Finite Group Databasebeta

← #16807889

Subgroups — #16807889

Order 3328.

2202 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131382C212yesmaximal, complemented
2#13131376C212yesmaximal, complemented
3#13131370C212yesmaximal, complemented
4#13131359C212yesmaximal, complemented
5#13131359C212yesmaximal, complemented
6#13131359C212yesmaximal, complemented
7#13131352C212yesmaximal, complemented
8#13131349C212yesmaximal, complemented
9#13131334C212yesmaximal, complemented
10#13131334C212yesmaximal, complemented
11#13131329C212yesmaximal, complemented
12#13131329C211yesmaximal, characteristic, complemented
13#13131325C211yesmaximal, characteristic
14#13131323C212yesmaximal, complemented
15#13131316C211yesmaximal, characteristic, complemented
16C22⋊Q8×#261C211yesmaximal, characteristic, complemented
17#121×#261C211yesmaximal, characteristic
18C2×#11719082C211yesmaximal, characteristic, complemented
19D13×#539C211yesmaximal, characteristic
20C2×Q8×#261C2211yescharacteristic
21C2×D4×#261C2212yes—
22C2×D4×#261C2211yescharacteristic
23C2×D4×#261C2212yes—
24C2×#88237C2212yes—
25C2×#88237C2212yes—
26C22×C4⋊#261C2211yescharacteristic
27C22×C4×#261C2211yescharacteristic
28C13×#539C411yescharacteristic, complemented
29#11719412C412yescomplemented
30D13×#126C2212yes—
31#11719397C412yescomplemented
32D13×#125C2212yes—
33#11719370C412yescomplemented
34#11719365C412yescomplemented
35D13×#123C2212yes—
36D13×#123C2212yes—
37#11719350C411yescharacteristic, complemented
38#11719343C412yescomplemented
39D13×C22⋊Q8C2211yescharacteristic
40D13×C22⋊Q8C2212yes—
41D13×#121C2211yescharacteristic
42#11719307C411yescharacteristic, complemented
43#11719269C412yescomplemented
44C4×D4×D13C2212yes—
45#11719220C411yescharacteristic, complemented
46C2×C4⋊C4×D13C2211yescharacteristic
47(C2×#261)⋊Q8C2211yescharacteristic
48(C2×#261)⋊Q8C2212yes—
49#11719151C2211yescharacteristic
50#11719150C2212yes—
51#11719150C2212yes—
52#11719150C2212yes—
53#11719136C2211yescharacteristic
54#11719136C2211yescharacteristic
55#11719136C2212yes—
56#11719136C2212yes—
57#11719136C2212yes—
58C2×(C2×#261)⋊C4C2211yescharacteristic
59C2×(C2×#261)⋊C4C2211yescharacteristic
60C2×(C2×#261)⋊C4C2211yescharacteristic
61C2×(C2×#261)⋊C4C2211yescharacteristic
62C2×(C2×#261)⋊C4C2212yes—
63#11719083C2211yescharacteristic
64#11719083C2211yescharacteristic
65#11719083C2212yes—
66#11719083C2212yes—
67#11719083C2212yes—
68#11719083C2212yes—
69#11719083C2212yes—
70#11719083C2212yes—
71#11719083C2212yes—
72#11719083C2212yes—
73#11719083C2212yes—
74#11719082C2212yes—
75#11719082C2212yes—
76#11719082C2212yes—
77#11719082C2212yes—
78#11719082C2212yes—
79#11719082C2212yes—
80#11719082C2212yes—
81#11719082C2212yes—
82#11719082C2212yes—
83#11719082C2212yes—
84#11719082C2212yes—
85#11719082C2212yes—
86#11719082C2212yes—
87#11719082C2212yes—
88C4⋊C4×#261C2211yescharacteristic
89C4⋊C4×#261C2211yescharacteristic
90C4⋊C4×#261C2212yes—
91C4⋊C4×#261C2212yes—
92C4⋊C4×#261C2212yes—
93#11719071C2212yes—
94#11719071C2212yes—
95#11719071C2212yes—
96#11719071C2212yes—
97#11719071C2212yes—
98#11719071C2212yes—
99#11719071C2212yes—
100#11719071C2212yes—
101#11719070C2212yes—
102#11719070C2212yes—
103#11719070C2212yes—
104#11719070C2212yes—
105#11719070C2212yes—
106#11719070C2212yes—
107#11719070C2212yes—
108C22⋊C4×#261C2212yes—
109C22⋊C4×#261C2212yes—
110C22⋊C4×#261C2212yes—
111C22⋊C4×#261C2212yes—
112C22⋊C4×#261C2212yes—
113#11719060C2212yes—
114#11719060C2212yes—
115C4×C4⋊#261C2212yes—
116C4×C4⋊#261C2212yes—
117C23×#261C2311yescharacteristic
118C23×#261C2311yescharacteristic
119C23×#261C2312yes—
120C23×#261C2311yescharacteristic
