Finite Group Databasebeta

← D13×#3501 #16770814

Subgroups — D13×#3501 #16770814

Order 3328.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128639C211yesmaximal, characteristic, complemented
2#13128638C212yesmaximal, complemented
3#13128637C212yesmaximal, complemented
4#13128636C214yesmaximal, complemented
5#13128635C218yesmaximal, complemented
6#13128634C212yesmaximal, complemented
7#13128633C214yesmaximal, complemented
8#13128632C214yesmaximal, complemented
9#13128631C214yesmaximal, complemented
10D13×#554C218yesmaximal, complemented
11D13×#554C214yesmaximal, complemented
12D4×Q8×D13C214yesmaximal, complemented
13D13×#544C212yesmaximal, complemented
14D13×#543C214yesmaximal, complemented
15D13×#533C212yesmaximal, complemented
16C2×D13×C22⋊Q8C214yesmaximal, complemented
17D13×#518C212yesmaximal
18C2×C4×D4×D13C211yesmaximal, characteristic
19C13×#3501C211yesmaximal, characteristic, complemented
20C22×Q8×D13C2214yescomplemented
21C22×D4×D13C2211yescharacteristic
22C23×C4×D13C2212yes—
23C13×#554C2214yescomplemented
24C13×#554C2218yescomplemented
25D4×Q8×C13C2214yescomplemented
26C13×#544C2212yescomplemented
27C13×#543C2214yescomplemented
28C13×#533C2212yescomplemented
29C2×C13×C22⋊Q8C2214yescomplemented
30C13×#518C2212yes—
31C2×C4×D4×C13C2211yescharacteristic
32Q8×C22⋊D13C2218yescomplemented
33C2×#88200C2214yescomplemented
34#11719503C2212yes—
35C2×D4×Dic13C2211yescharacteristic
36C2×C4×C22⋊D13C2212yes—
37C2×#88178C2214yescomplemented
38#11719435C2218yescomplemented
39#11719435C2214yescomplemented
40#11719434C2218yescomplemented
41#11719433C2212yescomplemented
42#11719433C2212yescomplemented
43#11719432C2214yescomplemented
44#11719432C2218yescomplemented
45D13×C4⋊Q8C2218yescomplemented
46D13×C4⋊Q8C2212yescomplemented
47D13×C4⋊Q8C2212yescomplemented
48#11719395C2218yescomplemented
49#11719395C2218yescomplemented
50#11719395C2218yescomplemented
51#11719394C2218yescomplemented
52#11719393C2214yescomplemented
53D13×#125C2218yescomplemented
54D13×#125C2214yescomplemented
55#11719341C22116yescomplemented
56#11719341C22116yescomplemented
57#11719341C22116yescomplemented
58#11719340C2218yescomplemented
59#11719340C22116yescomplemented
60#11719339C2218yescomplemented
61#11719339C2218yescomplemented
62#11719339C22116yescomplemented
63#11719339C22116yescomplemented
64#11719337C2218yescomplemented
65#11719337C22116yescomplemented
66D13×C22⋊Q8C2214yes—
67D13×C22⋊Q8C2218yes—
68D13×C22⋊Q8C2214yes—
69D13×C22⋊Q8C2218yescomplemented
70D13×C22⋊Q8C2218yescomplemented
71D13×C22⋊Q8C22116yescomplemented
72D13×C22⋊Q8C22116yescomplemented
73D13×C22⋊Q8C2218yescomplemented
74D13×C22⋊Q8C2218yescomplemented
75D13×C22⋊Q8C2218yescomplemented
76D13×C22⋊Q8C2218yescomplemented
77#11719328C2218yescomplemented
78#11719327C2214yescomplemented
79#11719327C2214yescomplemented
80#11719284C2214yescomplemented
81#11719284C2218yescomplemented
82#11719283C2214yescomplemented
83#11719283C2214yescomplemented
84Q8×D52C2214yescomplemented
85C4×Q8×D13C2214yescomplemented
86C4×Q8×D13C2214yescomplemented
87#11719250C2218yes—
88#11719250C2218yes—
89C4×D4×D13C2214yes—
90C4×D4×D13C2214yes—
91C4×D4×D13C2214yes—
92C4×D4×D13C2214yes—
93C4×D4×D13C2218yes—
94C4×D4×D13C2218yes—
95#11719248C2214yescomplemented
96#11719248C2218yescomplemented
97#11719244C2218yescomplemented
98#11719244C2218yescomplemented
99#11719244C2218yescomplemented
100D4×Dic26C2214yescomplemented
101D4×Dic26C2218yescomplemented
102#11719226C2214yes—
103D13×#117C2214yes—
104#11719224C2214yescomplemented
105#11719222C2214yescomplemented
106#11719216C2218yescomplemented
107#11719216C22116yescomplemented
108C2×#88151C2214yescomplemented
109C2×#88150C2218yescomplemented
110C2×#88147C2211yescharacteristic
111C2×C4⋊C4×D13C2211yescharacteristic
112C2×C4⋊C4×D13C2214yescomplemented
113C2×C4⋊C4×D13C2218yescomplemented
114#11719205C2212yescomplemented
115#11719191C2218yes—
116C2×#88135C2212yes—
117C2×C22⋊C4×D13C2212yes—
118C2×C22⋊C4×D13C2218yes—
119#11719188C2218yescomplemented
120#11719188C2214yescomplemented
121C2×#88132C2218yescomplemented
