Finite Group Databasebeta

← C2×#13128322 #16769877

Subgroups — C2×#13128322 #16769877

Order 3328.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D13C212yesmaximal, complemented
2#13128322C2132yesmaximal, direct product factor
3C2×#11719423C211yesmaximal, characteristic, complemented
4C2×#11719432C211yesmaximal, characteristic, complemented
5C2×#11719382C212yesmaximal, complemented
6C2×#11719431C211yesmaximal, characteristic, complemented
7C2×#11719316C212yesmaximal, complemented
8C2×#11719381C212yesmaximal, complemented
9C2×#11719315C214yesmaximal, complemented
10C2×#11719422C211yesmaximal, characteristic, complemented
11C2×#11719314C212yesmaximal, complemented
12C2×#11719253C212yesmaximal, complemented
13C2×#11719252C214yesmaximal, complemented
14C2×#11719533C212yesmaximal, complemented
15C2×C4×#6127C211yesmaximal, characteristic, complemented
16C22×C4×D52C211yesmaximal, characteristic, complemented
17C2×C4×D4×D13C212yesmaximal, complemented
18C2×C13×#532C211yesmaximal, characteristic, complemented
19C22×C13×#41C2212yescomplemented
20C2×#41×D13—232no—
21C2×#41×D13C22132yescomplemented
22C22×#6131C2212yescomplemented
23C22×Q8×D13C2212yescomplemented
24C22×#6129C2214yescomplemented
25C22×#6129C2212yescomplemented
26C22×D4×D13C2212yes—
27C22×D4×D13C2214yescomplemented
28C22×D4×D13C2212yescomplemented
29C22×#6127C2211yescharacteristic
30C22×#6127C2214yescomplemented
31C23×D52C2211yescharacteristic
32C23×C4×D13C2214yescomplemented
33C23×C4×D13C2212yescomplemented
34C13×#532C22116yescomplemented
35C2×C13×C4⋊Q8C2211yescharacteristic, complemented
36C2×C13×#127C2211yescharacteristic, complemented
37C2×C13×#124C2212yescomplemented
38C2×C13×#121C2212yescomplemented
39C2×C13×#121C2212yescomplemented
40C2×C4×D4×C13C2212yescomplemented
41C2×C4×D4×C13C2212yescomplemented
42C22×C42×C13C2211yescharacteristic, complemented
43#11719533C22132yescomplemented
44C2×#88200C2212yescomplemented
45C2×#88200C2212yescomplemented
46C2×#88194C2212yescomplemented
47C2×#88193C2214yescomplemented
48C2×#88192C2212yescomplemented
49C2×#88192C2212yescomplemented
50C2×#88192C2212yescomplemented
51C2×#88191C2214yescomplemented
52C2×#88191C2214yescomplemented
53C2×#88189C2214yescomplemented
54C2×D4×Dic13C2212yescomplemented
55C2×C4×C22⋊D13C2214yescomplemented
56C2×C4×C22⋊D13C2212yescomplemented
57C2×C4×C22⋊D13C2212yescomplemented
58C2×C4×C22⋊D13C2214yescomplemented
59C22×#6103C2212yescomplemented
60C2×#88180C2211yescharacteristic, complemented
61C22×C4⋊Dic13C2211yescharacteristic, complemented
62#11719432C22116yescomplemented
63#11719431C22116yescomplemented
64#11719423C22116yescomplemented
65#11719422C22116yescomplemented
66#11719382C22132yescomplemented
67#11719381C22132yescomplemented
68#11719316C22132yescomplemented
69#11719315C22164yescomplemented
70#11719314C22132yescomplemented
71#11719253C22132yescomplemented
72#11719252C22164yescomplemented
73C4×D4×D13C22132yescomplemented
74C2×#88150C2214yescomplemented
75C2×#88149C2212yescomplemented
76C2×#88148C2214yescomplemented
77C2×#88147C2212yes—
78C2×C4⋊C4×D13C2212yescomplemented
79C2×#88142C2212yescomplemented
80C2×#88139C2214yescomplemented
81C2×#88138C2214yescomplemented
82C2×#88138C2214yescomplemented
83C2×#88137C2214yescomplemented
84C2×#88136C2214yescomplemented
85C2×#88135C2214yescomplemented
86C2×C22⋊C4×D13C2214yescomplemented
87C2×#88132C2214yescomplemented
88C4×#6127C22116yescomplemented
89C2×C4×D52C2211yescharacteristic
90C2×C4×D52C2211yescharacteristic
91C2×C4×D52C22116yescomplemented
92C2×C4×D52C2212yescomplemented
93C2×C4×D52C2211yescharacteristic, complemented
94C2×C4×D52C2212yescomplemented
95C2×C4×D52C2211yescharacteristic, complemented
