Finite Group Databasebeta

← #15878604

Subgroups — #15878604

Order 3328.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#6099C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic, complemented
3C22×#88077C211yesmaximal, characteristic, complemented
4#13117281C211yesmaximal, characteristic, complemented
5#13115756C211yesmaximal, characteristic, complemented
6#13115669C211yesmaximal, characteristic, complemented
7#13115285C211yesmaximal, characteristic, complemented
8#13115280C211yesmaximal, characteristic, complemented
9#13115139C211yesmaximal, characteristic, complemented
10#13115139C211yesmaximal, characteristic, complemented
11#13114856C211yesmaximal, characteristic, complemented
12#13114780C211yesmaximal, characteristic, complemented
13#13114780C211yesmaximal, characteristic, complemented
14#13114646C211yesmaximal, characteristic, complemented
15D4×C13×#41C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C13×#550C411yescharacteristic, complemented
19D4×Q8×C13C411yescharacteristic, complemented
20C13×#548C411yescharacteristic, complemented
21C13×#548C411yescharacteristic, complemented
22C13×#547—21no—
23C13×#547C411yescharacteristic, complemented
24C13×#546—21no—
25C13×#546—21no—
26C13×#546C411yescharacteristic, complemented
27C13×#546C411yescharacteristic, complemented
28D42×C13—21no—
29D42×C13C411yescharacteristic, complemented
30C13×#532—21no—
31C13×#532C2211yescharacteristic
32C13×#525—21no—
33C13×#525—21no—
34C13×#525C2211yescharacteristic
35C13×#525C2211yescharacteristic
36C4×C13×#41C2211yescharacteristic
37C2×C4×D4×C13—21no—
38C2×C4×D4×C13C2211yescharacteristic
39C2×#88180C2211yescharacteristic, complemented
40C22×C4×Dic13C2211yescharacteristic, complemented
41C22×#6099C2211yescharacteristic, complemented
42C22×#6099C2211yescharacteristic, complemented
43#11718897—24no—
44C2×#88077—24no—
45C2×#88077C2211yescharacteristic
46C2×#88077C2211yescharacteristic
47C2×#88077C2211yescharacteristic
48C2×#88077C2211yescharacteristic
49C2×#88077C2211yescharacteristic, complemented
50C2×#88077C2211yescharacteristic, complemented
51C2×#88077C2211yescharacteristic, complemented
52C2×#88077C2211yescharacteristic, complemented
53C2×#88077C2211yescharacteristic, complemented
54C2×#88077C2211yescharacteristic, complemented
55C2×#88077C2211yescharacteristic, complemented
56C2×#88077C2211yescharacteristic, complemented
57#11718881—21no—
58C4×C22⋊Dic13C2211yescharacteristic, complemented
59C4×C22⋊Dic13C2211yescharacteristic, complemented
60#11718868C2211yescharacteristic, complemented
61#11718868C2211yescharacteristic, complemented
62#11718673—21no—
63#11718672—21no—
64#11718672—21no—
65D4×#1055—21no—
66#11718642—21no—
67#11718612—21no—
68#11718611—21no—
69C4×C4⋊Dic13C2211yescharacteristic, complemented
70#11718593C2211yescharacteristic, complemented
71#11718585C2211yescharacteristic, complemented
72C4×#6099C2211yescharacteristic, complemented
73#11718124C2211yescharacteristic, complemented
74#11718124C2211yescharacteristic, complemented
75#11718124C2211yescharacteristic, complemented
76#11718124C2211yescharacteristic, complemented
77C2×C13×#41—21no—
78C2×C13×#41—21no—
79C2×C13×#41—21no—
80C2×C13×#41—21no—
81C2×C13×#41—22no—
82C2×C13×#41—22no—
83C2×C13×#41—22no—
84C2×C13×#41—22no—
85C2×C13×#41—41no—
86C2×C13×#41—41no—
87C2×C13×#41—41no—
88C2×C13×#41—41no—
89C2×C13×#41C2×C411yescharacteristic
90C2×C13×#41C2×C411yescharacteristic
91C2×C13×#41C2×C411yescharacteristic, complemented
92C2×C13×#41C2×C411yescharacteristic, complemented
93C2×C13×#41C2311yescharacteristic
94C2×C13×#41C2311yescharacteristic
