Finite Group Databasebeta

← #16728154

Subgroups — #16728154

Order 3328.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128394C211yesmaximal, characteristic
2#13124007C212yesmaximal, complemented
3#13124002C212yesmaximal, complemented
4#13123989C212yesmaximal, complemented
5#13123978C212yesmaximal, complemented
6#13123976C212yesmaximal, complemented
7#13123971C212yesmaximal, complemented
8#13123956C212yesmaximal, complemented
9#13123948C212yesmaximal, complemented
10#13123779C211yesmaximal, characteristic, complemented
11#13123776C211yesmaximal, characteristic, complemented
12D4×#6099C211yesmaximal, characteristic, complemented
13#13123557C211yesmaximal, characteristic, complemented
14#13123557C211yesmaximal, characteristic, complemented
15#13123539C211yesmaximal, characteristic, complemented
16#13123530C211yesmaximal, characteristic, complemented
17#13123490C211yesmaximal, characteristic, complemented
18#13123490C211yesmaximal, characteristic, complemented
19#13123485C211yesmaximal, characteristic, complemented
20#13123401C211yesmaximal, characteristic, complemented
21#13123399C211yesmaximal, characteristic, complemented
22C2×#11718763C211yesmaximal, characteristic, complemented
23C2×C13×#435C211yesmaximal, characteristic, complemented
24C22×C13×M16C2211yescharacteristic
25C23×C8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27#11719511C412yes—
28#11719496C2211yescharacteristic
29#11719496C2211yescharacteristic
30C2×#88180C2211yescharacteristic
31C2×#88180C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33C22×#6099C2211yescharacteristic
34C2×#88155C2211yescharacteristic
35C2×#88155C2211yescharacteristic
36#11719270C411yescharacteristic
37#11719270C411yescharacteristic
38#11719268C411yescharacteristic
39#11719262C2212yes—
40#11719260C411yescharacteristic
41#11719248C411yescharacteristic
42#11719247C411yescharacteristic
43#11719246C411yescharacteristic
44#11719246C411yescharacteristic
45#11719243C2212yes—
46#11719243C2212yes—
47C4×#6129C2212yes—
48#11719218C412yes—
49#11719200C412yes—
50#11719200C412yes—
51C4×#6127C2211yescharacteristic
52#11719175C2211yescharacteristic
53C13×#435C2211yescharacteristic
54C13×#435C2211yescharacteristic
55C13×#435C2211yescharacteristic
56C13×#435C2211yescharacteristic
57C13×#435C2211yescharacteristic
58C13×#435C2211yescharacteristic
59C13×#435C2211yescharacteristic
60C13×#435C2211yescharacteristic
61C2×C13×C4⋊C8C2211yescharacteristic
62C2×C13×C22⋊C8C2211yescharacteristic
63C2×C13×C22⋊C8C2211yescharacteristic
64C2×C13×#97C2211yescharacteristic
65#11718868C2211yescharacteristic
66#11718868C2211yescharacteristic
67#11718789C2212yescomplemented
68#11718789C2212yescomplemented
69#11718788C2212yescomplemented
70#11718788C2212yescomplemented
71#11718780C2212yescomplemented
72#11718780C2212yescomplemented
73#11718779C2212yescomplemented
74#11718779C2212yescomplemented
75#11718772C2212yescomplemented
76#11718772C2212yescomplemented
77#11718771C2211yescharacteristic
78#11718771C2211yescharacteristic
79C8×C22⋊D13C2212yescomplemented
80C8×C22⋊D13C2212yescomplemented
81#11718763C2211yescharacteristic
82#11718763C2211yescharacteristic
83#11718763C2211yescharacteristic
84#11718763C2211yescharacteristic
85#11718763C2211yescharacteristic
86#11718763C2211yescharacteristic
87#11718763C2211yescharacteristic
88#11718763C2211yescharacteristic
89#11718763C2212yescomplemented
90#11718763C2212yescomplemented
91#11718762C2211yescharacteristic
92#11718762C2211yescharacteristic
93#11718762C2211yescharacteristic
94#11718762C2211yescharacteristic
95C2×#88054C2212yescomplemented
96C2×#88054C2212yescomplemented
97#11718673C2212yes—
98#11718672C2212yes—
99#11718672C2212yes—