121C23×#261C2311yescharacteristic
122C23×#261C2312yes—
123C2×Q8×D13C2311yescharacteristic
124C2×D4×D13C2312yes—
125C2×D4×D13C2311yescharacteristic
126C22×C4×D13C2311yescharacteristic
127C22×C4×D13C2311yescharacteristic
128C22×C4×D13C2311yescharacteristic
129C22×C4×D13C2312yes—
130C2×C22⋊#261C2312yes—
131C2×C22⋊#261C2312yes—
132C2×C22⋊#261C2312yes—
133C2×C22⋊#261C2312yes—
134C2×C22⋊#261C2312yes—
135C2×C22⋊#261C2312yes—
136C2×C22⋊#261C2312yes—
137C2×C22⋊#261C2312yes—
138Q8×#261—42no—
139D4×#261—42no—
140D4×#261—44no—
141D4×#261—44no—
142#88237—44no—
143#88237—44no—
144C2×C4⋊#261—42no—
145C2×C4⋊#261C2312yes—
146C2×C4⋊#261C2312yes—
147C2×C4⋊#261C2312yes—
148C2×C4⋊#261C2312yes—
149C2×C4⋊#261C2312yes—
150C2×C4⋊#261C2312yes—
151C2×C4⋊#261C2312yes—
152C2×C4⋊#261C2312yes—
153C2×C4⋊#261C2312yes—
154C2×C4⋊#261C2311yescharacteristic
155C2×C4⋊#261C2312yes—
156C2×C4⋊#261C2312yes—
157C2×C4⋊#261C2312yes—
158C2×C4⋊#261C2311yescharacteristic
159C2×C4⋊#261C2311yescharacteristic
160C2×C4⋊#261C2311yescharacteristic
161C2×C4×#261—42no—
162C2×C4×#261C2312yes—
163C2×C4×#261C2311yescharacteristic
164C2×C4×#261C2311yescharacteristic
165C2×C4×#261C2312yes—
166C2×C4×#261C2312yes—
167C2×C4×#261C2312yes—
168C2×C4×#261C2312yes—
169C2×C4×#261C2312yes—
170C2×C4×#261C2311yescharacteristic
171C2×C4×#261C2312yes—
172C2×C4×#261C2312yes—
173C2×C4×#261C2311yescharacteristic
174C13×#126C2×C412yescomplemented
175C13×#125C2×C412yescomplemented
176C13×#123C2×C412yescomplemented
177C13×#123C2×C412yescomplemented
178C13×C22⋊Q8C2×C412yescomplemented
179C13×C22⋊Q8C2×C411yescharacteristic, complemented
180C13×#121C2×C411yescharacteristic
181C4×D4×C13C2×C412yescomplemented
182C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
183#88200C2×C411yescharacteristic, complemented
184#88200C2×C412yescomplemented
185#88193C2×C412yes—
186#88192C2×C411yescharacteristic
187#88189C2×C412yescomplemented
188#88189C2×C412yescomplemented
189D4×Dic13C2×C412yescomplemented
190#88184C2×C411yescharacteristic
191#88183C2×C412yescomplemented
192#88183C2×C412yescomplemented
193C4×C22⋊D13C2×C412yescomplemented
194C4×C22⋊D13C2×C412yescomplemented
195C2×C4⋊Dic13C2×C411yescharacteristic, complemented
196#88178C2×C411yescharacteristic, complemented
197#88178C2×C412yescomplemented
198C2×#6101C2×C411yescharacteristic, complemented
199C2×#6101C2×C411yescharacteristic, complemented
200#88152C2×C412yescomplemented
201#88152C2×C412yescomplemented
202#88152C2×C412yescomplemented
203#88151C2×C412yescomplemented
204#88151C2×C411yescharacteristic, complemented
205#88150C2×C412yescomplemented
206#88150C2×C412yescomplemented
207#88150C2×C412yescomplemented
208#88149C2×C411yescharacteristic
209#88148C2×C412yescomplemented
210#88148C2×C412yescomplemented
211#88148C2×C412yescomplemented
212#88148C2×C412yescomplemented
213#88147C2×C412yescomplemented
214C4⋊C4×D13C2×C412yescomplemented
215C4⋊C4×D13C2×C412yescomplemented
216C4⋊C4×D13C2312yes—
217C4⋊C4×D13C2312yes—
218C4⋊C4×D13C2312yes—
219C4⋊C4×D13C2311yescharacteristic
220C4⋊C4×D13C2312yes—
221C4⋊C4×D13C2312yes—
222C4⋊C4×D13C2311yescharacteristic
223C4⋊C4×D13C2312yes—
224#88144C2×C412yescomplemented
225#88144C2×C412yescomplemented
226#88143C2×C412yescomplemented
227#88143C2×C412yescomplemented
228#88143C2×C412yescomplemented
229#88143C2×C412yescomplemented
230#88140C2×C412yescomplemented
231#88140C2×C412yescomplemented
232#88138C2×C412yes—
233#88137C2×C412yescomplemented
234#88137C2×C412yescomplemented
235#88137C2×C412yescomplemented
236#88137C2×C412yescomplemented
237#88135C2×C412yescomplemented
238#88135C2×C412yescomplemented
239C22⋊C4×D13C2312yes—
240C22⋊C4×D13C2312yes—