96C2×C4×D52C2211yescharacteristic, complemented
97C2×C4×D52C2211yescharacteristic, complemented
98C2×#88126C2212yescomplemented
99C2×C42×D13C2212yescomplemented
100C2×C4×Dic26C2211yescharacteristic, complemented
101C2×C4×Dic26C2211yescharacteristic, complemented
102C24×D13C2314yes—
103C24×D13C2312yes—
104C2×C13×#41—216no—
105C2×C13×#41C23116yescomplemented
106C22×Q8×C13C2312yes—
107C22×D4×C13C2312yes—
108C22×D4×C13C2314yes—
109C22×D4×C13C2312yes—
110C22×D4×C13C2312yes—
111C23×C4×C13C2311yescharacteristic
112C23×C4×C13C2314yes—
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C22×C22⋊D13C2314yes—
116C22×C22⋊D13C2314yes—
117C22×C22⋊D13C2314yes—
118C22×C22⋊D13C2314yes—
119C22×C22⋊D13C2312yes—
120C23×Dic13C2314yes—
121C23×Dic13C2312yes—
122#41×D13—2256no—
123C2×#6131—216no—
124C2×#6131C23116yescomplemented
125C2×Q8×D13—216no—
126C2×Q8×D13C23116yescomplemented
127C2×#6129—232no—
128C2×#6129—216no—
129C2×#6129C23132yescomplemented
130C2×#6129C23116yescomplemented
131C2×D4×D13—232no—
132C2×D4×D13—216no—
133C2×D4×D13—216no—
134C2×D4×D13C23116yes—
135C2×D4×D13C23132yescomplemented
136C2×D4×D13C23116yescomplemented
137C2×#6127—232no—
138C2×#6127D4116yescomplemented
139C2×#6127C2318yes—
140C2×#6127C23132yescomplemented
141C22×D52—28no—
142C22×D52C2312yes—
143C22×D52C2311yescharacteristic
144C22×D52C2318yes—
145C22×D52C2314yes—
146C22×D52C2311yescharacteristic
147C22×D52C2311yescharacteristic
148C22×C4×D13—216no—
149C22×C4×D13—232no—
150C22×C4×D13C2312yes—
151C22×C4×D13C2312yes—
152C22×C4×D13C2312yes—
153C22×C4×D13C2312yes—
154C22×C4×D13C2312yes—
155C22×C4×D13C2314yes—
156C22×C4×D13C2314yes—
157C22×C4×D13C2312yes—
158C22×C4×D13C2312yes—
159C22×C4×D13C23116yescomplemented
160C22×C4×D13C23132yescomplemented
161C22×Dic26C2314yes—
162C22×Dic26C2311yescharacteristic
163C13×C4⋊Q8C2318yescomplemented
164C13×#127C2318yescomplemented
165C13×#124C23116yescomplemented
166C13×#121C23116yescomplemented
167C13×#121C23116yescomplemented
168C4×D4×C13C23116yescomplemented
169C4×D4×C13C23116yescomplemented
170C2×C13×C4⋊C4C2312yes—
171C2×C13×C4⋊C4C2312yes—
172C2×C13×C22⋊C4C2314yes—
173C2×C13×C22⋊C4C2314yes—
174C2×C42×C13C2311yescharacteristic
175C2×C42×C13C2311yescharacteristic
176C2×C42×C13C2311yescharacteristic
177C2×C42×C13C2311yescharacteristic
178C2×C42×C13C2318yescomplemented
179C2×C22⋊Dic13C2314yes—
180C2×C22⋊Dic13C2314yes—
181C2×C22⋊Dic13C2312yes—
182#88200C23116yescomplemented
183#88200C23116yescomplemented
184#88194C23116yescomplemented
185#88193C23132yescomplemented
186#88192C23116yescomplemented
187#88192C23116yescomplemented
188#88192C23116yescomplemented
189#88191C23132yescomplemented
190#88191C23132yescomplemented
191#88189C23132yescomplemented
192D4×Dic13C23116yescomplemented
193C4×C22⋊D13C23116yescomplemented
194C4×C22⋊D13C23116yescomplemented
195C4×C22⋊D13C23132yescomplemented
196C4×C22⋊D13C23132yescomplemented
197C2×#6103C2312yes—
198C2×#6103C2312yes—
199C2×#6103C2312yes—
200C2×#6103C2312yes—
201C2×#6103C2312yes—
202C2×#6103C2312yes—
203C2×#6103C2314yes—
204C2×#6103C2314yes—
205C2×#6103C23116yescomplemented
206#88180C2318yescomplemented
207C2×C4⋊Dic13C2311yescharacteristic
208C2×C4⋊Dic13C2311yescharacteristic
209C2×C4⋊Dic13C2311yescharacteristic
210C2×C4⋊Dic13C2311yescharacteristic
211C2×C4⋊Dic13C2312yes—
212C2×C4⋊Dic13C2318yescomplemented
213C2×#6101C2312yes—
214C2×#6101C2312yes—
215C2×#6101C2314yes—
216C2×#6101C2314yes—
217C2×C4×Dic13C2312yes—
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220#88150C23132yescomplemented
221#88149C23116yescomplemented
222#88148C23132yescomplemented
223#88147C23116yes—
224C4⋊C4×D13C23116yescomplemented
