Finite Group Databasebeta

← C2×#13128508 #16771317

Subgroups — C2×#13128508 #16771317

Order 3328.

11438 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88257C211yesmaximal, characteristic, complemented
2C23×#6127C211yesmaximal, characteristic, complemented
3#13128508C2132yesmaximal, direct product factor
4C2×D4×Dic26C212yesmaximal, complemented
5C2×#11719257C212yesmaximal, complemented
6C2×#11719256C212yesmaximal, complemented
7C2×#11719360C214yesmaximal, complemented
8C2×#11719255C212yesmaximal, complemented
9C2×#11719296C214yesmaximal, complemented
10C2×#11719313C212yesmaximal, complemented
11C2×#11719538C211yesmaximal, characteristic, complemented
12C2×#11719231C211yesmaximal, characteristic, complemented
13C2×#11719333C212yesmaximal, complemented
14C2×#11719311C212yesmaximal, complemented
15C22×#88178C211yesmaximal, characteristic, complemented
16C2×D13×C22⋊Q8C212yesmaximal, complemented
17C2×#11719228C211yesmaximal, characteristic, complemented
18C2×C13×#525C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic, complemented
20C24×C4×C13C2211yescharacteristic
21C23×C22⋊D13C2212yes—
22C2×#88257—216no—
23C2×#88257C22116yescomplemented
24C22×Q8×D13C2212yescomplemented
25C22×#6129C2214yescomplemented
26C22×#6129C2212yescomplemented
27C22×#6127—216no—
28C22×#6127C2212yes—
29C22×#6127C2211yescharacteristic
30C22×#6127C2211yescharacteristic
31C22×#6127C2212yes—
32C22×#6127C2211yescharacteristic
33C22×#6127C2211yescharacteristic
34C22×#6127C22116yescomplemented
35C22×#6127C2212yescomplemented
36C23×D52C2211yescharacteristic
37C23×C4×D13C2212yes—
38C23×Dic26C2211yescharacteristic
39C23×Dic26C2212yescomplemented
40C23×Dic26C2211yescharacteristic, complemented
41C13×#525C22116yescomplemented
42C2×C13×#123C2212yescomplemented
43C2×C13×C22⋊Q8C2211yescharacteristic
44C2×C13×C22⋊Q8C2211yescharacteristic, complemented
45C2×C13×#121C2211yescharacteristic
46C2×C13×#121C2211yescharacteristic, complemented
47C2×C13×#120C2212yes—
48C2×C4×D4×C13C2212yes—
49C2×C4×D4×C13C2212yescomplemented
50C2×C13×#117C2211yescharacteristic, complemented
51C22×C22⋊Dic13C2212yes—
52#11719538C22116yescomplemented
53C2×#88200C2212yescomplemented
54C2×#88193C2214yescomplemented
55C2×#88193C2214yescomplemented
56C2×#88192C2214yescomplemented
57C2×#88192C2212yescomplemented
58C2×#88191C2214yes—
59C2×D4×Dic13C2214yes—
60C2×#88184C2212yescomplemented
61C22×C4⋊Dic13C2211yescharacteristic, complemented
62C2×#88178C2212yes—
63C2×#88178C2212yes—
64C2×#88178C2212yescomplemented
