Finite Group Databasebeta

← #16022486

Subgroups — #16022486

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719311C211yesmaximal, characteristic
2C2×C4×#6129C211yesmaximal, characteristic, complemented
3C22×#88146C211yesmaximal, characteristic, complemented
4#13117879C211yesmaximal, characteristic, complemented
5#13117870C211yesmaximal, characteristic, complemented
6#13117865C211yesmaximal, characteristic, complemented
7#13117862C211yesmaximal, characteristic, complemented
8#13117856C211yesmaximal, characteristic, complemented
9#13117841C211yesmaximal, characteristic, complemented
10#13117839C211yesmaximal, characteristic, complemented
11#13117831C212yesmaximal, complemented
12#13117827C212yesmaximal, complemented
13#13117816C212yesmaximal, complemented
14#13117813C212yesmaximal, complemented
15#13117323C211yesmaximal, characteristic, complemented
16#13117317C211yesmaximal, characteristic, complemented
17#13117296C212yesmaximal, complemented
18#13117276C212yesmaximal, complemented
19#13117272C212yesmaximal, complemented
20C4×D4×Dic13C212yesmaximal, complemented
21C4×#88146C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic, complemented
23C13×#2361C211yesmaximal, characteristic, complemented
24C22×#6129C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13C2212yes—
28C2×C4×D4×C13C2211yescharacteristic, complemented
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88192C2211yescharacteristic
31C2×#88191C2212yes—
32C2×D4×Dic13C2212yes—
33C2×D4×Dic13C2212yes—
34C2×D4×Dic13C2211yescharacteristic, complemented
35C2×C4×C22⋊D13C2212yes—
36C22×#6103C2212yes—
37C22×C4⋊Dic13C2211yescharacteristic
38C2×#88178C2211yescharacteristic
39C22×C4×Dic13C2212yes—
40C22×C4×Dic13C2212yescomplemented
41#11719311C4116yescomplemented
42C4×#6129—28no—
43C2×#88151C2211yescharacteristic
44C2×#88146—28no—
45C2×#88146C2212yes—
46C2×#88146C2212yes—
47C2×#88146C2211yescharacteristic
48C2×#88146C2211yescharacteristic
49C2×#88146C2211yescharacteristic
50C2×#88146C2211yescharacteristic
51C2×#88146C2211yescharacteristic
52C2×#88141C2211yescharacteristic, complemented
53C2×#88137C2212yes—
54C2×#88135C2212yes—
55C2×#88135C2212yes—
56C2×C22⋊C4×D13C2211yescharacteristic
57C2×C22⋊C4×D13C2211yescharacteristic
58C2×#88131C2212yescomplemented
59C2×C42×D13C2211yescharacteristic
60C2×C42×D13C2211yescharacteristic
61C2×C4×Dic26C2211yescharacteristic, complemented
62C13×#390C2211yescharacteristic, complemented
63C13×#389C2211yescharacteristic, complemented
64C13×#388C2212yescomplemented
65C13×#386C2212yes—
66C13×#385C2212yescomplemented
67C4×C13×C4⋊C4C2211yescharacteristic, complemented
68C4×C13×C22⋊C4C2211yescharacteristic
69#11718882C2211yescharacteristic, complemented
70#11718881C2212yes—
71#11718874C2212yes—
72#11718871C2212yes—
73C4×C22⋊Dic13C2212yes—
74C4×C22⋊Dic13C2211yescharacteristic
75C4×C22⋊Dic13C2212yescomplemented
76#11718651C2212yes—
77#11718650C2212yes—
78#11718646C2211yescharacteristic, complemented
79#11718639C2212yescomplemented
80C4⋊C4×Dic13C2212yescomplemented
81C4⋊C4×Dic13C2212yescomplemented
82C4⋊C4×Dic13C2211yescharacteristic, complemented
83C4⋊C4×Dic13C2211yescharacteristic, complemented
84#11718635C2211yescharacteristic, complemented
85#11718634C2211yescharacteristic, complemented
86#11718633C2212yescomplemented
87#11718619C2212yes—
88#11718618C2212yes—
89#11718618C2212yes—
90#11718617C2212yes—
91#11718617C2212yes—
92#11718612C2212yescomplemented
93#11718611C2212yescomplemented
94#11718607C2212yes—
95#11718606C2212yescomplemented