95C2×C13×#41C2311yescharacteristic
96C22×Q8×C13C2×C411yescharacteristic
97C22×Q8×C13C2×C411yescharacteristic, complemented
98C22×D4×C13—21no—
99C22×D4×C13—21no—
100C22×D4×C13—21no—
101C22×D4×C13C2×C411yescharacteristic
102C22×D4×C13C2×C411yescharacteristic, complemented
103C22×D4×C13D411yescharacteristic
104C23×C4×C13—21no—
105C23×C4×C13—21no—
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C23×Dic13—21no—
109C13×C4⋊Q8—21no—
110C13×C4⋊Q8C2×C411yescharacteristic, complemented
111C13×#127—21no—
112C13×#127C2×C411yescharacteristic, complemented
113C13×#124—21no—
114C13×#124—21no—
115C13×#124C2×C411yescharacteristic, complemented
116C13×#124C2×C411yescharacteristic, complemented
117C13×#123—21no—
118C13×#123—21no—
119C13×#123—21no—
120C13×#123—21no—
121C13×#123—21no—
122C13×#123—21no—
123C13×C22⋊Q8—21no—
124C13×C22⋊Q8—21no—
125C13×C22⋊Q8—21no—
126C13×C22⋊Q8—21no—
127C13×C22⋊Q8C2×C411yescharacteristic
128C13×C22⋊Q8C2×C411yescharacteristic
129C13×C22⋊Q8C2×C411yescharacteristic, complemented
130C13×C22⋊Q8C2×C411yescharacteristic, complemented
131C13×#121—21no—
132C13×#121—21no—
133C13×#121—21no—
134C13×#121—21no—
135C13×#121—21no—
136C13×#121—21no—
137C13×#121—21no—
138C13×#121—21no—
139C13×#121—21no—
140C13×#121—21no—
141C13×#121C2×C411yescharacteristic
142C13×#121C2×C411yescharacteristic
143C13×#121C2×C411yescharacteristic, complemented
144C13×#121C2×C411yescharacteristic, complemented
145C13×#120—21no—
146C13×#120—21no—
147C13×#120—21no—
148C13×#120—21no—
149C13×#120—21no—
150C13×#120—21no—
151C4×Q8×C13C2×C411yescharacteristic, complemented
152C4×Q8×C13C2×C411yescharacteristic, complemented
153C4×D4×C13—21no—
154C4×D4×C13—21no—
155C4×D4×C13—21no—
156C4×D4×C13—21no—
157C4×D4×C13—21no—
158C4×D4×C13—21no—
159C4×D4×C13—21no—
160C4×D4×C13—21no—
161C4×D4×C13—21no—
162C4×D4×C13—21no—
163C4×D4×C13—21no—
164C4×D4×C13—21no—
165C4×D4×C13C2×C411yescharacteristic
166C4×D4×C13C2×C411yescharacteristic
167C4×D4×C13C2×C411yescharacteristic
168C4×D4×C13C2×C411yescharacteristic
169C4×D4×C13C2×C411yescharacteristic, complemented
170C4×D4×C13C2×C411yescharacteristic, complemented
171C4×D4×C13D411yescharacteristic
172C4×D4×C13D411yescharacteristic
173C4×D4×C13D411yescharacteristic
174C4×D4×C13D411yescharacteristic
175C13×#117—21no—
176C13×#117C2311yescharacteristic
177C2×C13×C4⋊C4—21no—
178C2×C13×C4⋊C4D411yescharacteristic
179C2×C13×C22⋊C4—21no—
180C2×C13×C22⋊C4—21no—
181C2×C13×C22⋊C4D411yescharacteristic
182C2×C13×C22⋊C4D411yescharacteristic
183C2×C42×C13—21no—
184C2×C42×C13C2311yescharacteristic
185C2×C22⋊Dic13—21no—
186C2×C22⋊Dic13—21no—
187C2×C22⋊Dic13—21no—
188#88180—22no—
189#88180—41no—
190C2×C4⋊Dic13—21no—
191C2×C4⋊Dic13—21no—
192C2×C4×Dic13—22no—
193C2×C4×Dic13—21no—
194C2×C4×Dic13—41no—
195C2×C4×Dic13C2311yescharacteristic
196C2×C4×Dic13C2311yescharacteristic
197C2×C4×Dic13C2311yescharacteristic
198C2×C4×Dic13C2311yescharacteristic
199C2×#6099—21no—
200C2×#6099—21no—
201C2×#6099—22no—
202C2×#6099—22no—
203C2×#6099—41no—
204C2×#6099—41no—
205C2×#6099C2311yescharacteristic
206C2×#6099C2311yescharacteristic
207C2×#6099C2311yescharacteristic
208C2×#6099C2311yescharacteristic
209C22×#1055—21no—
210C22×#1055—21no—
211#88077—22no—
212#88077—22no—
213#88077—22no—
214#88077—22no—
215#88077—22no—
216#88077—22no—
217#88077—22no—
218#88077—41no—
219#88077—41no—
220#88077—41no—
221#88077—41no—
222#88077D414yescomplemented
223#88071—21no—
224#88071—21no—
225#88071—21no—
226#88071—21no—
227#88071—21no—
228C22⋊#1055—21no—
229C22⋊#1055—21no—
230C22⋊#1055—21no—
231C22⋊#1055—21no—
232C4⋊#1055—21no—
233C4⋊#1055—21no—
234#88043—21no—
235C4×#1055—21no—