65C2×#88178C2212yescomplemented
66C2×#88178C2212yescomplemented
67C2×#88178C22116yescomplemented
68C22×#6101C2212yescomplemented
69#11719360C22164yescomplemented
70#11719333C22132yescomplemented
71D13×C22⋊Q8C22132yescomplemented
72#11719313C22132yescomplemented
73#11719311C22132yescomplemented
74#11719296C22164yescomplemented
75#11719257C22132yescomplemented
76#11719256C22132yescomplemented
77#11719255C22132yescomplemented
78D4×Dic26C22132yescomplemented
79#11719231C22116yescomplemented
80#11719228C22116yescomplemented
81C2×#88151C2212yescomplemented
82C2×#88151C2212yescomplemented
83C2×#88150C2214yescomplemented
84C2×#88148C2214yescomplemented
85C2×#88146C2212yescomplemented
86C2×C4⋊C4×D13C2212yescomplemented
87C2×C4⋊C4×D13C2214yescomplemented
88C2×#88142C2214yescomplemented
89C2×#88140C2214yescomplemented
90C2×#88139C2214yescomplemented
91C2×#88138C2214yescomplemented
92C2×#88137C2214yescomplemented
93C2×#88137C2214yescomplemented
94C2×#88135C2214yescomplemented
95C2×#88135C2214yescomplemented
96C2×C22⋊C4×D13C2214yes—
97C2×#88132C2214yes—
98C2×#88132C2214yescomplemented
99C2×#88129C2212yescomplemented
100C2×C4×D52C2212yescomplemented
101C2×#88123C2212yescomplemented
102C2×C4×Dic26C2212yescomplemented
103C25×C13C2311yescharacteristic
104C24×D13C2312yes—
105C2×C13×#41—28no—
106C2×C13×#41C2318yescomplemented
107C22×Q8×C13C2311yescharacteristic
108C22×D4×C13C2312yes—
109C22×D4×C13C2311yescharacteristic
110C22×D4×C13C2312yes—
111C22×D4×C13C2312yes—
112C23×C4×C13—28no—
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C23×C4×C13C2311yescharacteristic
116C23×C4×C13C2311yescharacteristic
117C23×C4×C13C2311yescharacteristic
118C23×C4×C13C2318yes—
119C23×C4×C13C2312yes—
120C23×C4×C13C2311yescharacteristic
121C22×C22⋊D13—216no—
122C22×C22⋊D13C2312yes—
123C22×C22⋊D13C2314yes—
124C22×C22⋊D13C2312yes—
125C22×C22⋊D13C2312yes—
126C22×C22⋊D13C23116yes—
127C22×C22⋊D13C2314yes—
128C22×C22⋊D13C2312yes—
129C23×Dic13C2312yes—
130C23×Dic13C2314yes—
131C23×Dic13C2312yes—
132C23×Dic13C2312yes—
133#88257—2128no—
134C2×Q8×D13—216no—
135C2×Q8×D13C23116yescomplemented
136C2×#6129—232no—
137C2×#6129—216no—
138C2×#6129C23132yescomplemented
139C2×#6129C23116yescomplemented
140C2×#6127—28no—
141C2×#6127—216no—
142C2×#6127—2128no—
143C2×#6127—28no—
144C2×#6127—216no—
145C2×#6127—216no—
146C2×#6127—28no—
147C2×#6127D4116yescomplemented
148C2×#6127C2318yes—
149C2×#6127C2318yes—
150C2×#6127C2318yes—
151C2×#6127C23116yes—
152C2×#6127C23116yes—
153C2×#6127C2318yes—
154C2×#6127C23116yescomplemented