96#11718605C2212yescomplemented
97C22⋊C4×Dic13C2211yescharacteristic
98C22⋊C4×Dic13C2212yes—
99C22⋊C4×Dic13C2211yescharacteristic
100C22⋊C4×Dic13C2212yescomplemented
101C22⋊C4×Dic13C2212yescomplemented
102C22⋊C4×Dic13C2212yescomplemented
103#11718601C2212yes—
104C4×#6103C2212yes—
105C4×#6103C2211yescharacteristic
106C4×#6103C2211yescharacteristic
107C4×C4⋊Dic13C2212yescomplemented
108C4×C4⋊Dic13C2211yescharacteristic, complemented
109C42×Dic13C2212yescomplemented
110#11718590C2211yescharacteristic, complemented
111#11718589C2211yescharacteristic, complemented
112#11718331C2212yes—
113#11718330C2212yes—
114#11718329C2212yes—
115#11718327C2211yescharacteristic
116#11718327C2211yescharacteristic
117#11718327C2212yes—
118D13×#95C2211yescharacteristic
119D13×#95C2211yescharacteristic
120#11718316C2212yescomplemented
121#11718315C2212yescomplemented
122#11718314C2212yescomplemented
123#11718310C2212yescomplemented
124#11718309C2212yescomplemented
125#11718308C2212yescomplemented
126C24×D13C2311yescharacteristic
127C22×D4×C13C2312yes—
128C22×D4×C13C2311yescharacteristic
129C23×C4×C13C2312yes—
130C23×C4×C13C2312yes—
131C23×C4×C13C2311yescharacteristic
132C22×C22⋊D13C2312yes—
133C22×C22⋊D13C2312yes—
134C23×Dic13C2312yes—
135C23×Dic13C2312yes—
136C23×Dic13C2312yes—
137C23×Dic13C2311yescharacteristic
138C2×#6129—24no—
139C2×#6129—24no—
140C2×#6129C2×C418yescomplemented
141C22×C4×D13—24no—
142C22×C4×D13—24no—
143C22×C4×D13C2×C418yescomplemented
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×C4×D13C2311yescharacteristic
151C22×C4×D13C2311yescharacteristic
152C22×Dic26C2311yescharacteristic
153C13×#121C2×C418yescomplemented
154C4×D4×C13—24no—
155C4×D4×C13—28no—
156C2×C13×C4⋊C4—24no—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C4⋊C4C2311yescharacteristic
161C2×C13×C4⋊C4C2311yescharacteristic
162C2×C13×C22⋊C4C2311yescharacteristic
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C13×C22⋊C4C2312yes—
167C2×C13×C22⋊C4C2311yescharacteristic
168C2×C42×C13C2311yescharacteristic
169C2×C42×C13C2311yescharacteristic
170C2×C42×C13C2312yes—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2311yescharacteristic
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2312yes—
176C2×C22⋊Dic13C2312yes—
177C2×C22⋊Dic13C2311yescharacteristic
178#88192C2×C418yescomplemented
179#88191C2×C4116yescomplemented
180D4×Dic13—28no—
181D4×Dic13—24no—
182D4×Dic13C2×C4116yescomplemented
183C4×C22⋊D13—28no—
184C2×#6103—28no—
185C2×#6103C2311yescharacteristic
186C2×#6103C2311yescharacteristic
187C2×#6103C2311yescharacteristic
188C2×#6103C2311yescharacteristic
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2312yes—
192C2×#6103C2312yes—
193C2×#6103C2312yes—
194C2×#6103C2312yes—
195C2×C4⋊Dic13—24no—
196C2×C4⋊Dic13C2312yes—
197C2×C4⋊Dic13C2311yescharacteristic
198C2×C4⋊Dic13C2312yes—
199C2×C4⋊Dic13C2312yes—
200C2×C4⋊Dic13C2311yescharacteristic
201C2×C4⋊Dic13C2311yescharacteristic
202#88178C2×C418yescomplemented
203C2×#6101C2312yes—
204C2×#6101C2312yes—
205C2×#6101C2312yes—
206C2×#6101C2312yes—
207C2×#6101C2312yes—
208C2×C4×Dic13—28no—
209C2×C4×Dic13—28no—
210C2×C4×Dic13C2312yes—
211C2×C4×Dic13C2311yescharacteristic
212C2×C4×Dic13C2311yescharacteristic
213C2×C4×Dic13C2311yescharacteristic
214C2×C4×Dic13C2311yescharacteristic
215C2×C4×Dic13C2311yescharacteristic
216C2×C4×Dic13C2311yescharacteristic
217C2×C4×Dic13C2312yes—
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220C2×C4×Dic13C2312yes—
221C2×C4×Dic13C2312yes—
222C2×C4×Dic13C2312yes—
