Finite Group Databasebeta

← C2×#13131373 #16807610

Subgroups — C2×#13131373 #16807610

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131373C2116yesmaximal, direct product factor
2C2×#11719083C211yesmaximal, characteristic, complemented
3C2×#11719071C211yesmaximal, characteristic
4C2×#11719071C211yesmaximal, characteristic
5C2×#11719071C211yesmaximal, characteristic
6C2×#11719082C211yesmaximal, characteristic, complemented
7C2×#11719082C211yesmaximal, characteristic, complemented
8C2×#11719082C211yesmaximal, characteristic, complemented
9C2×#11719070C211yesmaximal, characteristic
10C2×C4⋊C4×#261C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×#261C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊#261C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#261C211yesmaximal, characteristic
14C2×C22⋊C4×#261C211yesmaximal, characteristic
15C2×#11719057C211yesmaximal, characteristic, complemented
16C2×D13×#126C211yesmaximal, characteristic
17C24×#261C2211yescharacteristic
18C22×C22⋊#261C2211yescharacteristic
19C22×C22⋊#261C2211yescharacteristic
20C22×C22⋊#261C2211yescharacteristic
21C22×C4⋊#261C2211yescharacteristic
22C22×C4⋊#261C2211yescharacteristic
23C22×C4⋊#261C2211yescharacteristic
24C22×C4⋊#261C2211yescharacteristic
25C22×C4⋊#261C2211yescharacteristic
26C22×C4×#261C2211yescharacteristic
27C22×C4×#261C2211yescharacteristic
28C22×C4×#261C2211yescharacteristic
29C22×C4×#261C2211yescharacteristic
30C22×C4×#261C2211yescharacteristic
31C22×C4×#261C2211yescharacteristic
32C22×C4×#261C2211yescharacteristic
33C2×C13×#126C411yescharacteristic, complemented
34D13×#126C418yescomplemented
35D13×#126C2218yes—
36C2×#88152C411yescharacteristic, complemented
37C2×#88152C411yescharacteristic, complemented
38C2×#88152C411yescharacteristic, complemented
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×C4⋊C4×D13C2211yescharacteristic
42C2×C22⋊C4×D13C2211yescharacteristic
43C2×C22⋊C4×D13C2211yescharacteristic
44C2×C22⋊C4×D13C2211yescharacteristic
45C2×#88133C411yescharacteristic, complemented
46C2×#88133C411yescharacteristic, complemented
47C2×#88133C411yescharacteristic, complemented
48C2×#88130C411yescharacteristic, complemented
49C2×C42×D13C2211yescharacteristic
50C2×(C2×#261)⋊C4C2211yescharacteristic
51C2×(C2×#261)⋊C4C2211yescharacteristic
52C2×(C2×#261)⋊C4C2211yescharacteristic
53C2×(C2×#261)⋊C4C2211yescharacteristic
54C2×(C2×#261)⋊C4C2211yescharacteristic
55C2×(C2×#261)⋊C4C2211yescharacteristic
56C2×(C2×#261)⋊C4C2211yescharacteristic
57C2×(C2×#261)⋊C4C2211yescharacteristic
58C2×(C2×#261)⋊C4C2211yescharacteristic
59C2×(C2×#261)⋊C4C2211yescharacteristic
60C2×(C2×#261)⋊C4C2211yescharacteristic
61C2×(C2×#261)⋊C4C2211yescharacteristic
62#11719083C2218yescomplemented
63#11719082C2218yescomplemented
64#11719082C2218yescomplemented