225#88142C23116yescomplemented
226#88139C23132yescomplemented
227#88138C23132yescomplemented
228#88138C23132yescomplemented
229#88137C23132yescomplemented
230#88136C23132yescomplemented
231#88135C23132yescomplemented
232C22⋊C4×D13C23132yescomplemented
233#88132C23132yescomplemented
234C4×D52C2318yes—
235C4×D52C2318yes—
236C4×D52C2318yescomplemented
237C4×D52C2318yescomplemented
238C4×D52C23116yescomplemented
239C4×D52C2318yescomplemented
240C4×D52C23116yescomplemented
241C4×D52C2318yescomplemented
242#88126C23116yescomplemented
243C42×D13C23116yescomplemented
244C4×Dic26C2318yescomplemented
245C4×Dic26C2318yescomplemented
246C2×D4×#41—131nomaximal, Sylow
247C24×C13C2414yes—
248C24×C13C2411yescharacteristic
249C23×D13—28no—
250C23×D13—216no—
251C23×D13—28no—
252C23×D13—216no—
253C23×D13—48no—
254C23×D13—44no—
255C23×D13C2412yes—
256C23×D13C24116yes—
257C23×D13C2418yes—
258C23×D13C2412yes—
259C23×D13C2412yes—
260C13×#41—264no—
261C2×Q8×C13—28no—
262C2×Q8×C13C2418yes—
263C2×D4×C13—216no—
264C2×D4×C13—28no—
265C2×D4×C13—28no—
266C2×D4×C13—44no—
267C2×D4×C13C2418yes—
268C2×D4×C13C24116yes—
269C2×D4×C13C2418yes—
270C2×D4×C13C2418yes—
271C22×C4×C13—216no—
272C22×C4×C13—24no—
273C22×C4×C13—42no—
274C22×C4×C13C2×D418yescomplemented
275C22×C4×C13C2411yescharacteristic
276C22×C4×C13C2411yescharacteristic
277C22×C4×C13C2411yescharacteristic
278C22×C4×C13C2414yes—
279C22×C4×C13C2414yes—
280C22×C4×C13C24116yes—
281C22×C4×C13C2414yes—
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2414yes—
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2411yescharacteristic
286C2×C22⋊D13—216no—
287C2×C22⋊D13—216no—
288C2×C22⋊D13—216no—
289C2×C22⋊D13—48no—
290C2×C22⋊D13C2×D4116yescomplemented
291C2×C22⋊D13C24116yes—
292C2×C22⋊D13C24116yes—
293C2×C22⋊D13C24116yes—
294C2×C22⋊D13C24116yes—
295C2×C22⋊D13C2418yes—
296C22×Dic13—28no—
297C22×Dic13—216no—
298C22×Dic13C24116yes—
299C22×Dic13C2412yes—
300C22×Dic13C2412yes—
301C22×Dic13C2412yes—
302C22×Dic13C2412yes—
303C22×Dic13C2418yes—
304C22×Dic13C2412yes—
305#6131—264no—
306Q8×D13—264no—
307#6129—2128no—
308#6129—264no—
309D4×D13—2128no—
310D4×D13—264no—
311D4×D13—264no—
312#6127—2128no—
313#6127C2×D4164yescomplemented
314C2×D52—216no—
315C2×D52—28no—
316C2×D52—24no—
317C2×D52—232no—
318C2×D52C2×D418yescomplemented
319C2×D52#4118yescomplemented
320C2×D52C2418yes—
321C2×D52C2414yes—
322C2×D52C24116yes—
323C2×D52C2414yes—
324C2×D52C2414yes—
325C2×C4×D13—216no—
326C2×C4×D13—28no—
327C2×C4×D13—28no—
328C2×C4×D13—28no—
329C2×C4×D13—28no—
330C2×C4×D13—264no—
331C2×C4×D13—28no—
332C2×C4×D13—216no—
333C2×C4×D13—2128no—
334C2×C4×D13—44no—
335C2×C4×D13C2×D4116yescomplemented
336C2×C4×D13C2418yes—
337C2×C4×D13C2418yes—
338C2×C4×D13C2418yes—
339C2×C4×D13C2418yes—
340C2×C4×D13C2418yes—
341C2×C4×D13C24116yes—
342C2×C4×D13C24116yes—
343C2×C4×D13C2418yes—
344C2×C4×D13C2418yes—
345C2×Dic26—216no—
346C2×Dic26C2×D418yescomplemented
347C2×Dic26C24116yes—
348C2×Dic26C2414yes—
349C13×C4⋊C4C2418yes—
350C13×C4⋊C4C2418yes—
351C13×C22⋊C4C24116yes—
352C13×C22⋊C4C24116yes—
353C42×C13C2414yes—
354C42×C13C2414yes—
355C42×C13C2414yes—
356C42×C13C2414yes—
357C22⋊Dic13C24116yes—
358C22⋊Dic13C24116yes—
359C22⋊Dic13C2418yes—
360#6103C2418yes—
361#6103C2418yes—
362#6103C2418yes—
363#6103C2418yes—
364#6103C2418yes—
365#6103C2418yes—
366#6103C24116yes—
367#6103C24116yes—
368C4⋊Dic13C2414yes—
369C4⋊Dic13C2414yes—
370C4⋊Dic13C2414yes—
371C4⋊Dic13C2414yes—
372C4⋊Dic13C2418yes—
373#6101C2418yes—
374#6101C2418yes—
375#6101C24116yes—
376#6101C24116yes—
377C4×Dic13C2418yes—
378C4×Dic13C2418yes—
379C4×Dic13C2418yes—
380C23×#41—132no—
381D4×#41—1332no—
382C2×#550—131no—
383C2×D4×Q8—131no—