241C22⋊C4×D13C2312yes—
242C22⋊C4×D13C2312yes—
243C22⋊C4×D13C2312yes—
244#88133C2×C412yescomplemented
245#88133C2×C412yescomplemented
246#88133C2×C412yescomplemented
247#88132C2×C412yescomplemented
248#88132C2×C412yescomplemented
249#88132C2×C412yescomplemented
250#88130C2×C412yescomplemented
251C4×D52C2×C412yescomplemented
252C42×D13C2312yes—
253#88124C2×C412yescomplemented
254(C2×#261)⋊C4C2312yes—
255(C2×#261)⋊C4C2312yes—
256(C2×#261)⋊C4C2312yes—
257(C2×#261)⋊C4C2312yes—
258(C2×#261)⋊C4C2312yes—
259(C2×#261)⋊C4C2312yes—
260(C2×#261)⋊C4C2312yes—
261(C2×#261)⋊C4C2312yes—
262(C2×#261)⋊C4C2312yes—
263(C2×#261)⋊C4C2312yes—
264(C2×#261)⋊C4C2312yes—
265(C2×#261)⋊C4C2312yes—
266(C2×#261)⋊C4C2312yes—
267(C2×#261)⋊C4C2312yes—
268(C2×#261)⋊C4C2312yes—
269(C2×#261)⋊C4C2312yes—
270(C2×#261)⋊C4C2312yes—
271(C2×#261)⋊C4C2312yes—
272(C2×#261)⋊C4C2312yes—
273(C2×#261)⋊C4C2312yes—
274(C2×#261)⋊C4C2312yes—
275(C2×#261)⋊C4C2312yes—
276(C2×#261)⋊C4C2312yes—
277(C2×#261)⋊C4C2312yes—
278#34427—131nomaximal, Sylow
279C23×D13C2412yes—
280C23×D13C2411yescharacteristic
281C22×#261—22no—
282C22×#261—22no—
283C22×#261—22no—
284C22×#261—22no—
285C22×#261—22no—
286C22×#261—22no—
287C22×#261—24no—
288C22×#261—41no—
289C22×#261—41no—
290C22×#261—41no—
291C22×#261—42no—
292C22×#261—42no—
293C22×#261—42no—
294C22×#261—41no—
295C22×#261—42no—
296C22×#261—42no—
297C22×#261—41no—
298C22×#261—41no—
299C22×#261C2411yescharacteristic
300C22×#261C2412yes—
301C22×#261C2412yes—
302C22×#261C2411yescharacteristic
303C22×#261C2412yes—
304C22×#261C2412yes—
305C22×#261C2412yes—
306C22×#261C2412yes—
307C22×#261C2411yescharacteristic
308C22×#261C2411yescharacteristic
309C2×Q8×C13C22×C411yescharacteristic
310C2×D4×C13C22×C412yes—
311C2×D4×C13C22×C411yescharacteristic
312C22×C4×C13C22×C411yescharacteristic
313C22×C4×C13C22×C411yescharacteristic
314C22×C4×C13C22×C411yescharacteristic
315C22×C4×C13C22×C412yes—
316C2×C22⋊D13C22×C412yes—
317C2×C22⋊D13C22×C412yes—
318C2×C22⋊D13C22×C412yes—
319C22×Dic13C22×C411yescharacteristic
320C22×Dic13C22×C412yes—
321C22×Dic13C22×C411yescharacteristic
322C22×Dic13C22×C411yescharacteristic
323Q8×D13—41no—
324Q8×D13—41no—
325D4×D13—24no—
326D4×D13—24no—
327D4×D13—41no—
328D4×D13—41no—
329C2×D52C22×C412yes—
330C2×D52C22×C411yescharacteristic
331C2×C4×D13—22no—
332C2×C4×D13—22no—
333C2×C4×D13—41no—
334C2×C4×D13—41no—
335C2×C4×D13—42no—
336C2×C4×D13—41no—
337C2×C4×D13—42no—
338C2×C4×D13—41no—
339C2×C4×D13C22×C412yes—
340C2×C4×D13C22×C412yes—
341C2×C4×D13C22×C412yes—
342C2×C4×D13C22×C412yes—
343C2×C4×D13C22×C411yescharacteristic
344C2×C4×D13C22×C411yescharacteristic
345C2×C4×D13C2412yes—
346C2×C4×D13C2412yes—
347C2×C4×D13C2412yes—
348C2×C4×D13C2412yes—
349C2×C4×D13C2412yes—
350C2×C4×D13C2411yescharacteristic
351C2×C4×D13C2411yescharacteristic
352C2×Dic26C22×C412yes—
353C2×Dic26C22×C411yescharacteristic
354C22⋊#261—24no—
355C22⋊#261—24no—
356C22⋊#261—24no—
357C22⋊#261—42no—
358C22⋊#261—42no—
359C22⋊#261—42no—
360C22⋊#261—42no—
361C22⋊#261—42no—
362C4⋊#261—24no—
363C4⋊#261—24no—
364C4⋊#261—42no—
365C4⋊#261—42no—
366C4⋊#261—42no—
367C4⋊#261—41no—
368C4⋊#261—42no—
369C4⋊#261—41no—
370C4⋊#261—42no—
371C4⋊#261—42no—
372C4⋊#261—42no—
373C4⋊#261—41no—
374C4⋊#261—42no—
375C4⋊#261—42no—
376C4⋊#261—42no—
377C4⋊#261—41no—
378C4×#261—22no—
379C4×#261—22no—
380C4×#261—24no—
381C4×#261—41no—
382C4×#261—41no—
383C4×#261—42no—
384C4×#261—42no—
385C4×#261—42no—
386C4×#261—42no—
387C4×#261—42no—
388C4×#261—42no—
389C4×#261—42no—
390C13×C4⋊C4C22×C411yescharacteristic
391C13×C4⋊C4C22×C412yes—
392C13×C4⋊C4C22×C412yes—
393C13×C4⋊C4C22×C412yes—
394C13×C4⋊C4C22×C412yes—
395C13×C4⋊C4C22×C412yes—