155C22×D52—28no—
156C22×D52C2311yescharacteristic
157C22×D52C2312yes—
158C22×D52C2318yes—
159C22×D52C2311yescharacteristic
160C22×C4×D13—216no—
161C22×C4×D13C2314yes—
162C22×C4×D13C2312yes—
163C22×C4×D13C2312yes—
164C22×C4×D13C2312yes—
165C22×C4×D13C23116yes—
166C22×C4×D13C2314yes—
167C22×C4×D13C2312yes—
168C22×Dic26—28no—
169C22×Dic26—28no—
170C22×Dic26—216no—
171C22×Dic26C2311yescharacteristic
172C22×Dic26C2312yes—
173C22×Dic26C2314yes—
174C22×Dic26C2312yes—
175C22×Dic26C2312yes—
176C22×Dic26C2318yes—
177C22×Dic26C2311yescharacteristic
178C22×Dic26C2318yescomplemented
179C22×Dic26C23116yescomplemented
180C13×#123C23116yescomplemented
181C13×C22⋊Q8C2318yes—
182C13×C22⋊Q8C2318yescomplemented
183C13×#121C2318yes—
184C13×#121C2318yescomplemented
185C13×#120C23116yes—
186C4×D4×C13C23116yes—
187C4×D4×C13C23116yescomplemented
188C13×#117C2318yescomplemented
189C2×C13×C4⋊C4C2312yes—
190C2×C13×C4⋊C4C2312yes—
191C2×C13×C4⋊C4C2311yescharacteristic
192C2×C13×C4⋊C4C2311yescharacteristic
193C2×C13×C22⋊C4C2312yes—
194C2×C13×C22⋊C4C2312yes—
195C2×C13×C22⋊C4C2312yes—
196C2×C13×C22⋊C4C2312yes—
197C2×C13×C22⋊C4C2312yes—
198C2×C42×C13C2312yes—
199C2×C22⋊Dic13C2314yes—
200C2×C22⋊Dic13C2314yes—
201C2×C22⋊Dic13C2314yes—
202C2×C22⋊Dic13C23116yes—
203#88200C23116yescomplemented
204#88193C23132yescomplemented
205#88193C23132yescomplemented
206#88192C23132yescomplemented
207#88192C23116yescomplemented
208#88191C23132yes—
209D4×Dic13C23132yes—
210#88184C23116yescomplemented
211C2×#6103C2314yes—
212C2×#6103C2314yes—
213C2×#6103C2314yes—
214C2×#6103C2314yes—
215C2×C4⋊Dic13C2312yes—
216C2×C4⋊Dic13C2314yes—
217C2×C4⋊Dic13C2314yes—
218C2×C4⋊Dic13C2312yes—
219C2×C4⋊Dic13C2318yescomplemented
220#88178C23116yes—
221#88178C23116yes—
222#88178C23116yescomplemented
223#88178C23116yescomplemented
224#88178C23116yescomplemented
225C2×#6101C2314yes—
226C2×#6101C2314yes—
227C2×#6101C2314yes—
228C2×#6101C2314yes—
229C2×#6101C23116yescomplemented
230C2×C4×Dic13C2314yes—
231#88151C23116yescomplemented
232#88151C23116yescomplemented
233#88150C23132yescomplemented
234#88148C23132yescomplemented
235#88146C23116yescomplemented
236C4⋊C4×D13C23116yescomplemented
237C4⋊C4×D13C23132yescomplemented
238#88142C23132yescomplemented
239#88140C23132yescomplemented
240#88139C23132yescomplemented
241#88138C23132yescomplemented
242#88137C23132yescomplemented
243#88137C23132yescomplemented
244#88135C23132yescomplemented
245#88135C23132yescomplemented
246C22⋊C4×D13C23132yes—
247#88132C23132yes—