236#22434—131nomaximal, Sylow
237C24×C13—21no—
238C24×C13—21no—
239C24×C13C2×D411yescharacteristic
240C24×C13C2×D411yescharacteristic
241C13×#41—21no—
242C13×#41—21no—
243C13×#41—22no—
244C13×#41—22no—
245C13×#41—22no—
246C13×#41—22no—
247C13×#41—21no—
248C13×#41—21no—
249C13×#41—21no—
250C13×#41—21no—
251C13×#41—21no—
252C13×#41—21no—
253C13×#41—21no—
254C13×#41—21no—
255C13×#41—42no—
256C13×#41—42no—
257C13×#41—42no—
258C13×#41—42no—
259C13×#41—41no—
260C13×#41—41no—
261C13×#41—41no—
262C13×#41—41no—
263C13×#41—42no—
264C13×#41—42no—
265C13×#41—42no—
266C13×#41—42no—
267C13×#41C2×D412yes—
268C13×#41#4112yes—
269C2×Q8×C13—21no—
270C2×Q8×C13—21no—
271C2×Q8×C13—22no—
272C2×Q8×C13—22no—
273C2×Q8×C13—41no—
274C2×Q8×C13—41no—
275C2×Q8×C13C22×C411yescharacteristic
276C2×Q8×C13C22×C411yescharacteristic
277C2×Q8×C13C22×C411yescharacteristic
278C2×D4×C13—21no—
279C2×D4×C13—22no—
280C2×D4×C13—22no—
281C2×D4×C13—21no—
282C2×D4×C13—21no—
283C2×D4×C13—21no—
284C2×D4×C13—21no—
285C2×D4×C13—21no—
286C2×D4×C13—21no—
287C2×D4×C13—21no—
288C2×D4×C13—21no—
289C2×D4×C13—21no—
290C2×D4×C13—21no—
291C2×D4×C13—21no—
292C2×D4×C13—21no—
293C2×D4×C13—21no—
294C2×D4×C13—21no—
295C2×D4×C13—41no—
296C2×D4×C13—41no—
297C2×D4×C13—42no—
298C2×D4×C13—42no—
299C2×D4×C13—42no—
300C2×D4×C13—42no—
301C2×D4×C13—42no—
302C2×D4×C13—44no—
303C2×D4×C13C22⋊C411yescharacteristic
304C2×D4×C13C22⋊C411yescharacteristic
305C2×D4×C13C22⋊C411yescharacteristic
306C2×D4×C13C22⋊C411yescharacteristic
307C2×D4×C13C22×C411yescharacteristic
308C2×D4×C13C22×C411yescharacteristic
309C2×D4×C13C22×C411yescharacteristic
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—21no—
315C22×C4×C13—21no—
316C22×C4×C13—21no—
317C22×C4×C13—21no—
318C22×C4×C13—21no—
319C22×C4×C13—21no—
320C22×C4×C13—21no—
321C22×C4×C13—21no—
322C22×C4×C13—21no—
323C22×C4×C13—21no—
324C22×C4×C13—21no—
325C22×C4×C13—21no—
326C22×C4×C13—21no—
327C22×C4×C13—21no—
328C22×C4×C13—21no—
329C22×C4×C13—42no—
330C22×C4×C13—42no—
331C22×C4×C13—42no—
332C22×C4×C13—42no—
333C22×C4×C13C22×C411yescharacteristic
334C22×C4×C13C22×C411yescharacteristic
335C22×C4×C13C22×C411yescharacteristic
336C22×C4×C13C22×C411yescharacteristic
337C22×C4×C13C2×D411yescharacteristic
338C22×C4×C13C2×D411yescharacteristic
339C22×C4×C13C2×D411yescharacteristic
340C22×C4×C13C2×D411yescharacteristic
341C22×C4×C13C2×D411yescharacteristic
342C22×C4×C13C2×D411yescharacteristic
343C22×C4×C13C2×D411yescharacteristic
344C22×C4×C13C2×D411yescharacteristic
345C22×C4×C13C2411yescharacteristic
346C22×Dic13—21no—
347C22×Dic13—21no—
348C22×Dic13—21no—
349C22×Dic13—21no—
350C22×Dic13—42no—
351C22×Dic13—42no—
352C22×Dic13—42no—
353C13×C4⋊C4—21no—
354C13×C4⋊C4—21no—
355C13×C4⋊C4—21no—
356C13×C4⋊C4—21no—
357C13×C4⋊C4—21no—
358C13×C4⋊C4—21no—
359C13×C4⋊C4—21no—
360C13×C4⋊C4—21no—
361C13×C4⋊C4C22⋊C411yescharacteristic
362C13×C4⋊C4C22⋊C411yescharacteristic
363C13×C4⋊C4C22⋊C411yescharacteristic
364C13×C4⋊C4C22⋊C411yescharacteristic
365C13×C4⋊C4C22×C411yescharacteristic
366C13×C4⋊C4C22×C411yescharacteristic
367C13×C22⋊C4—21no—
368C13×C22⋊C4—21no—
369C13×C22⋊C4—21no—
370C13×C22⋊C4—21no—
371C13×C22⋊C4—21no—
372C13×C22⋊C4—21no—
373C13×C22⋊C4—21no—
374C13×C22⋊C4—21no—
375C13×C22⋊C4—21no—
376C13×C22⋊C4—21no—
377C13×C22⋊C4—21no—
378C13×C22⋊C4—21no—
379C13×C22⋊C4—21no—
380C13×C22⋊C4—21no—
381C13×C22⋊C4—21no—
382C13×C22⋊C4C22⋊C411yescharacteristic
383C13×C22⋊C4C22⋊C411yescharacteristic
384C13×C22⋊C4C22⋊C411yescharacteristic
385C13×C22⋊C4C22⋊C411yescharacteristic
386C13×C22⋊C4C22⋊C411yescharacteristic
387C13×C22⋊C4C22⋊C411yescharacteristic