100D4×#1055C2212yes—
101#11718585C2211yescharacteristic
102C4×#6099C2211yescharacteristic
103#11718500C2212yescomplemented
104#11718500C2212yescomplemented
105#11718498C2212yescomplemented
106D13×C4⋊C8C2212yescomplemented
107#11718492C2212yescomplemented
108#11718491C2212yescomplemented
109#11718489C2212yescomplemented
110#11718489C2212yescomplemented
111#11718391C2212yescomplemented
112#11718391C2212yescomplemented
113#11718390C2212yescomplemented
114#11718390C2212yescomplemented
115#11718389C2212yescomplemented
116#11718389C2212yescomplemented
117#11718386C2212yescomplemented
118#11718386C2212yescomplemented
119#11718381C2212yescomplemented
120#11718381C2212yescomplemented
121#11718381C2212yescomplemented
122#11718381C2212yescomplemented
123#11718380C2212yescomplemented
124#11718380C2212yescomplemented
125#11718379C2212yescomplemented
126#11718379C2212yescomplemented
127#11718370C2212yescomplemented
128#11718370C2212yescomplemented
129#11718366C2212yescomplemented
130#11718366C2212yescomplemented
131#11718362C2212yescomplemented
132#11718362C2212yescomplemented
133#11718362C2212yescomplemented
134#11718362C2212yescomplemented
135C22×D4×C13C2×C411yescharacteristic
136C23×C4×C13C2311yescharacteristic
137C23×C4×C13C2311yescharacteristic
138C2×#6129C2×C412yes—
139C2×#6127C2311yescharacteristic
140C2×C13×M16—42no—
141C2×C13×M16C2311yescharacteristic
142C2×C13×M16C2311yescharacteristic
143C2×C13×M16C2311yescharacteristic
144C2×C13×M16C2311yescharacteristic
145C22×C8×C13—42no—
146C22×C8×C13C2311yescharacteristic
147C22×C8×C13C2311yescharacteristic
148C22×C8×C13C2311yescharacteristic
149C22×C8×C13C2311yescharacteristic
150C22×C8×C13C2311yescharacteristic
151C22×C8×C13C2311yescharacteristic
152C22×C8×C13C2311yescharacteristic
153C22×C8×C13C2311yescharacteristic
154C4×D4×C13C2×C411yescharacteristic
155C4×D4×C13C2×C411yescharacteristic
156C4×D4×C13C2×C411yescharacteristic
157C4×D4×C13C2×C411yescharacteristic
158C4×D4×C13C2311yescharacteristic
159C4×D4×C13C2311yescharacteristic
160C4×D4×C13C2311yescharacteristic
161C4×D4×C13C2311yescharacteristic
162C2×C13×C4⋊C4C2×C411yescharacteristic
163C2×C13×C22⋊C4C2×C411yescharacteristic
164C2×C13×C22⋊C4C2×C411yescharacteristic
165C2×C42×C13C2311yescharacteristic
166#88207C2×C412yes—
167#88207C2×C412yes—
168C2×C22⋊Dic13C2×C412yes—
169C2×C22⋊Dic13C2×C412yes—
170#88193C2×C412yes—
171#88193C2×C412yes—
172#88192C2×C412yes—
173#88190C2×C412yes—
174#88189C2×C412yes—
175#88189C2×C412yes—
176D4×Dic13C2×C412yes—
177#88184C2×C411yescharacteristic
178#88184C2×C411yescharacteristic
179#88184C2×C411yescharacteristic
180#88184C2×C411yescharacteristic
181#88183C2×C412yes—
182#88183C2×C412yes—
183C4×C22⋊D13C2×C412yes—
184C4×C22⋊D13C2×C412yes—
185C4×C22⋊D13C2312yes—
186C4×C22⋊D13C2312yes—
187C4×C22⋊D13C2312yes—
188C4×C22⋊D13C2312yes—
189#88180C2×C412yes—
190#88180C2×C412yes—
191#88180C2×C411yescharacteristic
192#88180C2×C411yescharacteristic
193#88180C2×C411yescharacteristic
194#88180C2×C411yescharacteristic
195#88180C2311yescharacteristic
196#88180C2311yescharacteristic
197#88180C2311yescharacteristic
198#88180C2312yes—
199#88180C2312yes—
200C2×C4⋊Dic13C2×C411yescharacteristic
201C2×C4⋊Dic13C2×C411yescharacteristic
202C2×C4⋊Dic13C2×C411yescharacteristic
203C2×C4⋊Dic13C2×C411yescharacteristic
204#88178C2×C412yes—
205#88178C2×C412yes—
206#88178C2×C411yescharacteristic
207#88178C2×C411yescharacteristic
208#88178C2×C411yescharacteristic
209#88178C2×C411yescharacteristic
210C2×C4×Dic13C2312yes—
211C2×C4×Dic13C2312yes—
212C2×#6099—42no—
213C2×#6099—42no—
214C2×#6099C2311yescharacteristic
215C2×#6099C2311yescharacteristic
216C2×#6099C2311yescharacteristic
217C2×#6099C2311yescharacteristic