65#11719082C2218yescomplemented
66C4⋊C4×#261C2218yescomplemented
67C4⋊C4×#261C2218yescomplemented
68#11719071C2218yes—
69#11719071C2218yes—
70#11719071C2218yes—
71#11719070C2218yes—
72C22⋊C4×#261C2218yes—
73C22⋊C4×#261C2218yes—
74C4×C4⋊#261C2218yescomplemented
75#11719057C2218yescomplemented
76C24×D13C2311yescharacteristic
77C23×#261—24no—
78C23×#261—24no—
79C23×#261—42no—
80C23×#261C2311yescharacteristic
81C23×#261C2311yescharacteristic
82C23×#261C2311yescharacteristic
83C23×#261C2311yescharacteristic
84C23×#261C2314yes—
85C23×#261C2311yescharacteristic
86C23×#261C2311yescharacteristic
87C23×#261C2311yescharacteristic
88C23×#261C2311yescharacteristic
89C22×C4×D13C2311yescharacteristic
90C22×C4×D13C2311yescharacteristic
91C22×C4×D13C2311yescharacteristic
92C22×C4×D13C2311yescharacteristic
93C22×C4×D13C2311yescharacteristic
94C22×C4×D13C2311yescharacteristic
95C2×C22⋊#261—24no—
96C2×C22⋊#261—24no—
97C2×C22⋊#261—42no—
98C2×C22⋊#261C2314yes—
99C2×C22⋊#261C2314yes—
100C2×C22⋊#261C2314yes—
101C2×C4⋊#261—24no—
102C2×C4⋊#261—24no—
103C2×C4⋊#261—24no—
104C2×C4⋊#261—24no—
105C2×C4⋊#261—42no—
106C2×C4⋊#261C2314yes—
107C2×C4⋊#261C2314yes—
108C2×C4⋊#261C2314yes—
109C2×C4⋊#261C2314yes—
110C2×C4⋊#261C2314yes—
111C2×C4×#261—24no—
112C2×C4×#261—24no—
113C2×C4×#261—24no—
114C2×C4×#261—24no—
115C2×C4×#261—42no—
116C2×C4×#261—42no—
117C2×C4×#261—42no—
118C2×C4×#261C2314yes—
119C2×C4×#261C2314yes—
120C2×C4×#261C2314yes—
121C2×C4×#261C2314yes—
122C2×C4×#261C2314yes—
123C2×C4×#261C2314yes—
124C2×C4×#261C2314yes—
125C13×#126C2×C418yescomplemented
126C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
127C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
128C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
129C2×C13×C22⋊C4C2×C411yescharacteristic
130C2×C13×C22⋊C4C2×C411yescharacteristic
131C2×C13×C22⋊C4C2×C411yescharacteristic
132C2×C42×C13C2×C411yescharacteristic, complemented
133C2×C22⋊Dic13C2×C411yescharacteristic
134C2×C22⋊Dic13C2×C411yescharacteristic
135C2×C22⋊Dic13C2×C411yescharacteristic
136C2×#6103C2×C411yescharacteristic
137C2×#6103C2×C411yescharacteristic
138C2×#6103C2×C411yescharacteristic
139C2×#6103C2×C411yescharacteristic
140C2×#6103C2×C411yescharacteristic
141C2×#6103C2×C411yescharacteristic
142C2×C4⋊Dic13C2×C411yescharacteristic, complemented
143C2×C4⋊Dic13C2×C411yescharacteristic, complemented
144C2×C4⋊Dic13C2×C411yescharacteristic, complemented
145C2×#6101C2×C411yescharacteristic, complemented
146C2×#6101C2×C411yescharacteristic, complemented
147C2×#6101C2×C411yescharacteristic, complemented
148C2×#6101C2×C411yescharacteristic, complemented
149C2×#6101C2×C411yescharacteristic, complemented
150C2×#6101C2×C411yescharacteristic, complemented
151C2×C4×Dic13C2×C411yescharacteristic, complemented
152C2×C4×Dic13C2×C411yescharacteristic, complemented
