Finite Group Databasebeta

← C2×#13128166 #16769754

Subgroups — C2×#13128166 #16769754

Order 3328.

11662 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6127C211yesmaximal, characteristic, complemented
2C22×#41×D13C211yesmaximal, characteristic, complemented
3#13128166C2132yesmaximal, direct product factor
4C2×#11719334C212yesmaximal, complemented
5C2×#11719313C212yesmaximal, complemented
6C2×#11719333C212yesmaximal, complemented
7C2×#11719353C212yesmaximal, complemented
8C2×#11719312C212yesmaximal, complemented
9C2×#11719297C212yesmaximal, complemented
10C2×#11719358C212yesmaximal, complemented
11C2×#11719294C212yesmaximal, complemented
12C2×#11719253C214yesmaximal, complemented
13C2×#11719229C211yesmaximal, characteristic, complemented
14C2×#11719496C211yesmaximal, characteristic, complemented
15C2×#11719252C214yesmaximal, complemented
16C2×#11719533C211yesmaximal, characteristic, complemented
17C2×D13×#117C211yesmaximal, characteristic, complemented
18C2×C13×#525C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic, complemented
21C23×C22⋊D13C2211yescharacteristic
22C23×C22⋊D13C2211yescharacteristic, complemented
23C2×#41×D13—216no—
24C2×#41×D13C22116yescomplemented
25C22×#6131C2211yescharacteristic, complemented
26C22×Q8×D13C2211yescharacteristic, complemented
27C22×#6129C2212yes—
28C22×#6129C2211yescharacteristic, complemented
29C22×D4×D13C2212yes—
30C22×D4×D13C2211yescharacteristic, complemented
31C22×#6127—216no—
32C22×#6127C2212yes—
33C22×#6127C2211yescharacteristic
34C22×#6127C2212yes—
35C22×#6127C2212yescomplemented
36C22×#6127C2212yescomplemented
37C22×#6127C2212yescomplemented
38C22×#6127C22116yescomplemented
39C23×D52C2211yescharacteristic
40C23×C4×D13C2211yescharacteristic
41C23×C4×D13C2211yescharacteristic, complemented
42C23×C4×D13C2212yescomplemented
43C23×Dic26C2211yescharacteristic, complemented
44C13×#525C22116yescomplemented
45C2×C13×#123C2212yescomplemented
46C2×C13×C22⋊Q8C2212yescomplemented
47C2×C13×#121C2212yescomplemented
48C2×C13×#120C2212yescomplemented
49C2×C4×D4×C13C2214yescomplemented
50C2×C13×#117C2211yescharacteristic, complemented
51C2×#88207C2212yescomplemented
52#11719533C22116yescomplemented
53C2×#88200C2212yescomplemented
54C2×#88194C2214yescomplemented
55C2×#88193C2214yescomplemented
56C2×#88192C2212yescomplemented
57C2×#88192C2214yescomplemented
58C2×#88191C2212yescomplemented
59C2×#88191C2214yescomplemented
60C2×#88189C2212yescomplemented
61#11719496C22116yescomplemented
62C2×#88184C2212yescomplemented
63C2×#88183C2212yescomplemented
64C2×C4×C22⋊D13C2214yescomplemented
65C2×C4×C22⋊D13C2214yescomplemented
66C2×#88180C2211yescharacteristic, complemented
67C2×#88178C2212yescomplemented
68#11719358C22132yescomplemented
69#11719353C22132yescomplemented
70#11719334C22132yescomplemented
71#11719333C22132yescomplemented
72#11719313C22132yescomplemented
73#11719312C22132yescomplemented
74#11719297C22132yescomplemented
75#11719294C22132yescomplemented
76#11719253C22164yescomplemented
77#11719252C22164yescomplemented
78#11719229C22116yescomplemented
79D13×#117C22116yescomplemented
80C2×#88151C2212yescomplemented
81C2×#88150C2214yescomplemented
82C2×#88149C2212yescomplemented
83C2×#88149C2214yescomplemented
84C2×#88148C2214yescomplemented
85C2×#88146C2212yescomplemented
86C2×C4⋊C4×D13C2212yescomplemented
87C2×#88142C2214yescomplemented
88C2×#88140C2212yescomplemented
89C2×#88139C2214yescomplemented
90C2×#88139C2214yescomplemented
91C2×#88138C2214yescomplemented
92C2×#88138C2214yescomplemented
93C2×#88138C2214yescomplemented
94C2×#88137C2214yescomplemented
95C2×#88136C2214yescomplemented
96C2×#88136C2212yescomplemented
