Finite Group Databasebeta

← #16021684

Subgroups — #16021684

Order 3328.

3134 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719311C211yesmaximal, characteristic
2C2×C4×#6129C211yesmaximal, characteristic, complemented
3C2×D13×#117C211yesmaximal, characteristic, complemented
4#13117532C211yesmaximal, characteristic, complemented
5#13117531C211yesmaximal, characteristic, complemented
6#13117523C211yesmaximal, characteristic, complemented
7#13117519C211yesmaximal, characteristic, complemented
8#13117518C211yesmaximal, characteristic, complemented
9#13117516C211yesmaximal, characteristic, complemented
10#13117514C211yesmaximal, characteristic, complemented
11#13117506C212yesmaximal, complemented
12#13117503C212yesmaximal, complemented
13#13117495C212yesmaximal, complemented
14#13117492C212yesmaximal, complemented
15#13117323C211yesmaximal, characteristic, complemented
16#13117317C211yesmaximal, characteristic, complemented
17#13117298C212yesmaximal, complemented
18#13117296C212yesmaximal, complemented
19#13117276C212yesmaximal, complemented
20#13117272C212yesmaximal, complemented
21#13117218C211yesmaximal, characteristic, complemented
22C4×#88146C211yesmaximal, characteristic, complemented
23C13×#2324C211yesmaximal, characteristic, complemented
24C22×#6129C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic, complemented
28C2×C13×#117C2211yescharacteristic
29C2×#88192C2211yescharacteristic
30C2×#88191C2212yes—
31C2×D4×Dic13C2212yes—
32C2×D4×Dic13C2211yescharacteristic, complemented
33C2×C4×C22⋊D13C2212yes—
34C2×#88180C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×C4×Dic13C2212yescomplemented
37#11719311C4116yescomplemented
38C4×#6129—28no—
39D13×#117—28no—
40C2×#88151C2211yescharacteristic
41C2×#88146C2211yescharacteristic
42C2×#88146C2211yescharacteristic
43C2×#88146C2211yescharacteristic
44C2×#88146C2211yescharacteristic
45C2×#88146C2211yescharacteristic
46C2×C4⋊C4×D13C2211yescharacteristic
47C2×C4⋊C4×D13C2211yescharacteristic
48C2×#88141C2211yescharacteristic, complemented
49C2×#88137C2212yes—
50C2×#88135C2212yes—
51C2×#88135C2212yes—
52C2×C22⋊C4×D13C2211yescharacteristic
53C2×C22⋊C4×D13C2211yescharacteristic
54C2×#88131C2211yescharacteristic
55C2×#88131C2211yescharacteristic
56C2×#88131C2212yescomplemented
57C2×#88126C2211yescharacteristic
58C2×#88126C2211yescharacteristic
59C2×C42×D13C2211yescharacteristic
60C2×C42×D13C2211yescharacteristic
61C2×C4×Dic26C2211yescharacteristic, complemented
62C13×#390C2212yes—
63C13×#390C2211yescharacteristic, complemented
64C13×#389C2211yescharacteristic, complemented
65C13×#388C2212yescomplemented
66C13×#386C2212yes—
67C13×#385C2212yescomplemented
68C13×#380C2211yescharacteristic
69C4×C13×C4⋊C4C2211yescharacteristic, complemented
70#11718882C2212yes—
71#11718882C2211yescharacteristic, complemented
72#11718881C2212yes—
73#11718874C2212yes—
74#11718873C2211yescharacteristic
75#11718871C2212yescomplemented
76#11718651C2212yes—
77#11718650C2212yes—
78#11718648C2211yescharacteristic
79#11718648C2211yescharacteristic
80#11718646C2211yescharacteristic, complemented
81#11718639C2212yescomplemented
82C4⋊C4×Dic13C2211yescharacteristic, complemented
83C4⋊C4×Dic13C2211yescharacteristic, complemented
84C4⋊C4×Dic13C2212yescomplemented
85#11718635C2211yescharacteristic, complemented
86#11718634C2212yescomplemented
87#11718634C2211yescharacteristic, complemented
88#11718633C2212yescomplemented
89#11718619C2212yes—
90#11718618C2212yes—
91#11718618C2212yes—
