Finite Group Databasebeta

← D13×#2362 #16022454

Subgroups — D13×#2362 #16022454

Order 3328.

3310 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D13C211yesmaximal, characteristic, complemented
3C2×D13×#117C211yesmaximal, characteristic
4#13117868C211yesmaximal, characteristic, complemented
5#13117867C211yesmaximal, characteristic, complemented
6#13117866C212yesmaximal, complemented
7#13117865C211yesmaximal, characteristic, complemented
8#13117864C212yesmaximal, complemented
9#13117863C211yesmaximal, characteristic, complemented
10#13117862C211yesmaximal, characteristic, complemented
11#13117861C211yesmaximal, characteristic, complemented
12#13117860C212yesmaximal, complemented
13#13117859C211yesmaximal, characteristic, complemented
14#13117858C212yesmaximal, complemented
15D13×#391C211yesmaximal, characteristic, complemented
16D13×#389C211yesmaximal, characteristic, complemented
17D13×#388C212yesmaximal
18D13×#388C212yesmaximal
19D13×#387C212yesmaximal, complemented
20C4×C4⋊C4×D13C212yesmaximal, complemented
21C4×C4⋊C4×D13C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic
23C13×#2362C211yesmaximal, characteristic, complemented
24C22×Q8×D13C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic, complemented
28C2×C13×#117C2211yescharacteristic
29C2×#88200C2211yescharacteristic
30C2×Q8×Dic13C2211yescharacteristic, complemented
31C2×#88180C2211yescharacteristic
32C2×#88178C2211yescharacteristic
33D13×C22⋊Q8C4116yescomplemented
34C4×Q8×D13—28no—
35D13×#117—28no—
36C2×#88151C2211yescharacteristic
37C2×#88150C2212yes—
38C2×#88146C2211yescharacteristic
39C2×#88146C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×C4⋊C4×D13C2212yes—
42C2×C4⋊C4×D13C2212yes—
43C2×C4⋊C4×D13C2212yes—
44C2×C4⋊C4×D13C2211yescharacteristic
45C2×C4⋊C4×D13C2211yescharacteristic
46C2×#88141C2212yescomplemented
47C2×#88141C2211yescharacteristic, complemented
48C2×C22⋊C4×D13C2212yes—
49C2×C22⋊C4×D13C2211yescharacteristic
50C2×C22⋊C4×D13C2211yescharacteristic
51C2×C22⋊C4×D13C2212yes—
52C2×#88132C2212yes—
53C2×#88131C2212yes—
54C2×#88126C2212yes—
55C2×C42×D13C2212yes—
56C2×C42×D13C2212yes—
57C2×C42×D13C2211yescharacteristic
58C2×C42×D13C2212yes—
59C2×C42×D13C2211yescharacteristic
60C2×C4×Dic26C2211yescharacteristic, complemented
61C2×C4×Dic26C2212yescomplemented
62C13×#391C2211yescharacteristic, complemented
63C13×#389C2211yescharacteristic, complemented
64C13×#388C2212yes—
65C13×#388C2212yes—
66C13×#387C2212yescomplemented
67C4×C13×C4⋊C4C2212yescomplemented
68C4×C13×C4⋊C4C2211yescharacteristic, complemented
69C4×C13×C22⋊C4C2211yescharacteristic
70#11718891C2211yescharacteristic, complemented
71C4×C22⋊Dic13C2211yescharacteristic
72#11718651C2212yes—
73#11718651C2212yes—
74#11718646C2211yescharacteristic, complemented
75#11718642C2212yescomplemented
76#11718639C2212yescomplemented
77C4⋊C4×Dic13C2212yescomplemented
78C4⋊C4×Dic13C2211yescharacteristic, complemented
79C4⋊C4×Dic13C2212yescomplemented
80C4⋊C4×Dic13C2211yescharacteristic, complemented
81#11718635C2211yescharacteristic, complemented
82#11718634C2211yescharacteristic, complemented
83#11718633C2212yescomplemented
84#11718612C2212yes—
85#11718612C2212yes—
86#11718606C2212yes—
87#11718606C2212yes—
88#11718605C2212yes—
89#11718605C2212yes—
90C22⋊C4×Dic13C2211yescharacteristic
91C22⋊C4×Dic13C2211yescharacteristic
92#11718601C2212yes—
93#11718601C2212yes—
94C4×#6103C2211yescharacteristic