396C13×C4⋊C4C22×C412yes—
397C13×C4⋊C4C22×C411yescharacteristic
398C13×C22⋊C4C22×C412yes—
399C13×C22⋊C4C22×C412yes—
400C13×C22⋊C4C22×C412yes—
401C13×C22⋊C4C22×C412yes—
402C13×C22⋊C4C22×C412yes—
403C42×C13C22×C412yes—
404C22⋊Dic13C22×C412yes—
405C22⋊Dic13C22×C412yes—
406C22⋊Dic13C22×C412yes—
407C22⋊Dic13C22×C412yes—
408C22⋊Dic13C22×C412yes—
409#6103C22×C412yes—
410#6103C22×C412yes—
411#6103C22×C412yes—
412#6103C22×C412yes—
413#6103C22×C412yes—
414#6103C22×C412yes—
415#6103C22×C412yes—
416#6103C22×C412yes—
417#6103C22×C412yes—
418#6103C22×C412yes—
419C4⋊Dic13C22×C412yes—
420C4⋊Dic13C22×C412yes—
421C4⋊Dic13C22×C412yes—
422C4⋊Dic13C22×C412yes—
423C4⋊Dic13C22×C411yescharacteristic
424C4⋊Dic13C22×C412yes—
425C4⋊Dic13C22×C412yes—
426C4⋊Dic13C22×C411yescharacteristic
427#6101C22×C412yes—
428#6101C22×C412yes—
429#6101C22×C412yes—
430#6101C22×C412yes—
431#6101C22×C412yes—
432#6101C22×C412yes—
433#6101C22×C412yes—
434#6101C22×C412yes—
435#6101C22×C412yes—
436#6101C22×C412yes—
437#6101C22×C412yes—
438#6101C22×C412yes—
439#6101C22×C412yes—
440#6101C22×C412yes—
441C4×Dic13C22×C412yes—
442C4×Dic13C22×C412yes—
443C4×Dic13C22×C412yes—
444C2×#539—131no—
445#2382—132no—
446#2376—132no—
447#2370—132no—
448#2359—132no—
449#2359—132no—
450#2359—132no—
451#2352—132no—
452#2349—132no—
453#2334—132no—
454#2334—132no—
455#2329—132no—
456#2329—131no—
457#2325—131no—
458#2323—132no—
459#2316—131no—
460C4×C22⋊Q8—131no—
461C4×#121—131no—
462C2×#387—131no—
463C23×C13C23×C412yes—
464C23×C13C23×C411yescharacteristic
465C22×D13—21no—
466C22×D13—21no—
467C22×D13—21no—
468C22×D13—21no—
469C22×D13—22no—
470C22×D13—22no—
471C22×D13—22no—
472C22×D13—22no—
473C22×D13—22no—
474C22×D13—22no—
475C22×D13C23×C412yes—
476C22×D13C23×C411yescharacteristic
477C22×D13H(5,𝔽2)12yes—
478C22×D132−1+412yes—
479C22×D13C2511yescharacteristic
480C2×#261—21no—
481C2×#261—21no—
482C2×#261—21no—
483C2×#261—21no—
484C2×#261—21no—
485C2×#261—22no—
486C2×#261—21no—
487C2×#261—22no—
488C2×#261—22no—
489C2×#261—22no—
490C2×#261—22no—
491C2×#261—22no—
492C2×#261—22no—
493C2×#261—22no—
494C2×#261—21no—
495C2×#261—22no—
496C2×#261—21no—
497C2×#261—22no—
498C2×#261—21no—
499C2×#261—22no—
500C2×#261—22no—
501C2×#261—22no—
502C2×#261—22no—
503C2×#261—22no—
504C2×#261—22no—
505C2×#261—22no—
506C2×#261—22no—
507C2×#261—21no—
508C2×#261—44no—
509C2×#261—44no—
510C2×#261—84no—
511C2×#261—82no—
512C2×#261—82no—
513C2×#261—84no—
514C2×#261H(5,𝔽2)12yes—
515C2×#2612−1+412yes—
516Q8×C13—41no—
517D4×C13—24no—
518D4×C13—41no—
519C2×C4×C13—22no—
520C2×C4×C13—42no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13C23×C412yes—
524C2×C4×C13C23×C412yes—
525C2×C4×C13C23×C412yes—
526C2×C4×C13C23×C411yescharacteristic
527C2×C4×C13C23×C412yes—
528C2×C4×C13C23×C411yescharacteristic
529C2×C4×C13C23×C412yes—
530C22⋊D13—24no—
531C22⋊D13—24no—
532C22⋊D13—42no—
533C2×Dic13—22no—
534C2×Dic13—42no—
535C2×Dic13—41no—
536C2×Dic13—41no—
537C2×Dic13C23×C412yes—
538C2×Dic13C23×C412yes—
539C2×Dic13C23×C412yes—
540C2×Dic13C23×C411yescharacteristic
541C2×Dic13C23×C412yes—
542C2×Dic13C23×C412yes—
543C2×Dic13C23×C411yescharacteristic
544D52—24no—
545D52—41no—
546C4×D13—24no—
547C4×D13—21no—
548C4×D13—21no—
549C4×D13—22no—
550C4×D13—22no—
551C4×D13—22no—
552C4×D13—22no—
553C4×D13—22no—
554C4×D13—22no—
555C4×D13—22no—
556C4×D13—22no—
557C4×D13—22no—
558C4×D13—21no—
559C4×D13—22no—
560C4×D13—21no—
561C4×D13—42no—
562C4×D13—41no—
563C4×D13—42no—
564C4×D13—42no—
565C4×D13—41no—
566Dic26—42no—
567Dic26—41no—
568#539—132no—
569#539—132no—
570#539—132no—
571#539—132no—
572#539—132no—
573#539—131no—
574#539—131no—
575#539—132no—
576#539—131no—