97C2×C22⋊C4×D13C2212yes—
98C2×#88132C2214yescomplemented
99C2×#88131C2212yescomplemented
100C2×C4×D52C2214yescomplemented
101C2×#88126C2212yescomplemented
102C2×C42×D13C2212yescomplemented
103C25×C13C2311yescharacteristic
104C24×D13C2311yescharacteristic
105C24×D13C2312yes—
106C24×D13C2311yescharacteristic
107C2×C13×#41—28no—
108C2×C13×#41C2318yes—
109C22×Q8×C13C2311yescharacteristic
110C22×D4×C13C2312yes—
111C22×D4×C13C2311yescharacteristic
112C22×D4×C13C2314yes—
113C23×C4×C13—28no—
114C23×C4×C13C2312yes—
115C23×C4×C13C2312yes—
116C23×C4×C13C2312yes—
117C23×C4×C13C2311yescharacteristic
118C23×C4×C13C2311yescharacteristic
119C23×C4×C13C2318yescomplemented
120C22×C22⋊D13—28no—
121C22×C22⋊D13—28no—
122C22×C22⋊D13C2312yes—
123C22×C22⋊D13C2312yes—
124C22×C22⋊D13C2312yes—
125C22×C22⋊D13C2312yes—
126C22×C22⋊D13C2312yes—
127C22×C22⋊D13C2312yes—
128C22×C22⋊D13C2312yes—
129C22×C22⋊D13C2318yes—
130C22×C22⋊D13C2314yes—
131C22×C22⋊D13C2314yes—
132C22×C22⋊D13C2318yescomplemented
133C23×Dic13C2312yes—
134C23×Dic13C2311yescharacteristic
135C23×Dic13C2311yescharacteristic
136#41×D13—2128no—
137C2×#6131—28no—
138C2×#6131C2318yescomplemented
139C2×Q8×D13—28no—
140C2×Q8×D13C2318yescomplemented
141C2×#6129—216no—
142C2×#6129—28no—
143C2×#6129C23116yes—
144C2×#6129C2318yescomplemented
145C2×D4×D13—216no—
146C2×D4×D13—28no—
147C2×D4×D13C23116yes—
148C2×D4×D13C2318yescomplemented
149C2×#6127—28no—
150C2×#6127—216no—
151C2×#6127—216no—
152C2×#6127—216no—
153C2×#6127—216no—
154C2×#6127—216no—
155C2×#6127—2128no—
156C2×#6127C2318yes—
157C2×#6127C23116yes—
158C2×#6127C23116yes—
159C2×#6127C23116yescomplemented
160C2×#6127C23116yescomplemented
161C2×#6127C23116yescomplemented
162C22×D52—28no—
163C22×D52C2312yes—
164C22×D52C2312yes—
165C22×D52C2312yes—
166C22×D52C2311yescharacteristic
167C22×D52C2318yes—
168C22×D52C2314yes—
169C22×C4×D13—28no—
170C22×C4×D13—216no—
171C22×C4×D13D4116yescomplemented
172C22×C4×D13C2312yes—
173C22×C4×D13C2312yes—
174C22×C4×D13C2312yes—
175C22×C4×D13C2312yes—
176C22×C4×D13C2312yes—
177C22×C4×D13C2314yes—
178C22×C4×D13C2311yescharacteristic
179C22×C4×D13C2311yescharacteristic
180C22×C4×D13C2311yescharacteristic
181C22×C4×D13C2311yescharacteristic
182C22×C4×D13C2318yes—
183C22×C4×D13C2318yescomplemented
184C22×C4×D13C23116yescomplemented
185C22×Dic26—28no—
186C22×Dic26C2312yes—
187C22×Dic26C2312yes—
188C22×Dic26C2312yes—
189C22×Dic26C2311yescharacteristic
190C22×Dic26C2318yescomplemented
191C13×#123C23116yescomplemented
192C13×C22⋊Q8C23116yescomplemented
193C13×#121C23116yescomplemented
194C13×#120C23116yescomplemented
195C4×D4×C13C23132yescomplemented
196C13×#117C2318yescomplemented
197C2×C13×C4⋊C4C2314yes—
198C2×C13×C4⋊C4C2312yes—
199C2×C13×C22⋊C4C2312yes—
200C2×C13×C22⋊C4C2314yes—
201C2×C13×C22⋊C4C2314yes—
202C2×C42×C13C2312yes—
203#88207C23116yescomplemented
204C2×C22⋊Dic13C2312yes—
205C2×C22⋊Dic13C2314yes—
206C2×C22⋊Dic13C2314yes—
207#88200C23116yescomplemented
208#88194C23132yescomplemented
209#88193C23132yescomplemented
210#88192C23132yescomplemented
211#88192C23116yescomplemented
212#88191C23132yescomplemented
213#88191C23116yescomplemented
214#88189C23116yescomplemented
215#88184C23116yescomplemented
216#88183C23116yescomplemented
217C4×C22⋊D13C23132yescomplemented
218C4×C22⋊D13C23132yescomplemented
219C2×#6103C2314yes—
220C2×#6103C2314yes—
221C2×#6103C2314yes—
222C2×#6103C2314yes—
223C2×#6103C2314yes—
224#88180C2318yescomplemented
225C2×C4⋊Dic13C2314yes—
226C2×C4⋊Dic13C2312yes—
227#88178C23116yescomplemented
228C2×#6101C2314yes—
229C2×#6101C2314yes—
230C2×#6101C2314yes—
231C2×C4×Dic13C2312yes—
232C2×C4×Dic13C2314yes—
233#88151C23116yescomplemented