388C13×C22⋊C4C22⋊C411yescharacteristic
389C13×C22⋊C4C22⋊C411yescharacteristic
390C42×C13—21no—
391C42×C13—21no—
392C42×C13—21no—
393C42×C13C22×C411yescharacteristic
394C42×C13C22×C411yescharacteristic
395C42×C13C2×D411yescharacteristic
396C42×C13C2×D411yescharacteristic
397C22⋊Dic13—42no—
398C22⋊Dic13—42no—
399C22⋊Dic13—42no—
400C4⋊Dic13—42no—
401C4⋊Dic13—42no—
402C4×Dic13—21no—
403C4×Dic13—21no—
404C4×Dic13—21no—
405C4×Dic13—21no—
406C4×Dic13—21no—
407C4×Dic13—21no—
408C4×Dic13—21no—
409C4×Dic13—42no—
410C4×Dic13C2×D412yescomplemented
411#6099—21no—
412#6099—21no—
413#6099—21no—
414#6099—21no—
415#6099—21no—
416#6099—21no—
417#6099—21no—
418#6099—42no—
419#6099—42no—
420#6099C2×D412yescomplemented
421C2×#1055—21no—
422C2×#1055—21no—
423C2×#1055—21no—
424C2×#1055—21no—
425C2×#1055—42no—
426C2×#1055—42no—
427D4×#41D1311yescharacteristic
428D4×M16—131no—
429C2×#421—131no—
430C22×#104—131no—
431#2290—131no—
432#1980—131no—
433#1963—131no—
434#1897—131no—
435#1896—131no—
436#1871—131no—
437#1871—131no—
438#1806—131no—
439#1789—131no—
440#1789—131no—
441#1759—131no—
442C23×C13—21no—
443C23×C13—21no—
444C23×C13—21no—
445C23×C13—22no—
446C23×C13—21no—
447C23×C13—21no—
448C23×C13—21no—
449C23×C13—21no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—42no—
454C23×C13—42no—
455C23×C13—42no—
456C23×C13—42no—
457C23×C13—81no—
458C23×C13—81no—
459C23×C13C2×C22⋊C411yescharacteristic
460C23×C13C2×C22⋊C411yescharacteristic
461C23×C13C2×C22⋊C411yescharacteristic
462C23×C13C2×C22⋊C411yescharacteristic
463C23×C13C22×D411yescharacteristic
464Q8×C13—21no—
465Q8×C13—21no—
466Q8×C13—21no—
467Q8×C13—21no—
468Q8×C13—21no—
469Q8×C13—42no—
470Q8×C13—42no—
471Q8×C13C4×D412yes—
472D4×C13—22no—
473D4×C13—22no—
474D4×C13—22no—
475D4×C13—22no—
476D4×C13—21no—
477D4×C13—21no—
478D4×C13—21no—
479D4×C13—21no—
480D4×C13—21no—
481D4×C13—41no—
482D4×C13—41no—
483D4×C13—42no—
484D4×C13—42no—
485D4×C13—42no—
486D4×C13—42no—
487D4×C13—42no—
488D4×C13—42no—
489D4×C13—42no—
490D4×C13—42no—
491D4×C13—41no—
492D4×C13—41no—
493D4×C13—41no—
494D4×C13—41no—
495D4×C13—42no—
496D4×C13—81no—
497D4×C13—81no—
498D4×C13—81no—
499D4×C13C4×D412yes—
500C2×C4×C13—21no—
501C2×C4×C13—21no—
502C2×C4×C13—21no—
503C2×C4×C13—21no—
504C2×C4×C13—21no—
505C2×C4×C13—21no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—21no—
509C2×C4×C13—21no—
510C2×C4×C13—21no—
511C2×C4×C13—21no—
512C2×C4×C13—21no—
513C2×C4×C13—21no—
514C2×C4×C13—21no—
515C2×C4×C13—21no—
516C2×C4×C13—21no—
517C2×C4×C13—22no—
518C2×C4×C13—21no—
519C2×C4×C13—21no—
520C2×C4×C13—21no—
521C2×C4×C13—21no—
522C2×C4×C13—22no—
523C2×C4×C13—21no—
524C2×C4×C13—21no—
525C2×C4×C13—21no—
526C2×C4×C13—21no—
527C2×C4×C13—41no—
528C2×C4×C13—41no—
529C2×C4×C13—42no—
530C2×C4×C13—42no—
531C2×C4×C13—42no—
532C2×C4×C13—42no—
533C2×C4×C13—42no—
534C2×C4×C13—42no—
535C2×C4×C13—42no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—81no—
541C2×C4×C13C2×C22⋊C411yescharacteristic
542C2×C4×C13C2×C22⋊C411yescharacteristic
543C2×C4×C13C2×C22⋊C411yescharacteristic
544C2×C4×C13C2×C22⋊C411yescharacteristic
545C2×C4×C13C2×C22⋊C411yescharacteristic
546C2×C4×C13C2×C22⋊C411yescharacteristic
547C2×C4×C13C2×C22⋊C411yescharacteristic
548C2×C4×C13C2×C22⋊C411yescharacteristic
549C2×C4×C13C23×C411yescharacteristic
550C2×C4×C13C22×D411yescharacteristic
551C2×C4×C13C22×D411yescharacteristic
552C2×C4×C13C2×#4111yescharacteristic
553C2×C4×C13H(5,𝔽2)11yescharacteristic
554C2×C4×C13H(5,𝔽2)11yescharacteristic
555C2×Dic13—22no—
556C2×Dic13—22no—
557C2×Dic13—41no—
558C2×Dic13—41no—
559C2×Dic13—41no—
560C2×Dic13—48no—
561C2×Dic13—41no—
562C2×Dic13—41no—