122C2×C4×D52C2211yescharacteristic
123C2×C42×D13C2211yescharacteristic
124#11719175C2212yescomplemented
125C24×D13C2312yes—
126C22×Q8×C13C2314yescomplemented
127C22×D4×C13C2311yescharacteristic
128C23×C4×C13C2312yes—
129C22×C22⋊D13C2312yes—
130C23×Dic13C2312yes—
131C2×Q8×D13—416no—
132C2×Q8×D13C2314yes—
133C2×Q8×D13C2318yes—
134C2×Q8×D13C2314yes—
135C2×Q8×D13C2318yescomplemented
136C2×Q8×D13C2318yescomplemented
137C2×D4×D13Q8116yescomplemented
138C2×D4×D13C2314yes—
139C2×D4×D13C2314yes—
140C22×D52C2311yescharacteristic
141C22×C4×D13—48no—
142C22×C4×D13C2311yescharacteristic
143C22×C4×D13C2314yes—
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2312yes—
146C22×C4×D13C2312yes—
147C22×C4×D13C2318yes—
148C22×C4×D13C2318yes—
149C22×C4×D13C2312yes—
150C22×C4×D13C2314yes—
151C22×C4×D13C2314yes—
152C22×C4×D13C2314yes—
153C22×C4×D13C2311yescharacteristic
154C22×Dic26C2318yescomplemented
155C22×Dic26C2314yescomplemented
156C13×C4⋊Q8C2312yescomplemented
157C13×C4⋊Q8C2318yescomplemented
158C13×C4⋊Q8C2312yescomplemented
159C13×#125C2314yescomplemented
160C13×#125C2318yescomplemented
161C13×C22⋊Q8C2314yes—
162C13×C22⋊Q8C2318yes—
163C13×C22⋊Q8C2314yes—
164C13×C22⋊Q8C2318yescomplemented
165C13×C22⋊Q8C2318yescomplemented
166C13×C22⋊Q8C23116yescomplemented
167C13×C22⋊Q8C23116yescomplemented
168C4×Q8×C13C2314yescomplemented
169C4×Q8×C13C2314yescomplemented
170C4×D4×C13C2318yes—
171C4×D4×C13C2314yes—
172C4×D4×C13C2314yes—
173C4×D4×C13C2318yes—
174C13×#117C2314yes—
175C2×C13×C4⋊C4C2311yescharacteristic
176C2×C13×C4⋊C4C2318yescomplemented
177C2×C13×C4⋊C4C2314yescomplemented
178C2×C13×C22⋊C4C2318yes—
179C2×C13×C22⋊C4C2312yes—
180C2×C42×C13C2311yescharacteristic
181C2×C22⋊Dic13C2318yes—
182C2×C22⋊Dic13C2312yes—
183#88200C2314yes—
184#88200C2314yes—
185#88200C2318yes—
186#88200C23116yescomplemented
187#88200C2318yescomplemented
188#88200C2318yescomplemented
189#88200C23116yescomplemented
190Q8×Dic13C2314yescomplemented
191Q8×Dic13C2314yescomplemented
192#88198C23116yescomplemented
193#88198C2314yescomplemented
194#88198C2314yescomplemented
195D4×Dic13C2314yes—
196D4×Dic13C2318yes—
197D4×Dic13C2318yes—
198D4×Dic13C2314yes—
199C4×C22⋊D13C23116yes—
200C4×C22⋊D13C23116yes—
201C4×C22⋊D13C2318yes—
202C4×C22⋊D13C2318yes—
203C2×#6103C2312yes—
204C2×#6103C2312yes—
205C2×#6103C2318yes—
206C2×#6103C2318yes—
207#88180C2314yes—
208C2×C4⋊Dic13C2311yescharacteristic
209C2×C4⋊Dic13C2318yescomplemented
210C2×C4⋊Dic13C2314yescomplemented
211#88178C2314yes—
212#88178C2314yes—
213#88178C2318yes—
214#88178C23116yescomplemented
215#88178C23116yescomplemented
216#88178C2318yescomplemented
217#88178C2318yescomplemented
218C2×#6101C2312yes—
219C2×#6101C2318yescomplemented
220C2×#6101C2318yescomplemented
221C2×#6101C2318yescomplemented
222C2×C4×Dic13C2311yescharacteristic
223C2×C4×Dic13C2311yescharacteristic
224C2×C4×Dic13C2311yescharacteristic
225#88151C2314yes—
226#88151C2314yes—
227#88151C2318yes—
228#88151C2318yescomplemented
229#88151C23116yescomplemented
230#88151C2318yescomplemented
231#88151C23116yescomplemented
232#88150C23116yes—
233#88150C2318yes—
234#88150C2318yes—
235#88150C23116yescomplemented
236#88150C23116yescomplemented
237#88150C23116yescomplemented
238#88150C23116yescomplemented
239#88150C23116yescomplemented
240#88150C23116yescomplemented
241#88147C2318yes—
242#88147C2314yes—
243#88147C2314yes—
244#88147C2318yes—
245#88146C2314yes—
246#88146C2314yes—
247C4⋊C4×D13C2314yes—
248C4⋊C4×D13C2314yes—
249C4⋊C4×D13C2314yes—
250C4⋊C4×D13C23116yes—
251C4⋊C4×D13C2314yes—
252C4⋊C4×D13C2314yes—
253C4⋊C4×D13C2314yes—
254C4⋊C4×D13C2318yes—
255C4⋊C4×D13C2318yes—
256C4⋊C4×D13C2318yes—
257C4⋊C4×D13C2318yescomplemented
258C4⋊C4×D13C23116yescomplemented
259C4⋊C4×D13C23116yescomplemented
260C4⋊C4×D13C2318yescomplemented
261#88144C2314yescomplemented
262#88144C2314yescomplemented
263#88144C2318yescomplemented
264#88144C2318yescomplemented
265#88143C23116yescomplemented
266#88143C2318yescomplemented
267#88143C23116yescomplemented
268#88143C2318yescomplemented
269#88142C2314yescomplemented