234#88150C23132yescomplemented
235#88149C23116yescomplemented
236#88149C23132yescomplemented
237#88148C23132yescomplemented
238#88146C23116yescomplemented
239C4⋊C4×D13C23116yescomplemented
240#88142C23132yescomplemented
241#88140C23116yescomplemented
242#88139C23132yescomplemented
243#88139C23132yescomplemented
244#88138C23132yescomplemented
245#88138C23132yescomplemented
246#88138C23132yescomplemented
247#88137C23132yescomplemented
248#88136C23116yescomplemented
249#88136C23132yescomplemented
250C22⋊C4×D13C23116yes—
251#88132C23132yescomplemented
252#88131C23116yescomplemented
253C4×D52C23132yescomplemented
254#88126C23116yescomplemented
255C42×D13C23116yescomplemented
256C2×#3449—131nomaximal, Sylow
257C24×C13—24no—
258C24×C13—44no—
259C24×C13C2412yes—
260C24×C13C2412yes—
261C24×C13C2411yescharacteristic
262C24×C13C2414yes—
263C23×D13—24no—
264C23×D13—28no—
265C23×D13—44no—
266C23×D13—48no—
267C23×D13—44no—
268C23×D13C2×D418yes—
269C23×D13C2412yes—
270C23×D13C2412yes—
271C23×D13C2411yescharacteristic
272C23×D13C2411yescharacteristic
273C23×D13C2414yes—
274C23×D13C2418yes—
275C23×D13C2414yes—
276C13×#41—232no—
277C2×Q8×C13—24no—
278C2×Q8×C13C2414yes—
279C2×D4×C13—28no—
280C2×D4×C13—24no—
281C2×D4×C13—48no—
282C2×D4×C13C2418yes—
283C2×D4×C13C2414yes—
284C2×D4×C13C24116yes—
285C22×C4×C13—24no—
286C22×C4×C13—28no—
287C22×C4×C13—28no—
288C22×C4×C13—28no—
289C22×C4×C13—232no—
290C22×C4×C13C2×D418yes—
291C22×C4×C13C2414yes—
292C22×C4×C13C2412yes—
293C22×C4×C13C2412yes—
294C22×C4×C13C2418yes—
295C22×C4×C13C2418yes—
296C22×C4×C13C2418yes—
297C22×C4×C13C2414yes—
298C22×C4×C13C2411yescharacteristic
299C22×C4×C13C2414yes—
300C22×C4×C13C2411yescharacteristic
301C2×C22⋊D13—28no—
302C2×C22⋊D13—28no—
303C2×C22⋊D13—28no—
304C2×C22⋊D13—232no—
305C2×C22⋊D13—28no—
306C2×C22⋊D13—28no—
307C2×C22⋊D13—28no—
308C2×C22⋊D13—232no—
309C2×C22⋊D13—28no—
310C2×C22⋊D13—48no—
311C2×C22⋊D13—48no—
312C2×C22⋊D13C2418yes—
313C2×C22⋊D13C2418yes—
314C2×C22⋊D13C2418yes—
315C2×C22⋊D13C2418yes—
316C2×C22⋊D13C2418yes—
317C2×C22⋊D13C2418yes—
318C2×C22⋊D13C2418yes—
319C2×C22⋊D13C24116yes—
320C2×C22⋊D13C24116yes—
321C22×Dic13—24no—
322C22×Dic13—28no—
323C22×Dic13C2×D418yes—
324C22×Dic13C2418yes—
325C22×Dic13C2414yes—
326C22×Dic13C2414yes—
327C22×Dic13C2412yes—
328C22×Dic13C2412yes—
329C22×Dic13C2414yes—
330C22×Dic13C2411yescharacteristic
331C22×Dic13C2411yescharacteristic
332#6131—232no—
333Q8×D13—232no—
334#6129—264no—
335#6129—232no—
336D4×D13—264no—
337D4×D13—232no—
338#6127—232no—
339#6127—264no—
340#6127—264no—
341#6127—264no—
342#6127—264no—
343#6127—264no—
344C2×D52—28no—
345C2×D52—28no—
346C2×D52—232no—
347C2×D52—28no—
348C2×D52—24no—
349C2×D52—48no—
350C2×D52C2418yes—
351C2×D52C2418yes—
352C2×D52C2418yes—
353C2×D52C2414yes—
354C2×D52C24116yes—
355C2×C4×D13—28no—
356C2×C4×D13—28no—
357C2×C4×D13—28no—
358C2×C4×D13—28no—
359C2×C4×D13—232no—
360C2×C4×D13—28no—
361C2×C4×D13—264no—
362C2×C4×D13—48no—
363C2×C4×D13C2×D418yes—
364C2×C4×D13C2×D418yes—
365C2×C4×D13C2×D418yes—
366C2×C4×D13C2×D418yes—
367C2×C4×D13C2×D4164yescomplemented
368C2×C4×D13C2418yes—
369C2×C4×D13C2418yes—
370C2×C4×D13C2418yes—
371C2×C4×D13C2418yes—
372C2×C4×D13C2418yes—
373C2×C4×D13C24116yes—
374C2×C4×D13C2414yes—
375C2×C4×D13C2414yes—
376C2×C4×D13C2414yes—
377C2×C4×D13C2414yes—
378C2×Dic26—24no—
379C2×Dic26—28no—
380C2×Dic26—28no—
381C2×Dic26—232no—
382C2×Dic26—28no—
383C2×Dic26C2418yes—
384C2×Dic26C2418yes—
385C2×Dic26C2418yes—
386C2×Dic26C2414yes—
387C13×C4⋊C4C24116yes—
388C13×C4⋊C4C2418yes—
389C13×C22⋊C4C2418yes—
390C13×C22⋊C4C24116yes—
391C13×C22⋊C4C24116yes—
392C42×C13C2418yes—
393C22⋊Dic13C2418yes—
394C22⋊Dic13C24116yes—