563C2×Dic13—41no—
564C2×Dic13—41no—
565C2×Dic13—41no—
566C2×Dic13—41no—
567C2×Dic13—41no—
568#1055—22no—
569#1055—41no—
570#1055—41no—
571#1055—41no—
572C22×#41C2×D1311yescharacteristic
573C22×#41C2×D1311yescharacteristic
574C22×M16—131no—
575C22×M16—131no—
576#550Dic1311yescharacteristic, complemented
577D4×Q8Dic1311yescharacteristic, complemented
578#548Dic1311yescharacteristic, complemented
579#548Dic1311yescharacteristic, complemented
580#547—21no—
581#547Dic1311yescharacteristic, complemented
582#546—21no—
583#546—21no—
584#546Dic1311yescharacteristic, complemented
585#546Dic1311yescharacteristic, complemented
586D42—21no—
587D42Dic1311yescharacteristic, complemented
588#532—21no—
589#532C2×D1311yescharacteristic
590#525—21no—
591#525—21no—
592#525C2×D1311yescharacteristic
593#525C2×D1311yescharacteristic
594C4×#41C2×D1311yescharacteristic
595C2×C4×D4—21no—
596C2×C4×D4C2×D1311yescharacteristic
597C2×#117—131no—
598C22×C42—131no—
599#436—261no—
600#435—261no—
601#435—261no—
602C8×D4—261no—
603#423—131no—
604#421—264no—
605C2×#104—131no—
606C2×#104—131no—
607C2×#104—131no—
608C2×#104—131no—
609C2×#104—131no—
610C2×#104—131no—
611C2×#104—131no—
612C2×#104—131no—
613C2×#104—131no—
614C2×#104—131no—
615C2×#104—131no—
616C2×#104—131no—
617C2×#104—264no—
618#407—131no—
619#407—131no—
620C4×M16—131no—
621#388—261no—
622#387—261no—
623#386—261no—
624#385—261no—
625C4×C4⋊C4—131no—
626C4×C22⋊C4—131no—
627C4×C22⋊C4—131no—
628#376—131no—
629#339—131no—
630#339—131no—
631#339—131no—
632#339—131no—
633C22×C13—21no—
634C22×C13—21no—
635C22×C13—21no—
636C22×C13—21no—
637C22×C13—21no—
638C22×C13—21no—
639C22×C13—21no—
640C22×C13—22no—
641C22×C13—21no—
642C22×C13—21no—
643C22×C13—21no—
644C22×C13—21no—
645C22×C13—21no—
646C22×C13—21no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—41no—
650C22×C13—41no—
651C22×C13—41no—
652C22×C13—41no—
653C22×C13—41no—
654C22×C13—41no—
655C22×C13—41no—
656C22×C13—41no—
657C22×C13—81no—
658C22×C13—81no—
659C22×C13—84no—
660C22×C13—84no—
661C22×C13#42112yescomplemented
662C22×C13C22×C22⋊C411yescharacteristic
663C22×C13D4211yescharacteristic
664C22×C13#54611yescharacteristic
665C4×C13—21no—
666C4×C13—21no—
667C4×C13—21no—
668C4×C13—21no—
669C4×C13—22no—
670C4×C13—21no—
671C4×C13—21no—
672C4×C13—21no—
673C4×C13—21no—
674C4×C13—41no—
675C4×C13—41no—
676C4×C13—41no—
677C4×C13—41no—
678C4×C13C2×C4×D411yescharacteristic
679C4×C13#51811yescharacteristic
680C4×C13D4211yescharacteristic
681C4×C13#54611yescharacteristic
682Dic13—42no—
683Dic13—42no—
684Dic13—81no—
685Dic13—81no—
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—21no—
689C2×#41—21no—
690C2×#41—22no—
691C2×#41—22no—
692C2×#41—22no—
693C2×#41—22no—
694C2×#41—41no—
695C2×#41—41no—
696C2×#41—41no—
697C2×#41—41no—
698C2×#41C2×Dic1311yescharacteristic
699C2×#41C2×Dic1311yescharacteristic
700C2×#41C2×Dic1311yescharacteristic, complemented
701C2×#41C2×Dic1311yescharacteristic, complemented
702C2×#41C22×D1311yescharacteristic
703C2×#41C22×D1311yescharacteristic
704C2×#41C22×D1311yescharacteristic
705C22×Q8C2×Dic1311yescharacteristic
706C22×Q8C2×Dic1311yescharacteristic, complemented
707C22×D4—21no—
708C22×D4—21no—
709C22×D4—21no—
710C22×D4C2×Dic1311yescharacteristic
711C22×D4C2×Dic1311yescharacteristic, complemented
712C22×D4C22⋊D1311yescharacteristic
713C23×C4—21no—
714C23×C4—21no—
715C23×C4—261no—
716C23×C4C22×D1311yescharacteristic
717C23×C4C22×D1311yescharacteristic
718C2×M16—131no—
719C2×M16—131no—
720C2×M16—131no—
721C2×M16—131no—
722C2×M16—261no—
723C2×M16—261no—
724C2×M16—262no—
725C2×M16—262no—
726C2×M16—521no—
727C2×M16—521no—