384C2×#548—132no—
385C2×#547—131no—
386C2×#547—132no—
387C2×#546—132no—
388C2×#546—134no—
389C2×D42—131no—
390C2×D42—132no—
391C2×#532—132no—
392C2×#532D1311yescharacteristic, complemented
393C2×#525—132no—
394C2×#525—134no—
395C2×C4×#41—131no—
396C22×C4×D4—131no—
397C22×C4×D4—132no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—28no—
401C23×C13—28no—
402C23×C13—28no—
403C23×C13C22×D414yes—
404C23×C13C2518yes—
405C23×C13C2512yes—
406C23×C13C2511yescharacteristic
407C22×D13—24no—
408C22×D13—24no—
409C22×D13—24no—
410C22×D13—24no—
411C22×D13—24no—
412C22×D13—216no—
413C22×D13—24no—
414C22×D13—24no—
415C22×D13—232no—
416C22×D13—216no—
417C22×D13—232no—
418C22×D13—416no—
419C22×D13—48no—
420C22×D13—464no—
421C22×D13—432no—
422C22×D13C22×D418yes—
423C22×D13C2×#4118yescomplemented
424C22×D13C2514yes—
425C22×D13C2514yes—
426C22×D13C2514yes—
427Q8×C13—216no—
428D4×C13—232no—
429D4×C13—216no—
430D4×C13—216no—
431D4×C13—48no—
432C2×C4×C13—28no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—232no—
437C2×C4×C13—28no—
438C2×C4×C13—44no—
439C2×C4×C13C22×D414yes—
440C2×C4×C13C22×D414yes—
441C2×C4×C13C22×D4116yescomplemented
442C2×C4×C13C2×#4114yescomplemented
443C2×C4×C13C2512yes—
444C2×C4×C13C2512yes—
445C2×C4×C13C2512yes—
446C2×C4×C13C2518yes—
447C2×C4×C13C2512yes—
448C2×C4×C13C2512yes—
449C2×C4×C13C2512yes—
450C22⋊D13—232no—
451C22⋊D13—232no—
452C22⋊D13—232no—
453C22⋊D13—416no—
454C22⋊D13C22×D4132yescomplemented
455C2×Dic13—24no—
456C2×Dic13—24no—
457C2×Dic13—216no—
458C2×Dic13—24no—
459C2×Dic13—24no—
460C2×Dic13—232no—
461C2×Dic13C22×D418yes—
462C2×Dic13C2514yes—
463C2×Dic13C2514yes—
464C2×Dic13C2514yes—
465C2×Dic13C2514yes—
466C2×Dic13C2514yes—
467D52—232no—
468D52—216no—
469D52—28no—
470D52C22×D4116yescomplemented
471D52C2×#41116yescomplemented
472C4×D13—232no—
473C4×D13—216no—
474C4×D13—216no—
475C4×D13—216no—
476C4×D13—216no—
477C4×D13—216no—
478C4×D13—232no—
479C4×D13—48no—
480C4×D13C22×D4132yescomplemented
481Dic26—232no—
482Dic26C22×D4116yescomplemented
483C22×#41—1332no—
484C22×#41—132no—
485C22×#41—134no—
486C22×#41—132no—
487C22×#41—131no—
488C22×#41—134no—
489C22×#41—2632no—
490C22×#41C2×D1312yescomplemented
491C23×Q8—132no—
492C23×D4—134no—
493C23×D4—132no—
494C23×D4—132no—
495C23×D4—131no—
496C24×C4—134no—
497C24×C4—132no—
498#550—1316no—
499D4×Q8—1316no—
500#548—1332no—
501#547—1316no—
502#547—1332no—
503#546—1332no—
504#546—1364no—
505D42—1316no—
506D42—1332no—
507#532—1332no—
508#532C2×D13116yescomplemented
509C2×C4⋊Q8—132no—
510C2×C4⋊Q8C2×D1311yescharacteristic, complemented
511C2×#127—132no—
512C2×#127C2×D1311yescharacteristic, complemented
513C2×#124—134no—
514C2×#124C2×D1312yescomplemented
515#525—1332no—
516#525—1364no—
517C2×#123—134no—
518C2×#123—134no—
519C2×#123—134no—
520C2×C22⋊Q8—132no—
521C2×C22⋊Q8—132no—
522C2×C22⋊Q8—134no—
523C2×C22⋊Q8—134no—
524C2×#121—132no—
525C2×#121—132no—
526C2×#121—132no—
527C2×#121—134no—
528C2×#121—132no—
529C2×#121—134no—
530C2×#121—134no—
531C2×#121C2×D1312yescomplemented
532C2×#121C2×D1312yescomplemented
533C2×#120—134no—
534C2×#120—134no—
535C2×#120—134no—
536C4×#41—1316no—
537C2×C4×Q8—131no—
538C2×C4×Q8—131no—
539C2×C4×D4—132no—
540C2×C4×D4—134no—
541C2×C4×D4—132no—
542C2×C4×D4—132no—
543C2×C4×D4—134no—
544C2×C4×D4—1332no—
545C2×C4×D4—132no—
546C2×C4×D4—134no—
547C2×C4×D4—131no—
548C2×C4×D4—131no—
549C2×C4×D4—132no—
550C2×C4×D4—131no—
551C2×C4×D4—132no—
552C2×C4×D4—131no—
553C2×C4×D4—131no—
554C2×C4×D4—131no—
555C2×C4×D4—1316no—
556C2×C4×D4C2×D1312yescomplemented
557C2×C4×D4C2×D1312yescomplemented
558C2×#117—131no—
559C2×#117—132no—
560C22×C4⋊C4—131no—
561C22×C4⋊C4—132no—
562C22×C22⋊C4—132no—