395C22⋊Dic13C24116yes—
396#6103C24116yes—
397#6103C24116yes—
398#6103C24116yes—
399#6103C24116yes—
400#6103C24116yes—
401C4⋊Dic13C24116yes—
402C4⋊Dic13C2418yes—
403#6101C24116yes—
404#6101C24116yes—
405#6101C24116yes—
406C4×Dic13C2418yes—
407C4×Dic13C24116yes—
408C23×#41—131no—
409C23×#41—131no—
410#3449—1332no—
411C2×#537—132no—
412C2×#537—132no—
413C2×#536—132no—
414C2×#536—132no—
415C2×#535—132no—
416C2×#535—132no—
417C2×#534—132no—
418C2×#534—132no—
419C2×#532—134no—
420C2×#525—131no—
421C2×#525—131no—
422C2×#525—134no—
423C2×#525—131no—
424C2×#525D1311yescharacteristic, complemented
425C22×#117—131no—
426C23×C13—24no—
427C23×C13—24no—
428C23×C13—28no—
429C23×C13—24no—
430C23×C13—24no—
431C23×C13—28no—
432C23×C13—24no—
433C23×C13—48no—
434C23×C13—416no—
435C23×C13C22×D414yes—
436C23×C13C2514yes—
437C23×C13C2514yes—
438C23×C13C2512yes—
439C23×C13C2511yescharacteristic
440C22×D13—24no—
441C22×D13—24no—
442C22×D13—28no—
443C22×D13—24no—
444C22×D13—24no—
445C22×D13—24no—
446C22×D13—28no—
447C22×D13—24no—
448C22×D13—216no—
449C22×D13—416no—
450C22×D13—48no—
451C22×D13—416no—
452C22×D13—48no—
453C22×D13—432no—
454C22×D13—416no—
455C22×D13C22×D414yes—
456C22×D13C22×D414yes—
457C22×D13C22×D4116yes—
458C22×D13C2514yes—
459C22×D13C2514yes—
460C22×D13C2512yes—
461C22×D13C2512yes—
462Q8×C13—28no—
463D4×C13—216no—
464D4×C13—28no—
465D4×C13—416no—
466C2×C4×C13—28no—
467C2×C4×C13—24no—
468C2×C4×C13—24no—
469C2×C4×C13—28no—
470C2×C4×C13—216no—
471C2×C4×C13—216no—
472C2×C4×C13—216no—
473C2×C4×C13C22×D414yes—
474C2×C4×C13C22×D414yes—
475C2×C4×C13C22×D4116yes—
476C2×C4×C13C2518yes—
477C2×C4×C13C2514yes—
478C2×C4×C13C2514yes—
479C2×C4×C13C2512yes—
480C2×C4×C13C2512yes—
481C22⋊D13—216no—
482C22⋊D13—216no—
483C22⋊D13—216no—
484C22⋊D13—216no—
485C22⋊D13—216no—
486C22⋊D13—216no—
487C22⋊D13—216no—
488C22⋊D13—416no—
489C22⋊D13—416no—
490C2×Dic13—28no—
491C2×Dic13—24no—
492C2×Dic13—24no—
493C2×Dic13—28no—
494C2×Dic13—216no—
495C2×Dic13C22×D414yes—
496C2×Dic13C22×D414yes—
497C2×Dic13C22×D4116yes—
498C2×Dic13C2518yes—
499C2×Dic13C2514yes—
500C2×Dic13C2514yes—
501C2×Dic13C2512yes—
502C2×Dic13C2512yes—
503D52—216no—
504D52—216no—
505D52—216no—
506D52—28no—
507D52—416no—
508C4×D13—216no—
509C4×D13—216no—
510C4×D13—216no—
511C4×D13—216no—
512C4×D13—216no—
513C4×D13—416no—
514C4×D13C22×D4116yes—
515C4×D13C22×D4116yes—
516C4×D13C22×D4116yes—
517C4×D13C22×D4116yes—
518Dic26—28no—
519Dic26—216no—
520Dic26—216no—
521Dic26—216no—
522C22×#41—1316no—
523C22×#41—131no—
524C22×#41—132no—
525C22×#41—131no—
526C22×#41—132no—
527C22×#41—131no—
528C22×#41—132no—
529C22×#41—132no—
530C22×#41—132no—
531C22×#41—132no—
532C22×#41—1316no—
533C22×#41—2616no—
534C22×#41—2616no—
535C22×#41C2×D1311yescharacteristic
536C23×Q8—131no—
537C23×Q8—131no—
538C23×D4—131no—
539C23×D4—131no—
540C23×D4—132no—
541C23×D4—131no—
542C23×D4—131no—
543C24×C4—131no—
544C24×C4—132no—
545C24×C4—131no—
546C24×C4C2×D1311yescharacteristic, complemented
547#537—1332no—
548#537—1332no—
549#536—1332no—
550#536—1332no—
551#535—1332no—
552#535—1332no—
553#534—1332no—
554#534—1332no—
555#532—1364no—
556C2×C4⋊Q8—134no—
557C2×#127—134no—
558C2×#124—134no—
559C2×#124—134no—
560#525—1316no—
561#525—1316no—
562#525—1364no—
563#525—1316no—
564#525C2×D13116yescomplemented
565C2×#123—132no—
566C2×#123—132no—
567C2×#123—134no—
568C2×#123—134no—
569C2×#123—132no—
570C2×#123C2×D1312yescomplemented
571C2×C22⋊Q8—132no—
572C2×C22⋊Q8—132no—
573C2×C22⋊Q8—134no—
574C2×C22⋊Q8—132no—
575C2×C22⋊Q8—134no—
576C2×C22⋊Q8C2×D1312yescomplemented
577C2×#121—132no—
578C2×#121—134no—
579C2×#121—134no—
580C2×#121—132no—
581C2×#121—132no—
582C2×#121—134no—