95C4×#6103C2211yescharacteristic
96C4×C4⋊Dic13C2212yescomplemented
97C4×C4⋊Dic13C2211yescharacteristic, complemented
98#11718594C2212yescomplemented
99C4×#6101C2212yescomplemented
100C4×#6101C2212yescomplemented
101C4×#6101C2212yescomplemented
102#11718590C2211yescharacteristic, complemented
103#11718589C2211yescharacteristic, complemented
104#11718331C2212yes—
105#11718331C2212yes—
106#11718330C2212yes—
107#11718330C2212yes—
108#11718327C2211yescharacteristic
109#11718327C2211yescharacteristic
110D13×#95C2211yescharacteristic
111D13×#95C2212yes—
112D13×#95C2212yes—
113D13×#95C2212yes—
114D13×#95C2212yes—
115D13×#95C2211yescharacteristic
116#11718316C2212yescomplemented
117#11718315C2212yescomplemented
118#11718314C2212yescomplemented
119#11718313C2212yescomplemented
120#11718310C2212yescomplemented
121#11718310C2212yescomplemented
122#11718310C2212yescomplemented
123#11718308C2212yescomplemented
124#11718307C2212yescomplemented
125#11718307C2212yescomplemented
126C24×D13C2311yescharacteristic
127C22×Q8×C13C2311yescharacteristic
128C23×C4×C13C2311yescharacteristic
129C23×Dic13C2311yescharacteristic
130C2×Q8×D13—24no—
131C2×Q8×D13—24no—
132C2×Q8×D13C2×C418yes—
133C22×C4×D13—24no—
134C22×C4×D13—24no—
135C22×C4×D13C2×C418yes—
136C22×C4×D13C2312yes—
137C22×C4×D13C2311yescharacteristic
138C22×C4×D13C2311yescharacteristic
139C22×C4×D13C2311yescharacteristic
140C22×C4×D13C2312yes—
141C22×C4×D13C2312yes—
142C22×C4×D13C2311yescharacteristic
143C22×C4×D13C2311yescharacteristic
144C22×C4×D13C2312yes—
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×Dic26C2312yes—
149C22×Dic26C2311yescharacteristic
150C13×C22⋊Q8C2×C418yescomplemented
151C4×Q8×C13—24no—
152C13×#117—24no—
153C2×C13×C4⋊C4C2312yes—
154C2×C13×C4⋊C4C2312yes—
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2311yescharacteristic
159C2×C13×C22⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2311yescharacteristic
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C42×C13C2311yescharacteristic
164C2×C42×C13C2311yescharacteristic
165C2×C42×C13C2312yes—
166C2×C42×C13C2312yes—
167C2×C42×C13C2312yes—
168C2×C22⋊Dic13C2312yes—
169C2×C22⋊Dic13C2311yescharacteristic
170C2×C22⋊Dic13C2311yescharacteristic
171C2×C22⋊Dic13C2312yes—
172#88200C2×C418yescomplemented
173Q8×Dic13—24no—
174C2×#6103C2312yes—
175C2×#6103C2312yes—
176C2×#6103C2311yescharacteristic
177C2×#6103C2311yescharacteristic
178C2×#6103C2311yescharacteristic
179C2×#6103C2311yescharacteristic
180C2×#6103C2312yes—
181C2×#6103C2312yes—
182#88180—24no—
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2311yescharacteristic
185C2×C4⋊Dic13C2312yes—
186C2×C4⋊Dic13C2312yes—
187C2×C4⋊Dic13C2311yescharacteristic
188C2×C4⋊Dic13C2311yescharacteristic
189#88178C2×C418yescomplemented
190C2×#6101C2312yes—
191C2×#6101C2312yes—
192C2×#6101C2312yes—
193C2×#6101C2312yes—
194C2×#6101C2312yes—
195C2×#6101C2312yes—
196C2×#6101C2312yes—
197C2×#6101C2312yes—
198C2×#6101C2312yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C2311yescharacteristic
201C2×C4×Dic13C2312yes—
202C2×C4×Dic13C2312yes—
203C2×C4×Dic13C2312yes—
204C2×C4×Dic13C2311yescharacteristic
205C2×C4×Dic13C2312yes—
206C2×C4×Dic13C2312yes—
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2311yescharacteristic
209C2×C4×Dic13C2311yescharacteristic
210C2×C4×Dic13C2312yes—
211C2×C4×Dic13C2312yes—
212C2×C4×Dic13C2312yes—