577#539#26111yescharacteristic, complemented
578C2×#126—132no—
579C2×#125—132no—
580C2×#123—132no—
581C2×#123—132no—
582C2×C22⋊Q8—132no—
583C2×C22⋊Q8—131no—
584C2×#121—131no—
585C2×C4×Q8—131no—
586C2×C4×D4—132no—
587C2×C4×D4—132no—
588C2×C4×D4—132no—
589C2×C4×D4—131no—
590C2×#117—132no—
591C2×#117—132no—
592C22×C4⋊C4—131no—
593C22×C4⋊C4—131no—
594C22×C42—131no—
595#391—132no—
596#391—131no—
597#390—131no—
598#389—132no—
599#389—132no—
600#389—132no—
601#389—132no—
602#389—132no—
603#389—132no—
604#389—132no—
605#389—132no—
606#389—131no—
607#389—132no—
608#389—131no—
609#388—132no—
610#388—132no—
611#388—132no—
612#388—132no—
613#388—132no—
614#388—132no—
615#388—132no—
616#388—132no—
617#387—132no—
618#387—132no—
619#387—132no—
620#387—132no—
621#387—132no—
622#387—132no—
623#387—132no—
624#387—132no—
625#387—132no—
626#387—132no—
627#387—132no—
628#387—132no—
629#387—132no—
630#387—132no—
631#386—132no—
632#386—132no—
633#386—132no—
634#385—132no—
635#385—132no—
636#385—132no—
637#385—132no—
638#385—132no—
639#385—132no—
640#385—132no—
641#382—132no—
642#382—132no—
643#380—131no—
644#380—131no—
645#380—132no—
646#380—132no—
647#380—132no—
648C4×C4⋊C4—132no—
649C4×C4⋊C4—131no—
650C4×C4⋊C4—132no—
651C4×C4⋊C4—132no—
652C4×C4⋊C4—132no—
653C4×C4⋊C4—132no—
654C4×C4⋊C4—131no—
655C4×C22⋊C4—132no—
656C4×C22⋊C4—132no—
657C4×C22⋊C4—132no—
658C4×C22⋊C4—132no—
659C4×C22⋊C4—132no—
660C2×#95—131no—
661C2×#95—132no—
662C2×#95—131no—
663C2×#95—131no—
664C2×#95—131no—
665C22×C13—21no—
666C22×C13—21no—
667C22×C13—22no—
668C22×C13—22no—
669C22×C13—22no—
670C22×C13#52012yes—
671C22×C13C24×C411yescharacteristic
672C2×D13—21no—
673C2×D13—21no—
674C2×D13—22no—
675C2×D13—22no—
676C2×D13—22no—
677C2×D13—22no—
678C2×D13—22no—
679C2×D13—22no—
680C2×D13—22no—
681C2×D13—42no—
682C2×D13—42no—
683C2×D13—42no—
684C2×D13—42no—
685C2×D13#52012yes—
686C2×D13C2×H(5,𝔽2)11yescharacteristic
687C2×D13C2×H(5,𝔽2)11yescharacteristic
688C2×D13C2×2−1+411yescharacteristic
689C2×D13C2×2−1+411yescharacteristic
690C2×D13#58511yescharacteristic
691C2×D13#58511yescharacteristic
692#261—22no—
693#261—22no—
694#261—41no—
695#261—42no—
696#261—42no—
697#261—41no—
698#261—42no—
699#261—42no—
700#261—42no—
701#261—42no—
702C4×C13—22no—
703C4×C13—22no—
704C4×C13—21no—
705C4×C13—22no—
706C4×C13—22no—
707C4×C13—21no—
708C4×C13—22no—
709Dic13—22no—
710Dic13—22no—
711Dic13—21no—
712Dic13—22no—
713Dic13—22no—
714Dic13—21no—
715Dic13—22no—
716C22×Q8—131no—
717C22×D4—132no—
718C22×D4—131no—
719C23×C4—131no—
720C23×C4—131no—
721C23×C4—131no—
722C23×C4—132no—
723C23×C4—131no—
724C23×C4—131no—
725C23×C4—131no—
726C23×C4—131no—
727C23×C4—132no—
728C23×C4—132no—
729#126—132no—
730#126—132no—
731#126—132no—
732#126—132no—
733#126—132no—
734#126—132no—
735#126—132no—
736#126C2×#26112yescomplemented
737#125—132no—
738#125—132no—
739#125—132no—
740#125—132no—
741#125—132no—
742#125—132no—
743#125—132no—
744#125C2×#26112yescomplemented
745#123—132no—
746#123—132no—
747#123—132no—
748#123—132no—
749#123—132no—
750#123—132no—
751#123—132no—
752#123—132no—
753#123—132no—
754#123—132no—
755#123—132no—
756#123—132no—
757#123—132no—
758#123—132no—
759#123C2×#26112yescomplemented
760#123C2×#26112yescomplemented
761C22⋊Q8—131no—
762C22⋊Q8—132no—
763C22⋊Q8—131no—
764C22⋊Q8—132no—
765C22⋊Q8—132no—
766C22⋊Q8—132no—
767C22⋊Q8—132no—
768C22⋊Q8—131no—
769C22⋊Q8—132no—
770C22⋊Q8—132no—
771C22⋊Q8—132no—
772C22⋊Q8—132no—
773C22⋊Q8C2×#26111yescharacteristic, complemented
774C22⋊Q8C2×#26112yescomplemented
775#121—131no—
776#121—132no—
777#121—131no—
778#121—131no—
779#121—132no—
780#121C2×#26111yescharacteristic
781C4×Q8—522no—
782C4×D4—132no—