223C2×C4×Dic13C2312yes—
224C2×C4×Dic13C2312yes—
225C2×C4×Dic13C2312yes—
226#88151C2×C418yescomplemented
227#88146—24no—
228#88146—24no—
229#88146—28no—
230#88146—24no—
231#88146—28no—
232#88146C2×C418yescomplemented
233#88146D418yescomplemented
234#88141—24no—
235#88137C2×C4116yescomplemented
236#88135—28no—
237#88135C2×C4116yescomplemented
238C22⋊C4×D13—24no—
239C22⋊C4×D13—24no—
240#88131—28no—
241C42×D13—24no—
242C42×D13—24no—
243C4×Dic26—24no—
244C13×#95C2311yescharacteristic
245C13×#95C2311yescharacteristic
246C13×#95C2312yes—
247C13×#95C2312yes—
248#88071C2312yes—
249#88071C2312yes—
250#88071C2312yes—
251#88071C2312yes—
252#88071C2312yes—
253#88071C2311yescharacteristic
254#88071C2312yes—
255#88071C2311yescharacteristic
256#88071C2312yes—
257#88071C2312yes—
258#88071C2311yescharacteristic
259#88071C2311yescharacteristic
260#88071C2311yescharacteristic
261#88071C2311yescharacteristic
262#88071C2312yes—
263#88071C2312yes—
264#34136—131nomaximal, Sylow
265C24×C13C2412yes—
266C24×C13C2411yescharacteristic
267C23×D13—22no—
268C23×D13—22no—
269C23×D13—22no—
270C23×D13—22no—
271C23×D13—41no—
272C23×D13—41no—
273C23×D13C22×C414yes—
274C23×D13C2411yescharacteristic
275C23×D13C2411yescharacteristic
276C2×D4×C13—24no—
277C2×D4×C13—24no—
278C2×D4×C13—22no—
279C2×D4×C13—22no—
280C2×D4×C13C22×C418yes—
281C2×D4×C13C22×C414yes—
282C22×C4×C13—22no—
283C22×C4×C13—22no—
284C22×C4×C13—24no—
285C22×C4×C13—24no—
286C22×C4×C13—24no—
287C22×C4×C13—24no—
288C22×C4×C13—42no—
289C22×C4×C13—42no—
290C22×C4×C13C22×C414yes—
291C22×C4×C13C2411yescharacteristic
292C22×C4×C13C2412yes—
293C22×C4×C13C2411yescharacteristic
294C22×C4×C13C2412yes—
295C22×C4×C13C2411yescharacteristic
296C22×C4×C13C2412yes—
297C22×C4×C13C2411yescharacteristic
298C22×C4×C13C2411yescharacteristic
299C22×C4×C13C2411yescharacteristic
300C2×C22⋊D13—24no—
301C2×C22⋊D13—24no—
302C2×C22⋊D13—42no—
303C2×C22⋊D13—42no—
304C2×C22⋊D13C22×C418yes—
305C2×C22⋊D13C22×C418yes—
306C22×Dic13—24no—
307C22×Dic13—22no—
308C22×Dic13—22no—
309C22×Dic13—24no—
310C22×Dic13—24no—
311C22×Dic13—24no—
312C22×Dic13—24no—
313C22×Dic13—24no—
314C22×Dic13—42no—
315C22×Dic13—42no—
316C22×Dic13C22×C418yes—
317C22×Dic13C22×C414yes—
318C22×Dic13C2411yescharacteristic
319C22×Dic13C2411yescharacteristic
320C22×Dic13C2412yes—
321C22×Dic13C2411yescharacteristic
322C22×Dic13C2412yes—
323C22×Dic13C2412yes—
324C22×Dic13C2412yes—
325C22×Dic13C2411yescharacteristic
326C22×Dic13C2411yescharacteristic
327C22×Dic13C2411yescharacteristic
328#6129—232no—
329C2×C4×D13—22no—
330C2×C4×D13—22no—
331C2×C4×D13—22no—
332C2×C4×D13—22no—
333C2×C4×D13—22no—
334C2×C4×D13—22no—
335C2×C4×D13—232no—
336C2×C4×D13—22no—
337C2×C4×D13—22no—
338C2×C4×D13—22no—
339C2×C4×D13—22no—
340C2×C4×D13—22no—
341C2×C4×D13—22no—
342C2×C4×D13—22no—
343C2×C4×D13—22no—
344C2×C4×D13—41no—
345C2×C4×D13—41no—
346C2×C4×D13—41no—
347C2×C4×D13—41no—
348C2×C4×D13C22×C414yes—
349C2×C4×D13C22×C414yes—
350C2×C4×D13C22×C414yes—
351C2×C4×D13C22×C414yes—
352C2×C4×D13C2×D414yes—
353C2×C4×D13#4114yes—
354C2×Dic26—22no—
355C2×Dic26—22no—
356C2×Dic26C22×C414yes—
357C13×C4⋊C4—24no—
358C13×C4⋊C4—22no—
359C13×C4⋊C4—24no—
360C13×C4⋊C4C22×C414yes—
361C13×C4⋊C4C2×D414yes—
362C13×C22⋊C4—22no—
363C13×C22⋊C4—24no—
364C13×C22⋊C4—24no—
365C13×C22⋊C4—42no—
366C13×C22⋊C4C22×C418yes—
367C13×C22⋊C4#4114yescomplemented
368C42×C13—22no—
369C42×C13—22no—
370C42×C13—24no—
371C22⋊Dic13—22no—
372C22⋊Dic13—24no—
373C22⋊Dic13—24no—
374C22⋊Dic13—42no—
375C22⋊Dic13C22×C418yes—
376C22⋊Dic13C22×C418yes—