218C2×#6099C2312yes—
219C2×#6099C2312yes—
220C22×#1055C2312yes—
221C22×#1055C2312yes—
222#88155—42no—
223#88155—42no—
224C2×#6094C2312yes—
225C2×#6094C2312yes—
226C2×C8×D13C2312yes—
227C2×C8×D13C2312yes—
228#88152C2×C412yes—
229#88152C2×C412yes—
230#88151C2×C412yes—
231#88146C2×C412yes—
232#88144C2×C412yes—
233#88143C2×C412yes—
234#88143C2×C412yes—
235#88141C2×C412yes—
236#88140C2×C412yes—
237#88140C2×C412yes—
238#88139C2×C412yes—
239#88139C2×C412yes—
240#88137C2×C412yes—
241#88137C2×C412yes—
242#88135C2×C412yes—
243#88135C2×C412yes—
244#88133C2×C412yes—
245#88133C2×C412yes—
246#88133C2×C412yes—
247#88133C2×C412yes—
248#88132C2×C412yes—
249#88132C2×C412yes—
250#88131C2×C412yes—
251#88131C2×C412yes—
252C4×D52C2×C411yescharacteristic
253C4×D52C2×C411yescharacteristic
254#88126C2312yes—
255C42×D13C2312yes—
256#88124C2×C411yescharacteristic
257#88124C2×C411yescharacteristic
258#88123C2×C411yescharacteristic
259#88123C2×C411yescharacteristic
260C4×Dic26C2×C411yescharacteristic
261C4×Dic26C2×C411yescharacteristic
262C4×Dic26C2312yes—
263C4×Dic26C2312yes—
264C13×C4⋊C8C2311yescharacteristic
265C13×C4⋊C8C2311yescharacteristic
266C13×C4⋊C8C2311yescharacteristic
267C13×C4⋊C8C2311yescharacteristic
268C13×C22⋊C8C2311yescharacteristic
269C13×C22⋊C8C2311yescharacteristic
270C13×C22⋊C8C2311yescharacteristic
271C13×C22⋊C8C2311yescharacteristic
272C13×C22⋊C8C2311yescharacteristic
273C13×C22⋊C8C2311yescharacteristic
274C13×C22⋊C8C2311yescharacteristic
275C13×C22⋊C8C2311yescharacteristic
276C13×#97C2311yescharacteristic
277C13×#97C2311yescharacteristic
278C13×#97C2311yescharacteristic
279C13×#97C2311yescharacteristic
280C22⋊#1055C2312yes—
281C22⋊#1055C2312yes—
282C22⋊#1055C2312yes—
283C22⋊#1055C2312yes—
284#88060C2312yes—
285#88060C2312yes—
286#88060C2312yes—
287#88060C2312yes—
288#88055C2312yes—
289#88055C2312yes—
290#88055C2312yes—
291#88055C2312yes—
292#88054C2312yes—
293#88054C2312yes—
294#88054C2312yes—
295#88054C2312yes—
296#88054C2312yes—
297#88054C2312yes—
298#88054C2312yes—
299#88054C2312yes—
300#88054C2312yes—
301#88054C2312yes—
302#88054C2312yes—
303#88054C2312yes—
304#88054C2312yes—
305#88054C2312yes—
306#88054C2312yes—
307#88054C2312yes—
308C8×Dic13C2312yes—
309C8×Dic13C2312yes—
310C8×Dic13C2312yes—
311C8×Dic13C2312yes—
312C4⋊#1055C2312yes—
313C4⋊#1055C2312yes—
314#88043C2312yes—
315C4×#1055C2312yes—
316#60272—131nomaximal, Sylow
317C24×C13C22×C411yescharacteristic
318C24×C13C22×C411yescharacteristic
319C2×D4×C13—42no—
320C2×D4×C13C22×C411yescharacteristic
321C2×D4×C13C22×C411yescharacteristic
322C2×D4×C13C22×C411yescharacteristic
323C2×D4×C13C22×C411yescharacteristic
324C22×C4×C13—22no—
325C22×C4×C13—22no—
326C22×C4×C13—22no—
327C22×C4×C13—22no—
328C22×C4×C13C22×C411yescharacteristic
329C22×C4×C13C22×C411yescharacteristic
330C22×C4×C13C22×C411yescharacteristic
331C22×C4×C13C22×C411yescharacteristic
332C22×C4×C13C22×C411yescharacteristic
333C22×C4×C13C22×C411yescharacteristic
334C22×C4×C13C22×C411yescharacteristic
335C22×C4×C13C22×C411yescharacteristic
336C22×C4×C13C2411yescharacteristic
337C22×C4×C13C2411yescharacteristic
338C22×C4×C13C2411yescharacteristic
339C22×C4×C13C2411yescharacteristic
340C22×C4×C13C2411yescharacteristic
341C2×C22⋊D13C22×C412yes—
342C2×C22⋊D13C22×C412yes—
343C2×C22⋊D13C22×C412yes—
344C2×C22⋊D13C22×C412yes—
345C2×C22⋊D13C22×C412yes—
346C22×Dic13C22×C412yes—
347C22×Dic13C22×C412yes—
348C22×Dic13C22×C412yes—
349C22×Dic13C22×C412yes—
350#6129—44no—
351#6127—22no—
352#6127—22no—
353C2×D52C22×C411yescharacteristic
354C2×C4×D13C22×C412yes—
355C2×C4×D13C22×C412yes—
356C2×C4×D13C2412yes—
357C2×Dic26C22×C411yescharacteristic
358C2×Dic26C22×C412yes—
359C2×Dic26C22×C412yes—
360C13×M16—41no—
361C13×M16—41no—