153C2×C4×Dic13C2×C411yescharacteristic, complemented
154#88152C2×C418yescomplemented
155#88152C2×C418yescomplemented
156#88152C2×C418yescomplemented
157C4⋊C4×D13C2×C414yescomplemented
158C4⋊C4×D13C2×C414yescomplemented
159C4⋊C4×D13C2×C414yescomplemented
160C4⋊C4×D13C2314yes—
161C4⋊C4×D13C2314yes—
162C4⋊C4×D13C2314yes—
163C22⋊C4×D13C2×C414yes—
164C22⋊C4×D13C2×C414yes—
165C22⋊C4×D13C2×C414yes—
166C22⋊C4×D13C2314yes—
167C22⋊C4×D13C2314yes—
168C22⋊C4×D13C2314yes—
169#88133C2×C418yescomplemented
170#88133C2×C418yescomplemented
171#88133C2×C418yescomplemented
172#88130C2×C418yescomplemented
173C42×D13C2×C414yescomplemented
174C42×D13C2314yes—
175(C2×#261)⋊C4C2314yes—
176(C2×#261)⋊C4C2314yes—
177(C2×#261)⋊C4C2314yes—
178(C2×#261)⋊C4C2314yes—
179(C2×#261)⋊C4C2314yes—
180(C2×#261)⋊C4C2314yes—
181(C2×#261)⋊C4C2314yes—
182(C2×#261)⋊C4C2314yes—
183(C2×#261)⋊C4C2314yes—
184(C2×#261)⋊C4C2314yes—
185(C2×#261)⋊C4C2314yes—
186(C2×#261)⋊C4C2314yes—
187C2×#2373—131nomaximal, Sylow
188C24×C13C22×C411yescharacteristic
189C23×D13—22no—
190C23×D13—22no—
191C23×D13—22no—
192C23×D13—22no—
193C23×D13—22no—
194C23×D13—22no—
195C23×D13C22×C412yes—
196C23×D13C22×C411yescharacteristic
197C23×D13C2412yes—
198C23×D13C2411yescharacteristic
199C22×#261—22no—
200C22×#261—22no—
201C22×#261—22no—
202C22×#261—22no—
203C22×#261—22no—
204C22×#261—22no—
205C22×#261—22no—
206C22×#261—22no—
207C22×#261—22no—
208C22×#261—22no—
209C22×#261—22no—
210C22×#261—22no—
211C22×#261—22no—
212C22×#261—22no—
213C22×#261—22no—
214C22×#261—22no—
215C22×#261—22no—
216C22×#261—22no—
217C22×#261—22no—
218C22×#261—22no—
219C22×#261—28no—
220C22×#261—28no—
221C22×#261—44no—
222C22×#261—416no—
223C22×#261#4114yes—
224C22×#261#4114yes—
225C22×#261#4114yes—
226C22×#261#4114yes—
227C22×#261C2412yes—
228C22×#261C2412yes—
229C22×#261C2412yes—
230C22×#261C2412yes—
231C22×#261C2412yes—
232C22×#261C2412yes—
233C22×#261C2412yes—
234C22×#261C2412yes—
235C22×C4×C13C22×C411yescharacteristic
236C22×C4×C13C22×C411yescharacteristic
237C22×C4×C13C22×C411yescharacteristic
238C22×C4×C13C22×C411yescharacteristic
239C22×C4×C13C22×C411yescharacteristic
240C22×C4×C13C22×C411yescharacteristic
241C22×Dic13C22×C411yescharacteristic
242C22×Dic13C22×C411yescharacteristic
243C22×Dic13C22×C411yescharacteristic
244C22×Dic13C22×C411yescharacteristic
245C22×Dic13C22×C411yescharacteristic
246C22×Dic13C22×C411yescharacteristic
247C2×C4×D13—22no—
248C2×C4×D13—22no—
249C2×C4×D13—22no—
250C2×C4×D13—22no—
251C2×C4×D13—22no—
252C2×C4×D13—22no—
253C2×C4×D13—22no—
254C2×C4×D13—22no—
255C2×C4×D13—22no—
256C2×C4×D13—22no—
257C2×C4×D13—22no—
258C2×C4×D13—22no—
259C2×C4×D13C22×C412yes—
260C2×C4×D13C22×C412yes—
261C2×C4×D13C22×C412yes—
262C2×C4×D13C22×C412yes—
263C2×C4×D13C22×C412yes—
264C2×C4×D13C22×C412yes—
265C2×C4×D13C2412yes—