248#88132C23132yescomplemented
249#88129C23116yescomplemented
250C4×D52C23116yescomplemented
251#88123C23116yescomplemented
252C4×Dic26C23116yescomplemented
253C2×#3489—131nomaximal, Sylow
254C24×C13—24no—
255C24×C13—24no—
256C24×C13—42no—
257C24×C13C2411yescharacteristic
258C24×C13C2412yes—
259C24×C13C2414yes—
260C24×C13C2411yescharacteristic
261C24×C13C2411yescharacteristic
262C23×D13—28no—
263C23×D13—28no—
264C23×D13—44no—
265C23×D13C2412yes—
266C23×D13C2418yes—
267C23×D13C2412yes—
268C13×#41—232no—
269C2×Q8×C13—24no—
270C2×Q8×C13C2414yes—
271C2×D4×C13—28no—
272C2×D4×C13—28no—
273C2×D4×C13—24no—
274C2×D4×C13—44no—
275C2×D4×C13C2418yes—
276C2×D4×C13C2414yes—
277C2×D4×C13C2418yes—
278C2×D4×C13C2418yes—
279C22×C4×C13—24no—
280C22×C4×C13—24no—
281C22×C4×C13—28no—
282C22×C4×C13—24no—
283C22×C4×C13—24no—
284C22×C4×C13—24no—
285C22×C4×C13—232no—
286C22×C4×C13C2×D418yes—
287C22×C4×C13C2412yes—
288C22×C4×C13C2411yescharacteristic
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2412yes—
291C22×C4×C13C2412yes—
292C22×C4×C13C2414yes—
293C22×C4×C13C2414yes—
294C22×C4×C13C2414yes—
295C22×C4×C13C2414yes—
296C22×C4×C13C2414yes—
297C22×C4×C13C2418yes—
298C22×C4×C13C2411yescharacteristic
299C22×C4×C13C2411yescharacteristic
300C22×C4×C13C2414yes—
301C2×C22⋊D13—28no—
302C2×C22⋊D13—28no—
303C2×C22⋊D13—216no—
304C2×C22⋊D13—264no—
305C2×C22⋊D13—28no—
306C2×C22⋊D13—48no—
307C2×C22⋊D13C2×D4116yes—
308C2×C22⋊D13C2418yes—
309C2×C22⋊D13C24116yes—
310C2×C22⋊D13C2418yes—
311C2×C22⋊D13C2418yes—
312C2×C22⋊D13C24116yes—
313C2×C22⋊D13C2418yes—
314C22×Dic13—28no—
315C22×Dic13—28no—
316C22×Dic13—216no—
317C22×Dic13—44no—
318C22×Dic13C2418yes—
319C22×Dic13C24116yes—
320C22×Dic13C2418yes—
321C22×Dic13C2414yes—
322C22×Dic13C2412yes—
323C22×Dic13C2414yes—
324C22×Dic13C2418yes—
325C22×Dic13C2412yes—
326Q8×D13—264no—
327#6129—2128no—
328#6129—264no—
329#6127—232no—
330#6127—264no—
331#6127—232no—
332#6127—264no—
333#6127—264no—
334#6127—232no—
335#6127C2×D4164yescomplemented
336C2×D52—28no—
337C2×D52—24no—
338C2×D52—232no—
339C2×D52C2×D418yes—
340C2×D52C2414yes—
341C2×D52C2418yes—
342C2×D52C2414yes—
343C2×C4×D13—28no—
344C2×C4×D13—216no—
345C2×C4×D13—28no—
346C2×C4×D13—28no—
347C2×C4×D13—264no—
348C2×C4×D13—48no—
349C2×C4×D13C2×D4116yes—
350C2×C4×D13C24116yes—
351C2×C4×D13C2418yes—
352C2×C4×D13C2418yes—
353C2×C4×D13C2418yes—
354C2×C4×D13C24116yes—
355C2×C4×D13C2418yes—
356C2×Dic26—28no—
357C2×Dic26—24no—
358C2×Dic26—28no—
359C2×Dic26—232no—
360C2×Dic26—28no—
361C2×Dic26—216no—
362C2×Dic26—232no—