362C13×M16—41no—
363C13×M16—41no—
364C2×C8×C13—22no—
365C2×C8×C13—22no—
366C2×C8×C13—22no—
367C2×C8×C13—22no—
368C2×C8×C13—41no—
369C2×C8×C13—41no—
370C2×C8×C13—41no—
371C2×C8×C13—41no—
372C2×C8×C13C2411yescharacteristic
373C2×C8×C13C2411yescharacteristic
374C2×C8×C13C2411yescharacteristic
375C2×C8×C13C2411yescharacteristic
376C2×C8×C13C2411yescharacteristic
377C2×C8×C13C2411yescharacteristic
378C2×C8×C13C2411yescharacteristic
379C2×C8×C13C2411yescharacteristic
380C13×C4⋊C4C22×C411yescharacteristic
381C13×C4⋊C4C22×C411yescharacteristic
382C13×C4⋊C4C22×C411yescharacteristic
383C13×C4⋊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
390C13×C22⋊C4C22×C411yescharacteristic
391C13×C22⋊C4C22×C411yescharacteristic
392C42×C13C22×C411yescharacteristic
393C42×C13C22×C411yescharacteristic
394C42×C13C2411yescharacteristic
395C42×C13C2411yescharacteristic
396C22⋊Dic13C22×C412yes—
397C22⋊Dic13C22×C412yes—
398C22⋊Dic13C22×C412yes—
399C22⋊Dic13C22×C412yes—
400C22⋊Dic13C22×C412yes—
401C22⋊Dic13C22×C412yes—
402C22⋊Dic13C22×C412yes—
403C22⋊Dic13C22×C412yes—
404C22⋊Dic13C22×C412yes—
405C22⋊Dic13C22×C412yes—
406C22⋊Dic13C22×C412yes—
407#6103C22×C412yes—
408#6103C22×C412yes—
409#6103C22×C412yes—
410#6103C22×C412yes—
411#6103C22×C412yes—
412#6103C22×C412yes—
413C4⋊Dic13C22×C411yescharacteristic
414C4⋊Dic13C22×C411yescharacteristic
415C4⋊Dic13C22×C412yes—
416C4⋊Dic13C22×C412yes—
417C4⋊Dic13C22×C411yescharacteristic
418C4⋊Dic13C22×C411yescharacteristic
419C4⋊Dic13C22×C411yescharacteristic
420C4⋊Dic13C22×C411yescharacteristic
421C4⋊Dic13C22×C412yes—
422C4⋊Dic13C22×C412yes—
423C4⋊Dic13C22×C412yes—
424C4⋊Dic13C22×C412yes—
425#6101C22×C412yes—
426#6101C22×C412yes—
427#6101C22×C412yes—
428#6101C22×C412yes—
429#6101C22×C412yes—
430#6101C22×C412yes—
431#6101C22×C412yes—
432#6101C22×C412yes—
433#6101C22×C412yes—
434#6101C22×C412yes—
435C4×Dic13C22×C412yes—
436C4×Dic13C22×C412yes—
437C4×Dic13C22×C412yes—
438C4×Dic13C22×C412yes—
439C4×Dic13C22×C412yes—
440C4×Dic13C22×C412yes—
441C4×Dic13C2412yes—
442C4×Dic13C2412yes—
443C4×Dic13C2412yes—
444#6099—22no—
445#6099—22no—
446#6099—22no—
447#6099—22no—
448#6099—42no—
449#6099—42no—
450C2×#1055—42no—
451C2×#1055—42no—
452C2×#1055C2412yes—
453C2×#1055C2412yes—
454C2×#1055C2412yes—
455C2×#1055C2412yes—
456#6094—42no—
457#6094—42no—
458C8×D13—42no—
459C8×D13—42no—
460#3475—131no—
461#2995—132no—
462#2995—132no—
463#2994—132no—
464#2993—132no—
465#2992—132no—
466#2992—132no—
467#2990—132no—
468#2989—132no—
469#2962—131no—
470#2961—131no—
471D4×M16—131no—
472#2933—131no—
473#2933—131no—
474#2930—131no—
475#2929—131no—
476C2×#435D1311yescharacteristic, complemented
477#2924—131no—
478#2924—131no—
479#2923—131no—
480#2906—131no—
481#2905—131no—
482C2×#424—131no—
483C23×C13—22no—
484C23×C13—22no—
485C23×C13—22no—
486C23×C13—41no—
487C23×C13—41no—
488C23×C13—41no—
489C23×C13C23×C411yescharacteristic
490C23×C13C23×C411yescharacteristic
491C23×C13C23×C411yescharacteristic
492C23×C13C23×C411yescharacteristic
493C23×C13C23×C411yescharacteristic
494C22×D13C23×C412yes—
495D4×C13—22no—
496D4×C13—22no—
497D4×C13—41no—
498D4×C13—41no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
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—41no—
514C2×C4×C13—41no—
515C2×C4×C13C23×C411yescharacteristic
516C2×C4×C13C23×C411yescharacteristic
517C2×C4×C13C23×C411yescharacteristic
518C2×C4×C13C23×C411yescharacteristic
519C2×C4×C13C23×C411yescharacteristic
520C2×C4×C13C23×C411yescharacteristic
521C2×C4×C13C23×C411yescharacteristic
522C2×C4×C13C23×C411yescharacteristic
523C2×C4×C13C23×C411yescharacteristic
524C2×C4×C13H(5,𝔽2)12yes—
525C2×C4×C132−1+412yes—
526C2×C4×C13C2511yescharacteristic
527C22⋊D13—24no—