270#88142C2318yescomplemented
271#88142C2318yescomplemented
272#88142C2314yescomplemented
273#88142C23116yescomplemented
274#88142C2314yescomplemented
275#88142C2314yescomplemented
276#88141C2314yescomplemented
277#88141C2314yescomplemented
278#88141C2318yescomplemented
279#88141C2318yescomplemented
280#88135C2318yes—
281#88135C2318yes—
282#88135C23116yes—
283#88135C23116yes—
284C22⋊C4×D13C2318yes—
285C22⋊C4×D13C23116yes—
286C22⋊C4×D13C2318yes—
287C22⋊C4×D13C23116yes—
288C22⋊C4×D13C2318yes—
289C22⋊C4×D13C23116yes—
290#88132C2318yes—
291#88132C23116yes—
292#88132C2318yes—
293#88132C23116yescomplemented
294#88132C23116yescomplemented
295#88132C23116yescomplemented
296#88132C23116yescomplemented
297#88132C23116yescomplemented
298#88132C23116yescomplemented
299#88131C2318yes—
300C4×D52C2314yes—
301C4×D52C2318yes—
302C4×D52C2314yes—
303C4×D52C2318yes—
304#88126C2318yes—
305C42×D13C2312yes—
306C42×D13C2318yes—
307C42×D13C2312yes—
308C42×D13C2312yes—
309C42×D13C2312yes—
310#88124C2314yescomplemented
311#88124C2318yescomplemented
312#88123C2312yescomplemented
313#88123C2312yescomplemented
314#88123C2318yescomplemented
315C4×Dic26C2314yescomplemented
316C4×Dic26C2314yescomplemented
317C4×Dic26C2318yescomplemented
318C4×Dic26C2318yescomplemented
319C2×#3501—131nomaximal, Sylow
320C24×C13C2412yes—
321C23×D13—44no—
322C23×D13—44no—
323C23×D13C2×Q8116yescomplemented
324C23×D13C2411yescharacteristic
325C23×D13C2414yes—
326C23×D13C2412yes—
327C23×D13C2414yes—
328C2×Q8×C13—48no—
329C2×Q8×C13C2414yes—
330C2×Q8×C13C2418yes—
331C2×Q8×C13C2414yes—
332C2×D4×C13C2×Q818yescomplemented
333C2×D4×C13C2414yes—
334C22×C4×C13—44no—
335C22×C4×C13C2411yescharacteristic
336C22×C4×C13C2414yes—
337C22×C4×C13C2411yescharacteristic
338C22×C4×C13C2412yes—
339C22×C4×C13C2414yes—
340C22×C4×C13C2418yes—
341C22×C4×C13C2418yes—
342C22×C4×C13C2411yescharacteristic
343C2×C22⋊D13C2×Q8116yescomplemented
344C2×C22⋊D13C2418yes—
345C22×Dic13—44no—
346C22×Dic13C2411yescharacteristic
347C22×Dic13C2414yes—
348C22×Dic13C2411yescharacteristic
349C22×Dic13C2412yes—
350C22×Dic13C2418yes—
351C22×Dic13C2414yes—
352C22×Dic13C2418yes—
353C22×Dic13C2411yescharacteristic
354Q8×D13—216no—
355Q8×D13—416no—
356Q8×D13—416no—
357Q8×D13—416no—
358Q8×D13—48no—
359D4×D13C2×Q8132yescomplemented
360D4×D13C2×Q8132yescomplemented
361C2×D52C2×Q818yescomplemented
362C2×D52C2414yes—
363C2×C4×D13—24no—
364C2×C4×D13—216no—
365C2×C4×D13—48no—
366C2×C4×D13—44no—
367C2×C4×D13—48no—
368C2×C4×D13—44no—
369C2×C4×D13—48no—
370C2×C4×D13—44no—
371C2×C4×D13—416no—
372C2×C4×D13—42no—
373C2×C4×D13—416no—
374C2×C4×D13C2×Q818yescomplemented
375C2×C4×D13C2412yes—
376C2×C4×D13C2411yescharacteristic
377C2×C4×D13C2411yescharacteristic
378C2×C4×D13C2411yescharacteristic
379C2×C4×D13C2418yes—
380C2×C4×D13C2418yes—
381C2×C4×D13C2414yes—
382C2×C4×D13C2414yes—
383C2×C4×D13C2414yes—
384C2×C4×D13C2412yes—
385C2×C4×D13C2414yes—
386C2×C4×D13C24116yes—
387C2×C4×D13C24116yes—
388C2×C4×D13C2414yes—
389C2×C4×D13C2414yes—
390C2×C4×D13C2412yes—
391C2×C4×D13C2412yes—
392C2×C4×D13C2411yescharacteristic
393C2×Dic26—416no—
394C2×Dic26—48no—
395C2×Dic26C2414yes—
396C2×Dic26C2418yes—
397C2×Dic26C2414yes—
398C2×Dic26C2418yes—
399C2×Dic26C24116yes—
400C2×Dic26C2418yes—
401C13×C4⋊C4C2414yes—
402C13×C4⋊C4C2414yes—
403C13×C4⋊C4C2418yes—
404C13×C4⋊C4C2418yes—
405C13×C4⋊C4C2414yes—
406C13×C4⋊C4C2414yes—
407C13×C4⋊C4C24116yes—
408C13×C4⋊C4C2414yes—
409C13×C4⋊C4C2418yes—
410C13×C22⋊C4C2418yes—
411C13×C22⋊C4C2418yes—
412C13×C22⋊C4C24116yes—
413C42×C13C2412yes—
414C42×C13C2418yes—
415C42×C13C2412yes—
416C22⋊Dic13C2418yes—
417C22⋊Dic13C2418yes—
418C22⋊Dic13C24116yes—
419#6103C2418yes—
420#6103C2418yes—
421#6103C2418yes—
422#6103C24116yes—
423#6103C24116yes—
424#6103C2418yes—
425C4⋊Dic13C2414yes—
426C4⋊Dic13C2414yes—
427C4⋊Dic13C2418yes—
428C4⋊Dic13C2418yes—
429C4⋊Dic13C2414yes—
430C4⋊Dic13C2414yes—
431C4⋊Dic13C2414yes—
432C4⋊Dic13C24116yes—
433C4⋊Dic13C2418yes—
434#6101C2418yes—
435#6101C2418yes—
436#6101C2418yes—
437#6101C2418yes—
438#6101C2418yes—
