Finite Group Databasebeta

← #16733676

Subgroups — #16733676

Order 3328.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2#13125666C214yesmaximal, complemented
3#13125657C212yesmaximal, complemented
4#13125638C212yesmaximal, complemented
5#13125617C214yesmaximal, complemented
6#13125608C212yesmaximal, complemented
7#13125589C212yesmaximal, complemented
8#13124780C212yesmaximal, complemented
9#13124759C212yesmaximal, complemented
10#13124462C214yesmaximal, complemented
11#13124094C212yesmaximal, complemented
12#13124070C212yesmaximal, complemented
13C2×#11718868C211yesmaximal, characteristic, complemented
14C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
15C23×Q8×C13C2211yescharacteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C22×#6127C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8—21no—
21C2×C13×C22⋊Q8—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8C2212yes—
25C2×C13×C22⋊Q8C2212yes—
26C2×C13×C22⋊Q8C2212yes—
27C2×C13×C22⋊Q8C2212yescomplemented
28C2×C13×C22⋊Q8C2212yescomplemented
29C2×C13×C22⋊Q8C2212yescomplemented
30C22×C13×C4⋊C4—21no—
31C22×C13×C4⋊C4C2211yescharacteristic, complemented
32C22×C13×C22⋊C4—21no—
33C2×#88207—21no—
34C2×#88196C2214yescomplemented
35#11719496—21no—
36#11719496—21no—
37#11719496—21no—
38#11719496—21no—
39#11719496C2212yes—
40#11719496C2212yes—
41#11719496C2212yes—
42#11719496C2212yes—
43C2×#88184C2211yescharacteristic
44C2×#88184C2211yescharacteristic
45C2×#88183—21no—
46C2×C4×C22⋊D13—21no—
47C2×C4×C22⋊D13—21no—
48C2×#88180C2211yescharacteristic
49C2×#88178C2211yescharacteristic
50C2×#88178C2211yescharacteristic
51C22×#6099C2212yescomplemented
52#11718889C2214yescomplemented
53#11718889C2214yescomplemented
54#11718888C2214yescomplemented
55#11718888C2214yescomplemented
56#11718886C2214yescomplemented
57#11718868C2212yes—
58#11718868C2212yes—
59#11718868C2212yescomplemented
60#11718868C2212yescomplemented
61C2×C22⋊#1055C2212yes—
62C2×C22⋊#1055C2212yescomplemented
63#11718713C2218yescomplemented
64#11718712C2218yescomplemented
65#11718711C2214yescomplemented
66#11718710C2218yescomplemented
67#11718709C2218yescomplemented
68#11718708C2218yescomplemented
69#11718707C2214yescomplemented
70#11718706C2218yescomplemented
71#11718705C2214yescomplemented
72#11718704C2214yescomplemented
73#11718632C2214yescomplemented
74#11718631C2214yescomplemented
75#11718629C2214yescomplemented
76#11718628C2214yescomplemented
77#11718627C2214yescomplemented
78#11718625C2214yescomplemented
79C25×C13D411yescharacteristic
80C22×Q8×C13—21no—
81C22×Q8×C13—21no—
82C22×Q8×C13—21no—
83C22×Q8×C13—44no—
84C22×Q8×C13C2312yes—
85C22×Q8×C13C2312yes—
86C22×Q8×C13C2312yes—
87C23×C4×C13—21no—
88C23×C4×C13—21no—
89C23×C4×C13—44no—
90C23×C4×C13D411yescharacteristic
91C23×C4×C13D411yescharacteristic
92C23×C4×C13D411yescharacteristic
93C23×C4×C13D411yescharacteristic
94C23×C4×C13D411yescharacteristic
95C23×C4×C13D411yescharacteristic
96C23×C4×C13D411yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C22×C22⋊D13—21no—