363C2×Dic26—264no—
364C2×Dic26C2×D418yes—
365C2×Dic26C2414yes—
366C2×Dic26C2418yes—
367C2×Dic26C24116yes—
368C2×Dic26C2418yes—
369C2×Dic26C2418yes—
370C2×Dic26C2414yes—
371C13×C4⋊C4C2418yes—
372C13×C4⋊C4C2418yes—
373C13×C4⋊C4C2414yes—
374C13×C4⋊C4C2414yes—
375C13×C22⋊C4C2418yes—
376C13×C22⋊C4C2418yes—
377C13×C22⋊C4C2418yes—
378C13×C22⋊C4C2418yes—
379C13×C22⋊C4C2418yes—
380C42×C13C2418yes—
381C22⋊Dic13C24116yes—
382C22⋊Dic13C24116yes—
383C22⋊Dic13C24116yes—
384#6103C24116yes—
385#6103C24116yes—
386#6103C24116yes—
387#6103C24116yes—
388C4⋊Dic13C2418yes—
389C4⋊Dic13C24116yes—
390C4⋊Dic13C24116yes—
391C4⋊Dic13C2418yes—
392#6101C24116yes—
393#6101C24116yes—
394#6101C24116yes—
395#6101C24116yes—
396C4×Dic13C24116yes—
397C22×2−1+4—131no—
398C23×#41—131no—
399#3489—1332no—
400C2×D4×Q8—132no—
401C2×#548—132no—
402C2×#547—134no—
403C2×#547—132no—
404C2×#546—134no—
405C2×#546—132no—
406C2×#537—131no—
407C2×#537—132no—
408C2×#536—132no—
409C2×#536—131no—
410C2×#525—132no—
411C2×#525D1311yescharacteristic, complemented
412C22×C22⋊Q8—131no—
413C22×C22⋊Q8—132no—
414C2×#520—131no—
415C23×C13—22no—
416C23×C13—22no—
417C23×C13—22no—
418C23×C13—22no—
419C23×C13—24no—
420C23×C13—28no—
421C23×C13—22no—
422C23×C13—24no—
423C23×C13—22no—
424C23×C13—28no—
425C23×C13—24no—
426C23×C13—22no—
427C23×C13—44no—
428C23×C13—416no—
429C23×C13C22×D414yes—
430C23×C132−1+414yescomplemented
431C23×C13C2512yes—
432C23×C13C2514yes—
433C23×C13C2512yes—
434C23×C13C2512yes—
435C23×C13C2511yescharacteristic
436C22×D13—24no—
437C22×D13—24no—
438C22×D13—24no—
439C22×D13—24no—
440C22×D13—216no—
441C22×D13—24no—
442C22×D13—216no—
443C22×D13—48no—
444C22×D13—432no—
445C22×D13C22×D418yes—
446C22×D13C2514yes—
447C22×D13C2514yes—
448Q8×C13—28no—
449D4×C13—216no—
450D4×C13—216no—
451D4×C13—28no—
452D4×C13—48no—
453C2×C4×C13—24no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—28no—
457C2×C4×C13—24no—
458C2×C4×C13—24no—
459C2×C4×C13—28no—
460C2×C4×C13—216no—
461C2×C4×C13—28no—
462C2×C4×C13—28no—
463C2×C4×C13—28no—
464C2×C4×C13C22×D414yes—
465C2×C4×C13C22×D414yes—
466C2×C4×C13C22×D4116yes—
467C2×C4×C13C2514yes—
468C2×C4×C13C2512yes—
469C2×C4×C13C2512yes—
470C2×C4×C13C2514yes—
471C2×C4×C13C2514yes—
472C2×C4×C13C2512yes—
473C2×C4×C13C2512yes—
474C22⋊D13—216no—
475C22⋊D13—216no—
476C22⋊D13—232no—
477C22⋊D13—216no—
478C22⋊D13—416no—
479C22⋊D13C22×D4132yes—
480C2×Dic13—28no—
481C2×Dic13—24no—
482C2×Dic13—216no—
483C2×Dic13—28no—
484C2×Dic13—216no—
485C2×Dic13—232no—
486C2×Dic13—48no—