266C2×C4×D13C2412yes—
267C2×C4×D13C2412yes—
268C2×C4×D13C2412yes—
269C2×C4×D13C2412yes—
270C2×C4×D13C2412yes—
271C22⋊#261—28no—
272C22⋊#261—28no—
273C22⋊#261—44no—
274C4⋊#261—28no—
275C4⋊#261—28no—
276C4⋊#261—28no—
277C4⋊#261—28no—
278C4⋊#261—44no—
279C4×#261—28no—
280C4×#261—28no—
281C4×#261—28no—
282C4×#261—28no—
283C4×#261—44no—
284C4×#261—44no—
285C4×#261—44no—
286C13×C4⋊C4C22×C414yescomplemented
287C13×C4⋊C4C22×C414yescomplemented
288C13×C4⋊C4C22×C414yescomplemented
289C13×C22⋊C4C22×C414yes—
290C13×C22⋊C4C22×C414yes—
291C13×C22⋊C4C22×C414yes—
292C42×C13C22×C414yescomplemented
293C22⋊Dic13C22×C414yes—
294C22⋊Dic13C22×C414yes—
295C22⋊Dic13C22×C414yes—
296#6103C22×C414yes—
297#6103C22×C414yes—
298#6103C22×C414yes—
299#6103C22×C414yes—
300#6103C22×C414yes—
301#6103C22×C414yes—
302C4⋊Dic13C22×C414yescomplemented
303C4⋊Dic13C22×C414yescomplemented
304C4⋊Dic13C22×C414yescomplemented
305#6101C22×C414yescomplemented
306#6101C22×C414yescomplemented
307#6101C22×C414yescomplemented
308#6101C22×C414yescomplemented
309#6101C22×C414yescomplemented
310#6101C22×C414yescomplemented
311C4×Dic13C22×C414yescomplemented
312C4×Dic13C22×C414yescomplemented
313C4×Dic13C22×C414yescomplemented
314C22×#126—131no—
315#2373—1316no—
316C2×#389—131no—
317C2×#388—131no—
318C2×#388—131no—
319C2×#388—131no—
320C2×#387—131no—
321C2×#387—131no—
322C2×#387—131no—
323C2×#385—131no—
324C2×C4×C4⋊C4—131no—
325C2×C4×C4⋊C4—131no—
326C2×C4×C4⋊C4—131no—
327C2×C4×C22⋊C4—131no—
328C2×C4×C22⋊C4—131no—
329C2×#376—131no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13C23×C412yes—
334C23×C13C23×C411yescharacteristic
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—24no—
339C22×D13—24no—
340C22×D13—24no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13C23×C412yes—
352C22×D13C23×C411yescharacteristic
353C22×D13C2×#4112yes—
354C22×D13C2×#4112yes—
355C22×D13C2×#4112yes—
356C22×D13C2×#4112yes—
357C22×D13H(5,𝔽2)12yes—
358C22×D132−1+412yes—
359C22×D13C2511yescharacteristic
360C2×#261—28no—
361C2×#261—28no—
362C2×#261—28no—
363C2×#261—28no—
364C2×#261—22no—
365C2×#261—22no—
366C2×#261—22no—
367C2×#261—22no—
368C2×#261—22no—
369C2×#261—22no—
370C2×#261—22no—
371C2×#261—22no—
372C2×#261—22no—
373C2×#261—22no—
374C2×#261—22no—
375C2×#261—22no—
376C2×#261—22no—
377C2×#261—22no—
378C2×#261—22no—
379C2×#261—22no—
380C2×#261—22no—
381C2×#261—22no—
382C2×#261—22no—
383C2×#261—22no—
384C2×#261—416no—
385C2×#261—44no—
386C2×#261—44no—
387C2×#261—44no—
388C2×#261—44no—
389C2×#261C2×#4114yes—
390C2×#261C2×#4114yes—
391C2×#261C2×#4114yes—
392C2×#261C2×#4114yes—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13C23×C412yes—
400C2×C4×C13C23×C412yes—
401C2×C4×C13C23×C412yes—
402C2×C4×C13C23×C412yes—
403C2×C4×C13C23×C412yes—
404C2×C4×C13C23×C412yes—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13C23×C412yes—