213C2×C4×Dic13C2311yescharacteristic
214#88151C2×C418yescomplemented
215#88150C2×C4116yescomplemented
216#88146—24no—
217#88146—24no—
218C4⋊C4×D13—24no—
219C4⋊C4×D13—28no—
220C4⋊C4×D13—28no—
221C4⋊C4×D13C2×C418yes—
222C4⋊C4×D13C2×C4116yes—
223C4⋊C4×D13D418yes—
224#88141—24no—
225#88141—28no—
226C22⋊C4×D13—28no—
227C22⋊C4×D13—24no—
228C22⋊C4×D13—24no—
229C22⋊C4×D13C2×C4116yes—
230#88132C2×C4116yescomplemented
231#88131—28no—
232#88126—28no—
233C42×D13—28no—
234C42×D13—28no—
235C42×D13—24no—
236C42×D13—28no—
237C42×D13—24no—
238C4×Dic26—24no—
239C4×Dic26—28no—
240C13×#95C2311yescharacteristic
241C13×#95C2311yescharacteristic
242C13×#95C2312yes—
243C13×#95C2312yes—
244C13×#95C2312yes—
245C13×#95C2312yes—
246#88071C2312yes—
247#88071C2312yes—
248#88071C2312yes—
249#88071C2312yes—
250#88071C2312yes—
251#88071C2312yes—
252#88071C2312yes—
253#88071C2311yescharacteristic
254#88071C2312yes—
255#88071C2311yescharacteristic
256#88071C2312yes—
257#88071C2311yescharacteristic
258#88071C2312yes—
259#88071C2312yes—
260#88071C2311yescharacteristic
261#88071C2311yescharacteristic
262#88071C2311yescharacteristic
263#88071C2312yes—
264C2×#2362—131nomaximal, Sylow
265C24×C13C2411yescharacteristic
266C23×D13—22no—
267C23×D13—22no—
268C23×D13—22no—
269C23×D13—22no—
270C23×D13—22no—
271C23×D13—22no—
272C23×D13C22×C414yes—
273C23×D13C2411yescharacteristic
274C23×D13C2411yescharacteristic
275C2×Q8×C13—22no—
276C2×Q8×C13—22no—
277C2×Q8×C13C22×C414yes—
278C22×C4×C13—22no—
279C22×C4×C13—22no—
280C22×C4×C13C22×C414yes—
281C22×C4×C13C2411yescharacteristic
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2412yes—
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2412yes—
286C22×C4×C13C2412yes—
287C22×C4×C13C2412yes—
288C22×C4×C13C2411yescharacteristic
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2411yescharacteristic
291C22×Dic13—22no—
292C22×Dic13—22no—
293C22×Dic13C22×C414yes—
294C22×Dic13C2411yescharacteristic
295C22×Dic13C2411yescharacteristic
296C22×Dic13C2412yes—
297C22×Dic13C2411yescharacteristic
298C22×Dic13C2412yes—
299C22×Dic13C2412yes—
300C22×Dic13C2412yes—
301C22×Dic13C2411yescharacteristic
302C22×Dic13C2411yescharacteristic
303C22×Dic13C2411yescharacteristic
304Q8×D13—232no—
305C2×C4×D13—22no—
306C2×C4×D13—22no—
307C2×C4×D13—24no—
308C2×C4×D13—24no—
309C2×C4×D13—24no—
310C2×C4×D13—22no—
311C2×C4×D13—24no—
312C2×C4×D13—22no—
313C2×C4×D13—24no—
314C2×C4×D13—24no—
315C2×C4×D13—22no—
316C2×C4×D13—22no—
317C2×C4×D13—22no—
318C2×C4×D13—22no—
319C2×C4×D13—22no—
320C2×C4×D13—22no—
321C2×C4×D13—232no—
322C2×C4×D13—24no—
323C2×C4×D13—22no—
324C2×C4×D13—22no—
325C2×C4×D13—22no—
326C2×C4×D13—22no—
327C2×C4×D13—24no—
328C2×C4×D13—22no—
329C2×C4×D13—24no—
330C2×C4×D13—22no—
331C2×C4×D13C22×C418yes—
332C2×C4×D13C22×C418yes—
333C2×C4×D13C22×C414yes—
334C2×C4×D13C22×C414yes—
335C2×C4×D13C22×C414yes—
336C2×C4×D13C22×C414yes—
337C2×C4×D13C2×D418yes—
338C2×C4×D13C2×D414yes—
339C2×C4×D13#4114yes—
340C2×C4×D13#4114yes—
341C2×C4×D13#4114yes—
342C2×Dic26—22no—
343C2×Dic26—22no—
344C2×Dic26—24no—
345C2×Dic26—24no—
346C2×Dic26C22×C418yes—
347C2×Dic26C22×C414yes—
348C13×C4⋊C4—24no—
349C13×C4⋊C4—22no—
350C13×C4⋊C4—24no—
351C13×C4⋊C4C22×C418yes—
352C13×C4⋊C4C22×C414yes—
353C13×C4⋊C4C2×D414yes—
354C13×C22⋊C4—24no—
355C13×C22⋊C4—22no—
356C13×C22⋊C4—22no—
357C13×C22⋊C4C22×C418yes—
358C42×C13—24no—
359C42×C13—22no—
360C42×C13—24no—
361C42×C13—24no—
362C42×C13—22no—