728C22×C8—261no—
729C22×C8—261no—
730C4⋊Q8—21no—
731C4⋊Q8C2×Dic1311yescharacteristic, complemented
732#127—21no—
733#127C2×Dic1311yescharacteristic, complemented
734#124—21no—
735#124—21no—
736#124C2×Dic1311yescharacteristic, complemented
737#124C2×Dic1311yescharacteristic, complemented
738#123—21no—
739#123—21no—
740#123—21no—
741#123—21no—
742#123—21no—
743#123—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8C2×Dic1311yescharacteristic
749C22⋊Q8C2×Dic1311yescharacteristic
750C22⋊Q8C2×Dic1311yescharacteristic, complemented
751C22⋊Q8C2×Dic1311yescharacteristic, complemented
752#121—21no—
753#121—21no—
754#121—21no—
755#121—21no—
756#121—21no—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121C2×Dic1311yescharacteristic
763#121C2×Dic1311yescharacteristic
764#121C2×Dic1311yescharacteristic, complemented
765#121C2×Dic1311yescharacteristic, complemented
766#120—21no—
767#120—21no—
768#120—21no—
769#120—21no—
770#120—21no—
771#120—21no—
772C4×Q8C2×Dic1311yescharacteristic, complemented
773C4×Q8C2×Dic1311yescharacteristic, complemented
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—21no—
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4C2×Dic1311yescharacteristic
787C4×D4C2×Dic1311yescharacteristic
788C4×D4C2×Dic1311yescharacteristic
789C4×D4C2×Dic1311yescharacteristic
790C4×D4C2×Dic1311yescharacteristic, complemented
791C4×D4C2×Dic1311yescharacteristic, complemented
792C4×D4C22⋊D1311yescharacteristic
793C4×D4C22⋊D1311yescharacteristic
794C4×D4C22⋊D1311yescharacteristic
795C4×D4C22⋊D1311yescharacteristic
796#117—21no—
797#117—262no—
798#117—521no—
799#117C22×D1311yescharacteristic
800C2×C4⋊C4—21no—
801C2×C4⋊C4—261no—
802C2×C4⋊C4—261no—
803C2×C4⋊C4C22⋊D1311yescharacteristic
804C2×C22⋊C4—21no—
805C2×C22⋊C4—21no—
806C2×C22⋊C4—261no—
807C2×C22⋊C4—261no—
808C2×C22⋊C4—261no—
809C2×C22⋊C4C22⋊D1311yescharacteristic
810C2×C22⋊C4C22⋊D1311yescharacteristic
811C2×C42—21no—
812C2×C42—131no—
813C2×C42—131no—
814C2×C42—131no—
815C2×C42—131no—
816C2×C42—262no—
817C2×C42—261no—
818C2×C42—521no—
819C2×C42C22×D1311yescharacteristic
820C4⋊C8—261no—
821C4⋊C8—261no—
822#104—134no—
823#104—262no—
824#104—262no—
825#104—262no—
826#104—262no—
827#104—262no—
828#104—262no—
829#104—262no—
830#104—521no—
831#104—521no—
832#104—521no—
833#104—521no—
834C22⋊C8—261no—
835C22⋊C8—261no—
836C22⋊C8—261no—
837C22⋊C8—261no—
838#97—261no—
839C4×C8—261no—
840#95—261no—
841#95—261no—
842#95—261no—
843#95—261no—
844#95—261no—
845C2×C13—21no—
846C2×C13—21no—
847C2×C13—22no—
848C2×C13—41no—
849C2×C13—41no—
850C2×C13—41no—
851C2×C13—42no—
852C2×C13—81no—
853C2×C13—81no—
854C2×C13D4×C22⋊C411yescharacteristic
855C2×C13C2×#42111yescharacteristic
856C2×C13#290111yescharacteristic
857C24—21no—
858C24—21no—
859C24C2×C22⋊D1311yescharacteristic
860C24C2×C22⋊D1311yescharacteristic
861#41—21no—
862#41—21no—
863#41—22no—
864#41—22no—
865#41—22no—
866#41—22no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—42no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—41no—
880#41—41no—
881#41—41no—
882#41—41no—
883#41—42no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41D4×D1312yes—
888#41#612912yes—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—22no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8C22×Dic1311yescharacteristic
896C2×Q8C22×Dic1311yescharacteristic
897C2×Q8C22×Dic1311yescharacteristic
898C2×D4—21no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—41no—
916C2×D4—41no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4C22⋊Dic1311yescharacteristic
924C2×D4C22⋊Dic1311yescharacteristic
925C2×D4C22⋊Dic1311yescharacteristic