487C2×Dic13C22×D418yes—
488C2×Dic13C2518yes—
489C2×Dic13C2514yes—
490C2×Dic13C2518yes—
491C2×Dic13C2514yes—
492D52—216no—
493D52—28no—
494D52C22×D4116yes—
495C4×D13—216no—
496C4×D13—232no—
497C4×D13—216no—
498C4×D13—216no—
499C4×D13—416no—
500C4×D13C22×D4132yes—
501Dic26—216no—
502Dic26—28no—
503Dic26—216no—
504Dic26—216no—
505Dic26—232no—
506Dic26C22×D4116yes—
507C2×2−1+4—1316no—
508C2×2−1+4—2616no—
509C22×#41—132no—
510C22×#41—134no—
511C22×#41—131no—
512C22×#41—132no—
513C22×#41—131no—
514C22×#41—131no—
515C22×#41—132no—
516C22×#41—131no—
517C22×#41—1316no—
518C22×#41—132no—
519C22×#41—2616no—
520C22×#41C2×D1311yescharacteristic, complemented
521C23×Q8—132no—
522C23×Q8—131no—
523C23×Q8—131no—
524C23×Q8—132no—
525C23×D4—132no—
526C23×D4—131no—
527C24×C4—132no—
528C24×C4C2×D1311yescharacteristic
529D4×Q8—1332no—
530#548—1332no—
531#547—1364no—
532#547—1332no—
533#546—1364no—
534#546—1332no—
535#537—1316no—
536#537—1332no—
537#536—1332no—
538#536—1316no—
539C2×C4⋊Q8—134no—
540C2×C4⋊Q8—132no—
541C2×#124—134no—
542C2×#124—132no—
543#525—1332no—
544#525C2×D13116yescomplemented
545C2×#123—134no—
546C2×#123—134no—
547C2×#123—134no—
548C2×#123—134no—
549C2×#123C2×D1312yescomplemented
550C2×C22⋊Q8—132no—
551C2×C22⋊Q8—132no—
552C2×C22⋊Q8—132no—
553C2×C22⋊Q8—132no—
554C2×C22⋊Q8—132no—
555C2×C22⋊Q8—1316no—
556C2×C22⋊Q8—132no—
557C2×C22⋊Q8—1332no—
558C2×C22⋊Q8—134no—
559C2×C22⋊Q8—132no—
560C2×C22⋊Q8—132no—
561C2×C22⋊Q8—134no—
562C2×C22⋊Q8—134no—
563C2×C22⋊Q8C2×D1311yescharacteristic
564C2×C22⋊Q8C2×D1311yescharacteristic, complemented
565C2×#121—132no—
566C2×#121—134no—
567C2×#121—134no—
568C2×#121—134no—
569C2×#121—132no—
570C2×#121—134no—
571C2×#121C2×D1311yescharacteristic
572C2×#121C2×D1311yescharacteristic, complemented
573C2×#120—134no—
574C2×#120C2×D1312yes—
575#520—1316no—
576C2×C4×Q8—132no—
577C2×C4×D4—134no—
578C2×C4×D4—134no—
579C2×C4×D4—134no—
580C2×C4×D4—132no—
581C2×C4×D4C2×D1312yes—
582C2×C4×D4C2×D1312yescomplemented
583C2×#117—132no—
584C2×#117C2×D1311yescharacteristic, complemented
585C22×C4⋊C4—132no—
586C22×C4⋊C4—131no—
587C22×C4⋊C4—132no—
588C22×C4⋊C4—134no—
589C22×C22⋊C4—132no—
590C22×C22⋊C4—134no—
591C22×C13—22no—
592C22×C13—22no—
593C22×C13—22no—
594C22×C13—22no—
595C22×C13—28no—
596C22×C13—28no—
597C22×C13—24no—
598C22×C13—22no—
599C22×C13—24no—
600C22×C13—22no—
601C22×C13—24no—
602C22×C13—22no—
603C22×C13—416no—
604C22×C13—48no—
605C22×C13—44no—
606C22×C13C23×D414yes—
607C22×C13C23×D412yes—
608C22×C13C2×2−1+412yes—
609C22×C13C2×2−1+414yescomplemented