412C2×Dic13C23×C412yes—
413C2×Dic13C23×C412yes—
414C2×Dic13C23×C412yes—
415C2×Dic13C23×C412yes—
416C2×Dic13C23×C412yes—
417C4×D13—24no—
418C4×D13—24no—
419C4×D13—24no—
420C4×D13—24no—
421C4×D13—24no—
422C4×D13—24no—
423C4×D13—22no—
424C4×D13—22no—
425C4×D13—22no—
426C4×D13—22no—
427C4×D13—22no—
428C4×D13—22no—
429C4×D13—22no—
430C4×D13—22no—
431C4×D13—22no—
432C4×D13—22no—
433C4×D13—22no—
434C4×D13—22no—
435C24×C4—131no—
436C2×#126—138no—
437C2×#126—138no—
438C2×#126—131no—
439C2×#126—131no—
440C2×#126—131no—
441C2×#126—131no—
442C2×#126—131no—
443C2×#126—131no—
444C2×#126—131no—
445C2×#126#26111yescharacteristic, complemented
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463C22×C42—131no—
464C22×C42—131no—
465C22×C42—131no—
466C22×C42—131no—
467C22×C42—131no—
468#389—138no—
469#388—138no—
470#388—138no—
471#388—138no—
472#387—138no—
473#387—138no—
474#387—138no—
475#385—138no—
476C4×C4⋊C4—138no—
477C4×C4⋊C4—138no—
478C4×C4⋊C4—138no—
479C4×C22⋊C4—138no—
480C4×C22⋊C4—138no—
481#376—138no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C22×C13—22no—
495C22×C13—22no—
496C22×C13—22no—
497C22×C13—44no—
498C22×C13C4×#4112yes—
499C22×C13C4×#4112yes—
500C22×C13#52012yes—
501C22×C13C24×C411yescharacteristic
502C2×D13—22no—
503C2×D13—22no—
504C2×D13—22no—
505C2×D13—44no—
506C2×D13—48no—
507C2×D13—42no—
508C2×D13—42no—
509C2×D13—42no—
510C2×D13—42no—
511C2×D13C4×#4112yes—
512C2×D13C4×#4112yes—
513C2×D13#52012yes—
514C2×D13#55114yes—
515C2×D13#55214yes—
516C2×D13#55314yes—
517C2×D13#55614yes—
518C2×D13C22×#4111yescharacteristic
519C2×D13C22×#4111yescharacteristic
520C2×D13C22×#4111yescharacteristic
521C2×D13C22×#4111yescharacteristic
522C2×D13C2×H(5,𝔽2)11yescharacteristic
523C2×D13C2×2−1+411yescharacteristic
524#261—24no—
525#261—24no—
526#261—24no—
527#261—24no—
528#261—42no—
529#261—42no—
530#261—42no—
531#261—42no—
532C4×C13—22no—
533C4×C13—22no—
534C4×C13—22no—
535C4×C13—22no—
536C4×C13—22no—
537C4×C13—22no—
538Dic13—22no—
539Dic13—22no—
540Dic13—22no—
541Dic13—22no—
542Dic13—22no—
543Dic13—22no—
544C25—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—134no—
560C23×C4—264no—
561C23×C4—264no—
562C23×C4—522no—
563#126—138no—
564#126—138no—
565#126—138no—
566#126—138no—
567#126—138no—
568#126—138no—
569#126—138no—
570#126C2×#26118yescomplemented
571C2×C4⋊C4—131no—
572C2×C4⋊C4—131no—
573C2×C4⋊C4—131no—
574C2×C4⋊C4—131no—
575C2×C4⋊C4—131no—
576C2×C4⋊C4—131no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—134no—
591C2×C4⋊C4—264no—
592C2×C4⋊C4—264no—
593C2×C4⋊C4—264no—
594C2×C4⋊C4—264no—
595C2×C4⋊C4—522no—
596C2×C4⋊C4C2×#26111yescharacteristic, complemented
597C2×C4⋊C4C2×#26111yescharacteristic, complemented
598C2×C4⋊C4C2×#26111yescharacteristic, complemented
599C2×C22⋊C4—131no—
600C2×C22⋊C4—131no—