926C2×D4C22⋊Dic1311yescharacteristic
927C2×D4C22×Dic1311yescharacteristic
928C2×D4C22×Dic1311yescharacteristic
929C2×D4C22×Dic1311yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—261no—
954C22×C4—261no—
955C22×C4—261no—
956C22×C4—261no—
957C22×C4—522no—
958C22×C4—522no—
959C22×C4—522no—
960C22×C4C22×Dic1311yescharacteristic
961C22×C4C22×Dic1311yescharacteristic
962C22×C4C22×Dic1311yescharacteristic
963C22×C4C22×Dic1311yescharacteristic
964C22×C4C2×C22⋊D1311yescharacteristic
965C22×C4C2×C22⋊D1311yescharacteristic
966C22×C4C2×C22⋊D1311yescharacteristic
967C22×C4C2×C22⋊D1311yescharacteristic
968C22×C4C2×C22⋊D1311yescharacteristic
969C22×C4C2×C22⋊D1311yescharacteristic
970C22×C4C2×C22⋊D1311yescharacteristic
971C22×C4C2×C22⋊D1311yescharacteristic
972C22×C4C23×D1311yescharacteristic
973M16—132no—
974M16—261no—
975M16—261no—
976M16—261no—
977M16—261no—
978M16—261no—
979M16—261no—
980M16—261no—
981M16—522no—
982M16—522no—
983C2×C8—261no—
984C2×C8—261no—
985C2×C8—261no—
986C2×C8—261no—
987C2×C8—522no—
988C2×C8—522no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—522no—
998C4⋊C4—522no—
999C4⋊C4C22⋊Dic1311yescharacteristic
1000C4⋊C4C22⋊Dic1311yescharacteristic
1001C4⋊C4C22⋊Dic1311yescharacteristic
1002C4⋊C4C22⋊Dic1311yescharacteristic
1003C4⋊C4C22×Dic1311yescharacteristic
1004C4⋊C4C22×Dic1311yescharacteristic
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—21no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—522no—
1021C22⋊C4—522no—
1022C22⋊C4—522no—
1023C22⋊C4C22⋊Dic1311yescharacteristic
1024C22⋊C4C22⋊Dic1311yescharacteristic
1025C22⋊C4C22⋊Dic1311yescharacteristic
1026C22⋊C4C22⋊Dic1311yescharacteristic
1027C22⋊C4C22⋊Dic1311yescharacteristic
1028C22⋊C4C22⋊Dic1311yescharacteristic
1029C22⋊C4C22⋊Dic1311yescharacteristic
1030C22⋊C4C22⋊Dic1311yescharacteristic
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—132no—
1035C42—261no—
1036C42—261no—
1037C42—261no—
1038C42—261no—
1039C42—261no—
1040C42—261no—
1041C42—261no—
1042C42—522no—
1043C42C22×Dic1311yescharacteristic
1044C42C22×Dic1311yescharacteristic
1045C42C2×C22⋊D1311yescharacteristic
1046C42C2×C22⋊D1311yescharacteristic
1047C13#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C2×C22⋊Dic1311yescharacteristic
1066C23C2×C22⋊Dic1311yescharacteristic
1067C23C2×C22⋊Dic1311yescharacteristic
1068C23C2×C22⋊Dic1311yescharacteristic
1069C23C22×C22⋊D1311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×Dic1312yes—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—21no—
1087D4—41no—
1088D4—41no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—42no—
1102D4—81no—
1103D4—81no—
1104D4—81no—
1105D4D4×Dic1312yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—81no—
1147C2×C4—262no—
1148C2×C4—262no—
1149C2×C4—521no—
1150C2×C4—521no—
1151C2×C4—521no—
1152C2×C4—528no—
1153C2×C4—521no—
1154C2×C4—521no—
1155C2×C4—521no—
1156C2×C4—521no—
1157C2×C4—521no—
1158C2×C4—521no—
1159C2×C4—521no—
1160C2×C4C2×C22⋊Dic1311yescharacteristic
1161C2×C4C2×C22⋊Dic1311yescharacteristic
1162C2×C4C2×C22⋊Dic1311yescharacteristic
1163C2×C4C2×C22⋊Dic1311yescharacteristic
1164C2×C4C2×C22⋊Dic1311yescharacteristic
1165C2×C4C2×C22⋊Dic1311yescharacteristic
1166C2×C4C2×C22⋊Dic1311yescharacteristic
1167C2×C4C2×C22⋊Dic1311yescharacteristic
1168C2×C4C2×D4×D1311yescharacteristic
1169C2×C4C2×#612911yescharacteristic
1170C2×C4#8825111yescharacteristic
1171C2×C4#8825111yescharacteristic
1172C2×C4C23×Dic1311yescharacteristic
1173C2×C4C22×C22⋊D1311yescharacteristic
1174C8—262no—
1175C8—521no—
1176C8—521no—