377C22⋊Dic13#4114yescomplemented
378#6103—24no—
379#6103—24no—
380#6103—22no—
381#6103—22no—
382#6103—24no—
383#6103—22no—
384#6103—22no—
385#6103C22×C418yes—
386#6103C22×C418yes—
387#6103C2×D418yes—
388C4⋊Dic13—22no—
389C4⋊Dic13—24no—
390C4⋊Dic13—24no—
391C4⋊Dic13C22×C418yes—
392C4⋊Dic13C22×C414yes—
393C4⋊Dic13C2×D414yes—
394#6101—24no—
395#6101—24no—
396#6101—42no—
397#6101—42no—
398#6101C22×C418yes—
399C4×Dic13—22no—
400C4×Dic13—24no—
401C4×Dic13—24no—
402C4×Dic13—22no—
403C4×Dic13—24no—
404C4×Dic13—22no—
405C4×Dic13—22no—
406C4×Dic13—24no—
407C4×Dic13—24no—
408C4×Dic13—22no—
409C4×Dic13—22no—
410C4×Dic13—24no—
411C4×Dic13—42no—
412C4×Dic13—42no—
413C4×Dic13C22×C418yes—
414C4×Dic13C2×D418yes—
415C2×#525—131no—
416C2×C4×#41—131no—
417C22×#117—131no—
418#2363—131no—
419#2363—131no—
420#2362—131no—
421#2362—131no—
422#2361—131no—
423#2361D1311yescharacteristic, complemented
424#2360—131no—
425#2360—131no—
426#2359—132no—
427#2359—132no—
428#2358—132no—
429#2358—132no—
430#2297—131no—
431#2296—131no—
432#2293—132no—
433#2290—132no—
434#2290—132no—
435C42×D4—132no—
436C4×#117—131no—
437C2×C4×C22⋊C4—131no—
438C23×C13—21no—
439C23×C13—21no—
440C23×C13—21no—
441C23×C13—21no—
442C23×C13—22no—
443C23×C13—22no—
444C23×C13—22no—
445C23×C13—22no—
446C23×C13—22no—
447C23×C13—22no—
448C23×C13C23×C414yes—
449C23×C13C23×C412yes—
450C23×C13C2×#4112yes—
451C23×C13C2×#4112yes—
452C23×C13C2511yescharacteristic
453C22×D13—21no—
454C22×D13—21no—
455C22×D13—21no—
456C22×D13—21no—
457C22×D13—28no—
458C22×D13—21no—
459C22×D13—21no—
460C22×D13—21no—
461C22×D13—21no—
462C22×D13—21no—
463C22×D13—21no—
464C22×D13—28no—
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—216no—
475D4×C13—28no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—22no—
479C2×C4×C13—21no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—21no—
483C2×C4×C13—21no—
484C2×C4×C13—22no—
485C2×C4×C13—21no—
486C2×C4×C13—28no—
487C2×C4×C13—22no—
488C2×C4×C13—21no—
489C2×C4×C13—21no—
490C2×C4×C13—21no—
491C2×C4×C13—21no—
492C2×C4×C13—22no—
493C2×C4×C13—21no—
494C2×C4×C13—22no—
495C2×C4×C13—21no—
496C2×C4×C13—48no—
497C2×C4×C13—48no—
498C2×C4×C13C23×C414yes—
499C2×C4×C13C23×C412yes—
500C2×C4×C13C23×C412yes—
501C2×C4×C13C22×D414yes—
502C2×C4×C13C22×D412yes—
503C2×C4×C13C2×#4112yes—
504C2×C4×C13C2×#4112yes—
505C2×C4×C13C2×#4112yes—
506C22⋊D13—216no—
507C22⋊D13—48no—
508C2×Dic13—21no—
509C2×Dic13—21no—
510C2×Dic13—22no—
511C2×Dic13—21no—
512C2×Dic13—22no—
513C2×Dic13—22no—
514C2×Dic13—21no—
515C2×Dic13—21no—
516C2×Dic13—22no—
517C2×Dic13—22no—
518C2×Dic13—22no—
519C2×Dic13—21no—
520C2×Dic13—28no—
521C2×Dic13—216no—
522C2×Dic13—21no—
523C2×Dic13—22no—
524C2×Dic13—21no—
525C2×Dic13—22no—
526C2×Dic13—21no—
527C2×Dic13—21no—
528C2×Dic13—21no—
529C2×Dic13—22no—
530C2×Dic13—21no—
531C2×Dic13—48no—
532C2×Dic13—48no—
533C2×Dic13C23×C414yes—
534C2×Dic13C23×C414yes—
535C2×Dic13C23×C412yes—
536C2×Dic13C23×C412yes—
537C2×Dic13C22×D414yes—
538C2×Dic13C22×D412yes—
539C2×Dic13C2×#4112yes—
540C2×Dic13C2×#4112yes—
541C2×Dic13C2×#4112yes—
542C4×D13—28no—
543C4×D13—28no—
544C4×D13—28no—
545C4×D13—44no—
546C4×D13—44no—
547C4×D13—44no—
548C4×D13—44no—
549C4×D13C4×D4116yescomplemented
550Dic26—28no—
551C22×#41—131no—
552C24×C4—131no—
553#525—1316no—
554C2×#123—132no—
555C2×C22⋊Q8—131no—
556C2×C22⋊Q8—131no—
557C2×#121—131no—
558C2×#121C2×D1311yescharacteristic
559C2×#120—132no—
560C4×#41—268no—
561C2×C4×Q8—131no—
562C2×C4×Q8—131no—
563C2×C4×D4—132no—
564C2×C4×D4—132no—
565C2×C4×D4—131no—
566C2×C4×D4—132no—