92#11718617C2212yes—
93#11718617C2212yes—
94#11718616C2212yes—
95#11718612C2212yescomplemented
96#11718611C2212yescomplemented
97#11718607C2212yescomplemented
98#11718606C2212yes—
99#11718606C2212yes—
100#11718606C2212yescomplemented
101#11718605C2212yes—
102#11718605C2212yes—
103#11718605C2212yescomplemented
104C22⋊C4×Dic13C2212yes—
105C22⋊C4×Dic13C2212yescomplemented
106C22⋊C4×Dic13C2212yescomplemented
107#11718601C2212yes—
108C4×#6103C2212yes—
109C4×C4⋊Dic13C2211yescharacteristic, complemented
110C42×Dic13C2212yescomplemented
111#11718590C2211yescharacteristic, complemented
112#11718589C2212yescomplemented
113#11718589C2211yescharacteristic, complemented
114#11718331C2212yes—
115#11718330C2212yes—
116#11718329C2212yes—
117#11718327C2212yes—
118#11718327C2212yes—
119#11718325C2212yes—
120#11718316C2212yescomplemented
121#11718315C2212yescomplemented
122#11718314C2212yescomplemented
123#11718310C2212yescomplemented
124#11718309C2212yescomplemented
125#11718308C2212yescomplemented
126C24×D13C2311yescharacteristic
127C22×D4×C13C2311yescharacteristic
128C22×D4×C13C2312yes—
129C23×C4×C13C2311yescharacteristic
130C23×C4×C13C2312yes—
131C22×C22⋊D13C2312yes—
132C22×C22⋊D13C2312yes—
133C23×Dic13C2311yescharacteristic
134C23×Dic13C2312yes—
135C23×Dic13C2312yes—
136C2×#6129—24no—
137C2×#6129—24no—
138C2×#6129C2×C418yes—
139C22×C4×D13—24no—
140C22×C4×D13—24no—
141C22×C4×D13C2×C418yescomplemented
142C22×C4×D13C2311yescharacteristic
143C22×C4×D13C2311yescharacteristic
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×Dic26C2311yescharacteristic
151C13×#121C2×C418yescomplemented
152C4×D4×C13—24no—
153C13×#117—24no—
154C2×C13×C4⋊C4C2311yescharacteristic
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2311yescharacteristic
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2311yescharacteristic
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2311yescharacteristic
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C13×C22⋊C4C2312yes—
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2312yes—
169C2×C42×C13C2311yescharacteristic
170C2×C22⋊Dic13C2311yescharacteristic
171C2×C22⋊Dic13C2311yescharacteristic
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2312yes—
176C2×C22⋊Dic13C2312yes—
177C2×C22⋊Dic13C2312yes—
178#88192C2×C418yescomplemented
179#88191C2×C4116yescomplemented
180D4×Dic13—24no—
181D4×Dic13C2×C4116yescomplemented
182C4×C22⋊D13—28no—
183C2×#6103C2311yescharacteristic
184C2×#6103C2311yescharacteristic
185C2×#6103C2311yescharacteristic
186C2×#6103C2311yescharacteristic
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2312yes—
192C2×#6103C2312yes—
193#88180—24no—
194C2×C4⋊Dic13C2311yescharacteristic
195C2×C4⋊Dic13C2311yescharacteristic
196C2×C4⋊Dic13C2311yescharacteristic
197C2×C4⋊Dic13C2311yescharacteristic
198C2×C4⋊Dic13C2312yes—
199C2×C4⋊Dic13C2312yes—
200C2×C4⋊Dic13C2311yescharacteristic
201#88178C2×C418yescomplemented
202C2×#6101C2312yes—
203C2×#6101C2311yescharacteristic
204C2×#6101C2311yescharacteristic
205C2×#6101C2311yescharacteristic
206C2×#6101C2311yescharacteristic
207C2×#6101C2312yes—
208C2×#6101C2312yes—
209C2×#6101C2312yes—
210C2×#6101C2312yes—
211C2×C4×Dic13—28no—
212C2×C4×Dic13C2312yes—
213C2×C4×Dic13C2311yescharacteristic
214C2×C4×Dic13C2311yescharacteristic
215C2×C4×Dic13C2311yescharacteristic
216C2×C4×Dic13C2312yes—
217C2×C4×Dic13C2312yes—
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220C2×C4×Dic13C2312yes—
221C2×C4×Dic13C2312yes—
222C2×C4×Dic13C2312yes—