528C22⋊D13—24no—
529C22⋊D13—42no—
530C22⋊D13—42no—
531C22⋊D13—42no—
532C2×Dic13—24no—
533C2×Dic13—42no—
534C2×Dic13—42no—
535C2×Dic13—42no—
536C2×Dic13C23×C412yes—
537C2×Dic13C23×C412yes—
538C2×Dic13C23×C412yes—
539C2×Dic13C23×C412yes—
540C2×Dic13C23×C412yes—
541C2×Dic13C23×C412yes—
542C2×Dic13C23×C412yes—
543D52—22no—
544C4×D13—22no—
545C4×D13—22no—
546C4×D13—42no—
547C4×D13—42no—
548Dic26—22no—
549Dic26—42no—
550Dic26—42no—
551C8×C13—21no—
552C8×C13—21no—
553C8×C13—21no—
554C8×C13—21no—
555C8×C13—21no—
556C8×C13—21no—
557C8×C13—21no—
558C8×C13—21no—
559#1055—22no—
560#1055—22no—
561#1055—22no—
562#1055—22no—
563C2×#131—131no—
564C2×#131—131no—
565C22×M16—131no—
566C22×M16—131no—
567C22×M16C2×D1311yescharacteristic
568C23×C8C2×D1311yescharacteristic
569#556—131no—
570#555—131no—
571#554—131no—
572#553—131no—
573#553—131no—
574#552—131no—
575#552—131no—
576#552—132no—
577#551—132no—
578#551—132no—
579#547—131no—
580#546—132no—
581#533—131no—
582#529—132no—
583#529—132no—
584#529—132no—
585#525—131no—
586#525—131no—
587C4×#41—132no—
588C4×#41—131no—
589C2×C4×D4C2×D1311yescharacteristic
590C2×#117—131no—
591C2×#117—131no—
592#446—132no—
593#446—132no—
594#446—132no—
595#446—132no—
596#446—132no—
597#446—132no—
598#446—132no—
599C8×Q8—132no—
600#436—132no—
601#436—132no—
602#436—132no—
603#436—132no—
604#436—132no—
605#435—132no—
606#435—132no—
607#435—132no—
608#435—132no—
609#435—132no—
610#435—132no—
611#435—132no—
612#435—132no—
613#435—132no—
614#435—132no—
615#435C2×D1311yescharacteristic
616#435C2×D1311yescharacteristic
617#435C2×D1311yescharacteristic
618#435C2×D1311yescharacteristic
619#435C2×D1311yescharacteristic
620#435C2×D1311yescharacteristic
621#435C2×D1311yescharacteristic
622#435C2×D1311yescharacteristic
623C8×D4—132no—
624C8×D4—132no—
625C8×D4—132no—
626C8×D4—132no—
627C8×D4—132no—
628#433—132no—
629#433—132no—
630#433—132no—
631#433—132no—
632#433—132no—
633#433—132no—
634#432—132no—
635#432—132no—
636#432—132no—
637#432—132no—
638#431—132no—
639#431—132no—
640#424—132no—
641#424—132no—
642#424—131no—
643#424—131no—
644#424—131no—
645#424—131no—
646#424—132no—
647#424—132no—
648#424—131no—
649#424—131no—
650#424—131no—
651#424—131no—
652#424—132no—
653#424—132no—
654#423—132no—
655#423—132no—
656#423—131no—
657#423—132no—
658C2×C4⋊C8—132no—
659C2×C4⋊C8—132no—
660C2×C4⋊C8—132no—
661C2×C4⋊C8C2×D1311yescharacteristic
662#408—131no—
663#408—131no—
664#407—131no—
665#407—131no—
666C2×C22⋊C8C2×D1311yescharacteristic
667C2×C22⋊C8C2×D1311yescharacteristic
668#405—131no—
669#405—131no—
670#405—131no—
671#405—131no—
672C4×M16—131no—
673C2×#97C2×D1311yescharacteristic
674C22×C13—21no—
675C22×C13—21no—
676C22×C13—21no—
677C22×C13—21no—
678C22×C13—21no—
679C22×C13—21no—
680C22×C13—21no—
681C22×C13—21no—
682C22×C13—21no—
683C22×C13—21no—
684C22×C13—21no—
685C22×C13—21no—
686C22×C13—21no—
687C22×C13—44no—
688C22×C13—82no—
689C22×C13#52012yes—
690C22×C13#56812yes—
691C22×C13C24×C411yescharacteristic
692C2×D13—22no—
693C2×D13—22no—
694C2×D13—22no—
695C4×C13—21no—
696C4×C13—21no—
697C4×C13—21no—
698C4×C13—21no—
699C4×C13—21no—
700C4×C13—21no—
701C4×C13—21no—
702C4×C13—21no—
703C4×C13#52012yes—
704C4×C13C2×H(5,𝔽2)11yescharacteristic
705C4×C13C2×2−1+411yescharacteristic
706Dic13—22no—
707Dic13—22no—
708Dic13—22no—
709Dic13—22no—
710Dic13—22no—
711Dic13—22no—
712Dic13—22no—
713C2×#41—132no—
714C2×#41—131no—
715C22×D4C4×D1311yescharacteristic
716C23×C4C22×D1311yescharacteristic
717C23×C4C22×D1311yescharacteristic
718#131—522no—
719#131—522no—
720C2×M16—42no—
721C2×M16—131no—
722C2×M16—131no—
723C2×M16—131no—
724C2×M16—131no—
725C2×M16—132no—
726C2×M16—132no—
727C2×M16—132no—
728C2×M16—132no—