567C2×C4×D4—132no—
568C2×C4×D4—132no—
569C2×C4×D4C2×D1312yes—
570C2×C4×D4C2×D1311yescharacteristic, complemented
571C2×#117—131no—
572C2×#117—131no—
573C2×#117—132no—
574C2×#117—131no—
575C2×#117—131no—
576C2×#117—132no—
577C2×#117—131no—
578C2×#117—132no—
579C2×#117—268no—
580C22×C4⋊C4—131no—
581C22×C4⋊C4C2×D1311yescharacteristic
582C22×C22⋊C4—132no—
583C22×C22⋊C4—131no—
584C22×C22⋊C4—131no—
585C22×C42—132no—
586C22×C42—132no—
587C22×C42—131no—
588C22×C42—131no—
589#391—131no—
590#391—131no—
591#390—131no—
592#390—132no—
593#390—132no—
594#390C2×D1311yescharacteristic, complemented
595#389—132no—
596#389—131no—
597#389—131no—
598#389—131no—
599#389—132no—
600#389C2×D1311yescharacteristic, complemented
601#388—132no—
602#388—132no—
603#388—132no—
604#388—132no—
605#388—132no—
606#388—132no—
607#388—132no—
608#388C2×D1312yescomplemented
609#387—132no—
610#387—132no—
611#387—132no—
612#387—132no—
613#386—132no—
614#386—132no—
615#386—132no—
616#386—132no—
617#386—132no—
618#386C2×D1312yes—
619#385—132no—
620#385—132no—
621#385—132no—
622#385—132no—
623#385—132no—
624#385C2×D1312yescomplemented
625C4×C4⋊C4—132no—
626C4×C4⋊C4—131no—
627C4×C4⋊C4—131no—
628C4×C4⋊C4—132no—
629C4×C4⋊C4—132no—
630C4×C4⋊C4—131no—
631C4×C4⋊C4—132no—
632C4×C4⋊C4C2×D1311yescharacteristic, complemented
633C4×C22⋊C4—132no—
634C4×C22⋊C4—132no—
635C4×C22⋊C4—131no—
636C4×C22⋊C4—132no—
637C4×C22⋊C4—132no—
638C4×C22⋊C4—131no—
639C4×C22⋊C4—131no—
640C4×C22⋊C4—132no—
641C4×C22⋊C4—132no—
642C4×C22⋊C4—132no—
643C4×C22⋊C4—131no—
644C4×C22⋊C4—131no—
645C4×C22⋊C4—132no—
646C4×C22⋊C4—131no—
647C4×C22⋊C4—131no—
648C4×C22⋊C4C2×D1311yescharacteristic
649#376—132no—
650C2×#95—131no—
651C2×#95—131no—
652C43—132no—
653C22×C13—22no—
654C22×C13—22no—
655C22×C13—22no—
656C22×C13—22no—
657C22×C13—22no—
658C22×C13—22no—
659C22×C13—24no—
660C22×C13—24no—
661C22×C13—24no—
662C22×C13—42no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13—42no—
666C22×C13C4×#4114yescomplemented
667C22×C13C24×C411yescharacteristic
668C22×C13C23×D411yescharacteristic
669C22×C13C22×#4111yescharacteristic
670C22×C13C22×#4111yescharacteristic
671C22×C13C22×#4111yescharacteristic
672C22×C13#58511yescharacteristic
673C22×C13#58511yescharacteristic
674C2×D13—22no—
675C2×D13—22no—
676C2×D13—22no—
677C2×D13—22no—
678C2×D13—22no—
679C2×D13—22no—
680C2×D13—22no—
681C2×D13—22no—
682C2×D13—22no—
683C2×D13—416no—
684C2×D13—41no—
685C2×D13—41no—
686C2×D13—41no—
687C2×D13—41no—
688C2×D13C2×C4×D414yes—
689C4×C13—22no—
690C4×C13—24no—
691C4×C13—22no—
692C4×C13—24no—
693C4×C13—22no—
694C4×C13—41no—
695C4×C13—42no—
696C4×C13—41no—
697C4×C13C2×C4×D414yes—
698Dic13—24no—
699Dic13—22no—
700Dic13—24no—
701Dic13—22no—
702Dic13—24no—
703Dic13—22no—
704Dic13—41no—
705Dic13—42no—
706Dic13—41no—
707Dic13C2×C4×D414yes—
708C25—131no—
709C2×#41—138no—
710C2×#41—264no—
711C2×#41—264no—
712C22×Q8—131no—
713C22×D4—132no—
714C22×D4—132no—
715C22×D4C22×D1312yes—
716C22×D4C22×D1311yescharacteristic
717C23×C4—131no—
718C23×C4—132no—
719C23×C4—131no—
720C23×C4—138no—
721C23×C4—131no—
722C23×C4—131no—
723C23×C4—131no—
724C23×C4—132no—
725C23×C4—132no—
726C23×C4—131no—
727C23×C4—131no—
728C23×C4—131no—
729C23×C4—131no—
730C23×C4—264no—
731C23×C4—264no—
732C23×C4C22×D1312yes—
733C23×C4C22×D1312yes—
734C23×C4C22×D1311yescharacteristic
735#123—1316no—
736C22⋊Q8—138no—
737C22⋊Q8—138no—
738#121—138no—
739#121C4×D1318yescomplemented
740#120—1316no—
741C4×Q8—264no—
742C4×Q8—264no—
743C4×D4—24no—
744C4×D4—28no—
745C4×D4—1316no—
746C4×D4—1316no—