439#6101C2418yes—
440#6101C24116yes—
441#6101C24116yes—
442#6101C2418yes—
443#6101C2418yes—
444#6101C24116yes—
445#6101C2418yes—
446C4×Dic13C2412yes—
447C4×Dic13C2412yes—
448C4×Dic13C2418yes—
449C4×Dic13C2412yes—
450C4×Dic13C2412yes—
451C4×Dic13C2412yes—
452C4×Dic13C2412yes—
453C4×Dic13C2418yes—
454C4×Dic13C2418yes—
455#3501—134no—
456#3501—138no—
457#3501—134no—
458#3501—132no—
459#3501—134no—
460#3501—132no—
461#3501—134no—
462#3501—132no—
463#3501—131no—
464#3501D1311yescharacteristic, direct product factor
465C2×#554—134no—
466C2×#554—138no—
467C2×D4×Q8—134no—
468C2×#544—132no—
469C2×#543—134no—
470C2×#533—132no—
471C22×C22⋊Q8—134no—
472C2×#518—132no—
473C22×C4×D4—131no—
474C23×C13—42no—
475C23×C13—42no—
476C23×C13C22×Q818yescomplemented
477C23×C13C2511yescharacteristic
478C23×C13C2514yes—
479C22×D13—28no—
480C22×D13—22no—
481C22×D13—28no—
482C22×D13—22no—
483C22×D13—432no—
484C22×D13—42no—
485C22×D13—44no—
486C22×D13—42no—
487C22×D13—44no—
488C22×D13C22×Q814yes—
489C22×D13C22×Q8116yes—
490C22×D13C22×Q818yescomplemented
491C22×D13C22×Q8116yescomplemented
492C22×D13C2511yescharacteristic
493C22×D13C2514yes—
494C22×D13C2511yescharacteristic
495Q8×C13—28no—
496Q8×C13—48no—
497Q8×C13—44no—
498D4×C13C22×Q8116yescomplemented
499C2×C4×C13—28no—
500C2×C4×C13—22no—
501C2×C4×C13—48no—
502C2×C4×C13—42no—
503C2×C4×C13—44no—
504C2×C4×C13—41no—
505C2×C4×C13—48no—
506C2×C4×C13C22×Q814yescomplemented
507C2×C4×C13C2511yescharacteristic
508C2×C4×C13C2512yes—
509C2×C4×C13C2518yes—
510C2×C4×C13C2518yes—
511C2×C4×C13C2514yes—
512C2×C4×C13C2512yes—
513C2×C4×C13C2511yescharacteristic
514C22⋊D13C22×Q8132yescomplemented
515C2×Dic13—28no—
516C2×Dic13—22no—
517C2×Dic13—48no—
518C2×Dic13—42no—
519C2×Dic13—44no—
520C2×Dic13—41no—
521C2×Dic13—48no—
522C2×Dic13C22×Q814yescomplemented
523C2×Dic13C2511yescharacteristic
524C2×Dic13C2512yes—
525C2×Dic13C2518yes—
526C2×Dic13C2518yes—
527C2×Dic13C2514yes—
528C2×Dic13C2512yes—
529C2×Dic13C2511yescharacteristic
530D52C22×Q8116yescomplemented
531C4×D13—22no—
532C4×D13—28no—
533C4×D13—216no—
534C4×D13—216no—
535C4×D13—24no—
536C4×D13—22no—
537C4×D13—28no—
538C4×D13—22no—
539C4×D13—28no—
540C4×D13—44no—
541C4×D13—44no—
542C4×D13—44no—
543C4×D13—42no—
544C4×D13—416no—
545C4×D13—416no—
546C4×D13C22×Q818yes—
547C4×D13C22×Q818yescomplemented
548C4×D13H(5,𝔽2)14yes—
549Dic26—28no—
550Dic26—216no—
551Dic26—48no—
552Dic26—416no—
553Dic26—48no—
554Dic26—44no—
555C23×Q8—134no—
556C23×D4—131no—
557C24×C4—132no—
558#554—138no—
559#554—134no—
560#554—138no—
561#554—138no—
562#554—138no—
563#554—138no—
564#554—1316no—
565#554—1316no—
566#554—1316no—
567#554—1316no—
568#554—134no—
569#554—138no—
570#554—138no—
571#554—138no—
572#554—138no—
573#554—138no—
574#554—134no—
575#554—138no—
576#554—1316no—
577#554C2×D1314yescomplemented
578#554C2×D1318yescomplemented
579D4×Q8—138no—
580D4×Q8—138no—
581D4×Q8—134no—
582D4×Q8—138no—
583D4×Q8—1316no—
584D4×Q8—134no—
585D4×Q8—138no—
586D4×Q8—134no—
587D4×Q8C2×D1314yescomplemented
588#544—138no—
589#544—138no—
590#544—138no—
591#544—134no—
592#544—132no—
593#544C2×D1312yescomplemented
594#543—138no—
595#543—138no—
596#543—1316no—
597#543—1316no—
598#543—138no—
599#543—134no—
600#543C2×D1314yescomplemented
601#533—132no—
602#533—132no—
603#533—134no—
604#533—134no—
605#533—134no—
606#533—134no—
607#533—134no—
608#533—134no—
609#533—132no—
610#533C2×D1312yescomplemented
611C2×C4⋊Q8—132no—
612C2×C4⋊Q8—132no—
613C2×C4⋊Q8—138no—
614C2×#125—134no—
615C2×#125—138no—
616C2×C22⋊Q8—134no—
617C2×C22⋊Q8—134no—
618C2×C22⋊Q8—134no—
619C2×C22⋊Q8—138no—
620C2×C22⋊Q8—138no—
621C2×C22⋊Q8—138no—
622C2×C22⋊Q8—134no—
623C2×C22⋊Q8—138no—
624C2×C22⋊Q8—138no—
625C2×C22⋊Q8—138no—
626C2×C22⋊Q8—138no—
627C2×C22⋊Q8—1316no—
628C2×C22⋊Q8—1316no—
629C2×C22⋊Q8—138no—
630C2×C22⋊Q8—134no—
631C2×C22⋊Q8—138no—
632C2×C22⋊Q8C2×D1314yescomplemented
633#518—132no—
634#518—138no—
635#518—138no—
636#518—134no—
637#518—138no—
638#518C2×D1312yes—
639C2×C4×Q8—134no—
640C2×C4×Q8—134no—
641C2×C4×D4—131no—
642C2×C4×D4—132no—
643C2×C4×D4—134no—
644C2×C4×D4—134no—