583C2×#121—134no—
584C2×#121—134no—
585C2×#121—134no—
586C2×#121C2×D1312yescomplemented
587C2×#120—132no—
588C2×#120—132no—
589C2×#120—134no—
590C2×#120—134no—
591C2×#120—132no—
592C2×#120C2×D1312yescomplemented
593C2×C4×D4—134no—
594C2×C4×D4—134no—
595C2×C4×D4—134no—
596C2×C4×D4C2×D1314yescomplemented
597C2×#117—131no—
598C2×#117—1316no—
599C2×#117—132no—
600C2×#117—132no—
601C2×#117—132no—
602C2×#117C2×D1311yescharacteristic, complemented
603C22×C4⋊C4—132no—
604C22×C22⋊C4—132no—
605C22×C42—132no—
606C22×C13—24no—
607C22×C13—28no—
608C22×C13—24no—
609C22×C13—24no—
610C22×C13—24no—
611C22×C13—28no—
612C22×C13—24no—
613C22×C13—416no—
614C22×C13—48no—
615C22×C13—48no—
616C22×C13C23×D414yes—
617C22×C13C23×D412yes—
618C22×C13#58514yes—
619C22×C13C2611yescharacteristic
620C2×D13—24no—
621C2×D13—24no—
622C2×D13—28no—
623C2×D13—28no—
624C2×D13—24no—
625C2×D13—24no—
626C2×D13—24no—
627C2×D13—28no—
628C2×D13—24no—
629C2×D13—416no—
630C2×D13—432no—
631C2×D13—416no—
632C2×D13—48no—
633C2×D13—48no—
634C2×D13C23×D414yes—
635C2×D13C23×D414yes—
636C4×C13—24no—
637C4×C13—24no—
638C4×C13—28no—
639C4×C13C23×D414yes—
640C4×C13C23×D414yes—
641Dic13—24no—
642Dic13—24no—
643Dic13—28no—
644Dic13C23×D414yes—
645Dic13C23×D414yes—
646C25—131no—
647C25—132no—
648C25—131no—
649C25C22×D1311yescharacteristic
650C2×#41—28no—
651C2×#41—138no—
652C2×#41—1316no—
653C2×#41—138no—
654C2×#41—1316no—
655C2×#41—138no—
656C2×#41—1316no—
657C2×#41—1316no—
658C2×#41—1316no—
659C2×#41—1316no—
660C2×#41—2616no—
661C2×#41—2616no—
662C2×#41—2616no—
663C2×#41—2616no—
664C2×#41—26128no—
665C2×#41—2616no—
666C2×#41—2616no—
667C2×#41—268no—
668C2×#41—268no—
669C2×#41—26128no—
670C2×#41—268no—
671C2×#41C22×D1318yes—
672C22×Q8—138no—
673C22×Q8—132no—
674C22×Q8—131no—
675C22×Q8—132no—
676C22×Q8—132no—
677C22×Q8—138no—
678C22×Q8—268no—
679C22×Q8—268no—
680C22×Q8C22×D1311yescharacteristic
681C22×D4—132no—
682C22×D4—132no—
683C22×D4—132no—
684C22×D4—132no—
685C22×D4—132no—
686C22×D4—132no—
687C22×D4—132no—
688C22×D4—138no—
689C22×D4—138no—
690C22×D4—134no—
691C22×D4—134no—
692C22×D4—1316no—
693C22×D4—138no—
694C22×D4—132no—
695C22×D4—132no—
696C22×D4—132no—
697C22×D4—131no—
698C22×D4—138no—
699C22×D4—134no—
700C22×D4—268no—
701C22×D4—268no—
702C22×D4—268no—
703C22×D4—2616no—
704C22×D4—268no—
705C22×D4C22×D1312yes—
706C22×D4C22×D1311yescharacteristic
707C22×D4C22×D1314yes—
708C23×C4—28no—
709C23×C4—131no—
710C23×C4—1316no—
711C23×C4—131no—
712C23×C4—131no—
713C23×C4—138no—
714C23×C4—131no—
715C23×C4—131no—
716C23×C4—132no—
717C23×C4—131no—
718C23×C4—132no—
719C23×C4—132no—
720C23×C4—132no—
721C23×C4—1316no—
722C23×C4—138no—
723C23×C4—132no—
724C23×C4—132no—
725C23×C4—134no—
726C23×C4—2616no—
727C23×C4—268no—
728C23×C4C22×D1312yes—
729C23×C4C22×D1311yescharacteristic
730C23×C4C22×D1312yes—
731C23×C4C22×D1312yes—
732C23×C4C22×D1311yescharacteristic
733C23×C4C22×D1318yescomplemented
734C4⋊Q8—1332no—
735#127—1332no—
736#124—1332no—
737#124—1332no—
738#123—1316no—
739#123—1316no—
740#123—1332no—
741#123—1332no—
742#123—1316no—
743#123C22×D13116yescomplemented
744C22⋊Q8—1316no—
745C22⋊Q8—1316no—
746C22⋊Q8—1332no—
747C22⋊Q8—1316no—
748C22⋊Q8—1332no—
749C22⋊Q8C22×D13116yescomplemented
750#121—1316no—
751#121—1332no—
752#121—1332no—
753#121—1316no—
754#121—1316no—
755#121—1332no—
756#121—1332no—
757#121—1332no—
758#121—1332no—
759#121C22×D13116yescomplemented
760#120—1316no—
761#120—1316no—
762#120—1332no—
763#120—1332no—
764#120—1316no—
765#120C22×D13116yescomplemented
766C4×D4—1332no—
767C4×D4—1332no—
768C4×D4—1332no—
769C4×D4C22×D13132yescomplemented
770#117—138no—
771#117—1316no—
772#117—1316no—
773#117—1316no—