747C4×D4—268no—
748C4×D4—268no—
749C4×D4—268no—
750C4×D4—264no—
751#117—138no—
752#117—138no—
753#117—268no—
754#117—268no—
755#117—268no—
756#117—264no—
757#117—264no—
758#117—264no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—131no—
761C2×C4⋊C4—131no—
762C2×C4⋊C4—132no—
763C2×C4⋊C4—132no—
764C2×C4⋊C4—132no—
765C2×C4⋊C4—131no—
766C2×C4⋊C4—132no—
767C2×C4⋊C4—132no—
768C2×C4⋊C4—132no—
769C2×C4⋊C4—132no—
770C2×C4⋊C4—132no—
771C2×C4⋊C4—264no—
772C2×C4⋊C4C22×D1312yes—
773C2×C4⋊C4C22×D1311yescharacteristic
774C2×C4⋊C4C22×D1312yes—
775C2×C4⋊C4C22×D1311yescharacteristic
776C2×C4⋊C4C22×D1311yescharacteristic
777C2×C22⋊C4—131no—
778C2×C22⋊C4—132no—
779C2×C22⋊C4—132no—
780C2×C22⋊C4—132no—
781C2×C22⋊C4—132no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—131no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—132no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—132no—
789C2×C22⋊C4—131no—
790C2×C22⋊C4—131no—
791C2×C22⋊C4—131no—
792C2×C22⋊C4—131no—
793C2×C22⋊C4—132no—
794C2×C22⋊C4—264no—
795C2×C22⋊C4—268no—
796C2×C22⋊C4—264no—
797C2×C22⋊C4C22×D1311yescharacteristic
798C2×C22⋊C4C22×D1312yes—
799C2×C22⋊C4C22×D1312yes—
800C2×C22⋊C4C22×D1312yes—
801C2×C22⋊C4C22×D1312yes—
802C2×C22⋊C4C22×D1311yescharacteristic
803C2×C42—132no—
804C2×C42—132no—
805C2×C42—132no—
806C2×C42—131no—
807C2×C42—132no—
808C2×C42—132no—
809C2×C42—131no—
810C2×C42—132no—
811C2×C42—132no—
812C2×C42—132no—
813C2×C42—131no—
814C2×C42—131no—
815C2×C42—131no—
816C2×C42—131no—
817C2×C42—132no—
818C2×C42—132no—
819C2×C42—264no—
820C2×C42—264no—
821C2×C42—268no—
822C2×C42—268no—
823C2×C42C22×D1312yes—
824C2×C42C22×D1311yescharacteristic
825C2×C42C22×D1311yescharacteristic
826#95—131no—
827#95—131no—
828#95—131no—
829#95—131no—
830#95—131no—
831#95—131no—
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#95—132no—
842#95C22×D1311yescharacteristic
843#95C22×D1311yescharacteristic
844#95C22×D1312yes—
845#95C22×D1312yes—
846C2×C13—24no—
847C2×C13—44no—
848C2×C13C22×C4×D411yescharacteristic
849C2×C13C2×C4×#4111yescharacteristic
850C2×C13#342811yescharacteristic
851C2×C13D4×#4111yescharacteristic
852C2×C13D4×#4111yescharacteristic
853C2×C13#347511yescharacteristic
854C2×C13#347511yescharacteristic
855D13—24no—
856D13—42no—
857C24—131no—
858C24—131no—
859C24—134no—
860C24—262no—
861C24—262no—
862C24—262no—
863C24—262no—
864C24—521no—
865C24—521no—
866C24C23×D1312yes—
867C24C23×D1311yescharacteristic
868#41—2632no—
869C2×Q8—134no—
870C2×Q8—262no—
871C2×Q8—262no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—138no—
877C2×D4—138no—
878C2×D4—264no—
879C2×D4—264no—
880C2×D4—522no—
881C2×D4—522no—
882C2×D4C2×C4×D1318yes—
883C2×D4C2×C4×D1314yes—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—131no—
893C22×C4—134no—
894C22×C4—134no—
895C22×C4—134no—
896C22×C4—134no—
897C22×C4—138no—
898C22×C4—131no—
899C22×C4—131no—
900C22×C4—131no—
901C22×C4—132no—
902C22×C4—132no—
903C22×C4—132no—
904C22×C4—134no—
905C22×C4—134no—
906C22×C4—134no—
907C22×C4—131no—
908C22×C4—131no—
909C22×C4—132no—
910C22×C4—262no—
911C22×C4—262no—
912C22×C4—2632no—
913C22×C4—262no—
914C22×C4—262no—
915C22×C4—262no—
916C22×C4—262no—
917C22×C4—262no—
918C22×C4—262no—
919C22×C4—262no—
920C22×C4—262no—
921C22×C4—262no—
922C22×C4—264no—
923C22×C4—262no—
924C22×C4—264no—
925C22×C4—264no—
926C22×C4—264no—
927C22×C4—264no—
928C22×C4—262no—
929C22×C4—262no—
930C22×C4—264no—
931C22×C4—262no—
932C22×C4—262no—
933C22×C4—521no—
934C22×C4—521no—
935C22×C4—521no—
936C22×C4—521no—
937C22×C4—522no—