105C22×C22⋊D13—21no—
106C22×C22⋊D13—21no—
107C2×#6127—21no—
108C2×#6127—21no—
109C2×#6127—44no—
110C2×#6127C2312yes—
111C2×#6127C2312yes—
112C22×D52C2311yescharacteristic
113C22×C4×D13—21no—
114C22×Dic26C2311yescharacteristic
115C13×C22⋊Q8—22no—
116C13×C22⋊Q8—22no—
117C13×C22⋊Q8—22no—
118C13×C22⋊Q8—22no—
119C13×C22⋊Q8—22no—
120C13×C22⋊Q8—22no—
121C13×C22⋊Q8—22no—
122C13×C22⋊Q8—22no—
123C13×C22⋊Q8—22no—
124C13×C22⋊Q8—22no—
125C13×C22⋊Q8—22no—
126C13×C22⋊Q8—22no—
127C13×C22⋊Q8C2314yes—
128C13×C22⋊Q8C2314yes—
129C13×C22⋊Q8C2314yes—
130C13×C22⋊Q8C2314yes—
131C2×C13×C4⋊C4—22no—
132C2×C13×C4⋊C4—22no—
133C2×C13×C4⋊C4—22no—
134C2×C13×C4⋊C4—22no—
135C2×C13×C4⋊C4—22no—
136C2×C13×C4⋊C4—22no—
137C2×C13×C4⋊C4—21no—
138C2×C13×C4⋊C4—21no—
139C2×C13×C4⋊C4—21no—
140C2×C13×C4⋊C4C2312yes—
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C13×C22⋊C4—22no—
144C2×C13×C22⋊C4—22no—
145C2×C13×C22⋊C4—22no—
146C2×C13×C22⋊C4—22no—
147C2×C13×C22⋊C4—22no—
148C2×C13×C22⋊C4—22no—
149#88207—22no—
150#88207—22no—
151#88207—22no—
152#88207—22no—
153C2×C22⋊Dic13—21no—
154C2×C22⋊Dic13—21no—
155C2×C22⋊Dic13—21no—
156C2×#6107C2318yescomplemented
157#88196—48no—
158C2×#6106C2318yescomplemented
159#88184—21no—
160#88184—21no—
161#88184—21no—
162#88184—21no—
163#88184C2312yes—
164#88184C2312yes—
165#88184C2312yes—
166#88184C2312yes—
167#88183—22no—
168#88183—22no—
169#88183—22no—
170#88183—22no—
171C4×C22⋊D13—22no—
172C4×C22⋊D13—22no—
173C4×C22⋊D13—22no—
174C4×C22⋊D13—22no—
175C4×C22⋊D13—22no—
176C4×C22⋊D13—22no—
177C4×C22⋊D13—22no—
178C4×C22⋊D13—22no—
179C2×#6103—21no—
180C2×#6103—21no—
181#88180—21no—
182#88180—21no—
183#88180C2312yes—
184#88180C2312yes—
185C2×C4⋊Dic13C2311yescharacteristic
186C2×C4⋊Dic13C2311yescharacteristic
187#88178—21no—
188#88178—21no—
189#88178—21no—
190#88178—21no—
191#88178C2312yes—
192#88178C2312yes—
193#88178C2312yes—
194#88178C2312yes—
195C2×#6101—21no—
196C2×#6101—21no—
197C2×C4×Dic13—21no—
198C2×#6099—44no—
199C2×#6099C2314yes—
200C2×#6099C2314yes—
201C22×#1055C2314yes—
202#88075C2318yescomplemented
203#88075C2318yescomplemented
204C22⋊#1055C2314yes—
205C22⋊#1055C2314yes—
206C22⋊#1055C2314yes—
207C22⋊#1055C2314yes—
208#88050C2318yescomplemented
209#88049C2318yescomplemented
210#88048C2318yescomplemented
211#88047C2318yescomplemented
212#60751—131nomaximal, Sylow
213C24×C13—24no—
214C24×C13—42no—
215C24×C13—42no—
216C24×C13C2×D411yescharacteristic
217C24×C13C2×D411yescharacteristic
218C24×C13C2×D411yescharacteristic
219C24×C13C2×D411yescharacteristic
220C24×C13C2×D411yescharacteristic
221C24×C13C2×D411yescharacteristic
222C24×C13C2×D411yescharacteristic
223C23×D13—21no—
224C2×Q8×C13—22no—
225C2×Q8×C13—22no—
226C2×Q8×C13—22no—
227C2×Q8×C13—28no—
228C2×Q8×C13—44no—
229C2×Q8×C13—44no—
230C2×Q8×C13—44no—
231C2×Q8×C13—44no—
232C2×Q8×C13—44no—
233C2×Q8×C13C2414yes—
234C22×C4×C13—24no—
235C22×C4×C13—24no—
236C22×C4×C13—24no—
237C22×C4×C13—22no—
238C22×C4×C13—22no—
239C22×C4×C13—22no—