774#117C22×D1318yescomplemented
775C2×C4⋊C4—134no—
776C2×C4⋊C4—132no—
777C2×C4⋊C4—134no—
778C2×C4⋊C4—134no—
779C2×C4⋊C4—134no—
780C2×C4⋊C4—1316no—
781C2×C4⋊C4C22×D1312yes—
782C2×C4⋊C4C22×D1314yes—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—134no—
785C2×C22⋊C4—134no—
786C2×C22⋊C4—134no—
787C2×C22⋊C4—134no—
788C2×C22⋊C4—134no—
789C2×C22⋊C4—134no—
790C2×C22⋊C4—134no—
791C2×C22⋊C4—1316no—
792C2×C22⋊C4C22×D1312yes—
793C2×C22⋊C4C22×D1314yes—
794C2×C22⋊C4C22×D1314yes—
795C2×C42—134no—
796C2×C42—132no—
797C2×C42—1316no—
798C2×C42C22×D1312yes—
799C2×C13—24no—
800C2×C13—44no—
801C2×C13—44no—
802C2×C13#344914yescomplemented
803C2×C13C24×D411yescharacteristic
804C2×C13C2×#58512yes—
805D13—24no—
806D13—24no—
807D13—44no—
808D13—44no—
809C24—24no—
810C24—44no—
811C24—131no—
812C24—131no—
813C24—138no—
814C24—134no—
815C24—132no—
816C24—132no—
817C24—138no—
818C24—134no—
819C24—268no—
820C24—264no—
821C24—524no—
822C24—524no—
823C24—528no—
824C24C23×D1312yes—
825C24C23×D1312yes—
826C24C23×D1311yescharacteristic
827C24C23×D1314yes—
828#41—232no—
829#41—2664no—
830#41—2664no—
831#41—2664no—
832#41—2664no—
833#41—2664no—
834#41—2664no—
835#41—2632no—
836#41—2632no—
837#41—2632no—
838C2×Q8—24no—
839C2×Q8—138no—
840C2×Q8—134no—
841C2×Q8—138no—
842C2×Q8—138no—
843C2×Q8—268no—
844C2×Q8—268no—
845C2×Q8—2632no—
846C2×Q8—268no—
847C2×Q8—2632no—
848C2×Q8—264no—
849C2×Q8C23×D1314yes—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—48no—
853C2×D4—138no—
854C2×D4—138no—
855C2×D4—138no—
856C2×D4—138no—
857C2×D4—138no—
858C2×D4—138no—
859C2×D4—138no—
860C2×D4—1316no—
861C2×D4—1316no—
862C2×D4—138no—
863C2×D4—138no—
864C2×D4—138no—
865C2×D4—134no—
866C2×D4—1316no—
867C2×D4—268no—
868C2×D4—268no—
869C2×D4—2632no—
870C2×D4—268no—
871C2×D4—2632no—
872C2×D4—268no—
873C2×D4—268no—
874C2×D4—268no—
875C2×D4—2632no—
876C2×D4—2664no—
877C2×D4—268no—
878C2×D4—268no—
879C2×D4—2632no—
880C2×D4—268no—
881C2×D4—268no—
882C2×D4—264no—
883C2×D4—528no—
884C2×D4—528no—
885C2×D4—528no—
886C2×D4C23×D1318yes—
887C2×D4C23×D1314yes—
888C2×D4C23×D13116yes—
889C22×C4—24no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—232no—
893C22×C4—28no—
894C22×C4—138no—
895C22×C4—131no—
896C22×C4—131no—
897C22×C4—134no—
898C22×C4—138no—
899C22×C4—138no—
900C22×C4—138no—
901C22×C4—138no—
902C22×C4—1364no—
903C22×C4—134no—
904C22×C4—134no—
905C22×C4—134no—
906C22×C4—134no—
907C22×C4—134no—
908C22×C4—132no—
909C22×C4—132no—
910C22×C4—138no—
911C22×C4—134no—
912C22×C4—138no—
913C22×C4—138no—
914C22×C4—138no—
915C22×C4—138no—
916C22×C4—138no—
917C22×C4—1316no—
918C22×C4—268no—
919C22×C4—2664no—
920C22×C4—268no—
921C22×C4—268no—
922C22×C4—264no—
923C22×C4—268no—
924C22×C4—268no—
925C22×C4—268no—
926C22×C4—2632no—
927C22×C4—528no—
928C22×C4D4×D1318yes—
929C22×C4C23×D1314yes—
930C22×C4C23×D1312yes—
931C22×C4C23×D1312yes—
932C22×C4C23×D1318yes—
933C22×C4C23×D1318yes—
934C22×C4C23×D1318yes—
935C22×C4C23×D1314yes—
936C22×C4C23×D1311yescharacteristic
937C22×C4C23×D1314yes—
938C22×C4C23×D1311yescharacteristic
939C4⋊C4—1316no—
940C4⋊C4—138no—
941C4⋊C4—1316no—
942C4⋊C4—1316no—
943C4⋊C4—1316no—
944C4⋊C4C23×D1318yes—
945C4⋊C4C23×D13116yes—
946C22⋊C4—138no—
947C22⋊C4—1316no—
948C22⋊C4—1316no—
949C22⋊C4—1316no—
950C22⋊C4—1316no—
951C22⋊C4—1316no—
952C22⋊C4—1316no—
953C22⋊C4—1316no—
954C22⋊C4C23×D1318yes—
955C22⋊C4C23×D13116yes—
956C22⋊C4C23×D13116yes—
957C42—138no—
958C42—1316no—
959C42C23×D1318yes—
960C13C2×#344911yescharacteristic, complemented, Sylow
961C23—24no—
962C23—28no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—28no—
967C23—24no—
968C23—48no—
969C23—416no—
970C23—134no—
971C23—134no—
972C23—132no—
973C23—132no—