601C2×C22⋊C4—131no—
602C2×C22⋊C4—131no—
603C2×C22⋊C4—131no—
604C2×C22⋊C4—131no—
605C2×C22⋊C4—131no—
606C2×C22⋊C4—131no—
607C2×C22⋊C4—131no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—134no—
610C2×C22⋊C4—134no—
611C2×C22⋊C4—134no—
612C2×C22⋊C4—134no—
613C2×C22⋊C4—134no—
614C2×C22⋊C4—134no—
615C2×C22⋊C4—134no—
616C2×C22⋊C4—134no—
617C2×C22⋊C4—264no—
618C2×C22⋊C4—264no—
619C2×C22⋊C4—522no—
620C2×C22⋊C4C2×#26111yescharacteristic
621C2×C22⋊C4C2×#26111yescharacteristic
622C2×C22⋊C4C2×#26111yescharacteristic
623C2×C42—131no—
624C2×C42—131no—
625C2×C42—131no—
626C2×C42—134no—
627C2×C42—134no—
628C2×C42—134no—
629C2×C42—134no—
630C2×C42—134no—
631C2×C42—134no—
632C2×C42—134no—
633C2×C42—134no—
634C2×C42—134no—
635C2×C42—264no—
636C2×C42—264no—
637C2×C42—264no—
638C2×C42—264no—
639C2×C42—522no—
640C2×C42—522no—
641C2×C42—522no—
642C2×C42C2×#26111yescharacteristic, complemented
643#95—134no—
644#95—134no—
645#95—134no—
646#95—134no—
647#95—134no—
648#95—134no—
649#95—134no—
650#95—134no—
651#95—134no—
652#95—134no—
653#95—134no—
654#95—134no—
655C2×C13—42no—
656C2×C13#237314yescomplemented
657C2×C13C2×C4×#4111yescharacteristic
658C2×C13C2×C4×#4111yescharacteristic
659C2×C13C2×#52011yescharacteristic
660D13—42no—
661D13#237314yescomplemented
662D13C2×#55111yescharacteristic
663D13C2×#55211yescharacteristic
664D13C2×#55311yescharacteristic
665D13C2×#55611yescharacteristic
666C24—131no—
667C24—132no—
668C24—132no—
669C24—131no—
670C24—262no—
671C24—262no—
672C24—262no—
673C24—262no—
674C24—262no—
675C24—262no—
676C24C22×#26111yescharacteristic
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—134no—
682C22×C4—134no—
683C22×C4—134no—
684C22×C4—134no—
685C22×C4—131no—
686C22×C4—131no—
687C22×C4—131no—
688C22×C4—131no—
689C22×C4—131no—
690C22×C4—131no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—262no—
708C22×C4—262no—
709C22×C4—262no—
710C22×C4—262no—
711C22×C4—262no—
712C22×C4—262no—
713C22×C4—262no—
714C22×C4—262no—
715C22×C4—262no—
716C22×C4—262no—
717C22×C4—262no—
718C22×C4—262no—
719C22×C4—268no—
720C22×C4—268no—
721C22×C4—262no—
722C22×C4—262no—
723C22×C4—262no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—262no—
728C22×C4—262no—
729C22×C4—262no—
730C22×C4—262no—
731C22×C4—262no—
732C22×C4—262no—
733C22×C4—262no—
734C22×C4—262no—
735C22×C4—262no—
736C22×C4—262no—
737C22×C4—262no—
738C22×C4—262no—
739C22×C4—262no—
740C22×C4—262no—
741C22×C4—524no—
742C22×C4—5216no—
743C22×C4C22×#26111yescharacteristic
744C22×C4C22×#26111yescharacteristic
745C22×C4C22×#26111yescharacteristic
746C22×C4C22×#26111yescharacteristic
747C22×C4C22×#26111yescharacteristic
748C22×C4C22×#26111yescharacteristic
749C4⋊C4—134no—
750C4⋊C4—134no—
751C4⋊C4—134no—
752C4⋊C4—134no—
753C4⋊C4—134no—
754C4⋊C4—134no—
755C4⋊C4—134no—
756C4⋊C4—134no—