223C2×C4×Dic13C2311yescharacteristic
224C2×C4×Dic13C2311yescharacteristic
225C2×C4×Dic13C2311yescharacteristic
226#88151C2×C418yescomplemented
227#88146—24no—
228#88146—24no—
229#88146—24no—
230#88146—24no—
231#88146C2×C418yescomplemented
232C4⋊C4×D13—24no—
233C4⋊C4×D13—24no—
234#88141—24no—
235#88137C2×C4116yescomplemented
236#88135—28no—
237#88135C2×C4116yescomplemented
238C22⋊C4×D13—24no—
239C22⋊C4×D13—24no—
240#88131—24no—
241#88131—24no—
242#88131—28no—
243#88126—24no—
244#88126—24no—
245C42×D13—24no—
246C42×D13D418yescomplemented
247C4×Dic26—24no—
248C13×#95C2312yes—
249C13×#95C2312yes—
250C13×#95C2312yes—
251#88071C2312yes—
252#88071C2312yes—
253#88071C2312yes—
254#88071C2312yes—
255#88071C2312yes—
256#88071C2312yes—
257#88071C2312yes—
258#88071C2312yes—
259#88071C2312yes—
260#88071C2312yes—
261#88071C2312yes—
262#88071C2312yes—
263#88071C2312yes—
264#34065—131nomaximal, Sylow
265C24×C13C2411yescharacteristic
266C24×C13C2412yes—
267C23×D13—22no—
268C23×D13—22no—
269C23×D13—41no—
270C23×D13—41no—
271C23×D13—41no—
272C23×D13—41no—
273C23×D13C22×C414yes—
274C23×D13C2411yescharacteristic
275C23×D13C2411yescharacteristic
276C2×D4×C13—22no—
277C2×D4×C13—22no—
278C2×D4×C13—42no—
279C2×D4×C13—42no—
280C2×D4×C13C22×C414yes—
281C2×D4×C13C22×C418yes—
282C22×C4×C13—22no—
283C22×C4×C13—22no—
284C22×C4×C13—24no—
285C22×C4×C13—42no—
286C22×C4×C13—42no—
287C22×C4×C13C22×C414yes—
288C22×C4×C13C2412yes—
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2412yes—
291C22×C4×C13C2411yescharacteristic
292C22×C4×C13C2412yes—
293C22×C4×C13C2411yescharacteristic
294C22×C4×C13C2411yescharacteristic
295C22×C4×C13C2411yescharacteristic
296C22×C4×C13C2411yescharacteristic
297C2×C22⋊D13—24no—
298C2×C22⋊D13—24no—
299C2×C22⋊D13—42no—
300C2×C22⋊D13—42no—
301C2×C22⋊D13C22×C418yes—
302C2×C22⋊D13C22×C418yes—
303C22×Dic13—22no—
304C22×Dic13—24no—
305C22×Dic13—22no—
306C22×Dic13—24no—
307C22×Dic13—24no—
308C22×Dic13—42no—
309C22×Dic13—42no—
310C22×Dic13C22×C418yes—
311C22×Dic13C22×C414yes—
312C22×Dic13C2412yes—
313C22×Dic13C2411yescharacteristic
314C22×Dic13C2412yes—
315C22×Dic13C2411yescharacteristic
316C22×Dic13C2412yes—
317C22×Dic13C2412yes—
318C22×Dic13C2411yescharacteristic
319C22×Dic13C2411yescharacteristic
320C22×Dic13C2411yescharacteristic
321C22×Dic13C2411yescharacteristic
322#6129—232no—
323C2×C4×D13—22no—
324C2×C4×D13—22no—
325C2×C4×D13—22no—
326C2×C4×D13—22no—
327C2×C4×D13—22no—
328C2×C4×D13—22no—
329C2×C4×D13—232no—
330C2×C4×D13—22no—
331C2×C4×D13—22no—
332C2×C4×D13—41no—
333C2×C4×D13—41no—
334C2×C4×D13—41no—
335C2×C4×D13—41no—
336C2×C4×D13—41no—
337C2×C4×D13—41no—
338C2×C4×D13—41no—
339C2×C4×D13—41no—
340C2×C4×D13C22×C414yes—
341C2×C4×D13C22×C414yes—
342C2×C4×D13C22×C414yes—
343C2×C4×D13C22×C414yes—
344C2×C4×D13C2×D414yes—
345C2×C4×D13C2×D414yes—
346C2×C4×D13C2×D414yes—
347C2×C4×D13#4114yes—
348C2×Dic26—22no—
349C2×Dic26—22no—
350C2×Dic26C22×C414yes—
351C13×C4⋊C4—22no—
352C13×C4⋊C4—22no—
353C13×C4⋊C4—22no—
354C13×C4⋊C4—22no—
355C13×C4⋊C4—42no—
356C13×C4⋊C4C22×C414yes—
357C13×C22⋊C4—22no—
358C13×C22⋊C4—22no—
359C13×C22⋊C4—24no—
360C13×C22⋊C4—42no—
361C13×C22⋊C4—42no—
362C13×C22⋊C4—42no—
363C13×C22⋊C4C22×C418yes—
364C42×C13—22no—
365C42×C13—42no—
366C42×C13C2×D414yes—
367C22⋊Dic13—22no—
368C22⋊Dic13—22no—
369C22⋊Dic13—24no—
370C22⋊Dic13—42no—
371C22⋊Dic13—42no—
372C22⋊Dic13—42no—
373C22⋊Dic13C22×C418yes—
374C22⋊Dic13C22×C418yes—
375#6103—24no—
376#6103—24no—
377#6103—22no—
378#6103—22no—
379#6103—22no—
380#6103—22no—