563C22×C22⋊C4—134no—
564C22×C42—132no—
565C22×C42C2×D1311yescharacteristic, complemented
566C22×C13—22no—
567C22×C13—22no—
568C22×C13—28no—
569C22×C13—28no—
570C22×C13—28no—
571C22×C13—28no—
572C22×C13—416no—
573C22×C13C23×D414yes—
574C22×C13C23×D412yes—
575C22×C13C22×#4112yes—
576C22×C13#58512yes—
577C22×C13C2611yescharacteristic
578C2×D13—24no—
579C2×D13—24no—
580C2×D13—24no—
581C2×D13—24no—
582C2×D13—216no—
583C2×D13—216no—
584C2×D13—24no—
585C2×D13—24no—
586C2×D13—24no—
587C2×D13—464no—
588C2×D13—432no—
589C2×D13—48no—
590C2×D13C23×D418yes—
591C2×D13C22×#4118yescomplemented
592C4×C13—28no—
593C4×C13—22no—
594C4×C13—22no—
595C4×C13—22no—
596C4×C13C23×D414yes—
597C4×C13C23×D414yes—
598C4×C13C22×#4114yescomplemented
599Dic13—24no—
600Dic13—24no—
601Dic13—24no—
602Dic13—24no—
603Dic13C23×D418yes—
604C25—134no—
605C25—132no—
606C2×#41—216no—
607C2×#41—1316no—
608C2×#41—1332no—
609C2×#41—1316no—
610C2×#41—1316no—
611C2×#41—138no—
612C2×#41—1332no—
613C2×#41—2632no—
614C2×#41—2632no—
615C2×#41—2616no—
616C2×#41—2616no—
617C2×#41—26256no—
618C2×#41C22×D13116yescomplemented
619C22×Q8—1316no—
620C22×Q8—131no—
621C22×Q8—134no—
622C22×Q8—2616no—
623C22×Q8C22×D1312yes—
624C22×D4—132no—
625C22×D4—134no—
626C22×D4—134no—
627C22×D4—134no—
628C22×D4—134no—
629C22×D4—1316no—
630C22×D4—1332no—
631C22×D4—1316no—
632C22×D4—131no—
633C22×D4—131no—
634C22×D4—132no—
635C22×D4—131no—
636C22×D4—138no—
637C22×D4—134no—
638C22×D4—268no—
639C22×D4—2632no—
640C22×D4—2616no—
641C22×D4—2616no—
642C22×D4C22×D1312yes—
643C22×D4C22×D1314yes—
644C22×D4C22×D1312yes—
645C22×D4C22×D1312yes—
646C23×C4—132no—
647C23×C4—132no—
648C23×C4—134no—
649C23×C4—134no—
650C23×C4—132no—
651C23×C4—134no—
652C23×C4—132no—
653C23×C4—132no—
654C23×C4—1332no—
655C23×C4—1316no—
656C23×C4—132no—
657C23×C4—132no—
658C23×C4—132no—
659C23×C4—2632no—
660C23×C4—2616no—
661C23×C4C22×D1311yescharacteristic
662C23×C4C22×D1314yes—
663C23×C4C22×D1311yescharacteristic
664C23×C4C22×D1311yescharacteristic
665C4⋊Q8—1316no—
666C4⋊Q8C22×D1318yescomplemented
667#127—1316no—
668#127C22×D1318yescomplemented
669#124—1332no—
670#124C22×D13116yescomplemented
671#123—1332no—
672#123—1332no—
673#123—1332no—
674C22⋊Q8—1316no—
675C22⋊Q8—1316no—
676C22⋊Q8—1332no—
677C22⋊Q8—1332no—
678#121—1316no—
679#121—1316no—
680#121—1332no—
681#121—1316no—
682#121—1316no—
683#121—1332no—
684#121—1332no—
685#121C22×D13116yescomplemented
686#121C22×D13116yescomplemented
687#120—1332no—
688#120—1332no—
689#120—1332no—
690C4×Q8—138no—
691C4×Q8—138no—
692C4×D4—1316no—
693C4×D4—1332no—
694C4×D4—1316no—
695C4×D4—1316no—
696C4×D4—1332no—
697C4×D4—1316no—
698C4×D4—1332no—
699C4×D4—138no—
700C4×D4—1316no—
701C4×D4—138no—
702C4×D4—138no—
703C4×D4—1316no—
704C4×D4—138no—
705C4×D4—138no—
706C4×D4—138no—
707C4×D4C22×D13116yescomplemented
708C4×D4C22×D13116yescomplemented
709#117—138no—
710#117—1316no—
711C2×C4⋊C4—131no—
712C2×C4⋊C4—131no—
713C2×C4⋊C4—134no—
714C2×C4⋊C4—132no—
715C2×C4⋊C4—138no—
716C2×C4⋊C4—132no—
717C2×C4⋊C4—132no—
718C2×C4⋊C4—131no—
719C2×C4⋊C4—131no—
720C2×C4⋊C4—134no—
721C2×C4⋊C4—1316no—
722C2×C4⋊C4C22×D1312yes—
723C2×C4⋊C4C22×D1312yes—
724C2×C22⋊C4—134no—
725C2×C22⋊C4—132no—
726C2×C22⋊C4—134no—
727C2×C22⋊C4—132no—
728C2×C22⋊C4—134no—
729C2×C22⋊C4—132no—
730C2×C22⋊C4—132no—
731C2×C22⋊C4—132no—
732C2×C22⋊C4—1316no—
733C2×C22⋊C4—132no—
734C2×C22⋊C4—132no—
735C2×C22⋊C4—134no—
736C2×C22⋊C4—1332no—
737C2×C22⋊C4C22×D1314yes—
738C2×C22⋊C4C22×D1314yes—
739C2×C42—132no—
740C2×C42—132no—
741C2×C42—132no—
742C2×C42—1316no—
743C2×C42C22×D1311yescharacteristic
744C2×C42C22×D1311yescharacteristic
745C2×C42C22×D1311yescharacteristic
746C2×C42C22×D1311yescharacteristic