974C23—1316no—
975C23—134no—
976C23—134no—
977C23—2616no—
978C23—264no—
979C23—264no—
980C23—268no—
981C23—264no—
982C23—264no—
983C23—264no—
984C23—268no—
985C23—264no—
986C23—528no—
987C23—528no—
988C23—5216no—
989C23—5216no—
990C23—5216no—
991C23—5232no—
992C23C2×D4×D1314yes—
993C23C24×D1314yes—
994C23C24×D1314yes—
995C23C24×D1312yes—
996C23C24×D1311yescharacteristic
997Q8—28no—
998Q8—2616no—
999Q8—2616no—
1000Q8—2616no—
1001Q8—268no—
1002D4—216no—
1003D4—28no—
1004D4—416no—
1005D4—2616no—
1006D4—2616no—
1007D4—2616no—
1008D4—2616no—
1009D4—2616no—
1010D4—2616no—
1011D4—2616no—
1012D4—2616no—
1013D4—2616no—
1014D4—2616no—
1015D4—268no—
1016D4—5216no—
1017D4—5216no—
1018D4—5216no—
1019C2×C4—28no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—216no—
1024C2×C4—216no—
1025C2×C4—216no—
1026C2×C4—134no—
1027C2×C4—134no—
1028C2×C4—1316no—
1029C2×C4—132no—
1030C2×C4—132no—
1031C2×C4—1316no—
1032C2×C4—1316no—
1033C2×C4—1316no—
1034C2×C4—1316no—
1035C2×C4—138no—
1036C2×C4—134no—
1037C2×C4—134no—
1038C2×C4—2616no—
1039C2×C4—2616no—
1040C2×C4—2616no—
1041C2×C4—268no—
1042C2×C4—264no—
1043C2×C4—264no—
1044C2×C4—268no—
1045C2×C4—2616no—
1046C2×C4—2616no—
1047C2×C4—2616no—
1048C2×C4—5216no—
1049C2×C4C2×D4×D1314yes—
1050C2×C4C2×D4×D1314yes—
1051C2×C4C2×D4×D13116yes—
1052C2×C4C24×D1318yes—
1053C2×C4C24×D1314yes—
1054C2×C4C24×D1314yes—
1055C2×C4C24×D1312yes—
1056C2×C4C24×D1312yes—
1057C22—24no—
1058C22—28no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—28no—
1063C22—24no—
1064C22—416no—
1065C22—48no—
1066C22—48no—
1067C22—134no—
1068C22—134no—
1069C22—264no—
1070C22—264no—
1071C22—268no—
1072C22—268no—
1073C22—264no—
1074C22—264no—
1075C22—264no—
1076C22—268no—
1077C22—264no—
1078C22—5216no—
1079C22—5216no—
1080C22—5232no—
1081C22—528no—
1082C22—528no—
1083C22C22×D4×D1314yes—
1084C22C22×D4×D1312yes—
1085C22#1171964814yes—
1086C22C25×D1311yescharacteristic
1087C4—24no—
1088C4—24no—
1089C4—28no—
1090C4—134no—
1091C4—134no—
1092C4—264no—
1093C4—264no—
1094C4—268no—
1095C4C22×D4×D1314yes—
1096C4C22×D4×D1314yes—
1097C2—24no—
1098C2—44no—
1099C2—44no—
1100C2—264no—
1101C2—264no—
1102C2—524no—
1103C2—524no—
1104C2#1312816614yesdirect product factor
1105C2C23×D4×D1311yescharacteristic
1106C2C2×#1171964812yes—
subgroupG/H
centerC22×C4C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#525C2
socleC23×C13C25
hypercenterC2×#525D13
hypocenterC13C2×#3449
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C23×#6127C2semidirect
2. C22×#41×D13C2semidirect
3. #13128166C2direct (N × H)
4. C2×#11719334C2semidirect
5. C2×#11719313C2semidirect
6. C2×#11719333C2semidirect
7. C2×#11719353C2semidirect
8. C2×#11719312C2semidirect
9. C2×#11719297C2semidirect
10. C2×#11719358C2semidirect
11. C2×#11719294C2semidirect
12. C2×#11719253C2semidirect
13. C2×#11719229C2semidirect
14. C2×#11719496C2semidirect
15. C2×#11719252C2semidirect
16. C2×#11719533C2semidirect
17. C2×D13×#117C2semidirect
18. C2×C13×#525C2semidirect
20. C24×C4×C13C22semidirect
22. C23×C22⋊D13C22semidirect
24. C2×#41×D13C22semidirect
25. C22×#6131C22semidirect
26. C22×Q8×D13C22semidirect
28. C22×#6129C22semidirect
30. C22×D4×D13C22semidirect
35. C22×#6127C22semidirect
36. C22×#6127C22semidirect
37. C22×#6127C22semidirect
38. C22×#6127C22semidirect
41. C23×C4×D13C22semidirect
42. C23×C4×D13C22semidirect
43. C23×Dic26C22semidirect
44. C13×#525C22semidirect
45. C2×C13×#123C22semidirect
46. C2×C13×C22⋊Q8C22semidirect
47. C2×C13×#121C22semidirect
48. C2×C13×#120C22semidirect
49. C2×C4×D4×C13C22semidirect
50. C2×C13×#117C22semidirect
51. C2×#88207C22semidirect
52. #11719533C22semidirect
53. C2×#88200C22semidirect