783C4×D4—132no—
784C4×D4—132no—
785C4×D4—132no—
786C4×D4—132no—
787C4×D4—132no—
788C4×D4—132no—
789C4×D4—522no—
790C4×D4—524no—
791C4×D4—524no—
792C4×D4C2×#26112yescomplemented
793#117—524no—
794#117—524no—
795C2×C4⋊C4—131no—
796C2×C4⋊C4—131no—
797C2×C4⋊C4—131no—
798C2×C4⋊C4—132no—
799C2×C4⋊C4—132no—
800C2×C4⋊C4—132no—
801C2×C4⋊C4—132no—
802C2×C4⋊C4—132no—
803C2×C4⋊C4—131no—
804C2×C4⋊C4—132no—
805C2×C4⋊C4—132no—
806C2×C4⋊C4—131no—
807C2×C4⋊C4—132no—
808C2×C4⋊C4—132no—
809C2×C4⋊C4—132no—
810C2×C4⋊C4—132no—
811C2×C4⋊C4—132no—
812C2×C4⋊C4—132no—
813C2×C4⋊C4—132no—
814C2×C4⋊C4—131no—
815C2×C4⋊C4—132no—
816C2×C4⋊C4—132no—
817C2×C4⋊C4—132no—
818C2×C4⋊C4—131no—
819C2×C4⋊C4—132no—
820C2×C4⋊C4—132no—
821C2×C4⋊C4—131no—
822C2×C4⋊C4—131no—
823C2×C4⋊C4—132no—
824C2×C4⋊C4—522no—
825C2×C4⋊C4C2×#26111yescharacteristic, complemented
826C2×C22⋊C4—132no—
827C2×C22⋊C4—132no—
828C2×C22⋊C4—132no—
829C2×C22⋊C4—132no—
830C2×C22⋊C4—132no—
831C2×C22⋊C4—132no—
832C2×C22⋊C4—132no—
833C2×C22⋊C4—132no—
834C2×C22⋊C4—132no—
835C2×C22⋊C4—132no—
836C2×C22⋊C4—132no—
837C2×C22⋊C4—132no—
838C2×C22⋊C4—132no—
839C2×C42—132no—
840C2×C42—132no—
841C2×C42—131no—
842C2×C42—131no—
843C2×C42—132no—
844C2×C42—132no—
845C2×C42—132no—
846C2×C42—132no—
847C2×C42—132no—
848C2×C42—132no—
849C2×C42—131no—
850C2×C42—132no—
851C2×C42—131no—
852C2×C42—522no—
853#95—132no—
854#95—132no—
855#95—132no—
856#95—132no—
857#95—132no—
858#95—132no—
859#95—132no—
860#95—132no—
861#95—132no—
862#95—132no—
863#95—132no—
864#95—132no—
865#95—132no—
866#95—132no—
867#95—132no—
868#95—132no—
869#95—132no—
870#95—132no—
871#95—132no—
872#95—132no—
873#95—132no—
874#95—132no—
875#95—132no—
876#95—132no—
877C2×C13—22no—
878C2×C13—42no—
879C2×C13C2×#52011yescharacteristic
880C2×C13C4×H(5,𝔽2)11yescharacteristic
881C2×C13C4×2−1+411yescharacteristic
882D13—22no—
883D13—42no—
884D13#353511yescharacteristic
885D13#353611yescharacteristic
886D13#356011yescharacteristic
887D13#356311yescharacteristic
888C24—131no—
889C24—132no—
890C2×Q8—131no—
891C2×Q8—132no—
892C2×Q8—521no—
893C2×Q8—521no—
894C2×Q8C22×#26111yescharacteristic
895C2×D4—132no—
896C2×D4—132no—
897C2×D4—132no—
898C2×D4—132no—
899C2×D4—131no—
900C2×D4—264no—
901C2×D4—264no—
902C2×D4—521no—
903C2×D4—521no—
904C2×D4C22×#26112yes—
905C2×D4C22×#26111yescharacteristic
906C22×C4—131no—
907C22×C4—131no—
908C22×C4—131no—
909C22×C4—131no—
910C22×C4—131no—
911C22×C4—132no—
912C22×C4—132no—
913C22×C4—132no—
914C22×C4—132no—
915C22×C4—132no—
916C22×C4—131no—
917C22×C4—131no—
918C22×C4—132no—
919C22×C4—132no—
920C22×C4—132no—
921C22×C4—131no—
922C22×C4—131no—
923C22×C4—132no—
924C22×C4—132no—
925C22×C4—131no—
926C22×C4—132no—
927C22×C4—132no—
928C22×C4—131no—
929C22×C4—132no—
930C22×C4—132no—
931C22×C4—132no—
932C22×C4—132no—
933C22×C4—262no—
934C22×C4—262no—
935C22×C4—262no—
936C22×C4—262no—
937C22×C4—264no—
938C22×C4—262no—
939C22×C4—262no—
940C22×C4—262no—
941C22×C4—262no—
942C22×C4—521no—
943C22×C4—521no—
944C22×C4—522no—
945C22×C4—521no—
946C22×C4—522no—
947C22×C4—521no—
948C22×C4—521no—
949C22×C4—521no—
950C22×C4—521no—
951C22×C4—522no—
952C22×C4—522no—
953C22×C4—522no—
954C22×C4—521no—
955C22×C4—522no—
956C22×C4—522no—
957C22×C4—521no—
958C22×C4—521no—
959C22×C4C22×#26111yescharacteristic
960C22×C4C22×#26111yescharacteristic
961C22×C4C22×#26111yescharacteristic
962C22×C4C22×#26112yes—
963C4⋊C4—132no—
964C4⋊C4—132no—
965C4⋊C4—132no—
966C4⋊C4—132no—
967C4⋊C4—132no—
968C4⋊C4—132no—
969C4⋊C4—132no—
970C4⋊C4—132no—
971C4⋊C4—132no—
972C4⋊C4—132no—
973C4⋊C4—131no—
974C4⋊C4—132no—
975C4⋊C4—132no—
976C4⋊C4—132no—
977C4⋊C4—132no—
978C4⋊C4—132no—
979C4⋊C4—132no—