757C4⋊C4—134no—
758C4⋊C4—268no—
759C4⋊C4—268no—
760C4⋊C4—268no—
761C4⋊C4—268no—
762C4⋊C4—524no—
763C4⋊C4C22×#26114yescomplemented
764C4⋊C4C22×#26114yescomplemented
765C4⋊C4C22×#26114yescomplemented
766C22⋊C4—134no—
767C22⋊C4—134no—
768C22⋊C4—134no—
769C22⋊C4—134no—
770C22⋊C4—134no—
771C22⋊C4—134no—
772C22⋊C4—134no—
773C22⋊C4—134no—
774C22⋊C4—134no—
775C22⋊C4—268no—
776C22⋊C4—268no—
777C22⋊C4—524no—
778C22⋊C4C22×#26114yes—
779C22⋊C4C22×#26114yes—
780C22⋊C4C22×#26114yes—
781C42—134no—
782C42—134no—
783C42—134no—
784C42—268no—
785C42—268no—
786C42—268no—
787C42—268no—
788C42—524no—
789C42—524no—
790C42—524no—
791C42C22×#26114yescomplemented
792C13C2×#237311yescharacteristic, complemented, Sylow
793C23—22no—
794C23—22no—
795C23—22no—
796C23—132no—
797C23—132no—
798C23—132no—
799C23—132no—
800C23—132no—
801C23—132no—
802C23—131no—
803C23—131no—
804C23—132no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—264no—
811C23—264no—
812C23—264no—
813C23—262no—
814C23—262no—
815C23—262no—
816C23—262no—
817C23—524no—
818C23—524no—
819C23—524no—
820C23—524no—
821C23C23×#26112yes—
822C23C23×#26111yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—134no—
830C2×C4—134no—
831C2×C4—134no—
832C2×C4—134no—
833C2×C4—132no—
834C2×C4—132no—
835C2×C4—132no—
836C2×C4—132no—
837C2×C4—132no—
838C2×C4—132no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—264no—
850C2×C4—264no—
851C2×C4—264no—
852C2×C4—264no—
853C2×C4—264no—
854C2×C4—264no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—268no—
865C2×C4—268no—
866C2×C4—262no—
867C2×C4—268no—
868C2×C4—268no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—5216no—
888C2×C4—524no—
889C2×C4—524no—
890C2×C4—524no—
891C2×C4—524no—
892C2×C4C23×#26112yes—
893C2×C4C23×#26112yes—
894C2×C4C23×#26112yes—
895C2×C4C23×#26112yes—
896C2×C4C23×#26112yes—
897C2×C4C23×#26112yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—44no—
902C22—132no—
903C22—132no—
904C22—131no—
905C22—131no—
906C22—131no—
907C22—131no—
908C22—132no—
909C22—131no—
910C22—131no—
911C22—134no—
912C22—134no—
913C22—134no—
914C22—134no—
915C22—262no—
916C22—262no—
917C22—262no—
918C22—522no—
919C22—522no—
920C22—522no—
921C22—522no—
922C22—528no—
923C22—524no—
924C22#41×#26112yes—
925C22#41×#26112yes—
926C22#1171963112yes—
927C22C24×#26111yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—264no—
935C4—264no—
936C4—264no—
937C4—264no—
938C4—262no—
939C4—262no—
940C4—262no—
941C4—262no—
942C4—262no—
943C4—262no—
944C4—522no—
945C4—522no—
946C4—522no—
947C4—522no—
948C2—42no—
949C2—131no—
950C2—131no—
951C2—131no—
952C2—131no—
953C2—134no—
954C2—522no—
955C2#1313137314yesdirect product factor
956C2C2×#41×#26111yescharacteristic
957C2C2×#41×#26111yescharacteristic
958C2C2×#1171963111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#126C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC2×#126#261