240C22×C4×C13—22no—
241C22×C4×C13—22no—
242C22×C4×C13—22no—
243C22×C4×C13—42no—
244C22×C4×C13—42no—
245C22×C4×C13—42no—
246C22×C4×C13—42no—
247C22×C4×C13—42no—
248C22×C4×C13—42no—
249C22×C4×C13—42no—
250C22×C4×C13—42no—
251C22×C4×C13—42no—
252C22×C4×C13—42no—
253C22×C4×C13—42no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13C2×D411yescharacteristic
257C22×C4×C13C2×D411yescharacteristic
258C22×C4×C13C2×D411yescharacteristic
259C22×C4×C13C2×D411yescharacteristic
260C22×C4×C13C2×D411yescharacteristic
261C22×C4×C13C2×D411yescharacteristic
262C22×C4×C13C2×D411yescharacteristic
263C22×C4×C13C2×D411yescharacteristic
264C22×C4×C13C2×D411yescharacteristic
265C22×C4×C13C2×D411yescharacteristic
266C22×C4×C13C2×D411yescharacteristic
267C22×C4×C13C2×D411yescharacteristic
268C22×C4×C13C2×D411yescharacteristic
269C22×C4×C13C2×D411yescharacteristic
270C22×C4×C13C2×D411yescharacteristic
271C22×C4×C13C2×D411yescharacteristic
272C22×C4×C13C2×D411yescharacteristic
273C22×C4×C13C2×D411yescharacteristic
274C22×C4×C13C2×D411yescharacteristic
275C22×C4×C13C2×D411yescharacteristic
276C22×C4×C13C2×D411yescharacteristic
277C22×C4×C13C2411yescharacteristic
278C22×C4×C13C2411yescharacteristic
279C22×C4×C13C2411yescharacteristic
280C22×C4×C13C2411yescharacteristic
281C22×C4×C13C2411yescharacteristic
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2411yescharacteristic
284C2×C22⋊D13—22no—
285C2×C22⋊D13—22no—
286C2×C22⋊D13—22no—
287C2×C22⋊D13—22no—
288C2×C22⋊D13—22no—
289C2×C22⋊D13—22no—
290C2×C22⋊D13—44no—
291C2×C22⋊D13—44no—
292C2×C22⋊D13—44no—
293C22×Dic13—21no—
294C22×Dic13—21no—
295C22×Dic13—21no—
296#6127—28no—
297#6127—44no—
298#6127—44no—
299#6127—44no—
300C2×D52—21no—
301C2×D52—42no—
302C2×D52C2412yes—
303C2×C4×D13—22no—
304C2×C4×D13—22no—
305C2×C4×D13—44no—
306C2×Dic26—21no—
307C2×Dic26—42no—
308C2×Dic26C2412yes—
309C13×C4⋊C4—24no—
310C13×C4⋊C4—24no—
311C13×C4⋊C4—24no—
312C13×C4⋊C4—24no—
313C13×C4⋊C4—22no—
314C13×C4⋊C4—22no—
315C13×C4⋊C4—22no—
316C13×C4⋊C4C2414yes—
317C13×C22⋊C4—24no—
318C13×C22⋊C4—24no—
319C13×C22⋊C4—24no—
320C13×C22⋊C4—24no—
321C22⋊Dic13—22no—
322C22⋊Dic13—22no—
323C22⋊Dic13—22no—
324C22⋊Dic13—22no—
325C22⋊Dic13—22no—
326C22⋊Dic13—22no—
327#6107—48no—
328#6106—48no—
329#6103—22no—
330#6103—22no—
331#6103—22no—
332#6103—22no—
333C4⋊Dic13—21no—
334C4⋊Dic13—21no—
335C4⋊Dic13C2412yes—
336C4⋊Dic13C2412yes—
337#6101—22no—
338#6101—22no—
339#6101—22no—
340#6101—22no—
341C4×Dic13—22no—
342C4×Dic13—22no—
343#6099—28no—
344#6099—44no—
345C2×#1055—44no—
346C2×#1055C2418yes—
347C2×#525—131no—
348C22×C22⋊Q8D1311yescharacteristic, complemented
349#3196—134no—
350#3195—132no—
351#3193—132no—
352#3190—134no—
353#3189—132no—
354#3187—132no—
355#3095—132no—
356#3092—132no—
357#3056—134no—
358#3007—132no—
359#3004—132no—
360C2×#407—131no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—416no—
382C23×C13#13714yescomplemented
383C23×C13C22×D411yescharacteristic
384C23×C13C22×D411yescharacteristic