381#6103—42no—
382#6103—42no—
383#6103C22×C418yes—
384#6103C22×C418yes—
385C4⋊Dic13—22no—
386C4⋊Dic13—22no—
387C4⋊Dic13—22no—
388C4⋊Dic13—22no—
389C4⋊Dic13—42no—
390C4⋊Dic13C22×C418yes—
391C4⋊Dic13C22×C414yes—
392#6101—24no—
393#6101—22no—
394#6101—22no—
395#6101—22no—
396#6101—22no—
397#6101—24no—
398#6101—42no—
399#6101—42no—
400#6101C22×C418yes—
401C4×Dic13—24no—
402C4×Dic13—22no—
403C4×Dic13—22no—
404C4×Dic13—22no—
405C4×Dic13—24no—
406C4×Dic13—24no—
407C4×Dic13—24no—
408C4×Dic13—42no—
409C4×Dic13—42no—
410C4×Dic13—42no—
411C4×Dic13C22×C418yes—
412C4×Dic13C2×D414yes—
413C4×Dic13C2×D414yes—
414C4×Dic13C2×D414yes—
415C2×#525—131no—
416C2×C4×#41—131no—
417C22×#117—131no—
418#2324—131no—
419#2324—131no—
420#2324—131no—
421#2324D1311yescharacteristic, complemented
422#2323—131no—
423#2323—131no—
424#2323—131no—
425#2323—131no—
426#2322—132no—
427#2322—132no—
428#2321—132no—
429#2321—132no—
430#2297—131no—
431#2296—131no—
432#2293—132no—
433#2293—132no—
434#2290—132no—
435#2290—132no—
436#2280—131no—
437C4×#117—131no—
438C23×C13—21no—
439C23×C13—22no—
440C23×C13—22no—
441C23×C13—21no—
442C23×C13—21no—
443C23×C13—22no—
444C23×C13—22no—
445C23×C13—21no—
446C23×C13—22no—
447C23×C13—22no—
448C23×C13—21no—
449C23×C13—21no—
450C23×C13C23×C412yes—
451C23×C13C23×C414yes—
452C23×C13C2511yescharacteristic
453C22×D13—21no—
454C22×D13—21no—
455C22×D13—21no—
456C22×D13—21no—
457C22×D13—21no—
458C22×D13—21no—
459C22×D13—21no—
460C22×D13—21no—
461C22×D13—21no—
462C22×D13—21no—
463C22×D13—28no—
464C22×D13—44no—
465C22×D13—44no—
466C22×D13—44no—
467C22×D13—44no—
468C22×D13—44no—
469C22×D13—44no—
470C22×D13C23×C412yes—
471C22×D13C23×C412yes—
472C22×D13C22×D412yes—
473C22×D13C2×#4112yes—
474D4×C13—28no—
475D4×C13—48no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—21no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—21no—
482C2×C4×C13—21no—
483C2×C4×C13—21no—
484C2×C4×C13—28no—
485C2×C4×C13—22no—
486C2×C4×C13—21no—
487C2×C4×C13—21no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—21no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13—22no—
494C2×C4×C13—21no—
495C2×C4×C13—21no—
496C2×C4×C13—21no—
497C2×C4×C13—48no—
498C2×C4×C13C23×C414yes—
499C2×C4×C13C23×C412yes—
500C2×C4×C13C23×C412yes—
501C2×C4×C13C22×D412yes—
502C2×C4×C13C22×D412yes—
503C2×C4×C13C22×D412yes—
504C2×C4×C13C2×#4112yes—
505C22⋊D13—216no—
506C22⋊D13—48no—
507C2×Dic13—22no—
508C2×Dic13—21no—
509C2×Dic13—22no—
510C2×Dic13—21no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—22no—
514C2×Dic13—22no—
515C2×Dic13—21no—
516C2×Dic13—21no—
517C2×Dic13—28no—
518C2×Dic13—216no—
519C2×Dic13—21no—
520C2×Dic13—21no—
521C2×Dic13—22no—
522C2×Dic13—22no—
523C2×Dic13—22no—
524C2×Dic13—22no—
525C2×Dic13—21no—
526C2×Dic13—22no—
527C2×Dic13—21no—
528C2×Dic13—22no—
529C2×Dic13—21no—
530C2×Dic13—21no—
531C2×Dic13—48no—
532C2×Dic13C23×C414yes—
533C2×Dic13C23×C414yes—
534C2×Dic13C23×C412yes—
535C2×Dic13C23×C412yes—
536C2×Dic13C22×D412yes—
537C2×Dic13C22×D412yes—
538C2×Dic13C22×D412yes—
539C2×Dic13C2×#4112yes—
540C4×D13—28no—
541C4×D13—28no—
542C4×D13—28no—
543C4×D13—44no—
544C4×D13—44no—
545C4×D13—44no—
546C4×D13—44no—
547C4×D13C4×D4116yes—
548Dic26—28no—
549C22×#41—131no—
550C24×C4—131no—
551#525—1316no—
552C2×#123—132no—
553C2×C22⋊Q8—131no—
554C2×C22⋊Q8—131no—
555C2×#121—131no—
556C2×#121C2×D1311yescharacteristic
557C2×#120—132no—
558C4×#41—268no—
559C2×C4×Q8—131no—
560C2×C4×Q8—131no—
561C2×C4×D4—132no—
562C2×C4×D4—131no—
563C2×C4×D4—132no—
564C2×C4×D4—132no—