363C22⋊Dic13—24no—
364C22⋊Dic13—22no—
365C22⋊Dic13—22no—
366C22⋊Dic13C22×C418yes—
367#6103—24no—
368#6103—22no—
369#6103—22no—
370#6103—24no—
371#6103—22no—
372#6103—22no—
373#6103C22×C418yes—
374#6103C22×C418yes—
375C4⋊Dic13—22no—
376C4⋊Dic13—24no—
377C4⋊Dic13—24no—
378C4⋊Dic13C22×C418yes—
379C4⋊Dic13C22×C414yes—
380C4⋊Dic13C2×D414yes—
381#6101—24no—
382#6101—24no—
383#6101—24no—
384#6101—24no—
385#6101—24no—
386#6101C22×C418yes—
387#6101C22×C418yes—
388#6101C22×C418yes—
389#6101C2×D418yes—
390C4×Dic13—24no—
391C4×Dic13—24no—
392C4×Dic13—22no—
393C4×Dic13—24no—
394C4×Dic13—22no—
395C4×Dic13—24no—
396C4×Dic13—22no—
397C4×Dic13—24no—
398C4×Dic13—24no—
399C4×Dic13—22no—
400C4×Dic13—24no—
401C4×Dic13—24no—
402C4×Dic13—24no—
403C4×Dic13—22no—
404C4×Dic13—22no—
405C22×C22⋊Q8—131no—
406C22×C4×Q8—131no—
407C22×#117—131no—
408#2362—131no—
409#2362—131no—
410#2362—132no—
411#2362—132no—
412#2362—132no—
413#2362—132no—
414#2362—131no—
415#2362—131no—
416#2362—131no—
417#2362—131no—
418#2362—131no—
419#2362D1311yescharacteristic, direct product factor
420C2×#391—131no—
421C2×#389—131no—
422C2×#388—132no—
423C2×#388—132no—
424C2×#387—132no—
425C2×C4×C4⋊C4—131no—
426C2×C4×C4⋊C4—132no—
427C2×C4×C22⋊C4—131no—
428C23×C13—21no—
429C23×C13—21no—
430C23×C13—21no—
431C23×C13—21no—
432C23×C13—21no—
433C23×C13—21no—
434C23×C13C23×C412yes—
435C23×C13C2511yescharacteristic
436C22×D13—21no—
437C22×D13—21no—
438C22×D13—21no—
439C22×D13—21no—
440C22×D13—21no—
441C22×D13—21no—
442C22×D13—28no—
443C22×D13—28no—
444C22×D13—28no—
445C22×D13—44no—
446C22×D13—44no—
447C22×D13—44no—
448C22×D13—44no—
449C22×D13C23×C412yes—
450C22×D13C23×C412yes—
451C22×D13C22×D412yes—
452C22×D13C2×#4112yes—
453C22×D13C2×#4112yes—
454C22×D13C2×#4112yes—
455C22×D132−1+412yes—
456C22×D132−1+412yes—
457Q8×C13—28no—
458C2×C4×C13—21no—
459C2×C4×C13—21no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13—21no—
464C2×C4×C13—22no—
465C2×C4×C13—22no—
466C2×C4×C13—21no—
467C2×C4×C13—22no—
468C2×C4×C13—21no—
469C2×C4×C13—21no—
470C2×C4×C13—28no—
471C2×C4×C13—21no—
472C2×C4×C13—22no—
473C2×C4×C13—21no—
474C2×C4×C13—22no—
475C2×C4×C13—21no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—22no—
479C2×C4×C13—21no—
480C2×C4×C13C23×C412yes—
481C2×C4×C13C23×C414yes—
482C2×C4×C13C23×C414yes—
483C2×C4×C13C23×C412yes—
484C2×C4×C13C22×D414yes—
485C2×C4×C13C22×D412yes—
486C2×C4×C13C2×#4112yes—
487C2×C4×C13C2×#4112yes—
488C2×C4×C13C2×#4112yes—
489C2×Dic13—21no—
490C2×Dic13—21no—
491C2×Dic13—22no—
492C2×Dic13—22no—
493C2×Dic13—22no—
494C2×Dic13—21no—
495C2×Dic13—22no—
496C2×Dic13—22no—
497C2×Dic13—21no—
498C2×Dic13—22no—
499C2×Dic13—21no—
500C2×Dic13—21no—
501C2×Dic13—28no—
502C2×Dic13—21no—
503C2×Dic13—22no—
504C2×Dic13—21no—
505C2×Dic13—22no—
506C2×Dic13—21no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—22no—
510C2×Dic13—21no—
511C2×Dic13C23×C414yes—
512C2×Dic13C23×C412yes—
513C2×Dic13C23×C414yes—
514C2×Dic13C23×C412yes—
515C2×Dic13C22×D414yes—
516C2×Dic13C22×D412yes—
517C2×Dic13C2×#4112yes—
518C2×Dic13C2×#4112yes—
519C2×Dic13C2×#4112yes—
520C4×D13—28no—
521C4×D13—216no—
522C4×D13—216no—
523C4×D13—216no—
524C4×D13—28no—
525C4×D13—28no—
526C4×D13—28no—
527C4×D13—28no—
528C4×D13—44no—
529C4×D13—48no—
530C4×D13—44no—
531C4×D13C4×D4116yes—
532Dic26—28no—
533Dic26—216no—
534C23×Q8—131no—
535C24×C4—131no—
536C2×C22⋊Q8—131no—
537C2×C22⋊Q8—131no—
538C2×C22⋊Q8—1316no—