385C23×C13C22×D411yescharacteristic
386C23×C13C22×D411yescharacteristic
387C23×C13C22×D411yescharacteristic
388C23×C13C22×D411yescharacteristic
389C23×C13C22×D411yescharacteristic
390C22×D13—22no—
391C22×D13—42no—
392C22×D13—42no—
393C22×D13—42no—
394Q8×C13—28no—
395Q8×C13—44no—
396Q8×C13—44no—
397Q8×C13—44no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—24no—
414C2×C4×C13—24no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—44no—
428C2×C4×C13—44no—
429C2×C4×C13—44no—
430C2×C4×C13—44no—
431C2×C4×C13—44no—
432C2×C4×C13—44no—
433C2×C4×C13C22×D411yescharacteristic
434C2×C4×C13C22×D411yescharacteristic
435C2×C4×C13C22×D411yescharacteristic
436C2×C4×C13C22×D411yescharacteristic
437C2×C4×C13C22×D411yescharacteristic
438C2×C4×C13C22×D411yescharacteristic
439C2×C4×C13C22×D411yescharacteristic
440C2×C4×C13H(5,𝔽2)14yes—
441C2×C4×C13C2511yescharacteristic
442C22⋊D13—44no—
443C22⋊D13—44no—
444C22⋊D13—44no—
445C22⋊D13—44no—
446C22⋊D13—44no—
447C22⋊D13—44no—
448C2×Dic13—22no—
449C2×Dic13—22no—
450C2×Dic13—22no—
451C2×Dic13—42no—
452C2×Dic13—42no—
453C2×Dic13—42no—
454D52—24no—
455D52—42no—
456C4×D13—44no—
457C4×D13—44no—
458Dic26—24no—
459Dic26—42no—
460#1055—28no—
461C22×#41—131no—
462C23×Q8C2×D1311yescharacteristic, complemented
463C24×C4C2×D1311yescharacteristic
464C2×#137—134no—
465C22×M16—132no—
466#525—132no—
467#525—132no—
468#525—132no—
469#525—132no—
470#525—261no—
471#525—261no—
472#525—261no—
473#525—261no—
474C2×#123—261no—
475C2×C22⋊Q8—21no—
476C2×C22⋊Q8—21no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8—21no—
479C2×C22⋊Q8—21no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8—131no—
482C2×C22⋊Q8—131no—
483C2×C22⋊Q8C2×D1312yes—
484C2×C22⋊Q8C2×D1312yes—
485C2×C22⋊Q8C2×D1312yes—
486C2×C22⋊Q8C2×D1312yescomplemented
487C2×C22⋊Q8C2×D1312yescomplemented
488C2×C22⋊Q8C2×D1312yescomplemented
489C2×#121—131no—
490C2×#121—131no—
491C2×#120—261no—
492C2×C4×D4—261no—
493C2×C4×D4—261no—
494C2×#117—131no—
495C22×C4⋊C4—21no—
496C22×C4⋊C4C2×D1311yescharacteristic, complemented
497C22×C22⋊C4—21no—
498#485—138no—
499#484—134no—
500#484—134no—
501#483—134no—
502#483—134no—
503#481—134no—
504#480—134no—
505#470—138no—
506#468—138no—
507#467—138no—
508#465—138no—
509#452—138no—
510#451—134no—
511#451—134no—
512#451—134no—
513#450—134no—
514#448—134no—
515#448—134no—
516#428—134no—
517#419—134no—
518#417—134no—
519#407—132no—
520#407—132no—
521#407—132no—
522#407—132no—
523C2×C22⋊C8—132no—
524C2×C22⋊C8—132no—
525C22×C13—28no—
526C22×C13—21no—
527C22×C13—21no—
528C22×C13—21no—
529C22×C13—21no—
530C22×C13—21no—
531C22×C13—21no—
532C22×C13—21no—
533C22×C13—21no—
534C22×C13—21no—
535C22×C13—21no—
536C22×C13—21no—
537C22×C13—21no—
538C22×C13—21no—
539C22×C13—21no—
540C22×C13—21no—
541C22×C13—21no—
542C22×C13—44no—
543C22×C13—44no—
544C22×C13—44no—
545C22×C13—44no—
546C22×C13—44no—
547C22×C13—44no—
548C22×C13#53412yes—
549C22×C13C2×#13712yes—
550C22×C13C2×#13712yes—
551C22×C13C2×#13712yes—
552C22×C13#57512yes—