1177C8—521no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—22no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#1171889712yescomplemented
1207C22D4×C22⋊D1311yescharacteristic
1208C22#1171951111yescharacteristic
1209C22C22×C22⋊Dic1311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—22no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—522no—
1224C4—522no—
1225C4—1041no—
1226C4—1041no—
1227C4C2×D4×Dic1311yescharacteristic
1228C4#1171950311yescharacteristic
1229C4D4×C22⋊D1311yescharacteristic
1230C4#1171951111yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic1311yescharacteristic
1241C2C2×#1171889711yescharacteristic
1242C2#1312338311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalD4×C13×#41C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenterD4×#41D13
hypocenterC13#22434
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#6099C2semidirect
2. C2×#11718897C2semidirect
3. C22×#88077C2semidirect
4. #13117281C2semidirect
5. #13115756C2semidirect
6. #13115669C2semidirect
7. #13115285C2semidirect
8. #13115280C2semidirect
9. #13115139C2semidirect
10. #13115139C2semidirect
11. #13114856C2semidirect
12. #13114780C2semidirect
13. #13114780C2semidirect
14. #13114646C2semidirect
18. C13×#550C4semidirect
19. D4×Q8×C13C4semidirect
20. C13×#548C4semidirect
21. C13×#548C4semidirect
23. C13×#547C4semidirect
26. C13×#546C4semidirect
27. C13×#546C4semidirect
29. D42×C13C4semidirect
39. C2×#88180C22semidirect
40. C22×C4×Dic13C22semidirect
41. C22×#6099C22semidirect
42. C22×#6099C22semidirect
49. C2×#88077C22semidirect
50. C2×#88077C22semidirect
51. C2×#88077C22semidirect
52. C2×#88077C22semidirect
53. C2×#88077C22semidirect
54. C2×#88077C22semidirect
55. C2×#88077C22semidirect
56. C2×#88077C22semidirect
58. C4×C22⋊Dic13C22semidirect
59. C4×C22⋊Dic13C22semidirect
60. #11718868C22semidirect
61. #11718868C22semidirect
69. C4×C4⋊Dic13C22semidirect
70. #11718593C22semidirect
71. #11718585C22semidirect
72. C4×#6099C22semidirect
73. #11718124C22semidirect
74. #11718124C22semidirect
75. #11718124C22semidirect
76. #11718124C22semidirect
91. C2×C13×#41C2×C4semidirect
92. C2×C13×#41C2×C4semidirect
97. C22×Q8×C13C2×C4semidirect
102. C22×D4×C13C2×C4semidirect
110. C13×C4⋊Q8C2×C4semidirect
112. C13×#127C2×C4semidirect
115. C13×#124C2×C4semidirect
116. C13×#124C2×C4semidirect
129. C13×C22⋊Q8C2×C4semidirect
130. C13×C22⋊Q8C2×C4semidirect
143. C13×#121C2×C4semidirect
144. C13×#121C2×C4semidirect
151. C4×Q8×C13C2×C4semidirect
152. C4×Q8×C13C2×C4semidirect
169. C4×D4×C13C2×C4semidirect
170. C4×D4×C13C2×C4semidirect
222. #88077D4semidirect
410. C4×Dic13C2×D4semidirect
420. #6099C2×D4semidirect
576. #550Dic13semidirect
577. D4×Q8Dic13semidirect
578. #548Dic13semidirect
579. #548Dic13semidirect
581. #547Dic13semidirect
584. #546Dic13semidirect
585. #546Dic13semidirect
587. D42Dic13semidirect
661. C22×C13#421semidirect
700. C2×#41C2×Dic13semidirect
701. C2×#41C2×Dic13semidirect
706. C22×Q8C2×Dic13semidirect
711. C22×D4C2×Dic13semidirect
731. C4⋊Q8C2×Dic13semidirect
733. #127C2×Dic13semidirect
736. #124C2×Dic13semidirect
737. #124C2×Dic13semidirect
750. C22⋊Q8C2×Dic13semidirect
751. C22⋊Q8C2×Dic13semidirect
764. #121C2×Dic13semidirect
765. #121C2×Dic13semidirect
772. C4×Q8C2×Dic13semidirect
773. C4×Q8C2×Dic13semidirect
790. C4×D4C2×Dic13semidirect
791. C4×D4C2×Dic13semidirect
1047. C13#22434semidirect
1206. C22#11718897semidirect

Maximal subgroups

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

subgroupindex
D4×#60992
C2×#117188972
C22×#880772
#131172812
#131157562
#131156692
#131152852
#131152802
#131151392
#131148562
#131147802
#131146462
D4×C13×#412
#2243413