729C2×M16—522no—
730C2×M16—522no—
731C2×M16C22×D1311yescharacteristic
732C2×M16C22×D1311yescharacteristic
733C2×M16C22×D1311yescharacteristic
734C2×M16C22×D1311yescharacteristic
735C22×C8—42no—
736C22×C8—132no—
737C22×C8—132no—
738C22×C8—132no—
739C22×C8—132no—
740C22×C8C22×D1311yescharacteristic
741C22×C8C22×D1311yescharacteristic
742C22×C8C22×D1311yescharacteristic
743C22×C8C22×D1311yescharacteristic
744C22×C8C22×D1311yescharacteristic
745C22×C8C22×D1311yescharacteristic
746C22×C8C22×D1311yescharacteristic
747C22×C8C22×D1311yescharacteristic
748C4⋊Q8—131no—
749C4⋊Q8—131no—
750#126—132no—
751#126—132no—
752#126—132no—
753#126—132no—
754#126—132no—
755#126—132no—
756#125—132no—
757#125—132no—
758#125—132no—
759#125—131no—
760#125—131no—
761#124—132no—
762#124—132no—
763#124—132no—
764#123—132no—
765#123—132no—
766#123—132no—
767#123—132no—
768#123—132no—
769#123—132no—
770#123—132no—
771#123—132no—
772C22⋊Q8—131no—
773C22⋊Q8—131no—
774C22⋊Q8—131no—
775C22⋊Q8—131no—
776C22⋊Q8—132no—
777C22⋊Q8—132no—
778C22⋊Q8—132no—
779C22⋊Q8—132no—
780C22⋊Q8—132no—
781#121—132no—
782#121—132no—
783#121—132no—
784#121—131no—
785#121—131no—
786#121—131no—
787#121—131no—
788#120—132no—
789#120—132no—
790C4×Q8—132no—
791C4×Q8—131no—
792C4×Q8—131no—
793C4×Q8—132no—
794C4×Q8—132no—
795C4×D4—132no—
796C4×D4—132no—
797C4×D4—132no—
798C4×D4—132no—
799C4×D4—132no—
800C4×D4—132no—
801C4×D4—132no—
802C4×D4—132no—
803C4×D4—132no—
804C4×D4—131no—
805C4×D4—131no—
806C4×D4C4×D1311yescharacteristic
807C4×D4C4×D1311yescharacteristic
808C4×D4C4×D1311yescharacteristic
809C4×D4C4×D1311yescharacteristic
810C4×D4C22×D1311yescharacteristic
811C4×D4C22×D1311yescharacteristic
812C4×D4C22×D1311yescharacteristic
813C4×D4C22×D1311yescharacteristic
814#117—132no—
815#117—132no—
816#117—131no—
817#117—131no—
818#117—131no—
819#117—131no—
820#117—131no—
821#117—131no—
822#117—131no—
823#117—132no—
824#117—132no—
825#117—132no—
826#117—132no—
827#117—132no—
828#117—132no—
829C2×C4⋊C4—131no—
830C2×C4⋊C4—131no—
831C2×C4⋊C4—131no—
832C2×C4⋊C4—131no—
833C2×C4⋊C4C4×D1311yescharacteristic
834C2×C22⋊C4—132no—
835C2×C22⋊C4—132no—
836C2×C22⋊C4C4×D1311yescharacteristic
837C2×C22⋊C4C4×D1311yescharacteristic
838C2×C42—132no—
839C2×C42—132no—
840C2×C42—132no—
841C2×C42C22×D1311yescharacteristic
842C4⋊C8—132no—
843C4⋊C8—132no—
844C4⋊C8—132no—
845C4⋊C8—132no—
846C4⋊C8—132no—
847C4⋊C8—132no—
848C4⋊C8—132no—
849C4⋊C8—132no—
850C4⋊C8—132no—
851C4⋊C8—132no—
852C4⋊C8—132no—
853C4⋊C8—132no—
854C4⋊C8—132no—
855C4⋊C8—132no—
856C4⋊C8—132no—
857C4⋊C8—132no—
858C4⋊C8—132no—
859C4⋊C8—132no—
860C4⋊C8C22×D1311yescharacteristic
861C4⋊C8C22×D1311yescharacteristic
862C4⋊C8C22×D1311yescharacteristic
863C4⋊C8C22×D1311yescharacteristic
864C22⋊C8—132no—
865C22⋊C8—132no—
866C22⋊C8—132no—
867C22⋊C8—132no—
868C22⋊C8—132no—
869C22⋊C8—132no—
870C22⋊C8—132no—
871C22⋊C8—132no—
872C22⋊C8C22×D1311yescharacteristic
873C22⋊C8C22×D1311yescharacteristic
874C22⋊C8C22×D1311yescharacteristic
875C22⋊C8C22×D1311yescharacteristic
876C22⋊C8C22×D1311yescharacteristic
877C22⋊C8C22×D1311yescharacteristic
878C22⋊C8C22×D1311yescharacteristic
879C22⋊C8C22×D1311yescharacteristic
880#97—132no—
881#97—132no—
882#97—132no—
883#97—132no—
884#97—132no—
885#97C22×D1311yescharacteristic
886#97C22×D1311yescharacteristic
887#97C22×D1311yescharacteristic
888#97C22×D1311yescharacteristic
889C4×C8—132no—
890C4×C8—132no—
891C4×C8—132no—
892C4×C8—132no—
893C4×C8—132no—
894C2×C13—22no—
895C2×C13—22no—
896C2×C13—41no—
897C2×C13—41no—
898C2×C13—41no—
899C2×C13C2×#52011yescharacteristic
900C2×C13C2×#56811yescharacteristic
901C2×C13#357311yescharacteristic
902D13—42no—
903C24C2×C4×D1311yescharacteristic
904C24C2×C4×D1311yescharacteristic