553C22×C13C23×D411yescharacteristic
554C2×D13—42no—
555C2×D13—42no—
556C2×D13—42no—
557C2×D13—84no—
558C4×C13—21no—
559C4×C13—21no—
560C4×C13—21no—
561C4×C13—21no—
562C4×C13—21no—
563C4×C13—21no—
564C4×C13—44no—
565C4×C13—44no—
566C4×C13#53412yes—
567C4×C13C2×H(5,𝔽2)12yes—
568Dic13—42no—
569Dic13—42no—
570Dic13—42no—
571C25C22⋊D1311yescharacteristic
572C2×#41—132no—
573C2×#41—132no—
574C2×#41—261no—
575C2×#41—261no—
576C2×#41—524no—
577C22×Q8—21no—
578C22×Q8—21no—
579C22×Q8—21no—
580C22×Q8—44no—
581C22×Q8—131no—
582C22×Q8C22×D1312yes—
583C22×Q8C22×D1312yes—
584C22×Q8C22×D1312yes—
585C22×D4—131no—
586C22×D4—261no—
587C22×D4—261no—
588C22×D4—261no—
589C23×C4—21no—
590C23×C4—21no—
591C23×C4—44no—
592C23×C4—261no—
593C23×C4C22⋊D1311yescharacteristic
594C23×C4C22⋊D1311yescharacteristic
595C23×C4C22⋊D1311yescharacteristic
596C23×C4C22⋊D1311yescharacteristic
597C23×C4C22⋊D1311yescharacteristic
598C23×C4C22⋊D1311yescharacteristic
599C23×C4C22⋊D1311yescharacteristic
600C23×C4C22×D1311yescharacteristic
601C23×C4C22×D1311yescharacteristic
602C23×C4C22×D1311yescharacteristic
603C23×C4C22×D1311yescharacteristic
604C23×C4C22×D1311yescharacteristic
605C23×C4C22×D1311yescharacteristic
606C23×C4C22×D1311yescharacteristic
607#137—528no—
608C2×Q16—138no—
609C2×SD16—138no—
610C2×M16—134no—
611C2×M16—134no—
612C2×M16—524no—
613C22×C8—134no—
614#123—262no—
615#123—262no—
616#123—262no—
617#123—262no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—22no—
630C22⋊Q8—132no—
631C22⋊Q8—132no—
632C22⋊Q8—132no—
633C22⋊Q8—132no—
634C22⋊Q8—261no—
635C22⋊Q8—261no—
636C22⋊Q8—261no—
637C22⋊Q8—261no—
638C22⋊Q8C22×D1314yes—
639C22⋊Q8C22×D1314yes—
640C22⋊Q8C22×D1314yes—
641C22⋊Q8C22×D1314yes—
642#121—132no—
643#121—132no—
644#121—132no—
645#121—132no—
646#121—261no—
647#121—261no—
648#121—261no—
649#121—261no—
650#120—262no—
651#120—262no—
652#120—262no—
653#120—262no—
654C4×D4—262no—
655C4×D4—262no—
656C4×D4—262no—
657C4×D4—262no—
658C4×D4—262no—
659C4×D4—262no—
660C4×D4—262no—
661C4×D4—262no—
662#117—132no—
663#117—132no—
664#117—261no—
665#117—261no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—131no—
676C2×C4⋊C4—131no—
677C2×C4⋊C4—261no—
678C2×C4⋊C4—261no—
679C2×C4⋊C4C22×D1312yes—
680C2×C4⋊C4C22×D1312yes—
681C2×C4⋊C4C22×D1312yes—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—261no—
689C2×C22⋊C4—261no—
690C2×C22⋊C4—261no—
691C2×C22⋊C4—261no—
692C2×C22⋊C4—261no—
693C2×C42—261no—
694#107—138no—
695#106—138no—
696#103—138no—
697#103—138no—
698#103—138no—
699#102—138no—
700C22⋊C8—134no—
701C22⋊C8—134no—
702C22⋊C8—134no—
703C22⋊C8—134no—
704C2×C13—22no—
705C2×C13—22no—
706C2×C13—22no—
707C2×C13—22no—
708C2×C13—22no—
709C2×C13—41no—
710C2×C13—41no—
711C2×C13C2×#53411yescharacteristic
712C2×C13C22×#13711yescharacteristic
713C2×C13C2×#57511yescharacteristic
714D13—82no—
715C24—24no—
716C24—42no—
717C24—42no—
718C24—261no—
719C24C2×C22⋊D1311yescharacteristic
720C24C2×C22⋊D1311yescharacteristic
721C24C2×C22⋊D1311yescharacteristic