565C2×C4×D4—132no—
566C2×C4×D4C2×D1311yescharacteristic, complemented
567C2×#117—131no—
568C2×#117—131no—
569C2×#117—131no—
570C2×#117—131no—
571C2×#117—131no—
572C2×#117—131no—
573C2×#117—131no—
574C2×#117—131no—
575C2×#117—132no—
576C2×#117—131no—
577C2×#117—131no—
578C2×#117—268no—
579C2×#117C2×D1311yescharacteristic
580C22×C4⋊C4—131no—
581C22×C4⋊C4—131no—
582C22×C22⋊C4—131no—
583C22×C22⋊C4—131no—
584C22×C42—131no—
585C22×C42—132no—
586C22×C42—131no—
587#391—131no—
588#391—131no—
589#390—132no—
590#390—131no—
591#390—132no—
592#390—132no—
593#390C2×D1312yes—
594#390C2×D1311yescharacteristic, complemented
595#389—132no—
596#389—132no—
597#389—131no—
598#389—131no—
599#389—132no—
600#389—131no—
601#389—132no—
602#389C2×D1311yescharacteristic, complemented
603#388—132no—
604#388—132no—
605#388—132no—
606#388—132no—
607#388—132no—
608#388—132no—
609#388—132no—
610#388—132no—
611#388—132no—
612#388—132no—
613#388—132no—
614#388C2×D1312yescomplemented
615#387—132no—
616#387—132no—
617#387—132no—
618#387—132no—
619#386—132no—
620#386—132no—
621#386—132no—
622#386—132no—
623#386—132no—
624#386C2×D1312yes—
625#385—132no—
626#385—132no—
627#385—132no—
628#385—132no—
629#385—132no—
630#385C2×D1312yescomplemented
631#381—132no—
632#380—131no—
633#380—131no—
634#380—131no—
635#380C2×D1311yescharacteristic
636#379—132no—
637C4×C4⋊C4—131no—
638C4×C4⋊C4—131no—
639C4×C4⋊C4—132no—
640C4×C4⋊C4—131no—
641C4×C4⋊C4—132no—
642C4×C4⋊C4C2×D1311yescharacteristic, complemented
643C4×C22⋊C4—132no—
644C4×C22⋊C4—132no—
645C4×C22⋊C4—132no—
646C4×C22⋊C4—132no—
647C4×C22⋊C4—132no—
648C4×C22⋊C4—132no—
649#376—132no—
650C43—132no—
651C22×C13—24no—
652C22×C13—22no—
653C22×C13—24no—
654C22×C13—22no—
655C22×C13—24no—
656C22×C13—22no—
657C22×C13—42no—
658C22×C13—42no—
659C22×C13—41no—
660C22×C13—41no—
661C22×C13—41no—
662C22×C13—41no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13C24×C411yescharacteristic
666C22×C13C23×D411yescharacteristic
667C22×C13C22×#4111yescharacteristic
668C22×C13#58511yescharacteristic
669C22×C13#58511yescharacteristic
670C22×C13#58511yescharacteristic
671C22×C13#58511yescharacteristic
672C2×D13—22no—
673C2×D13—22no—
674C2×D13—22no—
675C2×D13—22no—
676C2×D13—22no—
677C2×D13—22no—
678C2×D13—22no—
679C2×D13—22no—
680C2×D13—22no—
681C2×D13—416no—
682C2×D13—41no—
683C2×D13—41no—
684C2×D13—41no—
685C2×D13—41no—
686C2×D13C2×C4×D414yes—
687C4×C13—22no—
688C4×C13—24no—
689C4×C13—22no—
690C4×C13—22no—
691C4×C13—41no—
692C4×C13—41no—
693C4×C13—42no—
694C4×C13—42no—
695C4×C13C2×C4×D414yes—
696Dic13—24no—
697Dic13—22no—
698Dic13—24no—
699Dic13—22no—
700Dic13—22no—
701Dic13—41no—
702Dic13—41no—
703Dic13—42no—
704Dic13—42no—
705Dic13C2×C4×D414yes—
706C25—131no—
707C2×#41—138no—
708C2×#41—264no—
709C2×#41—264no—
710C22×Q8—131no—
711C22×D4—132no—
712C22×D4—132no—
713C22×D4C22×D1311yescharacteristic
714C22×D4C22×D1312yes—
715C23×C4—131no—
716C23×C4—131no—
717C23×C4—132no—
718C23×C4—138no—
719C23×C4—131no—
720C23×C4—131no—
721C23×C4—131no—
722C23×C4—131no—
723C23×C4—131no—
724C23×C4—132no—
725C23×C4—131no—
726C23×C4—131no—
727C23×C4—264no—
728C23×C4—264no—
729C23×C4C22×D1311yescharacteristic
730C23×C4C22×D1312yes—
731#123—1316no—
732C22⋊Q8—138no—
733C22⋊Q8—138no—
734#121—138no—
735#121C4×D1318yescomplemented
736#120—1316no—
737C4×Q8—264no—
738C4×Q8—264no—
739C4×D4—24no—
740C4×D4—1316no—
741C4×D4—1316no—
742C4×D4—264no—
743C4×D4—268no—
744C4×D4—268no—
745#117—24no—
746#117—138no—
747#117—264no—
748#117—264no—
749#117—264no—