539C2×C22⋊Q8—132no—
540C2×C22⋊Q8—131no—
541C2×C22⋊Q8—132no—
542C2×C22⋊Q8C2×D1311yescharacteristic
543C2×C4×Q8—131no—
544C2×C4×Q8—132no—
545C2×C4×Q8—131no—
546C2×C4×Q8—132no—
547C2×C4×Q8—131no—
548C2×C4×Q8—268no—
549C2×C4×Q8C2×D1311yescharacteristic, complemented
550C2×#117—131no—
551C2×#117—131no—
552C2×#117—131no—
553C2×#117—132no—
554C2×#117—132no—
555C2×#117—268no—
556C2×#117C2×D1311yescharacteristic
557C22×C4⋊C4—131no—
558C22×C4⋊C4—132no—
559C22×C4⋊C4—131no—
560C22×C4⋊C4—131no—
561C22×C4⋊C4—132no—
562C22×C4⋊C4—132no—
563C22×C22⋊C4—132no—
564C22×C22⋊C4—132no—
565C22×C22⋊C4—131no—
566C22×C22⋊C4—131no—
567C22×C42—132no—
568C22×C42—131no—
569C22×C42—132no—
570C22×C42—131no—
571C22×C42—132no—
572#391—131no—
573#391—131no—
574#391—131no—
575#391—132no—
576#391—132no—
577#391C2×D1311yescharacteristic, complemented
578#389—132no—
579#389—131no—
580#389—131no—
581#389—131no—
582#389—132no—
583#389C2×D1311yescharacteristic, complemented
584#388—132no—
585#388—132no—
586#388—132no—
587#388—132no—
588#388—132no—
589#388—132no—
590#388—132no—
591#388—132no—
592#388—132no—
593#388—132no—
594#388—132no—
595#388—132no—
596#388—132no—
597#388—132no—
598#388C2×D1312yes—
599#388C2×D1312yes—
600#387—132no—
601#387—132no—
602#387—132no—
603#387—132no—
604#387—132no—
605#387—132no—
606#387—132no—
607#387C2×D1312yescomplemented
608C4×C4⋊C4—132no—
609C4×C4⋊C4—132no—
610C4×C4⋊C4—131no—
611C4×C4⋊C4—131no—
612C4×C4⋊C4—132no—
613C4×C4⋊C4—132no—
614C4×C4⋊C4—132no—
615C4×C4⋊C4—132no—
616C4×C4⋊C4—131no—
617C4×C4⋊C4—132no—
618C4×C4⋊C4—132no—
619C4×C4⋊C4—132no—
620C4×C4⋊C4C2×D1312yescomplemented
621C4×C4⋊C4C2×D1311yescharacteristic, complemented
622C4×C22⋊C4—131no—
623C4×C22⋊C4—131no—
624C4×C22⋊C4—131no—
625C4×C22⋊C4—131no—
626C4×C22⋊C4—131no—
627C4×C22⋊C4—131no—
628C4×C22⋊C4—131no—
629C4×C22⋊C4C2×D1311yescharacteristic
630C2×#95—131no—
631C2×#95—131no—
632C2×#95—132no—
633C2×#95—132no—
634C2×#95—132no—
635C2×#95—132no—
636C22×C13—22no—
637C22×C13—22no—
638C22×C13—22no—
639C22×C13—41no—
640C22×C13—41no—
641C22×C13—41no—
642C22×C13—41no—
643C22×C13C24×C411yescharacteristic
644C22×C13C23×D411yescharacteristic
645C22×C13C22×#4111yescharacteristic
646C22×C13C22×#4111yescharacteristic
647C22×C13C22×#4111yescharacteristic
648C22×C13C2×2−1+411yescharacteristic
649C22×C13C2×2−1+411yescharacteristic
650C2×D13—22no—
651C2×D13—22no—
652C2×D13—22no—
653C2×D13—41no—
654C2×D13—41no—
655C2×D13—41no—
656C2×D13—41no—
657C2×D13—416no—
658C2×D13C2×C4×D414yes—
659C2×D13C4×#4114yes—
660C2×D13#51914yes—
661C2×D13#54714yes—
662C2×D13#54814yes—
663C2×D13#55214yes—
664C2×D13#55614yes—
665C4×C13—24no—
666C4×C13—22no—
667C4×C13—24no—
668C4×C13—24no—
669C4×C13—22no—
670C4×C13—22no—
671C4×C13—41no—
672C4×C13—42no—
673C4×C13—41no—
674C4×C13C2×C4×D414yes—
675Dic13—24no—
676Dic13—22no—
677Dic13—24no—
678Dic13—24no—
679Dic13—22no—
680Dic13—22no—
681Dic13—41no—
682Dic13—42no—
683Dic13—41no—
684Dic13C2×C4×D414yes—
685C25—131no—
686C22×Q8—138no—
687C22×Q8—132no—
688C22×Q8—131no—
689C22×Q8—264no—
690C22×Q8—264no—
691C22×Q8C22×D1311yescharacteristic
692C23×C4—131no—
693C23×C4—131no—
694C23×C4—138no—
695C23×C4—132no—
696C23×C4—132no—
697C23×C4—132no—
698C23×C4—131no—
699C23×C4—131no—
700C23×C4—131no—
701C23×C4—131no—
702C23×C4—131no—
703C23×C4—132no—
704C23×C4—131no—
705C23×C4—131no—
706C23×C4—264no—
707C23×C4—264no—
708C23×C4C22×D1311yescharacteristic
709C22⋊Q8—138no—