hypocenterC13C2×#2373
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #13131373C2direct (N × H)
2. C2×#11719083C2semidirect
6. C2×#11719082C2semidirect
7. C2×#11719082C2semidirect
8. C2×#11719082C2semidirect
10. C2×C4⋊C4×#261C2semidirect
11. C2×C4⋊C4×#261C2semidirect
12. C2×C4×C4⋊#261C2semidirect
15. C2×#11719057C2semidirect
33. C2×C13×#126C4semidirect
34. D13×#126C4semidirect
36. C2×#88152C4semidirect
37. C2×#88152C4semidirect
38. C2×#88152C4semidirect
45. C2×#88133C4semidirect
46. C2×#88133C4semidirect
47. C2×#88133C4semidirect
48. C2×#88130C4semidirect
62. #11719083C22semidirect
63. #11719082C22semidirect
64. #11719082C22semidirect
65. #11719082C22semidirect
66. C4⋊C4×#261C22semidirect
67. C4⋊C4×#261C22semidirect
74. C4×C4⋊#261C22semidirect
75. #11719057C22semidirect
125. C13×#126C2×C4semidirect
126. C2×C13×C4⋊C4C2×C4semidirect
127. C2×C13×C4⋊C4C2×C4semidirect
128. C2×C13×C4⋊C4C2×C4semidirect
132. C2×C42×C13C2×C4semidirect
142. C2×C4⋊Dic13C2×C4semidirect
143. C2×C4⋊Dic13C2×C4semidirect
144. C2×C4⋊Dic13C2×C4semidirect
145. C2×#6101C2×C4semidirect
146. C2×#6101C2×C4semidirect
147. C2×#6101C2×C4semidirect
148. C2×#6101C2×C4semidirect
149. C2×#6101C2×C4semidirect
150. C2×#6101C2×C4semidirect
151. C2×C4×Dic13C2×C4semidirect
152. C2×C4×Dic13C2×C4semidirect
153. C2×C4×Dic13C2×C4semidirect
154. #88152C2×C4semidirect
155. #88152C2×C4semidirect
156. #88152C2×C4semidirect
157. C4⋊C4×D13C2×C4semidirect
158. C4⋊C4×D13C2×C4semidirect
159. C4⋊C4×D13C2×C4semidirect
169. #88133C2×C4semidirect
170. #88133C2×C4semidirect
171. #88133C2×C4semidirect
172. #88130C2×C4semidirect
173. C42×D13C2×C4semidirect
286. C13×C4⋊C4C22×C4semidirect
287. C13×C4⋊C4C22×C4semidirect
288. C13×C4⋊C4C22×C4semidirect
292. C42×C13C22×C4semidirect
302. C4⋊Dic13C22×C4semidirect
303. C4⋊Dic13C22×C4semidirect
304. C4⋊Dic13C22×C4semidirect
305. #6101C22×C4semidirect
306. #6101C22×C4semidirect
307. #6101C22×C4semidirect
308. #6101C22×C4semidirect
309. #6101C22×C4semidirect
310. #6101C22×C4semidirect
311. C4×Dic13C22×C4semidirect
312. C4×Dic13C22×C4semidirect
313. C4×Dic13C22×C4semidirect
445. C2×#126#261semidirect
570. #126C2×#261semidirect
596. C2×C4⋊C4C2×#261semidirect
597. C2×C4⋊C4C2×#261semidirect
598. C2×C4⋊C4C2×#261semidirect
642. C2×C42C2×#261semidirect
656. C2×C13#2373semidirect
661. D13#2373semidirect
763. C4⋊C4C22×#261semidirect
764. C4⋊C4C22×#261semidirect
765. C4⋊C4C22×#261semidirect
791. C42C22×#261semidirect
792. C13C2×#2373semidirect
955. C2#13131373direct (N × H)

Maximal subgroups

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

subgroupindex
#131313732
C2×#117190832
C2×#117190712
C2×#117190822
C2×#117190702
C2×C4⋊C4×#2612
C2×C4×C4⋊#2612
C2×C22⋊C4×#2612
C2×#117190572
C2×D13×#1262
C2×#237313