645C2×C4×D4—134no—
646C2×C4×D4—134no—
647C2×C4×D4—138no—
648C2×C4×D4—138no—
649C2×C4×D4—131no—
650C2×C4×D4—132no—
651C2×C4×D4—131no—
652C2×C4×D4C2×D1311yescharacteristic
653C2×#117—134no—
654C22×C4⋊C4—131no—
655C22×C4⋊C4—138no—
656C22×C4⋊C4—134no—
657C22×C22⋊C4—132no—
658C22×C22⋊C4—138no—
659C22×C42—131no—
660C22×C13—24no—
661C22×C13—21no—
662C22×C13—24no—
663C22×C13—21no—
664C22×C13—48no—
665C22×C13C23×Q812yes—
666C22×C13C23×Q818yes—
667C22×C13C2611yescharacteristic
668C2×D13—24no—
669C2×D13—21no—
670C2×D13—24no—
671C2×D13—21no—
672C2×D13—28no—
673C2×D13—232no—
674C2×D13—416no—
675C2×D13—48no—
676C2×D13C23×Q812yes—
677C2×D13C23×Q818yes—
678C2×D13C23×Q812yes—
679C2×D13C2×H(5,𝔽2)12yes—
680C2×D13#58512yes—
681C4×C13—28no—
682C4×C13—24no—
683C4×C13—21no—
684C4×C13—22no—
685C4×C13—28no—
686C4×C13C23×Q814yes—
687C4×C13C2×H(5,𝔽2)12yes—
688Dic13—28no—
689Dic13—24no—
690Dic13—21no—
691Dic13—22no—
692Dic13—28no—
693Dic13C23×Q814yes—
694Dic13C2×H(5,𝔽2)12yes—
695C25—132no—
696C22×Q8—134no—
697C22×Q8—134no—
698C22×Q8—138no—
699C22×Q8—138no—
700C22×Q8—138no—
701C22×Q8—138no—
702C22×Q8—134no—
703C22×Q8—5216no—
704C22×Q8C22×D1314yescomplemented
705C22×D4—132no—
706C22×D4—1316no—
707C22×D4—134no—
708C22×D4—134no—
709C22×D4—131no—
710C22×D4C22×D1311yescharacteristic
711C23×C4—131no—
712C23×C4—132no—
713C23×C4—134no—
714C23×C4—131no—
715C23×C4—131no—
716C23×C4—138no—
717C23×C4—138no—
718C23×C4—132no—
719C23×C4—134no—
720C23×C4—132no—
721C23×C4—134no—
722C23×C4—132no—
723C23×C4—134no—
724C23×C4—528no—
725C23×C4C22×D1312yes—
726C4⋊Q8—134no—
727C4⋊Q8—134no—
728C4⋊Q8—1316no—
729C4⋊Q8—134no—
730C4⋊Q8—134no—
731C4⋊Q8—134no—
732C4⋊Q8—134no—
733C4⋊Q8—1316no—
734C4⋊Q8—138no—
735C4⋊Q8—138no—
736C4⋊Q8—132no—
737C4⋊Q8—132no—
738C4⋊Q8—138no—
739C4⋊Q8C22×D1312yescomplemented
740C4⋊Q8C22×D1312yescomplemented
741C4⋊Q8C22×D1318yescomplemented
742#125—138no—
743#125—138no—
744#125—134no—
745#125—134no—
746#125—1316no—
747#125—1316no—
748#125—138no—
749#125—138no—
750#125—134no—
751#125—138no—
752#125C22×D1314yescomplemented
753#125C22×D1318yescomplemented
754C22⋊Q8—134no—
755C22⋊Q8—138no—
756C22⋊Q8—138no—
757C22⋊Q8—138no—
758C22⋊Q8—134no—
759C22⋊Q8—1316no—
760C22⋊Q8—1316no—
761C22⋊Q8—134no—
762C22⋊Q8—138no—
763C22⋊Q8—138no—
764C22⋊Q8—138no—
765C22⋊Q8—134no—
766C22⋊Q8—1316no—
767C22⋊Q8—1316no—
768C22⋊Q8—138no—
769C22⋊Q8—134no—
770C22⋊Q8—1316no—
771C22⋊Q8—138no—
772C22⋊Q8—1316no—
773C22⋊Q8—138no—
774C22⋊Q8—1316no—
775C22⋊Q8—138no—
776C22⋊Q8—138no—
777C22⋊Q8—134no—
778C22⋊Q8—1316no—
779C22⋊Q8—1316no—
780C22⋊Q8—1316no—
781C22⋊Q8—1316no—
782C22⋊Q8—1316no—
783C22⋊Q8—1316no—
784C22⋊Q8—138no—
785C22⋊Q8—1316no—
786C22⋊Q8—1316no—
787C22⋊Q8—1316no—
788C22⋊Q8—138no—
789C22⋊Q8—1316no—
790C22⋊Q8—1316no—
791C22⋊Q8—1316no—
792C22⋊Q8—1316no—
793C22⋊Q8C22×D1314yes—
794C22⋊Q8C22×D1318yes—
795C22⋊Q8C22×D1314yes—
796C22⋊Q8C22×D1318yescomplemented
797C22⋊Q8C22×D1318yescomplemented
798C22⋊Q8C22×D13116yescomplemented
799C22⋊Q8C22×D13116yescomplemented
800C4×Q8—134no—
801C4×Q8—134no—
802C4×Q8—138no—
803C4×Q8—134no—
804C4×Q8—134no—
805C4×Q8—138no—
806C4×Q8—138no—
807C4×Q8—134no—
808C4×Q8—138no—
809C4×Q8—134no—
810C4×Q8C22×D1314yescomplemented
811C4×Q8C22×D1314yescomplemented
812C4×D4—134no—
813C4×D4—134no—
814C4×D4—138no—
815C4×D4—138no—
816C4×D4—138no—
817C4×D4—138no—
818C4×D4—1316no—
819C4×D4—1316no—
820C4×D4—134no—
821C4×D4—134no—
822C4×D4—138no—
823C4×D4—138no—
824C4×D4—138no—
825C4×D4—138no—
826C4×D4—1316no—
827C4×D4—1316no—
828C4×D4—134no—
829C4×D4—134no—
830C4×D4—138no—
831C4×D4—138no—
832C4×D4C22×D1314yes—
833C4×D4C22×D1314yes—
834C4×D4C22×D1318yes—
835C4×D4C22×D1318yes—
836#117—134no—
837#117—134no—
838#117—134no—
839#117—138no—
840#117—138no—
841#117C22×D1314yes—
842C2×C4⋊C4—132no—
843C2×C4⋊C4—131no—
844C2×C4⋊C4—138no—
845C2×C4⋊C4—138no—
846C2×C4⋊C4—138no—
847C2×C4⋊C4—138no—
848C2×C4⋊C4—134no—
849C2×C4⋊C4—138no—
850C2×C4⋊C4—134no—
851C2×C4⋊C4—134no—
852C2×C4⋊C4—134no—
853C2×C4⋊C4—138no—
854C2×C4⋊C4—1316no—
855C2×C4⋊C4—1316no—
856C2×C4⋊C4—1316no—
857C2×C4⋊C4—138no—
858C2×C4⋊C4—138no—