905#41—262no—
906#41—262no—
907#41—524no—
908C2×Q8—131no—
909C2×Q8—132no—
910C2×Q8—132no—
911C2×D4—42no—
912C2×D4—132no—
913C2×D4—132no—
914C2×D4—132no—
915C2×D4—132no—
916C2×D4—132no—
917C2×D4—131no—
918C2×D4C2×C4×D1311yescharacteristic
919C2×D4C2×C4×D1311yescharacteristic
920C2×D4C2×C4×D1311yescharacteristic
921C2×D4C2×C4×D1311yescharacteristic
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—132no—
927C22×C4—132no—
928C22×C4—132no—
929C22×C4—132no—
930C22×C4—132no—
931C22×C4—132no—
932C22×C4—132no—
933C22×C4C2×C4×D1311yescharacteristic
934C22×C4C2×C4×D1311yescharacteristic
935C22×C4C2×C4×D1311yescharacteristic
936C22×C4C2×C4×D1311yescharacteristic
937C22×C4C2×C4×D1311yescharacteristic
938C22×C4C2×C4×D1311yescharacteristic
939C22×C4C2×C4×D1311yescharacteristic
940C22×C4C2×C4×D1311yescharacteristic
941C22×C4C23×D1311yescharacteristic
942C22×C4C23×D1311yescharacteristic
943C22×C4C23×D1311yescharacteristic
944C22×C4C23×D1311yescharacteristic
945C22×C4C23×D1311yescharacteristic
946M16—41no—
947M16—41no—
948M16—41no—
949M16—41no—
950M16—262no—
951M16—262no—
952M16—262no—
953M16—262no—
954M16—522no—
955M16—522no—
956M16—522no—
957M16—522no—
958C2×C8—22no—
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—22no—
962C2×C8—41no—
963C2×C8—41no—
964C2×C8—41no—
965C2×C8—41no—
966C2×C8—132no—
967C2×C8—132no—
968C2×C8—132no—
969C2×C8—132no—
970C2×C8—522no—
971C2×C8—522no—
972C2×C8—522no—
973C2×C8—522no—
974C2×C8C23×D1311yescharacteristic
975C2×C8C23×D1311yescharacteristic
976C2×C8C23×D1311yescharacteristic
977C2×C8C23×D1311yescharacteristic
978C2×C8C23×D1311yescharacteristic
979C2×C8C23×D1311yescharacteristic
980C2×C8C23×D1311yescharacteristic
981C2×C8C23×D1311yescharacteristic
982C4⋊C4—131no—
983C4⋊C4—131no—
984C4⋊C4—131no—
985C4⋊C4—131no—
986C4⋊C4—131no—
987C4⋊C4—131no—
988C4⋊C4—132no—
989C4⋊C4—132no—
990C4⋊C4—132no—
991C4⋊C4—132no—
992C4⋊C4—132no—
993C4⋊C4—132no—
994C4⋊C4—132no—
995C4⋊C4—132no—
996C4⋊C4—132no—
997C4⋊C4—132no—
998C4⋊C4—132no—
999C4⋊C4—132no—
1000C4⋊C4—132no—
1001C4⋊C4—132no—
1002C4⋊C4—132no—
1003C4⋊C4—132no—
1004C4⋊C4C2×C4×D1311yescharacteristic
1005C4⋊C4C2×C4×D1311yescharacteristic
1006C4⋊C4C2×C4×D1311yescharacteristic
1007C4⋊C4C2×C4×D1311yescharacteristic
1008C22⋊C4—132no—
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—132no—
1025C22⋊C4C2×C4×D1311yescharacteristic
1026C22⋊C4C2×C4×D1311yescharacteristic
1027C22⋊C4C2×C4×D1311yescharacteristic
1028C22⋊C4C2×C4×D1311yescharacteristic
1029C22⋊C4C2×C4×D1311yescharacteristic
1030C22⋊C4C2×C4×D1311yescharacteristic
1031C22⋊C4C2×C4×D1311yescharacteristic
1032C22⋊C4C2×C4×D1311yescharacteristic
1033C42—132no—
1034C42—132no—
1035C42—132no—
1036C42—132no—
1037C42—132no—
1038C42—132no—
1039C42—132no—
1040C42—132no—
1041C42—132no—
1042C42C2×C4×D1311yescharacteristic
1043C42C2×C4×D1311yescharacteristic
1044C42C23×D1311yescharacteristic
1045C42C23×D1311yescharacteristic
1046C13#6027211yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—132no—
1054C23C22×C4×D1311yescharacteristic
1055C23C22×C4×D1311yescharacteristic
1056C23C22×C4×D1311yescharacteristic
1057C23C22×C4×D1311yescharacteristic
1058C23C22×C4×D1311yescharacteristic
1059Q8—262no—
1060Q8—522no—
1061Q8—522no—
1062D4—22no—
1063D4—22no—
1064D4—41no—
1065D4—41no—
1066D4—264no—
1067D4—264no—
1068D4—262no—
1069D4—522no—
1070D4—522no—
1071D4—522no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—132no—
1089C2×C4—132no—
1090C2×C4—132no—
1091C2×C4—132no—
1092C2×C4—132no—
1093C2×C4—132no—
1094C2×C4—132no—
1095C2×C4—264no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—522no—
1099C2×C4—522no—
1100C2×C4—522no—
1101C2×C4—522no—
1102C2×C4—522no—
1103C2×C4C22×C4×D1311yescharacteristic