750#117—268no—
751#117—264no—
752#117—264no—
753#117—264no—
754#117—264no—
755#117—264no—
756#117—264no—
757C2×C4⋊C4—131no—
758C2×C4⋊C4—132no—
759C2×C4⋊C4—132no—
760C2×C4⋊C4—131no—
761C2×C4⋊C4—131no—
762C2×C4⋊C4—131no—
763C2×C4⋊C4—131no—
764C2×C4⋊C4—131no—
765C2×C4⋊C4—131no—
766C2×C4⋊C4—132no—
767C2×C4⋊C4—132no—
768C2×C4⋊C4—131no—
769C2×C4⋊C4—131no—
770C2×C4⋊C4—132no—
771C2×C4⋊C4—132no—
772C2×C4⋊C4—132no—
773C2×C4⋊C4—264no—
774C2×C4⋊C4—264no—
775C2×C4⋊C4C22×D1311yescharacteristic
776C2×C4⋊C4C22×D1311yescharacteristic
777C2×C4⋊C4C22×D1311yescharacteristic
778C2×C4⋊C4C22×D1311yescharacteristic
779C2×C4⋊C4C22×D1312yes—
780C2×C4⋊C4C22×D1311yescharacteristic
781C2×C22⋊C4—132no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—131no—
786C2×C22⋊C4—131no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—131no—
789C2×C22⋊C4—131no—
790C2×C22⋊C4—131no—
791C2×C22⋊C4—131no—
792C2×C22⋊C4—132no—
793C2×C22⋊C4—132no—
794C2×C22⋊C4—132no—
795C2×C22⋊C4—132no—
796C2×C22⋊C4—132no—
797C2×C22⋊C4—132no—
798C2×C22⋊C4—132no—
799C2×C22⋊C4—264no—
800C2×C22⋊C4—264no—
801C2×C22⋊C4C22×D1311yescharacteristic
802C2×C22⋊C4C22×D1311yescharacteristic
803C2×C22⋊C4C22×D1312yes—
804C2×C22⋊C4C22×D1312yes—
805C2×C22⋊C4C22×D1312yes—
806C2×C22⋊C4C22×D1312yes—
807C2×C22⋊C4C22×D1312yes—
808C2×C42—131no—
809C2×C42—131no—
810C2×C42—131no—
811C2×C42—132no—
812C2×C42—138no—
813C2×C42—131no—
814C2×C42—132no—
815C2×C42—131no—
816C2×C42—131no—
817C2×C42—132no—
818C2×C42—132no—
819C2×C42—132no—
820C2×C42—132no—
821C2×C42—132no—
822C2×C42—132no—
823C2×C42—264no—
824C2×C42—268no—
825C2×C42C22×D1311yescharacteristic
826C2×C42C22×D1312yes—
827C2×C42C22×D1311yescharacteristic
828#95—132no—
829#95—132no—
830#95—132no—
831#95—132no—
832#95—132no—
833#95—132no—
834#95—132no—
835#95—132no—
836#95—132no—
837#95—132no—
838#95—132no—
839#95—132no—
840#95—132no—
841#95C22×D1312yes—
842#95C22×D1312yes—
843#95C22×D1312yes—
844C2×C13—42no—
845C2×C13—44no—
846C2×C13C22×C4×D411yescharacteristic
847C2×C13#342811yescharacteristic
848C2×C13#342811yescharacteristic
849C2×C13#344911yescharacteristic
850C2×C13#344911yescharacteristic
851C2×C13#345511yescharacteristic
852C2×C13#345511yescharacteristic
853D13—24no—
854D13—42no—
855C24—131no—
856C24—131no—
857C24—134no—
858C24—262no—
859C24—262no—
860C24—521no—
861C24—521no—
862C24—521no—
863C24—521no—
864C24C23×D1311yescharacteristic
865C24C23×D1312yes—
866#41—2632no—
867C2×Q8—134no—
868C2×Q8—262no—
869C2×Q8—262no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—138no—
875C2×D4—138no—
876C2×D4—264no—
877C2×D4—264no—
878C2×D4—522no—
879C2×D4—522no—
880C2×D4C2×C4×D1314yes—
881C2×D4C2×C4×D1318yes—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—131no—
888C22×C4—134no—
889C22×C4—134no—
890C22×C4—134no—
891C22×C4—134no—
892C22×C4—138no—
893C22×C4—131no—
894C22×C4—132no—
895C22×C4—132no—
896C22×C4—131no—
897C22×C4—131no—
898C22×C4—134no—
899C22×C4—134no—
900C22×C4—134no—
901C22×C4—134no—
902C22×C4—134no—
903C22×C4—132no—
904C22×C4—131no—
905C22×C4—132no—
906C22×C4—131no—
907C22×C4—262no—
908C22×C4—262no—
909C22×C4—2632no—
910C22×C4—262no—
911C22×C4—262no—
912C22×C4—262no—
913C22×C4—262no—
914C22×C4—264no—
915C22×C4—262no—
916C22×C4—262no—
917C22×C4—264no—
918C22×C4—264no—
919C22×C4—262no—
920C22×C4—262no—
921C22×C4—521no—
922C22×C4—521no—
923C22×C4—521no—
924C22×C4—521no—
925C22×C4—521no—
926C22×C4—521no—
927C22×C4—521no—
928C22×C4—521no—
929C22×C4—522no—
930C22×C4—522no—
931C22×C4C2×C4×D1314yes—
932C22×C4C23×D1312yes—