980C4⋊C4—132no—
981C4⋊C4—131no—
982C4⋊C4—132no—
983C4⋊C4—132no—
984C4⋊C4—132no—
985C4⋊C4—264no—
986C4⋊C4—264no—
987C4⋊C4—522no—
988C4⋊C4—522no—
989C4⋊C4—522no—
990C4⋊C4—522no—
991C4⋊C4—521no—
992C4⋊C4—522no—
993C4⋊C4—522no—
994C4⋊C4—522no—
995C4⋊C4—521no—
996C4⋊C4—522no—
997C4⋊C4—522no—
998C4⋊C4—521no—
999C4⋊C4—522no—
1000C4⋊C4—521no—
1001C4⋊C4C22×#26112yes—
1002C4⋊C4C22×#26112yes—
1003C4⋊C4C22×#26112yes—
1004C4⋊C4C22×#26111yescharacteristic
1005C4⋊C4C22×#26112yes—
1006C4⋊C4C22×#26112yes—
1007C4⋊C4C22×#26111yescharacteristic
1008C4⋊C4C22×#26112yes—
1009C22⋊C4—132no—
1010C22⋊C4—132no—
1011C22⋊C4—132no—
1012C22⋊C4—132no—
1013C22⋊C4—132no—
1014C22⋊C4—132no—
1015C22⋊C4—132no—
1016C22⋊C4—132no—
1017C22⋊C4—132no—
1018C22⋊C4—132no—
1019C22⋊C4—132no—
1020C22⋊C4—132no—
1021C22⋊C4—132no—
1022C22⋊C4—132no—
1023C22⋊C4—132no—
1024C22⋊C4—264no—
1025C22⋊C4—264no—
1026C22⋊C4—264no—
1027C22⋊C4—522no—
1028C22⋊C4—522no—
1029C22⋊C4—522no—
1030C22⋊C4—522no—
1031C22⋊C4—522no—
1032C22⋊C4C22×#26112yes—
1033C22⋊C4C22×#26112yes—
1034C22⋊C4C22×#26112yes—
1035C22⋊C4C22×#26112yes—
1036C22⋊C4C22×#26112yes—
1037C42—132no—
1038C42—132no—
1039C42—132no—
1040C42—262no—
1041C42—262no—
1042C42—264no—
1043C42—521no—
1044C42—521no—
1045C42—522no—
1046C42—522no—
1047C42—522no—
1048C42—522no—
1049C42—522no—
1050C42—522no—
1051C42—522no—
1052C42C22×#26112yes—
1053C13#3442711yescharacteristic, complemented, Sylow
1054C23—131no—
1055C23—132no—
1056C23—132no—
1057C23—131no—
1058C23—132no—
1059C23—261no—
1060C23—261no—
1061C23—261no—
1062C23—261no—
1063C23—262no—
1064C23—262no—
1065C23—262no—
1066C23—262no—
1067C23—262no—
1068C23—262no—
1069C23C23×#26112yes—
1070C23C23×#26111yescharacteristic
1071Q8—41no—
1072Q8—522no—
1073Q8—521no—
1074D4—24no—
1075D4—41no—
1076D4—264no—
1077D4—264no—
1078D4—264no—
1079D4—521no—
1080D4—522no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—132no—
1086C2×C4—132no—
1087C2×C4—132no—
1088C2×C4—132no—
1089C2×C4—132no—
1090C2×C4—132no—
1091C2×C4—132no—
1092C2×C4—131no—
1093C2×C4—131no—
1094C2×C4—261no—
1095C2×C4—261no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—262no—
1099C2×C4—262no—
1100C2×C4—262no—
1101C2×C4—262no—
1102C2×C4—262no—
1103C2×C4—261no—
1104C2×C4—262no—
1105C2×C4—261no—
1106C2×C4—262no—
1107C2×C4—264no—
1108C2×C4—262no—
1109C2×C4—261no—
1110C2×C4—261no—
1111C2×C4—261no—
1112C2×C4—261no—
1113C2×C4—262no—
1114C2×C4—261no—
1115C2×C4—262no—
1116C2×C4—262no—
1117C2×C4—262no—
1118C2×C4—261no—
1119C2×C4—262no—
1120C2×C4—262no—
1121C2×C4—262no—
1122C2×C4—262no—
1123C2×C4—262no—
1124C2×C4—262no—
1125C2×C4—262no—
1126C2×C4—262no—
1127C2×C4—261no—
1128C2×C4—261no—
1129C2×C4—262no—
1130C2×C4—262no—
1131C2×C4—262no—
1132C2×C4—262no—
1133C2×C4—262no—
1134C2×C4—261no—
1135C2×C4—261no—
1136C2×C4—262no—
1137C2×C4—262no—
1138C2×C4—522no—
1139C2×C4—522no—
1140C2×C4—521no—
1141C2×C4—522no—
1142C2×C4—521no—
1143C2×C4—521no—
1144C2×C4—522no—
1145C2×C4—521no—
1146C2×C4—524no—
1147C2×C4—524no—
1148C2×C4—1044no—
1149C2×C4—1042no—
1150C2×C4—1042no—
1151C2×C4—1044no—
1152C2×C4C23×#26112yes—
1153C2×C4C23×#26112yes—
1154C2×C4C23×#26112yes—
1155C2×C4C23×#26112yes—
1156C2×C4C23×#26112yes—
1157C2×C4C23×#26111yescharacteristic
1158C2×C4C23×#26111yescharacteristic
1159C22—21no—
1160C22—21no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—131no—
1165C22—131no—
1166C22—131no—
1167C22—131no—
1168C22—131no—
1169C22—131no—
1170C22—132no—
1171C22—262no—
1172C22—262no—
1173C22—262no—
1174C22—262no—
1175C22—261no—
1176C22—261no—
1177C22—262no—
1178C22—262no—
1179C22—262no—
1180C22—522no—
1181C22—522no—
1182C22—522no—
1183C22—522no—
1184C22#1171963112yes—