1104C2×C4C22×C4×D1311yescharacteristic
1105C2×C4C22×C4×D1311yescharacteristic
1106C2×C4C22×C4×D1311yescharacteristic
1107C2×C4C22×C4×D1311yescharacteristic
1108C2×C4C22×C4×D1311yescharacteristic
1109C2×C4C22×C4×D1311yescharacteristic
1110C2×C4C22×C4×D1311yescharacteristic
1111C2×C4C22×C4×D1311yescharacteristic
1112C2×C4#8825112yes—
1113C2×C4#8825712yes—
1114C2×C4C24×D1311yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—21no—
1120C8—21no—
1121C8—21no—
1122C8—21no—
1123C8—262no—
1124C8—262no—
1125C8—262no—
1126C8—262no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—44no—
1141C22—82no—
1142C22—262no—
1143C22—262no—
1144C22—262no—
1145C22#1171925112yes—
1146C22#1171945012yes—
1147C22C23×C4×D1311yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—21no—
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—262no—
1157C4—262no—
1158C4—262no—
1159C4—262no—
1160C4—262no—
1161C4—262no—
1162C4—262no—
1163C4#1171925112yes—
1164C4C2×#8825111yescharacteristic
1165C4C2×#8825711yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—41no—
1170C2—41no—
1171C2—522no—
1172C2C2×#1171925111yescharacteristic
1173C2C2×#1171945011yescharacteristic
1174C2#1312954711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC2×C13×#435C2
prime radical#13128394C2
cosocleC2×C4×C13C25
hypercenterC2×#435D13
hypocenterC13#60272
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #13124007C2semidirect
3. #13124002C2semidirect
4. #13123989C2semidirect
5. #13123978C2semidirect
6. #13123976C2semidirect
7. #13123971C2semidirect
8. #13123956C2semidirect
9. #13123948C2semidirect
10. #13123779C2semidirect
11. #13123776C2semidirect
12. D4×#6099C2semidirect
13. #13123557C2semidirect
14. #13123557C2semidirect
15. #13123539C2semidirect
16. #13123530C2semidirect
17. #13123490C2semidirect
18. #13123490C2semidirect
19. #13123485C2semidirect
20. #13123401C2semidirect
21. #13123399C2semidirect
22. C2×#11718763C2semidirect
23. C2×C13×#435C2semidirect
67. #11718789C22semidirect
68. #11718789C22semidirect
69. #11718788C22semidirect
70. #11718788C22semidirect
71. #11718780C22semidirect
72. #11718780C22semidirect
73. #11718779C22semidirect
74. #11718779C22semidirect
75. #11718772C22semidirect
76. #11718772C22semidirect
79. C8×C22⋊D13C22semidirect
80. C8×C22⋊D13C22semidirect
89. #11718763C22semidirect
90. #11718763C22semidirect
95. C2×#88054C22semidirect
96. C2×#88054C22semidirect
103. #11718500C22semidirect
104. #11718500C22semidirect
105. #11718498C22semidirect
106. D13×C4⋊C8C22semidirect
107. #11718492C22semidirect
108. #11718491C22semidirect
109. #11718489C22semidirect
110. #11718489C22semidirect
111. #11718391C22semidirect
112. #11718391C22semidirect
113. #11718390C22semidirect
114. #11718390C22semidirect
115. #11718389C22semidirect
116. #11718389C22semidirect
117. #11718386C22semidirect
118. #11718386C22semidirect
119. #11718381C22semidirect
120. #11718381C22semidirect
121. #11718381C22semidirect
122. #11718381C22semidirect
123. #11718380C22semidirect
124. #11718380C22semidirect
125. #11718379C22semidirect
126. #11718379C22semidirect
127. #11718370C22semidirect
128. #11718370C22semidirect
129. #11718366C22semidirect
130. #11718366C22semidirect
131. #11718362C22semidirect
132. #11718362C22semidirect
133. #11718362C22semidirect
134. #11718362C22semidirect
476. C2×#435D13semidirect
1046. C13#60272semidirect

Maximal subgroups

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

subgroupindex
#131283942
#131240072
#131240022
#131239892
#131239782
#131239762
#131239712
#131239562
#131239482
#131237792
#131237762
D4×#60992
#131235572
#131235392
#131235302
#131234902
#131234852
#131234012
#131233992
C2×#117187632
C2×C13×#4352
#6027213