933C22×C4C23×D1311yescharacteristic
934C22×C4C23×D1312yes—
935C22×C4C23×D1311yescharacteristic
936C22×C4C23×D1312yes—
937C22×C4C23×D1311yescharacteristic
938C22×C4C23×D1311yescharacteristic
939C22×C4C23×D1311yescharacteristic
940C22×C4C23×D1311yescharacteristic
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—42no—
946C4⋊C4—134no—
947C4⋊C4—138no—
948C4⋊C4—138no—
949C4⋊C4—262no—
950C4⋊C4—262no—
951C4⋊C4—262no—
952C4⋊C4—262no—
953C4⋊C4—264no—
954C4⋊C4—262no—
955C4⋊C4—262no—
956C4⋊C4—264no—
957C4⋊C4—262no—
958C4⋊C4—262no—
959C4⋊C4—522no—
960C4⋊C4—522no—
961C4⋊C4—522no—
962C4⋊C4C2×C4×D1314yes—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—24no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—138no—
970C22⋊C4—138no—
971C22⋊C4—138no—
972C22⋊C4—138no—
973C22⋊C4—262no—
974C22⋊C4—262no—
975C22⋊C4—264no—
976C22⋊C4—264no—
977C22⋊C4—262no—
978C22⋊C4—262no—
979C22⋊C4—264no—
980C22⋊C4—262no—
981C22⋊C4—262no—
982C22⋊C4—522no—
983C22⋊C4—522no—
984C22⋊C4—522no—
985C22⋊C4—522no—
986C22⋊C4—522no—
987C22⋊C4C2×C4×D1318yes—
988C42—22no—
989C42—42no—
990C42—138no—
991C42—134no—
992C42—134no—
993C42—134no—
994C42—262no—
995C42—262no—
996C42—264no—
997C42—264no—
998C42—264no—
999C42—262no—
1000C42—264no—
1001C42—522no—
1002C42—522no—
1003C42—522no—
1004C42D4×D1314yes—
1005C13#3406511yescharacteristic, complemented, Sylow
1006C23—21no—
1007C23—22no—
1008C23—21no—
1009C23—22no—
1010C23—21no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—22no—
1018C23—132no—
1019C23—132no—
1020C23—132no—
1021C23—132no—
1022C23—268no—
1023C23—261no—
1024C23—261no—
1025C23—261no—
1026C23—261no—
1027C23—261no—
1028C23—261no—
1029C23—261no—
1030C23—261no—
1031C23—261no—
1032C23—261no—
1033C23—524no—
1034C23—524no—
1035C23—524no—
1036C23—524no—
1037C23—524no—
1038C23—524no—
1039C23C22×C4×D1312yes—
1040C23C22×C4×D1314yes—
1041C23C24×D1311yescharacteristic
1042Q8—268no—
1043D4—28no—
1044D4—48no—
1045D4—2616no—
1046D4—528no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—28no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—48no—
1069C2×C4—132no—
1070C2×C4—132no—
1071C2×C4—132no—
1072C2×C4—1316no—
1073C2×C4—134no—
1074C2×C4—132no—
1075C2×C4—134no—
1076C2×C4—132no—
1077C2×C4—132no—
1078C2×C4—268no—
1079C2×C4—268no—
1080C2×C4—268no—
1081C2×C4—2616no—
1082C2×C4—262no—
1083C2×C4—261no—
1084C2×C4—261no—
1085C2×C4—262no—
1086C2×C4—261no—
1087C2×C4—261no—
1088C2×C4—262no—
1089C2×C4—261no—
1090C2×C4—262no—
1091C2×C4—261no—
1092C2×C4—268no—
1093C2×C4—261no—
1094C2×C4—262no—
1095C2×C4—261no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—261no—
1099C2×C4—262no—
1100C2×C4—261no—
1101C2×C4—261no—
1102C2×C4—262no—
1103C2×C4—261no—
1104C2×C4—262no—
1105C2×C4—524no—
1106C2×C4—524no—
1107C2×C4—524no—
1108C2×C4—524no—
1109C2×C4—528no—
1110C2×C4C22×C4×D1314yes—
1111C2×C4C22×C4×D1312yes—
1112C2×C4C22×C4×D1312yes—
1113C2×C4C2×D4×D1312yes—
1114C2×C4C2×D4×D1312yes—
1115C2×C4C2×D4×D1312yes—
1116C2×C4#41×D1312yes—
1117C22—22no—
1118C22—24no—
1119C22—22no—
1120C22—24no—
1121C22—24no—
1122C22—22no—
1123C22—42no—
1124C22—41no—
1125C22—42no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—134no—
1132C22—262no—
1133C22—262no—
1134C22—262no—
1135C22—262no—
1136C22—262no—
1137C22—262no—
1138C22—262no—
1139C22—262no—
1140C22—262no—
1141C22—5216no—
1142C22—521no—
1143C22—521no—
1144C22—521no—
1145C22—521no—
1146C22C23×C4×D1311yescharacteristic
1147C22C22×D4×D1311yescharacteristic
1148C22C2×#41×D1311yescharacteristic
1149C22#1171965011yescharacteristic