1185C22C24×#26111yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—21no—
1190C4—22no—
1191C4—21no—
1192C4—22no—
1193C4—262no—
1194C4—262no—
1195C4—262no—
1196C4—262no—
1197C4—262no—
1198C4—261no—
1199C4—262no—
1200C4—261no—
1201C4—262no—
1202C4—522no—
1203C4—522no—
1204C4—521no—
1205C4—521no—
1206C4—522no—
1207C4—522no—
1208C4—522no—
1209C4—522no—
1210C2—22no—
1211C2—42no—
1212C2—131no—
1213C2—131no—
1214C2—131no—
1215C2—131no—
1216C2—262no—
1217C2—522no—
1218C2C2×#1171963111yescharacteristic
1219C2H(5,𝔽2)×#26111yescharacteristic
1220C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#539C4
prime radicalD13×#121C22
cosocleC22×D13C25
hypercenter#539#261
hypocenterC13#34427
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #13131382C2semidirect
2. #13131376C2semidirect
3. #13131370C2semidirect
4. #13131359C2semidirect
5. #13131359C2semidirect
6. #13131359C2semidirect
7. #13131352C2semidirect
8. #13131349C2semidirect
9. #13131334C2semidirect
10. #13131334C2semidirect
11. #13131329C2semidirect
12. #13131329C2semidirect
14. #13131323C2semidirect
15. #13131316C2semidirect
16. C22⋊Q8×#261C2semidirect
18. C2×#11719082C2semidirect
28. C13×#539C4semidirect
29. #11719412C4semidirect
31. #11719397C4semidirect
33. #11719370C4semidirect
34. #11719365C4semidirect
37. #11719350C4semidirect
38. #11719343C4semidirect
42. #11719307C4semidirect
43. #11719269C4semidirect
45. #11719220C4semidirect
174. C13×#126C2×C4semidirect
175. C13×#125C2×C4semidirect
176. C13×#123C2×C4semidirect
177. C13×#123C2×C4semidirect
178. C13×C22⋊Q8C2×C4semidirect
179. C13×C22⋊Q8C2×C4semidirect
181. C4×D4×C13C2×C4semidirect
182. C2×C13×C4⋊C4C2×C4semidirect
183. #88200C2×C4semidirect
184. #88200C2×C4semidirect
187. #88189C2×C4semidirect
188. #88189C2×C4semidirect
189. D4×Dic13C2×C4semidirect
191. #88183C2×C4semidirect
192. #88183C2×C4semidirect
193. C4×C22⋊D13C2×C4semidirect
194. C4×C22⋊D13C2×C4semidirect
195. C2×C4⋊Dic13C2×C4semidirect
196. #88178C2×C4semidirect
197. #88178C2×C4semidirect
198. C2×#6101C2×C4semidirect
199. C2×#6101C2×C4semidirect
200. #88152C2×C4semidirect
201. #88152C2×C4semidirect
202. #88152C2×C4semidirect
203. #88151C2×C4semidirect
204. #88151C2×C4semidirect
205. #88150C2×C4semidirect
206. #88150C2×C4semidirect
207. #88150C2×C4semidirect
209. #88148C2×C4semidirect
210. #88148C2×C4semidirect
211. #88148C2×C4semidirect
212. #88148C2×C4semidirect
213. #88147C2×C4semidirect
214. C4⋊C4×D13C2×C4semidirect
215. C4⋊C4×D13C2×C4semidirect
224. #88144C2×C4semidirect
225. #88144C2×C4semidirect
226. #88143C2×C4semidirect
227. #88143C2×C4semidirect
228. #88143C2×C4semidirect
229. #88143C2×C4semidirect
230. #88140C2×C4semidirect
231. #88140C2×C4semidirect
233. #88137C2×C4semidirect
234. #88137C2×C4semidirect
235. #88137C2×C4semidirect
236. #88137C2×C4semidirect
237. #88135C2×C4semidirect
238. #88135C2×C4semidirect
244. #88133C2×C4semidirect
245. #88133C2×C4semidirect
246. #88133C2×C4semidirect
247. #88132C2×C4semidirect
248. #88132C2×C4semidirect
249. #88132C2×C4semidirect
250. #88130C2×C4semidirect
251. C4×D52C2×C4semidirect
253. #88124C2×C4semidirect
577. #539#261semidirect
736. #126C2×#261semidirect
744. #125C2×#261semidirect
759. #123C2×#261semidirect
760. #123C2×#261semidirect
773. C22⋊Q8C2×#261semidirect
774. C22⋊Q8C2×#261semidirect
792. C4×D4C2×#261semidirect
825. C2×C4⋊C4C2×#261semidirect
1053. C13#34427semidirect

Maximal subgroups

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

subgroupindex
#131313822
#131313762
#131313702
#131313592
#131313522
#131313492
#131313342
#131313292
#131313252
#131313232
#131313162
C22⋊Q8×#2612
#121×#2612
C2×#117190822
D13×#5392
#3442713