710C22⋊Q8—138no—
711C22⋊Q8—1316no—
712C22⋊Q8—138no—
713C22⋊Q8—1316no—
714C22⋊Q8C4×D1318yescomplemented
715C4×Q8—24no—
716C4×Q8—268no—
717C4×Q8—264no—
718C4×Q8—268no—
719C4×Q8—264no—
720C4×Q8—264no—
721#117—24no—
722#117—268no—
723#117—268no—
724#117—264no—
725#117—264no—
726#117—264no—
727C2×C4⋊C4—132no—
728C2×C4⋊C4—131no—
729C2×C4⋊C4—132no—
730C2×C4⋊C4—132no—
731C2×C4⋊C4—132no—
732C2×C4⋊C4—132no—
733C2×C4⋊C4—131no—
734C2×C4⋊C4—138no—
735C2×C4⋊C4—1316no—
736C2×C4⋊C4—138no—
737C2×C4⋊C4—132no—
738C2×C4⋊C4—131no—
739C2×C4⋊C4—132no—
740C2×C4⋊C4—132no—
741C2×C4⋊C4—132no—
742C2×C4⋊C4—132no—
743C2×C4⋊C4—132no—
744C2×C4⋊C4—132no—
745C2×C4⋊C4—264no—
746C2×C4⋊C4—268no—
747C2×C4⋊C4—268no—
748C2×C4⋊C4C22×D1311yescharacteristic
749C2×C4⋊C4C22×D1312yes—
750C2×C4⋊C4C22×D1312yes—
751C2×C4⋊C4C22×D1312yes—
752C2×C4⋊C4C22×D1311yescharacteristic
753C2×C4⋊C4C22×D1311yescharacteristic
754C2×C22⋊C4—132no—
755C2×C22⋊C4—132no—
756C2×C22⋊C4—132no—
757C2×C22⋊C4—1316no—
758C2×C22⋊C4—132no—
759C2×C22⋊C4—131no—
760C2×C22⋊C4—131no—
761C2×C22⋊C4—132no—
762C2×C22⋊C4—132no—
763C2×C22⋊C4—131no—
764C2×C22⋊C4—131no—
765C2×C22⋊C4—131no—
766C2×C22⋊C4—131no—
767C2×C22⋊C4—268no—
768C2×C22⋊C4—264no—
769C2×C22⋊C4—264no—
770C2×C22⋊C4C22×D1312yes—
771C2×C22⋊C4C22×D1311yescharacteristic
772C2×C22⋊C4C22×D1311yescharacteristic
773C2×C22⋊C4C22×D1312yes—
774C2×C42—132no—
775C2×C42—132no—
776C2×C42—132no—
777C2×C42—131no—
778C2×C42—131no—
779C2×C42—131no—
780C2×C42—132no—
781C2×C42—132no—
782C2×C42—132no—
783C2×C42—131no—
784C2×C42—131no—
785C2×C42—131no—
786C2×C42—132no—
787C2×C42—132no—
788C2×C42—132no—
789C2×C42—268no—
790C2×C42—264no—
791C2×C42—268no—
792C2×C42—264no—
793C2×C42—268no—
794C2×C42C22×D1312yes—
795C2×C42C22×D1311yescharacteristic
796C2×C42C22×D1312yes—
797C2×C42C22×D1311yescharacteristic
798C2×C42C22×D1312yes—
799#95—131no—
800#95—131no—
801#95—131no—
802#95—131no—
803#95—131no—
804#95—131no—
805#95—132no—
806#95—132no—
807#95—132no—
808#95—132no—
809#95—132no—
810#95—132no—
811#95—132no—
812#95—132no—
813#95—132no—
814#95—132no—
815#95—132no—
816#95—132no—
817#95C22×D1311yescharacteristic
818#95C22×D1311yescharacteristic
819#95C22×D1312yes—
820#95C22×D1312yes—
821#95C22×D1312yes—
822#95C22×D1312yes—
823C2×C13—42no—
824C2×C13C22×C4×D411yescharacteristic
825C2×C13C2×C4×#4111yescharacteristic
826C2×C13C2×#51911yescharacteristic
827C2×C13C2×#54711yescharacteristic
828C2×C13C2×#54811yescharacteristic
829C2×C13C2×#55211yescharacteristic
830C2×C13C2×#55611yescharacteristic
831D13—42no—
832D13#236218yesdirect product factor
833C24—131no—
834C24—134no—
835C24—131no—
836C24—262no—
837C24—262no—
838C24—262no—
839C24—262no—
840C24—262no—
841C24—262no—
842C24C23×D1311yescharacteristic
843C2×Q8—22no—
844C2×Q8—22no—
845C2×Q8—138no—
846C2×Q8—134no—
847C2×Q8—264no—
848C2×Q8—264no—
849C2×Q8—2632no—
850C2×Q8—262no—
851C2×Q8—262no—
852C2×Q8C2×C4×D1314yes—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—131no—
856C22×C4—134no—
857C22×C4—134no—
858C22×C4—134no—
859C22×C4—134no—
860C22×C4—131no—
861C22×C4—131no—
862C22×C4—132no—
863C22×C4—132no—
864C22×C4—132no—
865C22×C4—131no—
866C22×C4—138no—
867C22×C4—138no—
868C22×C4—134no—
869C22×C4—134no—
870C22×C4—134no—
871C22×C4—138no—
872C22×C4—134no—
873C22×C4—134no—
874C22×C4—131no—
875C22×C4—132no—
876C22×C4—131no—
877C22×C4—262no—
878C22×C4—262no—
879C22×C4—2632no—
880C22×C4—262no—
881C22×C4—262no—
882C22×C4—264no—