747C2×C42C22×D1318yescomplemented
748C2×C13—24no—
749C2×C13—48no—
750C2×C13D4×#4114yescomplemented
751C2×C13C24×D411yescharacteristic
752C2×C13C23×#4111yescharacteristic
753C2×C13C2×#58511yescharacteristic
754D13—28no—
755D13—28no—
756D13—44no—
757C24—132no—
758C24—132no—
759C24—132no—
760C24—1316no—
761C24—138no—
762C24—2616no—
763C24—268no—
764C24—2616no—
765C24—268no—
766C24—524no—
767C24—528no—
768C24C23×D1314yes—
769C24C23×D1311yescharacteristic
770#41—264no—
771#41—1364no—
772#41—26128no—
773#41—26128no—
774#41—2664no—
775#41—2664no—
776C2×Q8—28no—
777C2×Q8—138no—
778C2×Q8—134no—
779C2×Q8—1316no—
780C2×Q8—2616no—
781C2×Q8—2664no—
782C2×Q8C23×D1318yes—
783C2×D4—216no—
784C2×D4—28no—
785C2×D4—28no—
786C2×D4—44no—
787C2×D4—1316no—
788C2×D4—138no—
789C2×D4—1316no—
790C2×D4—1316no—
791C2×D4—1316no—
792C2×D4—1316no—
793C2×D4—138no—
794C2×D4—138no—
795C2×D4—134no—
796C2×D4—134no—
797C2×D4—138no—
798C2×D4—134no—
799C2×D4—1316no—
800C2×D4—2632no—
801C2×D4—2616no—
802C2×D4—268no—
803C2×D4—2616no—
804C2×D4—26128no—
805C2×D4—2664no—
806C2×D4—2664no—
807C2×D4—2616no—
808C2×D4—2616no—
809C2×D4—264no—
810C2×D4—528no—
811C2×D4C23×D1318yes—
812C2×D4C23×D13116yes—
813C2×D4C23×D1318yes—
814C2×D4C23×D1318yes—
815C22×C4—216no—
816C22×C4—24no—
817C22×C4—42no—
818C22×C4—132no—
819C22×C4—1316no—
820C22×C4—138no—
821C22×C4—132no—
822C22×C4—132no—
823C22×C4—132no—
824C22×C4—132no—
825C22×C4—138no—
826C22×C4—1316no—
827C22×C4—138no—
828C22×C4—1316no—
829C22×C4—138no—
830C22×C4—138no—
831C22×C4—1316no—
832C22×C4—138no—
833C22×C4—138no—
834C22×C4—138no—
835C22×C4—2616no—
836C22×C4—26128no—
837C22×C4—2616no—
838C22×C4—2616no—
839C22×C4—268no—
840C22×C4—268no—
841C22×C4—268no—
842C22×C4—268no—
843C22×C4—268no—
844C22×C4—2664no—
845C22×C4—268no—
846C22×C4—524no—
847C22×C4D4×D1318yescomplemented
848C22×C4C23×D1311yescharacteristic
849C22×C4C23×D1311yescharacteristic
850C22×C4C23×D1311yescharacteristic
851C22×C4C23×D1314yes—
852C22×C4C23×D1314yes—
853C22×C4C23×D13116yes—
854C22×C4C23×D1314yes—
855C22×C4C23×D1311yescharacteristic
856C22×C4C23×D1314yes—
857C22×C4C23×D1311yescharacteristic
858C22×C4C23×D1311yescharacteristic
859C4⋊C4—134no—
860C4⋊C4—134no—
861C4⋊C4—1316no—
862C4⋊C4—138no—
863C4⋊C4—138no—
864C4⋊C4—138no—
865C4⋊C4—134no—
866C4⋊C4—134no—
867C4⋊C4—1316no—
868C4⋊C4C23×D1318yes—
869C4⋊C4C23×D1318yes—
870C22⋊C4—1316no—
871C22⋊C4—138no—
872C22⋊C4—1316no—
873C22⋊C4—138no—
874C22⋊C4—1316no—
875C22⋊C4—138no—
876C22⋊C4—138no—
877C22⋊C4—138no—
878C22⋊C4—138no—
879C22⋊C4—138no—
880C22⋊C4—1316no—
881C22⋊C4C23×D13116yes—
882C22⋊C4C23×D13116yes—
883C42—138no—
884C42—138no—
885C42—138no—
886C42C23×D1314yes—
887C42C23×D1314yes—
888C42C23×D1314yes—
889C42C23×D1314yes—
890C13C2×D4×#4111yescharacteristic, complemented, Sylow
891C23—22no—
892C23—22no—
893C23—28no—
894C23—28no—
895C23—28no—
896C23—138no—
897C23—138no—
898C23—134no—
899C23—134no—
900C23—134no—
901C23—2632no—
902C23—2616no—
903C23—2632no—
904C23—264no—
905C23—264no—
906C23—264no—
907C23—264no—
908C23—2616no—
909C23—264no—
910C23—264no—
911C23—264no—
912C23—528no—
913C23—5216no—
914C23—5232no—
915C23—5264no—
916C23C2×D4×D1314yes—
917C23C24×D1318yes—
918C23C24×D1312yes—
919C23C24×D1311yescharacteristic
920Q8—216no—
921Q8—1316no—
922Q8—2632no—
923D4—232no—
924D4—216no—
925D4—216no—
926D4—48no—
927D4—1332no—
928D4—1316no—
929D4—1316no—
930D4—2616no—
931D4—2632no—
932D4—2632no—
933D4—2632no—
934D4—2632no—
935D4—268no—
936D4—5216no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—232no—
942C2×C4—28no—
943C2×C4—44no—
944C2×C4—138no—
945C2×C4—134no—
946C2×C4—1332no—
947C2×C4—134no—
948C2×C4—134no—
949C2×C4—134no—
950C2×C4—134no—