610C22×C13#58512yes—
611C22×C13C2611yescharacteristic
612C2×D13—24no—
613C2×D13—24no—
614C2×D13—216no—
615C2×D13—24no—
616C2×D13—24no—
617C2×D13—24no—
618C2×D13—432no—
619C2×D13—48no—
620C2×D13C23×D418yes—
621C4×C13—24no—
622C4×C13—22no—
623C4×C13—22no—
624C4×C13—24no—
625C4×C13—24no—
626C4×C13C23×D414yes—
627C4×C13C23×D414yes—
628Dic13—28no—
629Dic13—24no—
630Dic13—28no—
631Dic13C23×D418yes—
632C25—132no—
633C25C22×D1311yescharacteristic
6342−1+4—26128no—
635C2×#41—28no—
636C2×#41—1316no—
637C2×#41—1332no—
638C2×#41—1316no—
639C2×#41—138no—
640C2×#41—1316no—
641C2×#41—138no—
642C2×#41—1316no—
643C2×#41—138no—
644C2×#41—1316no—
645C2×#41—138no—
646C2×#41—2616no—
647C2×#41—2616no—
648C2×#41—268no—
649C2×#41—2616no—
650C2×#41—268no—
651C2×#41—26128no—
652C2×#41—2616no—
653C2×#41—2632no—
654C2×#41—268no—
655C2×#41C22×D1318yescomplemented
656C22×Q8—1316no—
657C22×Q8—131no—
658C22×Q8—132no—
659C22×Q8—134no—
660C22×Q8—132no—
661C22×Q8—132no—
662C22×Q8—131no—
663C22×Q8—138no—
664C22×Q8—1316no—
665C22×Q8—138no—
666C22×Q8—268no—
667C22×Q8—2616no—
668C22×Q8—2616no—
669C22×Q8—268no—
670C22×Q8C22×D1311yescharacteristic
671C22×D4—132no—
672C22×D4—134no—
673C22×D4—132no—
674C22×D4—132no—
675C22×D4—132no—
676C22×D4—1316no—
677C22×D4—134no—
678C22×D4—131no—
679C22×D4—132no—
680C22×D4—131no—
681C22×D4—138no—
682C22×D4—268no—
683C22×D4—2616no—
684C22×D4C22×D1312yes—
685C22×D4C22×D1312yes—
686C22×D4C22×D1311yescharacteristic
687C22×D4C22×D1312yes—
688C23×C4—28no—
689C23×C4—132no—
690C23×C4—132no—
691C23×C4—134no—
692C23×C4—132no—
693C23×C4—132no—
694C23×C4—134no—
695C23×C4—132no—
696C23×C4—132no—
697C23×C4—132no—
698C23×C4—1316no—
699C23×C4—134no—
700C23×C4—2616no—
701C23×C4C22×D1311yescharacteristic
702C23×C4C22×D1311yescharacteristic
703C23×C4C22×D1312yes—
704C23×C4C22×D1311yescharacteristic
705C23×C4C22×D1311yescharacteristic
706C23×C4C22×D1311yescharacteristic
707C23×C4C22×D1318yes—
708C23×C4C22×D1311yescharacteristic
709C4⋊Q8—1332no—
710C4⋊Q8—1316no—
711#124—1332no—
712#124—1316no—
713#123—1332no—
714#123—1332no—
715#123—1332no—
716#123—1332no—
717#123C22×D13116yescomplemented
718C22⋊Q8—1316no—
719C22⋊Q8—1316no—
720C22⋊Q8—1316no—
721C22⋊Q8—1316no—
722C22⋊Q8—1316no—
723C22⋊Q8—1316no—
724C22⋊Q8—1316no—
725C22⋊Q8—1332no—
726C22⋊Q8—1316no—
727C22⋊Q8—1332no—
728C22⋊Q8—1332no—
729C22⋊Q8C22×D1318yes—
730C22⋊Q8C22×D1318yescomplemented
731#121—1316no—
732#121—1332no—
733#121—1332no—
734#121—1332no—
735#121—1316no—
736#121—1332no—
737#121C22×D1318yes—