883C22×C4—264no—
884C22×C4—264no—
885C22×C4—262no—
886C22×C4—264no—
887C22×C4—262no—
888C22×C4—264no—
889C22×C4—264no—
890C22×C4—262no—
891C22×C4—262no—
892C22×C4—264no—
893C22×C4—262no—
894C22×C4—262no—
895C22×C4—262no—
896C22×C4—262no—
897C22×C4—264no—
898C22×C4—262no—
899C22×C4—264no—
900C22×C4—262no—
901C22×C4—262no—
902C22×C4—262no—
903C22×C4—262no—
904C22×C4—262no—
905C22×C4C2×C4×D1314yes—
906C22×C4C23×D1311yescharacteristic
907C22×C4C23×D1312yes—
908C22×C4C23×D1311yescharacteristic
909C22×C4C23×D1311yescharacteristic
910C22×C4C23×D1312yes—
911C22×C4C23×D1312yes—
912C22×C4C23×D1312yes—
913C22×C4C23×D1311yescharacteristic
914C22×C4C23×D1311yescharacteristic
915C22×C4C23×D1311yescharacteristic
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—138no—
920C4⋊C4—138no—
921C4⋊C4—138no—
922C4⋊C4—134no—
923C4⋊C4—138no—
924C4⋊C4—138no—
925C4⋊C4—134no—
926C4⋊C4—264no—
927C4⋊C4—264no—
928C4⋊C4—264no—
929C4⋊C4—264no—
930C4⋊C4—264no—
931C4⋊C4—262no—
932C4⋊C4—264no—
933C4⋊C4—264no—
934C4⋊C4C2×C4×D1314yes—
935C4⋊C4C2×C4×D1318yes—
936C4⋊C4D4×D1314yes—
937C22⋊C4—24no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—138no—
941C22⋊C4—138no—
942C22⋊C4—138no—
943C22⋊C4—264no—
944C22⋊C4—262no—
945C22⋊C4—262no—
946C22⋊C4—264no—
947C22⋊C4—262no—
948C22⋊C4—262no—
949C22⋊C4—264no—
950C22⋊C4—262no—
951C22⋊C4—262no—
952C22⋊C4C2×C4×D1318yes—
953C42—24no—
954C42—24no—
955C42—22no—
956C42—24no—
957C42—22no—
958C42—264no—
959C42—264no—
960C42—262no—
961C42—264no—
962C42—264no—
963C42—262no—
964C42—262no—
965C42—264no—
966C42—264no—
967C42—262no—
968C42—264no—
969C42—264no—
970C42—262no—
971C42—264no—
972C42—262no—
973C13C2×#236211yescharacteristic, complemented, Sylow
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—132no—
981C23—132no—
982C23—132no—
983C23—132no—
984C23—132no—
985C23—132no—
986C23—132no—
987C23—132no—
988C23—268no—
989C23—268no—
990C23—268no—
991C23—261no—
992C23—261no—
993C23—261no—
994C23—261no—
995C23—261no—
996C23—261no—
997C23—524no—
998C23—524no—
999C23—524no—
1000C23—524no—
1001C23C22×C4×D1312yes—
1002C23C24×D1311yescharacteristic
1003Q8—28no—
1004Q8—2616no—
1005Q8—268no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—132no—
1029C2×C4—132no—
1030C2×C4—132no—
1031C2×C4—1316no—
1032C2×C4—134no—
1033C2×C4—134no—
1034C2×C4—132no—
1035C2×C4—134no—
1036C2×C4—132no—
1037C2×C4—132no—
1038C2×C4—268no—
1039C2×C4—2616no—
1040C2×C4—2616no—
1041C2×C4—268no—
1042C2×C4—268no—
1043C2×C4—268no—
1044C2×C4—2616no—
1045C2×C4—268no—
1046C2×C4—261no—
1047C2×C4—261no—
1048C2×C4—262no—
1049C2×C4—262no—
1050C2×C4—262no—
1051C2×C4—261no—
1052C2×C4—262no—
1053C2×C4—261no—
1054C2×C4—262no—
1055C2×C4—262no—
1056C2×C4—261no—
1057C2×C4—261no—
1058C2×C4—268no—
1059C2×C4—262no—
1060C2×C4—261no—
1061C2×C4—261no—
1062C2×C4—261no—
1063C2×C4—261no—
1064C2×C4—262no—
1065C2×C4—261no—
1066C2×C4—262no—
1067C2×C4—261no—
1068C2×C4—524no—
1069C2×C4—528no—
1070C2×C4—524no—
1071C2×C4C22×C4×D1314yes—
1072C2×C4C22×C4×D1314yes—
1073C2×C4C22×C4×D1312yes—
1074C2×C4C22×C4×D1312yes—
1075C2×C4C2×D4×D1314yes—
1076C2×C4C2×D4×D1312yes—
1077C2×C4#41×D1312yes—
1078C2×C4#41×D1312yes—
1079C2×C4#41×D1312yes—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—134no—
1088C22—134no—
1089C22—134no—
1090C22—134no—
1091C22—134no—
1092C22—134no—
1093C22—134no—
1094C22—262no—
1095C22—262no—
1096C22—262no—
1097C22—5216no—
1098C22—521no—
1099C22—521no—