859C2×C4⋊C4—134no—
860C2×C4⋊C4—134no—
861C2×C4⋊C4—138no—
862C2×C4⋊C4—134no—
863C2×C4⋊C4C22×D1311yescharacteristic
864C2×C4⋊C4C22×D1318yescomplemented
865C2×C4⋊C4C22×D1314yescomplemented
866C2×C22⋊C4—132no—
867C2×C22⋊C4—138no—
868C2×C22⋊C4—132no—
869C2×C22⋊C4—132no—
870C2×C22⋊C4—138no—
871C2×C22⋊C4—138no—
872C2×C22⋊C4—138no—
873C2×C22⋊C4—138no—
874C2×C22⋊C4—1316no—
875C2×C22⋊C4—138no—
876C2×C22⋊C4—1316no—
877C2×C22⋊C4—1316no—
878C2×C22⋊C4C22×D1312yes—
879C2×C22⋊C4C22×D1318yes—
880C2×C42—131no—
881C2×C42—131no—
882C2×C42—131no—
883C2×C42—138no—
884C2×C42—132no—
885C2×C42—132no—
886C2×C42—132no—
887C2×C42—132no—
888C2×C42C22×D1311yescharacteristic
889C2×C13—22no—
890C2×C13—28no—
891C2×C13C24×Q811yescharacteristic
892C2×C13C22×H(5,𝔽2)11yescharacteristic
893C2×C13C2×#58511yescharacteristic
894D13—22no—
895D13—28no—
896D13#350114yesdirect product factor
897C24—131no—
898C24—134no—
899C24—1316no—
900C24—134no—
901C24—132no—
902C24—524no—
903C24—524no—
904C24C23×D1312yes—
905C2×Q8—48no—
906C2×Q8—138no—
907C2×Q8—134no—
908C2×Q8—138no—
909C2×Q8—134no—
910C2×Q8—138no—
911C2×Q8—1316no—
912C2×Q8—2616no—
913C2×Q8—528no—
914C2×Q8—5216no—
915C2×Q8—5216no—
916C2×Q8—528no—
917C2×Q8—5216no—
918C2×Q8—5216no—
919C2×Q8C23×D1314yes—
920C2×Q8C23×D1314yes—
921C2×Q8C23×D1318yes—
922C2×D4—1316no—
923C2×D4—138no—
924C2×D4—1332no—
925C2×D4—1332no—
926C2×D4—138no—
927C2×D4—134no—
928C2×D4Q8×D1318yescomplemented
929C2×D4C23×D1314yes—
930C22×C4—44no—
931C22×C4—131no—
932C22×C4—138no—
933C22×C4—132no—
934C22×C4—131no—
935C22×C4—132no—
936C22×C4—131no—
937C22×C4—134no—
938C22×C4—131no—
939C22×C4—138no—
940C22×C4—138no—
941C22×C4—132no—
942C22×C4—134no—
943C22×C4—132no—
944C22×C4—131no—
945C22×C4—131no—
946C22×C4—131no—
947C22×C4—138no—
948C22×C4—138no—
949C22×C4—134no—
950C22×C4—134no—
951C22×C4—134no—
952C22×C4—132no—
953C22×C4—1316no—
954C22×C4—1316no—
955C22×C4—134no—
956C22×C4—134no—
957C22×C4—134no—
958C22×C4—264no—
959C22×C4—2616no—
960C22×C4—524no—
961C22×C4—528no—
962C22×C4—528no—
963C22×C4—524no—
964C22×C4—528no—
965C22×C4—524no—
966C22×C4—5216no—
967C22×C4—5216no—
968C22×C4—522no—
969C22×C4—524no—
970C22×C4C23×D1311yescharacteristic
971C22×C4C23×D1314yes—
972C22×C4C23×D1311yescharacteristic
973C22×C4C23×D1318yes—
974C22×C4C23×D1312yes—
975C22×C4C23×D1318yes—
976C22×C4C23×D1314yes—
977C22×C4C23×D1311yescharacteristic
978C4⋊C4—138no—
979C4⋊C4—138no—
980C4⋊C4—138no—
981C4⋊C4—138no—
982C4⋊C4—134no—
983C4⋊C4—138no—
984C4⋊C4—134no—
985C4⋊C4—1316no—
986C4⋊C4—138no—
987C4⋊C4—1316no—
988C4⋊C4—1316no—
989C4⋊C4—1316no—
990C4⋊C4—138no—
991C4⋊C4—134no—
992C4⋊C4—138no—
993C4⋊C4—134no—
994C4⋊C4—138no—
995C4⋊C4—138no—
996C4⋊C4—138no—
997C4⋊C4—138no—
998C4⋊C4—134no—
999C4⋊C4C23×D1318yes—
1000C4⋊C4C23×D1314yes—
1001C4⋊C4C23×D1314yes—
1002C4⋊C4C23×D1318yes—
1003C4⋊C4C23×D13116yes—
1004C4⋊C4C23×D1314yes—
1005C4⋊C4C23×D1314yes—
1006C4⋊C4C23×D1318yes—
1007C4⋊C4C23×D1314yes—
1008C22⋊C4—138no—
1009C22⋊C4—138no—
1010C22⋊C4—1316no—
1011C22⋊C4—138no—
1012C22⋊C4—138no—
1013C22⋊C4—138no—
1014C22⋊C4—1316no—
1015C22⋊C4—1316no—
1016C22⋊C4—138no—
1017C22⋊C4C23×D1318yes—
1018C22⋊C4C23×D1318yes—
1019C22⋊C4C23×D13116yes—
1020C42—132no—
1021C42—132no—
1022C42—132no—
1023C42—132no—
1024C42—132no—
1025C42—132no—
1026C42—138no—
1027C42—138no—
1028C42—138no—
1029C42C23×D1312yes—
1030C42C23×D1312yes—
1031C42C23×D1318yes—
1032C13C2×#350111yescharacteristic, complemented, Sylow
1033C23—42no—
1034C23—42no—
1035C23—131no—
1036C23—134no—
1037C23—1316no—
1038C23—131no—
1039C23—134no—
1040C23—1316no—
1041C23—138no—
1042C23—268no—
1043C23—262no—
1044C23—268no—
1045C23—262no—
1046C23—524no—
1047C23—522no—
1048C23—524no—
1049C23—522no—
1050C23—5232no—
1051C23C2×Q8×D1318yescomplemented
1052C23C24×D1311yescharacteristic
1053C23C24×D1314yes—
1054Q8—28no—
1055Q8—48no—
1056Q8—44no—
1057Q8—2616no—
1058Q8—268no—
1059Q8—528no—
1060Q8—524no—
1061Q8—528no—
1062Q8—5216no—
1063D4—1332no—
1064D4—1316no—
1065D4C2×Q8×D13116yescomplemented
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—44no—
1069C2×C4—42no—
1070C2×C4—48no—