1150C22#1171965011yescharacteristic
1151C22#1171965011yescharacteristic
1152C22#1171965211yescharacteristic
1153C4—22no—
1154C4—24no—
1155C4—22no—
1156C4—22no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—134no—
1162C4—262no—
1163C4—264no—
1164C4—264no—
1165C4—262no—
1166C4—262no—
1167C4—522no—
1168C4—521no—
1169C4—522no—
1170C4—521no—
1171C4C4×D4×D1314yes—
1172C2—42no—
1173C2—44no—
1174C2—264no—
1175C2—522no—
1176C2C2×C4×D4×D1311yescharacteristic
1177C2#1312803411yescharacteristic
1178C2#1312803611yescharacteristic
1179C2#1312816411yescharacteristic
1180C2#1312816711yescharacteristic
1181C2#1312822011yescharacteristic
1182C2#1312822311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2324C2
socle, cosocleC23×C13C25
prime radicalC2×#11719311C2
hypercenter#2324D13
hypocenterC13#34065
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6129C2semidirect
3. C2×D13×#117C2semidirect
4. #13117532C2semidirect
5. #13117531C2semidirect
6. #13117523C2semidirect
7. #13117519C2semidirect
8. #13117518C2semidirect
9. #13117516C2semidirect
10. #13117514C2semidirect
11. #13117506C2semidirect
12. #13117503C2semidirect
13. #13117495C2semidirect
14. #13117492C2semidirect
15. #13117323C2semidirect
16. #13117317C2semidirect
17. #13117298C2semidirect
18. #13117296C2semidirect
19. #13117276C2semidirect
20. #13117272C2semidirect
21. #13117218C2semidirect
22. C4×#88146C2semidirect
23. C13×#2324C2semidirect
27. C2×C4×D4×C13C22semidirect
32. C2×D4×Dic13C22semidirect
36. C22×C4×Dic13C22semidirect
37. #11719311C4semidirect
48. C2×#88141C22semidirect
56. C2×#88131C22semidirect
61. C2×C4×Dic26C22semidirect
63. C13×#390C22semidirect
64. C13×#389C22semidirect
65. C13×#388C22semidirect
67. C13×#385C22semidirect
69. C4×C13×C4⋊C4C22semidirect
71. #11718882C22semidirect
75. #11718871C22semidirect
80. #11718646C22semidirect
81. #11718639C22semidirect
82. C4⋊C4×Dic13C22semidirect
83. C4⋊C4×Dic13C22semidirect
84. C4⋊C4×Dic13C22semidirect
85. #11718635C22semidirect
86. #11718634C22semidirect
87. #11718634C22semidirect
88. #11718633C22semidirect
95. #11718612C22semidirect
96. #11718611C22semidirect
97. #11718607C22semidirect
100. #11718606C22semidirect
103. #11718605C22semidirect
105. C22⋊C4×Dic13C22semidirect
106. C22⋊C4×Dic13C22semidirect
109. C4×C4⋊Dic13C22semidirect
110. C42×Dic13C22semidirect
111. #11718590C22semidirect
112. #11718589C22semidirect
113. #11718589C22semidirect
120. #11718316C22semidirect
121. #11718315C22semidirect
122. #11718314C22semidirect
123. #11718310C22semidirect
124. #11718309C22semidirect
125. #11718308C22semidirect
141. C22×C4×D13C2×C4semidirect
151. C13×#121C2×C4semidirect
178. #88192C2×C4semidirect
179. #88191C2×C4semidirect
181. D4×Dic13C2×C4semidirect
201. #88178C2×C4semidirect
226. #88151C2×C4semidirect
231. #88146C2×C4semidirect
235. #88137C2×C4semidirect
237. #88135C2×C4semidirect
246. C42×D13D4semidirect
421. #2324D13semidirect
566. C2×C4×D4C2×D13semidirect
594. #390C2×D13semidirect
602. #389C2×D13semidirect
614. #388C2×D13semidirect
630. #385C2×D13semidirect
642. C4×C4⋊C4C2×D13semidirect
735. #121C4×D13semidirect
1005. C13#34065semidirect

Maximal subgroups

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

subgroupindex
C2×#117193112
C2×C4×#61292
C2×D13×#1172
#131175322
#131175312
#131175232
#131175192
#131175182
#131175162
#131175142
#131175062
#131175032
#131174952
#131174922
#131173232
#131173172
#131172982
#131172962
#131172762
#131172722
#131172182
C4×#881462
C13×#23242
#3406513