722C24C2×C22⋊D1311yescharacteristic
723C24C2×C22⋊D1311yescharacteristic
724C24C2×C22⋊D1311yescharacteristic
725C24C2×C22⋊D1311yescharacteristic
726#41—268no—
727#41—524no—
728#41—524no—
729#41—524no—
730C2×Q8—22no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—28no—
734C2×Q8—44no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—132no—
740C2×Q8—261no—
741C2×Q8—522no—
742C2×Q8C23×D1314yes—
743C2×D4—132no—
744C2×D4—262no—
745C2×D4—262no—
746C2×D4—262no—
747C2×D4—262no—
748C2×D4—262no—
749C2×D4—262no—
750C2×D4—261no—
751C2×D4—522no—
752C2×D4—524no—
753C2×D4—524no—
754C2×D4—524no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—262no—
781C22×C4—262no—
782C22×C4—524no—
783C22×C4C2×C22⋊D1311yescharacteristic
784C22×C4C2×C22⋊D1311yescharacteristic
785C22×C4C2×C22⋊D1311yescharacteristic
786C22×C4C2×C22⋊D1311yescharacteristic
787C22×C4C2×C22⋊D1311yescharacteristic
788C22×C4C2×C22⋊D1311yescharacteristic
789C22×C4C2×C22⋊D1311yescharacteristic
790C22×C4C2×C22⋊D1311yescharacteristic
791C22×C4C2×C22⋊D1311yescharacteristic
792C22×C4C2×C22⋊D1311yescharacteristic
793C22×C4C2×C22⋊D1311yescharacteristic
794C22×C4C2×C22⋊D1311yescharacteristic
795C22×C4C2×C22⋊D1311yescharacteristic
796C22×C4C2×C22⋊D1311yescharacteristic
797C22×C4C2×C22⋊D1311yescharacteristic
798C22×C4C2×C22⋊D1311yescharacteristic
799C22×C4C2×C22⋊D1311yescharacteristic
800C22×C4C2×C22⋊D1311yescharacteristic
801C22×C4C2×C22⋊D1311yescharacteristic
802C22×C4C2×C22⋊D1311yescharacteristic
803C22×C4C2×C22⋊D1311yescharacteristic
804C22×C4C23×D1311yescharacteristic
805C22×C4C23×D1311yescharacteristic
806C22×C4C23×D1311yescharacteristic
807C22×C4C23×D1311yescharacteristic
808C22×C4C23×D1311yescharacteristic
809C22×C4C23×D1311yescharacteristic
810C22×C4C23×D1311yescharacteristic
811Q16—528no—
812SD16—528no—
813M16—268no—
814M16—524no—
815C2×C8—138no—
816C2×C8—524no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—132no—
825C4⋊C4—132no—
826C4⋊C4—261no—
827C4⋊C4—261no—
828C4⋊C4—262no—
829C4⋊C4—262no—
830C4⋊C4—262no—
831C4⋊C4—262no—
832C4⋊C4C23×D1314yes—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—262no—
838C22⋊C4—262no—
839C22⋊C4—262no—
840C22⋊C4—262no—
841C22⋊C4—262no—
842C22⋊C4—262no—
843C22⋊C4—262no—
844C22⋊C4—262no—
845C22⋊C4—262no—
846C22⋊C4—262no—
847C42—262no—
848C42—262no—
849C13#6075111yescharacteristic, complemented, Sylow
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—262no—
872C23—522no—
873C23—522no—
874C23—522no—
875C23#8819614yescomplemented
876C23C22×C22⋊D1311yescharacteristic
877C23C22×C22⋊D1311yescharacteristic
878C23C22×C22⋊D1311yescharacteristic
879C23C22×C22⋊D1311yescharacteristic
880C23C22×C22⋊D1311yescharacteristic
881C23C22×C22⋊D1311yescharacteristic
882C23C22×C22⋊D1311yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—264no—
888Q8—522no—
889D4—264no—
890D4—522no—
891D4—524no—
892D4—524no—
893D4—524no—
894D4—524no—
895D4—524no—
896D4—524no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—524no—
936C2×C4—522no—
937C2×C4—522no—
