—
540C2×C4⋊C4C22×D6112yes—
541C2×C4⋊C4C22×D6112yes—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6114yes—
545C2×C4⋊C4C22×D6114yes—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—614no—
549C2×C22⋊C4—612no—
550C2×C22⋊C4—612no—
551C2×C22⋊C4—614no—
552C2×C22⋊C4—612no—
553C2×C22⋊C4C22×D6112yes—
554C2×C22⋊C4C22×D6112yes—
555C2×C42—614no—
556C2×C42—611no—
557C2×C42—614no—
558C2×C42—612no—
559C2×C42—612no—
560C2×C42—612no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—1228no—
565C2×C42—1224no—
566C2×C42C22×D6112yes—
567C2×C42C22×D6112yes—
568#95—614no—
569#95—612no—
570#95—614no—
571#95—614no—
572#95—612no—
573#95—614no—
574#95—612no—
575#95—612no—
576#95C22×D6114yes—
577#95C22×D6114yes—
578C24—612no—
579C24C23×D6111yescharacteristic
580#41—6164no—
581C2×Q8—614no—
582C2×Q8—614no—
583C2×Q8—614no—
584C2×D4—618no—
585C2×D4—618no—
586C2×D4—618no—
587C2×D4—614no—
588C2×D4—614no—
589C2×D4—614no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—612no—
594C22×C4—618no—
595C22×C4—618no—
596C22×C4—618no—
597C22×C4—611no—
598C22×C4—614no—
599C22×C4—611no—
600C22×C4—618no—
601C22×C4—6116no—
602C22×C4—611no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—611no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1228no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4—2444no—
618C22×C4—2444no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2441no—
623C22×C4—2442no—
624C22×C4—2441no—
625C22×C4C2×C4×D6114yes—
626C22×C4D4×D6114yes—
627C22×C4Q8×D6114yes—
628C22×C4C23×D6112yes—
629C22×C4C23×D6114yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6111yescharacteristic
634C22×C4C23×D6111yescharacteristic
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—618no—
642C4⋊C4—6116no—
643C4⋊C4—618no—
644C4⋊C4—1228no—
645C4⋊C4—1228no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—2444no—
653C4⋊C4—2444no—
654C4⋊C4—2444no—
655C4⋊C4—2442no—
656C4⋊C4—2442no—
657C4⋊C4C2×C4×D6114yes—
658C4⋊C4C2×C4×D6114yes—
659C22⋊C4—24no—
660C22⋊C4—6116no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1228no—
664C22⋊C4—1224no—
665C22⋊C4C2×C4×D6118yes—
666C42—24no—
667C42—6116no—
668C42—1224no—
669C42—1224no—
670C42—1228no—
671C42—1222no—
672C42—1222no—
673C42—1222no—
674C42—1222no—
675C42—1224no—
676C42C2×C4×D6118yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—614no—
682C23—614no—
683C23—614no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23C22×C4×D6112yes—
689C23C2×D4×D6112yes—
690C23C2×Q8×D6112yes—
691C23C24×D6111yescharacteristic
692Q8—6116no—
693D4—6132no—
694D4—6116no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—84no—
709C2×C4—614no—
710C2×C4—614no—
711C2×C4—614no—
712C2×C4—6132no—
713C2×C4—618no—
714C2×C4—612no—
715C2×C4—612no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1224no—
719C2×C4—1221no—
720C2×C4—1224no—
721C2×C4—1221no—
722C2×C4—1222no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1221no—
728C2×C4—1222no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1221no—
734C2×C4—4888no—
735C2×C4—24416no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2448no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4C4⋊C4×D61116yescomplemented
742C2×C4C22×C4×D6114yes—
743C2×C4C22×C4×D6114yes—
744C2×C4C22×C4×D6112yes—
745C2×C4C22×C4×D6112yes—
746C2×C4C2×D4×D6112yes—
747C2×C4C2×D4×D6112yes—
748C2×C4C2×Q8×D6112yes—
749C2×C4C2×Q8×D6112yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—618no—
757C22—1224no—
758C22—1224no—
759C22—1224no—
760C22—1224no—
761C22—1224no—
762C22—1224no—
763C22C2×C4⋊C4×D6114yes—
764C22C23×C4×D6111yescharacteristic
765C22C22×D4×D6111yescharacteristic
766C22C22×Q8×D6111yescharacteristic
767C22H(5,𝔽2)×D6111yescharacteristic
768C222−1+4×D6111yescharacteristic
769C22#1684059711yescharacteristic
770C22#1684059911yescharacteristic
771C4—24no—
772C4—24no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—618no—
777C4—1222no—
778C4—1222no—
779C4—1228no—
780C4—2442no—
781C4—2441no—
782C4—2442no—
783C4—2441no—
784C4C2×C4⋊C4×D6114yes—
785C4C2×C4⋊C4×D6114yes—
786C2—24no—
787C2—1228no—
788C2C22×C4⋊C4×D6111yescharacteristic
789C2#2145902511yescharacteristic
790C2#2145903011yescharacteristic
791C2#2145948611yescharacteristic
792C2#2145949711yescharacteristic
793C2#2145963411yescharacteristic
794C2#2145964211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2317C2
socle, cosocleC23×C61C25
prime radicalC22×#11758222C22
hypercenter#2317D61
hypocenterC61#34250
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. #21448736C2semidirect
5. #21448731C2semidirect
6. #21448727C2semidirect
7. #21448725C2semidirect
8. #21448719C2semidirect
9. #21448717C2semidirect
10. #21448441C2semidirect
11. #21448435C2semidirect
12. #21448434C2semidirect
13. #21448303C2semidirect
14. #21448300C2semidirect
15. C2×#16839658C2semidirect
16. #389×D61C2semidirect
17. C61×#2317C2semidirect
20. #16840242C4semidirect
100. C4×Dic122C2×C4semidirect
104. C4×D244C2×C4semidirect
111. #14519737C2×C4semidirect
114. #14519735C2×C4semidirect
116. C2×C4⋊Dic61C2×C4semidirect
136. C4⋊C4×D61C2×C4semidirect
164. #117×C61C2×C4semidirect
215. #11758222C4⋊C4semidirect
308. C2×C4×C61C2×C4⋊C4semidirect
317. C22⋊D61C2×C4⋊C4semidirect
345. D244C2×C4⋊C4semidirect
350. C4×D61C2×C4⋊C4semidirect
351. Dic122C2×C4⋊C4semidirect
399. #2317D61semidirect
483. C61#34250semidirect
517. #117C4×D61semidirect
741. C2×C4C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402432
C2×#168402422
C2×#168402302
#214487362
#214487312
#214487272
#214487252
#214487192
#214487172
#214484412
#214484352
#214484342
#214483032
#214483002
C2×#168396582
#389×D612
C61×#23172
#3425061