951C2×C4—2632no—
952C2×C4—2632no—
953C2×C4—2632no—
954C2×C4—264no—
955C2×C4—264no—
956C2×C4—2616no—
957C2×C4—264no—
958C2×C4—264no—
959C2×C4—2616no—
960C2×C4—2616no—
961C2×C4—2616no—
962C2×C4—2616no—
963C2×C4—2616no—
964C2×C4—528no—
965C2×C4C2×D4×D1314yes—
966C2×C4C2×D4×D1314yes—
967C2×C4C2×D4×D13116yescomplemented
968C2×C4#41×D1314yescomplemented
969C2×C4C24×D1312yes—
970C2×C4C24×D1312yes—
971C2×C4C24×D1312yes—
972C2×C4C24×D1318yes—
973C2×C4C24×D1312yes—
974C2×C4C24×D1312yes—
975C2×C4C24×D1312yes—
976C22—28no—
977C22—22no—
978C22—22no—
979C22—28no—
980C22—28no—
981C22—28no—
982C22—416no—
983C22—138no—
984C22—138no—
985C22—2616no—
986C22—2616no—
987C22—264no—
988C22—264no—
989C22—264no—
990C22—264no—
991C22—264no—
992C22—264no—
993C22—264no—
994C22—5232no—
995C22—5264no—
996C22—528no—
997C22C22×D4×D1314yes—
998C22C22×D4×D1312yes—
999C22C2×#41×D1312yes—
1000C22#1171964812yes—
1001C22C25×D1311yescharacteristic
1002C4—28no—
1003C4—22no—
1004C4—22no—
1005C4—22no—
1006C4—138no—
1007C4—264no—
1008C4—264no—
1009C4—264no—
1010C4—264no—
1011C4C22×D4×D1314yes—
1012C4C22×D4×D1314yes—
1013C4C2×#41×D1314yescomplemented
1014C2—24no—
1015C2—48no—
1016C2—268no—
1017C2—268no—
1018C2—524no—
1019C2#1312832214yesdirect product factor
1020C2C23×D4×D1311yescharacteristic
1021C2C22×#41×D1311yescharacteristic
1022C2C2×#1171964811yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#532C2
socleC23×C13C25
hypercenterC2×#532D13
hypocenterC13C2×D4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C22×#41×D13C2semidirect
2. #13128322C2direct (N × H)
3. C2×#11719423C2semidirect
4. C2×#11719432C2semidirect
5. C2×#11719382C2semidirect
6. C2×#11719431C2semidirect
7. C2×#11719316C2semidirect
8. C2×#11719381C2semidirect
9. C2×#11719315C2semidirect
10. C2×#11719422C2semidirect
11. C2×#11719314C2semidirect
12. C2×#11719253C2semidirect
13. C2×#11719252C2semidirect
14. C2×#11719533C2semidirect
15. C2×C4×#6127C2semidirect
16. C22×C4×D52C2semidirect
17. C2×C4×D4×D13C2semidirect
18. C2×C13×#532C2semidirect
19. C22×C13×#41C22semidirect
21. C2×#41×D13C22semidirect
22. C22×#6131C22semidirect
23. C22×Q8×D13C22semidirect
24. C22×#6129C22semidirect
25. C22×#6129C22semidirect
27. C22×D4×D13C22semidirect
28. C22×D4×D13C22semidirect
30. C22×#6127C22semidirect
32. C23×C4×D13C22semidirect
33. C23×C4×D13C22semidirect
34. C13×#532C22semidirect
35. C2×C13×C4⋊Q8C22semidirect
36. C2×C13×#127C22semidirect
37. C2×C13×#124C22semidirect
38. C2×C13×#121C22semidirect
39. C2×C13×#121C22semidirect
40. C2×C4×D4×C13C22semidirect
41. C2×C4×D4×C13C22semidirect
42. C22×C42×C13C22semidirect
43. #11719533C22semidirect
44. C2×#88200C22semidirect
45. C2×#88200C22semidirect
46. C2×#88194C22semidirect
47. C2×#88193C22semidirect
48. C2×#88192C22semidirect
49. C2×#88192C22semidirect
50. C2×#88192C22semidirect
51. C2×#88191C22semidirect
52. C2×#88191C22semidirect
53. C2×#88189C22semidirect
54. C2×D4×Dic13C22semidirect
55. C2×C4×C22⋊D13C22semidirect
56. C2×C4×C22⋊D13C22semidirect
57. C2×C4×C22⋊D13C22semidirect
58. C2×C4×C22⋊D13C22semidirect
59. C22×#6103C22semidirect
60. C2×#88180C22semidirect
61. C22×C4⋊Dic13C22semidirect
62. #11719432C22semidirect
63. #11719431C22semidirect
64. #11719423C22semidirect
65. #11719422C22semidirect
66. #11719382C22semidirect
67. #11719381C22semidirect
68. #11719316C22semidirect
69. #11719315C22semidirect
70. #11719314C22semidirect
71. #11719253C22semidirect
72. #11719252C22semidirect
73. C4×D4×D13C22semidirect
74. C2×#88150C22semidirect
75. C2×#88149C22semidirect
76. C2×#88148C22semidirect
78. C2×C4⋊C4×D13C22semidirect
79. C2×#88142C22semidirect
80. C2×#88139C22semidirect
81. C2×#88138C22semidirect