938C2×C4—522no—
939C2×C4—524no—
940C2×C4#8825114yes—
941C2×C4C22×C22⋊D1311yescharacteristic
942C2×C4C22×C22⋊D1311yescharacteristic
943C2×C4C22×C22⋊D1311yescharacteristic
944C2×C4C22×C22⋊D1311yescharacteristic
945C2×C4C22×C22⋊D1311yescharacteristic
946C2×C4C22×C22⋊D1311yescharacteristic
947C2×C4C22×C22⋊D1311yescharacteristic
948C2×C4C24×D1311yescharacteristic
949C8—268no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—522no—
974C22—522no—
975C22—522no—
976C22—1044no—
977C22#1171950912yes—
978C22C2×#8819612yes—
979C22C2×#8819612yes—
980C22C2×#8819612yes—
981C22#1171952712yes—
982C22C23×C22⋊D1311yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—522no—
992C4—522no—
993C4—522no—
994C4#1171950912yes—
995C4C2×#8825112yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—1042no—
1004C2C2×#1171950911yescharacteristic
1005C2C22×#8819611yescharacteristic
1006C2C2×#1171952711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×C22⋊Q8C2
socleC22×C13C23×D4
prime radicalC2×#11719496C2
hypercenterC22×C22⋊Q8D13
hypocenterC13#60751
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13125666C2semidirect
3. #13125657C2semidirect
4. #13125638C2semidirect
5. #13125617C2semidirect
6. #13125608C2semidirect
7. #13125589C2semidirect
8. #13124780C2semidirect
9. #13124759C2semidirect
10. #13124462C2semidirect
11. #13124094C2semidirect
12. #13124070C2semidirect
13. C2×#11718868C2semidirect
14. C22×C13×C22⋊Q8C2semidirect
15. C23×Q8×C13C22semidirect
27. C2×C13×C22⋊Q8C22semidirect
28. C2×C13×C22⋊Q8C22semidirect
29. C2×C13×C22⋊Q8C22semidirect
31. C22×C13×C4⋊C4C22semidirect
34. C2×#88196C22semidirect
51. C22×#6099C22semidirect
52. #11718889C22semidirect
53. #11718889C22semidirect
54. #11718888C22semidirect
55. #11718888C22semidirect
56. #11718886C22semidirect
59. #11718868C22semidirect
60. #11718868C22semidirect
62. C2×C22⋊#1055C22semidirect
63. #11718713C22semidirect
64. #11718712C22semidirect
65. #11718711C22semidirect
66. #11718710C22semidirect
67. #11718709C22semidirect
68. #11718708C22semidirect
69. #11718707C22semidirect
70. #11718706C22semidirect
71. #11718705C22semidirect
72. #11718704C22semidirect
73. #11718632C22semidirect
74. #11718631C22semidirect
75. #11718629C22semidirect
76. #11718628C22semidirect
77. #11718627C22semidirect
78. #11718625C22semidirect
156. C2×#6107C23semidirect
158. C2×#6106C23semidirect
202. #88075C23semidirect
203. #88075C23semidirect
208. #88050C23semidirect
209. #88049C23semidirect
210. #88048C23semidirect
211. #88047C23semidirect
348. C22×C22⋊Q8D13semidirect
382. C23×C13#137semidirect
462. C23×Q8C2×D13semidirect
486. C2×C22⋊Q8C2×D13semidirect
487. C2×C22⋊Q8C2×D13semidirect
488. C2×C22⋊Q8C2×D13semidirect
496. C22×C4⋊C4C2×D13semidirect
849. C13#60751semidirect
875. C23#88196semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
#131256662
#131256572
#131256382
#131256172
#131256082
#131255892
#131247802
#131247592
#131244622
#131240942
#131240702
C2×#117188682
C22×C13×C22⋊Q82
#6075113