938C22×C4—522no—
939C22×C4C2×C4×D1314yes—
940C22×C4C23×D1311yescharacteristic
941C22×C4C23×D1312yes—
942C22×C4C23×D1311yescharacteristic
943C22×C4C23×D1312yes—
944C22×C4C23×D1311yescharacteristic
945C22×C4C23×D1312yes—
946C22×C4C23×D1311yescharacteristic
947C22×C4C23×D1311yescharacteristic
948C22×C4C23×D1311yescharacteristic
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—134no—
953C4⋊C4—138no—
954C4⋊C4—138no—
955C4⋊C4—134no—
956C4⋊C4—264no—
957C4⋊C4—264no—
958C4⋊C4—264no—
959C4⋊C4—262no—
960C4⋊C4—264no—
961C4⋊C4—522no—
962C4⋊C4—522no—
963C4⋊C4C2×C4×D1314yes—
964C4⋊C4D4×D1314yes—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—42no—
969C22⋊C4—138no—
970C22⋊C4—138no—
971C22⋊C4—134no—
972C22⋊C4—138no—
973C22⋊C4—138no—
974C22⋊C4—138no—
975C22⋊C4—264no—
976C22⋊C4—262no—
977C22⋊C4—262no—
978C22⋊C4—264no—
979C22⋊C4—264no—
980C22⋊C4—264no—
981C22⋊C4—262no—
982C22⋊C4—264no—
983C22⋊C4—262no—
984C22⋊C4—262no—
985C22⋊C4—522no—
986C22⋊C4C2×C4×D1318yes—
987C22⋊C4#612914yescomplemented
988C42—22no—
989C42—24no—
990C42—22no—
991C42—138no—
992C42—138no—
993C42—262no—
994C42—262no—
995C42—264no—
996C42—264no—
997C42—264no—
998C42—262no—
999C42—262no—
1000C42—264no—
1001C42—264no—
1002C42—264no—
1003C42—262no—
1004C42—262no—
1005C42—522no—
1006C42—522no—
1007C13#3413611yescharacteristic, complemented, Sylow
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—132no—
1019C23—132no—
1020C23—132no—
1021C23—132no—
1022C23—268no—
1023C23—261no—
1024C23—261no—
1025C23—261no—
1026C23—261no—
1027C23—268no—
1028C23—261no—
1029C23—261no—
1030C23—261no—
1031C23—261no—
1032C23—261no—
1033C23—261no—
1034C23—524no—
1035C23—524no—
1036C23—524no—
1037C23—524no—
1038C23—524no—
1039C23C22×C4×D1314yes—
1040C23C22×C4×D1312yes—
1041C23C2×#612912yes—
1042C23#41×D1312yes—
1043C23C24×D1311yescharacteristic
1044Q8—268no—
1045D4—216no—
1046D4—28no—
1047D4—2616no—
1048D4—528no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—28no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—132no—
1072C2×C4—132no—
1073C2×C4—132no—
1074C2×C4—1316no—
1075C2×C4—134no—
1076C2×C4—132no—
1077C2×C4—134no—
1078C2×C4—134no—
1079C2×C4—132no—
1080C2×C4—132no—
1081C2×C4—268no—
1082C2×C4—268no—
1083C2×C4—268no—
1084C2×C4—2616no—
1085C2×C4—261no—
1086C2×C4—261no—
1087C2×C4—262no—
1088C2×C4—261no—
1089C2×C4—262no—
1090C2×C4—261no—
1091C2×C4—262no—
1092C2×C4—261no—
1093C2×C4—262no—
1094C2×C4—262no—
1095C2×C4—262no—
1096C2×C4—261no—
1097C2×C4—268no—
1098C2×C4—261no—
1099C2×C4—262no—
1100C2×C4—261no—
1101C2×C4—261no—
1102C2×C4—261no—
1103C2×C4—262no—
1104C2×C4—261no—
1105C2×C4—261no—
1106C2×C4—262no—
1107C2×C4—524no—
1108C2×C4—524no—
1109C2×C4—524no—
1110C2×C4—524no—
1111C2×C4—528no—
1112C2×C4—528no—
1113C2×C4C22×C4×D1314yes—
1114C2×C4C22×C4×D1312yes—
1115C2×C4C22×C4×D1312yes—
1116C2×C4C2×D4×D1314yes—
1117C2×C4C2×D4×D1312yes—
1118C2×C4C2×#612912yes—
1119C2×C4C2×#612912yes—
1120C2×C4#41×D1312yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—134no—
1135C22—262no—
1136C22—262no—
1137C22—262no—
1138C22—262no—
1139C22—262no—
1140C22—262no—
1141C22—262no—
1142C22—262no—
1143C22—262no—
1144C22—5216no—
1145C22—521no—
1146C22—521no—
1147C22—521no—
1148C22—521no—
1149C22C4×#612914yescomplemented
1150C22C23×C4×D1311yescharacteristic
1151C22C22×D4×D1311yescharacteristic
1152C22C22×#612911yescharacteristic
1153C22C2×#41×D1311yescharacteristic
1154C22C2×#41×D1311yescharacteristic
1155C22#1171965011yescharacteristic
1156C22#1171965211yescharacteristic
1157C4—22no—
1158C4—24no—
1159C4—22no—