1100C22—521no—
1101C22—521no—
1102C22C23×C4×D1311yescharacteristic
1103C22C22×D4×D1311yescharacteristic
1104C22C2×#41×D1311yescharacteristic
1105C22C2×#41×D1311yescharacteristic
1106C22C2×#41×D1311yescharacteristic
1107C22D13×2−1+411yescharacteristic
1108C22D13×2−1+411yescharacteristic
1109C4—22no—
1110C4—24no—
1111C4—24no—
1112C4—24no—
1113C4—22no—
1114C4—22no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—134no—
1119C4—262no—
1120C4—264no—
1121C4—264no—
1122C4—264no—
1123C4—262no—
1124C4—262no—
1125C4—521no—
1126C4—522no—
1127C4—521no—
1128C4C4×D4×D1314yes—
1129C2—42no—
1130C2—138no—
1131C2—522no—
1132C2C2×C4×D4×D1311yescharacteristic
1133C2C4×#41×D1311yescharacteristic
1134C2D13×#51911yescharacteristic
1135C2D13×#54711yescharacteristic
1136C2D13×#54811yescharacteristic
1137C2D13×#55211yescharacteristic
1138C2D13×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2362C2
socle, cosocleC23×C13C25
prime radicalC24×D13C23
hypercenter#2362D13
hypocenterC13C2×#2362
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D13C2semidirect
4. #13117868C2semidirect
5. #13117867C2semidirect
6. #13117866C2semidirect
7. #13117865C2semidirect
8. #13117864C2semidirect
9. #13117863C2semidirect
10. #13117862C2semidirect
11. #13117861C2semidirect
12. #13117860C2semidirect
13. #13117859C2semidirect
14. #13117858C2semidirect
15. D13×#391C2semidirect
16. D13×#389C2semidirect
19. D13×#387C2semidirect
20. C4×C4⋊C4×D13C2semidirect
21. C4×C4⋊C4×D13C2semidirect
23. C13×#2362C2semidirect
27. C2×C4×Q8×C13C22semidirect
30. C2×Q8×Dic13C22semidirect
33. D13×C22⋊Q8C4semidirect
46. C2×#88141C22semidirect
47. C2×#88141C22semidirect
60. C2×C4×Dic26C22semidirect
61. C2×C4×Dic26C22semidirect
62. C13×#391C22semidirect
63. C13×#389C22semidirect
66. C13×#387C22semidirect
67. C4×C13×C4⋊C4C22semidirect
68. C4×C13×C4⋊C4C22semidirect
70. #11718891C22semidirect
74. #11718646C22semidirect
75. #11718642C22semidirect
76. #11718639C22semidirect
77. C4⋊C4×Dic13C22semidirect
78. C4⋊C4×Dic13C22semidirect
79. C4⋊C4×Dic13C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. #11718635C22semidirect
82. #11718634C22semidirect
83. #11718633C22semidirect
96. C4×C4⋊Dic13C22semidirect
97. C4×C4⋊Dic13C22semidirect
98. #11718594C22semidirect
99. C4×#6101C22semidirect
100. C4×#6101C22semidirect
101. C4×#6101C22semidirect
102. #11718590C22semidirect
103. #11718589C22semidirect
116. #11718316C22semidirect
117. #11718315C22semidirect
118. #11718314C22semidirect
119. #11718313C22semidirect
120. #11718310C22semidirect
121. #11718310C22semidirect
122. #11718310C22semidirect
123. #11718308C22semidirect
124. #11718307C22semidirect
125. #11718307C22semidirect
150. C13×C22⋊Q8C2×C4semidirect
172. #88200C2×C4semidirect
189. #88178C2×C4semidirect
214. #88151C2×C4semidirect
215. #88150C2×C4semidirect
230. #88132C2×C4semidirect
419. #2362D13direct (N × H)
549. C2×C4×Q8C2×D13semidirect
577. #391C2×D13semidirect
583. #389C2×D13semidirect
607. #387C2×D13semidirect
620. C4×C4⋊C4C2×D13semidirect
621. C4×C4⋊C4C2×D13semidirect
714. C22⋊Q8C4×D13semidirect
832. D13#2362direct (N × H)
973. C13C2×#2362semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
C2×C4×Q8×D132
C2×D13×#1172
#131178682
#131178672
#131178662
#131178652
#131178642
#131178632
#131178622
#131178612
#131178602
#131178592
#131178582
D13×#3912
D13×#3892
D13×#3882
D13×#3872
C4×C4⋊C4×D132
C4×C22⋊C4×D132
C13×#23622
C2×#236213