1071C2×C4—41no—
1072C2×C4—48no—
1073C2×C4—134no—
1074C2×C4—132no—
1075C2×C4—131no—
1076C2×C4—138no—
1077C2×C4—138no—
1078C2×C4—134no—
1079C2×C4—132no—
1080C2×C4—131no—
1081C2×C4—138no—
1082C2×C4—138no—
1083C2×C4—134no—
1084C2×C4—262no—
1085C2×C4—268no—
1086C2×C4—262no—
1087C2×C4—268no—
1088C2×C4—2616no—
1089C2×C4—2616no—
1090C2×C4—264no—
1091C2×C4—262no—
1092C2×C4—268no—
1093C2×C4—262no—
1094C2×C4—268no—
1095C2×C4—5216no—
1096C2×C4—522no—
1097C2×C4—524no—
1098C2×C4—524no—
1099C2×C4—524no—
1100C2×C4—5216no—
1101C2×C4—528no—
1102C2×C4—521no—
1103C2×C4—524no—
1104C2×C4—522no—
1105C2×C4—528no—
1106C2×C4C2×Q8×D1314yescomplemented
1107C2×C4C24×D1312yes—
1108C2×C4C24×D1311yescharacteristic
1109C2×C4C24×D1318yes—
1110C2×C4C24×D1318yes—
1111C2×C4C24×D1314yes—
1112C2×C4C24×D1312yes—
1113C2×C4C24×D1311yescharacteristic
1114C22—24no—
1115C22—21no—
1116C22—24no—
1117C22—21no—
1118C22—48no—
1119C22—132no—
1120C22—132no—
1121C22—132no—
1122C22—132no—
1123C22—138no—
1124C22—2632no—
1125C22—268no—
1126C22—264no—
1127C22—261no—
1128C22—264no—
1129C22—261no—
1130C22—528no—
1131C22—5216no—
1132C22C22×Q8×D1312yes—
1133C22C22×Q8×D1318yes—
1134C22C25×D1311yescharacteristic
1135C4—21no—
1136C4—24no—
1137C4—28no—
1138C4—28no—
1139C4—22no—
1140C4—134no—
1141C4—132no—
1142C4—261no—
1143C4—264no—
1144C4—268no—
1145C4—268no—
1146C4—262no—
1147C4C22×Q8×D1314yes—
1148C4D13×H(5,𝔽2)12yes—
1149C2—22no—
1150C2—28no—
1151C2—134no—
1152C2—262no—
1153C2—268no—
1154C2C23×Q8×D1311yescharacteristic
1155C2C2×D13×H(5,𝔽2)11yescharacteristic
1156C2D13×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3501C2
prime radicalC22×D4×D13C22
hypercenter#3501D13
hypocenterC13C2×#3501
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13128639C2semidirect
2. #13128638C2semidirect
3. #13128637C2semidirect
4. #13128636C2semidirect
5. #13128635C2semidirect
6. #13128634C2semidirect
7. #13128633C2semidirect
8. #13128632C2semidirect
9. #13128631C2semidirect
10. D13×#554C2semidirect
11. D13×#554C2semidirect
12. D4×Q8×D13C2semidirect
13. D13×#544C2semidirect
14. D13×#543C2semidirect
15. D13×#533C2semidirect
16. C2×D13×C22⋊Q8C2semidirect
19. C13×#3501C2semidirect
20. C22×Q8×D13C22semidirect
23. C13×#554C22semidirect
24. C13×#554C22semidirect
25. D4×Q8×C13C22semidirect
26. C13×#544C22semidirect
27. C13×#543C22semidirect
28. C13×#533C22semidirect
29. C2×C13×C22⋊Q8C22semidirect
32. Q8×C22⋊D13C22semidirect
33. C2×#88200C22semidirect
37. C2×#88178C22semidirect
38. #11719435C22semidirect
39. #11719435C22semidirect
40. #11719434C22semidirect
41. #11719433C22semidirect
42. #11719433C22semidirect
43. #11719432C22semidirect
44. #11719432C22semidirect
45. D13×C4⋊Q8C22semidirect
46. D13×C4⋊Q8C22semidirect
47. D13×C4⋊Q8C22semidirect
48. #11719395C22semidirect
49. #11719395C22semidirect
50. #11719395C22semidirect
51. #11719394C22semidirect
52. #11719393C22semidirect
53. D13×#125C22semidirect
54. D13×#125C22semidirect
55. #11719341C22semidirect
56. #11719341C22semidirect
57. #11719341C22semidirect
58. #11719340C22semidirect
59. #11719340C22semidirect
60. #11719339C22semidirect
61. #11719339C22semidirect
62. #11719339C22semidirect
63. #11719339C22semidirect
64. #11719337C22semidirect
65. #11719337C22semidirect
69. D13×C22⋊Q8C22semidirect
70. D13×C22⋊Q8C22semidirect
71. D13×C22⋊Q8C22semidirect
72. D13×C22⋊Q8C22semidirect
73. D13×C22⋊Q8C22semidirect
74. D13×C22⋊Q8C22semidirect
75. D13×C22⋊Q8C22semidirect
76. D13×C22⋊Q8C22semidirect
77. #11719328C22semidirect
78. #11719327C22semidirect
79. #11719327C22semidirect
80. #11719284C22semidirect
81. #11719284C22semidirect
82. #11719283C22semidirect
83. #11719283C22semidirect
84. Q8×D52C22semidirect
85. C4×Q8×D13C22semidirect
86. C4×Q8×D13C22semidirect
95. #11719248C22semidirect
96. #11719248C22semidirect
97. #11719244C22semidirect
98. #11719244C22semidirect
99. #11719244C22semidirect
100. D4×Dic26C22semidirect
101. D4×Dic26C22semidirect
104. #11719224C22semidirect
105. #11719222C22semidirect
106. #11719216C22semidirect
107. #11719216C22semidirect
108. C2×#88151C22semidirect