82. C2×#88138C22semidirect
83. C2×#88137C22semidirect
84. C2×#88136C22semidirect
85. C2×#88135C22semidirect
86. C2×C22⋊C4×D13C22semidirect
87. C2×#88132C22semidirect
88. C4×#6127C22semidirect
91. C2×C4×D52C22semidirect
92. C2×C4×D52C22semidirect
93. C2×C4×D52C22semidirect
94. C2×C4×D52C22semidirect
95. C2×C4×D52C22semidirect
96. C2×C4×D52C22semidirect
97. C2×C4×D52C22semidirect
98. C2×#88126C22semidirect
99. C2×C42×D13C22semidirect
100. C2×C4×Dic26C22semidirect
101. C2×C4×Dic26C22semidirect
105. C2×C13×#41C23semidirect
124. C2×#6131C23semidirect
126. C2×Q8×D13C23semidirect
129. C2×#6129C23semidirect
130. C2×#6129C23semidirect
135. C2×D4×D13C23semidirect
136. C2×D4×D13C23semidirect
138. C2×#6127D4semidirect
140. C2×#6127C23semidirect
159. C22×C4×D13C23semidirect
160. C22×C4×D13C23semidirect
163. C13×C4⋊Q8C23semidirect
164. C13×#127C23semidirect
165. C13×#124C23semidirect
166. C13×#121C23semidirect
167. C13×#121C23semidirect
168. C4×D4×C13C23semidirect
169. C4×D4×C13C23semidirect
178. C2×C42×C13C23semidirect
182. #88200C23semidirect
183. #88200C23semidirect
184. #88194C23semidirect
185. #88193C23semidirect
186. #88192C23semidirect
187. #88192C23semidirect
188. #88192C23semidirect
189. #88191C23semidirect
190. #88191C23semidirect
191. #88189C23semidirect
192. D4×Dic13C23semidirect
193. C4×C22⋊D13C23semidirect
194. C4×C22⋊D13C23semidirect
195. C4×C22⋊D13C23semidirect
196. C4×C22⋊D13C23semidirect
205. C2×#6103C23semidirect
206. #88180C23semidirect
212. C2×C4⋊Dic13C23semidirect
220. #88150C23semidirect
221. #88149C23semidirect
222. #88148C23semidirect
224. C4⋊C4×D13C23semidirect
225. #88142C23semidirect
226. #88139C23semidirect
227. #88138C23semidirect
228. #88138C23semidirect
229. #88137C23semidirect
230. #88136C23semidirect
231. #88135C23semidirect
232. C22⋊C4×D13C23semidirect
233. #88132C23semidirect
236. C4×D52C23semidirect
237. C4×D52C23semidirect
238. C4×D52C23semidirect
239. C4×D52C23semidirect
240. C4×D52C23semidirect
241. C4×D52C23semidirect
242. #88126C23semidirect
243. C42×D13C23semidirect
244. C4×Dic26C23semidirect
245. C4×Dic26C23semidirect
274. C22×C4×C13C2×D4semidirect
290. C2×C22⋊D13C2×D4semidirect
313. #6127C2×D4semidirect
318. C2×D52C2×D4semidirect
319. C2×D52#41semidirect
335. C2×C4×D13C2×D4semidirect
346. C2×Dic26C2×D4semidirect
392. C2×#532D13semidirect
423. C22×D13C2×#41semidirect
441. C2×C4×C13C22×D4semidirect
442. C2×C4×C13C2×#41semidirect
454. C22⋊D13C22×D4semidirect
470. D52C22×D4semidirect
471. D52C2×#41semidirect
480. C4×D13C22×D4semidirect
482. Dic26C22×D4semidirect
490. C22×#41C2×D13semidirect
508. #532C2×D13semidirect
510. C2×C4⋊Q8C2×D13semidirect
512. C2×#127C2×D13semidirect
514. C2×#124C2×D13semidirect
531. C2×#121C2×D13semidirect
532. C2×#121C2×D13semidirect
556. C2×C4×D4C2×D13semidirect
557. C2×C4×D4C2×D13semidirect
565. C22×C42C2×D13semidirect
591. C2×D13C22×#41semidirect
598. C4×C13C22×#41semidirect
618. C2×#41C22×D13semidirect
666. C4⋊Q8C22×D13semidirect
668. #127C22×D13semidirect
670. #124C22×D13semidirect
685. #121C22×D13semidirect
686. #121C22×D13semidirect
707. C4×D4C22×D13semidirect
708. C4×D4C22×D13semidirect
747. C2×C42C22×D13semidirect
750. C2×C13D4×#41semidirect
847. C22×C4D4×D13semidirect
890. C13C2×D4×#41semidirect
967. C2×C4C2×D4×D13semidirect
968. C2×C4#41×D13semidirect
1013. C4C2×#41×D13semidirect
1019. C2#13128322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D132
#131283222
C2×#117194232
C2×#117194322
C2×#117193822
C2×#117194312
C2×#117193162
C2×#117193812
C2×#117193152
C2×#117194222
C2×#117193142
C2×#117192532
C2×#117192522
C2×#117195332
C2×C4×#61272
C22×C4×D522
C2×C4×D4×D132
C2×C13×#5322
C2×D4×#4113