1160C4—24no—
1161C4—22no—
1162C4—42no—
1163C4—41no—
1164C4—41no—
1165C4—134no—
1166C4—262no—
1167C4—264no—
1168C4—264no—
1169C4—264no—
1170C4—262no—
1171C4—262no—
1172C4—521no—
1173C4—522no—
1174C4—521no—
1175C4C4×D4×D1314yes—
1176C2—24no—
1177C2—44no—
1178C2—264no—
1179C2—522no—
1180C2C2×C4×D4×D1311yescharacteristic
1181C2C2×C4×#612911yescharacteristic
1182C2#1312803611yescharacteristic
1183C2D4×#612911yescharacteristic
1184C2#1312832511yescharacteristic
1185C2#1312839511yescharacteristic
1186C2#1312839911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2361C2
socle, cosocleC23×C13C25
prime radicalC2×#11719311C2
hypercenter#2361D13
hypocenterC13#34136
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6129C2semidirect
3. C22×#88146C2semidirect
4. #13117879C2semidirect
5. #13117870C2semidirect
6. #13117865C2semidirect
7. #13117862C2semidirect
8. #13117856C2semidirect
9. #13117841C2semidirect
10. #13117839C2semidirect
11. #13117831C2semidirect
12. #13117827C2semidirect
13. #13117816C2semidirect
14. #13117813C2semidirect
15. #13117323C2semidirect
16. #13117317C2semidirect
17. #13117296C2semidirect
18. #13117276C2semidirect
19. #13117272C2semidirect
20. C4×D4×Dic13C2semidirect
21. C4×#88146C2semidirect
22. C4×C22⋊C4×D13C2semidirect
23. C13×#2361C2semidirect
28. C2×C4×D4×C13C22semidirect
34. C2×D4×Dic13C22semidirect
40. C22×C4×Dic13C22semidirect
41. #11719311C4semidirect
52. C2×#88141C22semidirect
58. C2×#88131C22semidirect
61. C2×C4×Dic26C22semidirect
62. C13×#390C22semidirect
63. C13×#389C22semidirect
64. C13×#388C22semidirect
66. C13×#385C22semidirect
67. C4×C13×C4⋊C4C22semidirect
69. #11718882C22semidirect
75. C4×C22⋊Dic13C22semidirect
78. #11718646C22semidirect
79. #11718639C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. C4⋊C4×Dic13C22semidirect
82. C4⋊C4×Dic13C22semidirect
83. C4⋊C4×Dic13C22semidirect
84. #11718635C22semidirect
85. #11718634C22semidirect
86. #11718633C22semidirect
92. #11718612C22semidirect
93. #11718611C22semidirect
95. #11718606C22semidirect
96. #11718605C22semidirect
100. C22⋊C4×Dic13C22semidirect
101. C22⋊C4×Dic13C22semidirect
102. C22⋊C4×Dic13C22semidirect
107. C4×C4⋊Dic13C22semidirect
108. C4×C4⋊Dic13C22semidirect
109. C42×Dic13C22semidirect
110. #11718590C22semidirect
111. #11718589C22semidirect
120. #11718316C22semidirect
121. #11718315C22semidirect
122. #11718314C22semidirect
123. #11718310C22semidirect
124. #11718309C22semidirect
125. #11718308C22semidirect
140. C2×#6129C2×C4semidirect
143. C22×C4×D13C2×C4semidirect
153. C13×#121C2×C4semidirect
178. #88192C2×C4semidirect
179. #88191C2×C4semidirect
182. D4×Dic13C2×C4semidirect
202. #88178C2×C4semidirect
226. #88151C2×C4semidirect
232. #88146C2×C4semidirect
233. #88146D4semidirect
235. #88137C2×C4semidirect
237. #88135C2×C4semidirect
367. C13×C22⋊C4#41semidirect
377. C22⋊Dic13#41semidirect
423. #2361D13semidirect
549. C4×D13C4×D4semidirect
570. C2×C4×D4C2×D13semidirect
594. #390C2×D13semidirect
600. #389C2×D13semidirect
608. #388C2×D13semidirect
624. #385C2×D13semidirect
632. C4×C4⋊C4C2×D13semidirect
666. C22×C13C4×#41semidirect
739. #121C4×D13semidirect
987. C22⋊C4#6129semidirect
1007. C13#34136semidirect
1149. C22C4×#6129semidirect

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
C22×#881462
#131178792
#131178702
#131178652
#131178622
#131178562
#131178412
#131178392
#131178312
#131178272
#131178162
#131178132
#131173232
#131173172
#131172962
#131172762
#131172722
C4×D4×Dic132
C4×#881462
C4×C22⋊C4×D132
C13×#23612
#3413613