109. C2×#88150C22semidirect
112. C2×C4⋊C4×D13C22semidirect
113. C2×C4⋊C4×D13C22semidirect
114. #11719205C22semidirect
119. #11719188C22semidirect
120. #11719188C22semidirect
121. C2×#88132C22semidirect
124. #11719175C22semidirect
126. C22×Q8×C13C23semidirect
135. C2×Q8×D13C23semidirect
136. C2×Q8×D13C23semidirect
137. C2×D4×D13Q8semidirect
154. C22×Dic26C23semidirect
155. C22×Dic26C23semidirect
156. C13×C4⋊Q8C23semidirect
157. C13×C4⋊Q8C23semidirect
158. C13×C4⋊Q8C23semidirect
159. C13×#125C23semidirect
160. C13×#125C23semidirect
164. C13×C22⋊Q8C23semidirect
165. C13×C22⋊Q8C23semidirect
166. C13×C22⋊Q8C23semidirect
167. C13×C22⋊Q8C23semidirect
168. C4×Q8×C13C23semidirect
169. C4×Q8×C13C23semidirect
176. C2×C13×C4⋊C4C23semidirect
177. C2×C13×C4⋊C4C23semidirect
186. #88200C23semidirect
187. #88200C23semidirect
188. #88200C23semidirect
189. #88200C23semidirect
190. Q8×Dic13C23semidirect
191. Q8×Dic13C23semidirect
192. #88198C23semidirect
193. #88198C23semidirect
194. #88198C23semidirect
209. C2×C4⋊Dic13C23semidirect
210. C2×C4⋊Dic13C23semidirect
214. #88178C23semidirect
215. #88178C23semidirect
216. #88178C23semidirect
217. #88178C23semidirect
219. C2×#6101C23semidirect
220. C2×#6101C23semidirect
221. C2×#6101C23semidirect
228. #88151C23semidirect
229. #88151C23semidirect
230. #88151C23semidirect
231. #88151C23semidirect
235. #88150C23semidirect
236. #88150C23semidirect
237. #88150C23semidirect
238. #88150C23semidirect
239. #88150C23semidirect
240. #88150C23semidirect
257. C4⋊C4×D13C23semidirect
258. C4⋊C4×D13C23semidirect
259. C4⋊C4×D13C23semidirect
260. C4⋊C4×D13C23semidirect
261. #88144C23semidirect
262. #88144C23semidirect
263. #88144C23semidirect
264. #88144C23semidirect
265. #88143C23semidirect
266. #88143C23semidirect
267. #88143C23semidirect
268. #88143C23semidirect
269. #88142C23semidirect
270. #88142C23semidirect
271. #88142C23semidirect
272. #88142C23semidirect
273. #88142C23semidirect
274. #88142C23semidirect
275. #88142C23semidirect
276. #88141C23semidirect
277. #88141C23semidirect
278. #88141C23semidirect
279. #88141C23semidirect
293. #88132C23semidirect
294. #88132C23semidirect
295. #88132C23semidirect
296. #88132C23semidirect
297. #88132C23semidirect
298. #88132C23semidirect
310. #88124C23semidirect
311. #88124C23semidirect
312. #88123C23semidirect
313. #88123C23semidirect
314. #88123C23semidirect
315. C4×Dic26C23semidirect
316. C4×Dic26C23semidirect
317. C4×Dic26C23semidirect
318. C4×Dic26C23semidirect
323. C23×D13C2×Q8semidirect
332. C2×D4×C13C2×Q8semidirect
343. C2×C22⋊D13C2×Q8semidirect
359. D4×D13C2×Q8semidirect
360. D4×D13C2×Q8semidirect
361. C2×D52C2×Q8semidirect
374. C2×C4×D13C2×Q8semidirect
464. #3501D13direct (N × H)
476. C23×C13C22×Q8semidirect
490. C22×D13C22×Q8semidirect
491. C22×D13C22×Q8semidirect
498. D4×C13C22×Q8semidirect
506. C2×C4×C13C22×Q8semidirect
514. C22⋊D13C22×Q8semidirect
522. C2×Dic13C22×Q8semidirect
530. D52C22×Q8semidirect
547. C4×D13C22×Q8semidirect
577. #554C2×D13semidirect
578. #554C2×D13semidirect
587. D4×Q8C2×D13semidirect
593. #544C2×D13semidirect
600. #543C2×D13semidirect
610. #533C2×D13semidirect
632. C2×C22⋊Q8C2×D13semidirect
704. C22×Q8C22×D13semidirect
739. C4⋊Q8C22×D13semidirect
740. C4⋊Q8C22×D13semidirect
741. C4⋊Q8C22×D13semidirect
752. #125C22×D13semidirect
753. #125C22×D13semidirect
796. C22⋊Q8C22×D13semidirect
797. C22⋊Q8C22×D13semidirect
798. C22⋊Q8C22×D13semidirect
799. C22⋊Q8C22×D13semidirect
810. C4×Q8C22×D13semidirect
811. C4×Q8C22×D13semidirect
864. C2×C4⋊C4C22×D13semidirect
865. C2×C4⋊C4C22×D13semidirect
896. D13#3501direct (N × H)
928. C2×D4Q8×D13semidirect
1032. C13C2×#3501semidirect
1051. C23C2×Q8×D13semidirect
1065. D4C2×Q8×D13semidirect
1106. C2×C4C2×Q8×D13semidirect

Maximal subgroups

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

subgroupindex
#131286392
#131286382
#131286372
#131286362
#131286352
#131286342
#131286332
#131286322
#131286312
D13×#5542
D4×Q8×D132
D13×#5442
D13×#5432
D13×#5332
C2×D13×C22⋊Q82
D13×#5182
C2×C4×D4×D132
C13×#35012
C2×#350113