54. C2×#88194C22semidirect
55. C2×#88193C22semidirect
56. C2×#88192C22semidirect
57. C2×#88192C22semidirect
58. C2×#88191C22semidirect
59. C2×#88191C22semidirect
60. C2×#88189C22semidirect
61. #11719496C22semidirect
62. C2×#88184C22semidirect
63. C2×#88183C22semidirect
64. C2×C4×C22⋊D13C22semidirect
65. C2×C4×C22⋊D13C22semidirect
66. C2×#88180C22semidirect
67. C2×#88178C22semidirect
68. #11719358C22semidirect
69. #11719353C22semidirect
70. #11719334C22semidirect
71. #11719333C22semidirect
72. #11719313C22semidirect
73. #11719312C22semidirect
74. #11719297C22semidirect
75. #11719294C22semidirect
76. #11719253C22semidirect
77. #11719252C22semidirect
78. #11719229C22semidirect
79. D13×#117C22semidirect
80. C2×#88151C22semidirect
81. C2×#88150C22semidirect
82. C2×#88149C22semidirect
83. C2×#88149C22semidirect
84. C2×#88148C22semidirect
85. C2×#88146C22semidirect
86. C2×C4⋊C4×D13C22semidirect
87. C2×#88142C22semidirect
88. C2×#88140C22semidirect
89. C2×#88139C22semidirect
90. C2×#88139C22semidirect
91. C2×#88138C22semidirect
92. C2×#88138C22semidirect
93. C2×#88138C22semidirect
94. C2×#88137C22semidirect
95. C2×#88136C22semidirect
96. C2×#88136C22semidirect
98. C2×#88132C22semidirect
99. C2×#88131C22semidirect
100. C2×C4×D52C22semidirect
101. C2×#88126C22semidirect
102. C2×C42×D13C22semidirect
119. C23×C4×C13C23semidirect
132. C22×C22⋊D13C23semidirect
138. C2×#6131C23semidirect
140. C2×Q8×D13C23semidirect
144. C2×#6129C23semidirect
148. C2×D4×D13C23semidirect
159. C2×#6127C23semidirect
160. C2×#6127C23semidirect
161. C2×#6127C23semidirect
171. C22×C4×D13D4semidirect
183. C22×C4×D13C23semidirect
184. C22×C4×D13C23semidirect
190. C22×Dic26C23semidirect
191. C13×#123C23semidirect
192. C13×C22⋊Q8C23semidirect
193. C13×#121C23semidirect
194. C13×#120C23semidirect
195. C4×D4×C13C23semidirect
196. C13×#117C23semidirect
203. #88207C23semidirect
207. #88200C23semidirect
208. #88194C23semidirect
209. #88193C23semidirect
210. #88192C23semidirect
211. #88192C23semidirect
212. #88191C23semidirect
213. #88191C23semidirect
214. #88189C23semidirect
215. #88184C23semidirect
216. #88183C23semidirect
217. C4×C22⋊D13C23semidirect
218. C4×C22⋊D13C23semidirect
224. #88180C23semidirect
227. #88178C23semidirect
233. #88151C23semidirect
234. #88150C23semidirect
235. #88149C23semidirect
236. #88149C23semidirect
237. #88148C23semidirect
238. #88146C23semidirect
239. C4⋊C4×D13C23semidirect
240. #88142C23semidirect
241. #88140C23semidirect
242. #88139C23semidirect
243. #88139C23semidirect
244. #88138C23semidirect
245. #88138C23semidirect
246. #88138C23semidirect
247. #88137C23semidirect
248. #88136C23semidirect
249. #88136C23semidirect
251. #88132C23semidirect
252. #88131C23semidirect
253. C4×D52C23semidirect
254. #88126C23semidirect
255. C42×D13C23semidirect
367. C2×C4×D13C2×D4semidirect
424. C2×#525D13semidirect
546. C24×C4C2×D13semidirect
564. #525C2×D13semidirect
570. C2×#123C2×D13semidirect
576. C2×C22⋊Q8C2×D13semidirect
586. C2×#121C2×D13semidirect
592. C2×#120C2×D13semidirect
596. C2×C4×D4C2×D13semidirect
602. C2×#117C2×D13semidirect
733. C23×C4C22×D13semidirect
743. #123C22×D13semidirect
749. C22⋊Q8C22×D13semidirect
759. #121C22×D13semidirect
765. #120C22×D13semidirect
769. C4×D4C22×D13semidirect
774. #117C22×D13semidirect
802. C2×C13#3449semidirect
960. C13C2×#3449semidirect
1104. C2#13128166direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61272
C22×#41×D132
#131281662
C2×#117193342
C2×#117193132
C2×#117193332
C2×#117193532
C2×#117193122
C2×#117192972
C2×#117193582
C2×#117192942
C2×#117192532
C2×#117192292
C2×#117194962
C2×#117192522
C2×#117195332
C2×D13×#1172
C2×C13×#5252
C2×#344913