738#121C22×D1318yescomplemented
739#120—1332no—
740#120C22×D13116yes—
741C4×Q8—1316no—
742C4×D4—1332no—
743C4×D4—1332no—
744C4×D4—1332no—
745C4×D4—1316no—
746C4×D4C22×D13116yes—
747C4×D4C22×D13116yescomplemented
748#117—1316no—
749#117C22×D1318yescomplemented
750C2×C4⋊C4—132no—
751C2×C4⋊C4—134no—
752C2×C4⋊C4—134no—
753C2×C4⋊C4—132no—
754C2×C4⋊C4—138no—
755C2×C4⋊C4—134no—
756C2×C4⋊C4—134no—
757C2×C4⋊C4—134no—
758C2×C4⋊C4—1316no—
759C2×C4⋊C4—134no—
760C2×C4⋊C4—1316no—
761C2×C4⋊C4—1332no—
762C2×C4⋊C4C22×D1311yescharacteristic
763C2×C4⋊C4C22×D1312yes—
764C2×C4⋊C4C22×D1311yescharacteristic
765C2×C4⋊C4C22×D1312yes—
766C2×C22⋊C4—134no—
767C2×C22⋊C4—134no—
768C2×C22⋊C4—1316no—
769C2×C22⋊C4—134no—
770C2×C22⋊C4—134no—
771C2×C22⋊C4—134no—
772C2×C22⋊C4—134no—
773C2×C22⋊C4—134no—
774C2×C22⋊C4—1332no—
775C2×C22⋊C4C22×D1312yes—
776C2×C22⋊C4C22×D1312yes—
777C2×C22⋊C4C22×D1312yes—
778C2×C22⋊C4C22×D1312yes—
779C2×C22⋊C4C22×D1312yes—
780C2×C42—134no—
781C2×C42C22×D1312yes—
782C2×C13—24no—
783C2×C13—24no—
784C2×C13—44no—
785C2×C13—42no—
786C2×C13#348914yescomplemented
787C2×C13C24×D411yescharacteristic
788C2×C13C22×2−1+411yescharacteristic
789C2×C13C2×#58511yescharacteristic
790D13—28no—
791D13—44no—
792C24—24no—
793C24—24no—
794C24—42no—
795C24—132no—
796C24—132no—
797C24—138no—
798C24—268no—
799C24—268no—
800C24—524no—
801C24C23×D1311yescharacteristic
802C24C23×D1312yes—
803C24C23×D1314yes—
804C24C23×D1311yescharacteristic
805C24C23×D1311yescharacteristic
806#41—232no—
807#41—1364no—
808#41—2664no—
809#41—2664no—
810#41—2632no—
811#41—2664no—
812#41—2632no—
813#41—2664no—
814#41—26128no—
815#41—2632no—
816C2×Q8—24no—
817C2×Q8—138no—
818C2×Q8—134no—
819C2×Q8—138no—
820C2×Q8—1316no—
821C2×Q8—138no—
822C2×Q8—138no—
823C2×Q8—134no—
824C2×Q8—2616no—
825C2×Q8—268no—
826C2×Q8—2632no—
827C2×Q8—2664no—
828C2×Q8—2664no—
829C2×Q8—268no—
830C2×Q8—268no—
831C2×Q8—264no—
832C2×Q8—2632no—
833C2×Q8C23×D1314yes—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—44no—
838C2×D4—1316no—
839C2×D4—138no—
840C2×D4—1316no—
841C2×D4—138no—
842C2×D4—138no—
843C2×D4—138no—
844C2×D4—1316no—
845C2×D4—138no—
846C2×D4—134no—
847C2×D4—138no—
848C2×D4—134no—
849C2×D4—2632no—
850C2×D4—268no—
851C2×D4—268no—
852C2×D4—2664no—
853C2×D4—268no—
854C2×D4—2616no—
855C2×D4—268no—
856C2×D4—264no—
857C2×D4—528no—
858C2×D4C23×D1318yes—
859C2×D4C23×D1318yes—
860C2×D4C23×D1314yes—
861C2×D4C23×D1318yes—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—232no—
868C22×C4—28no—
869C22×C4—132no—
870C22×C4—1316no—
871C22×C4—138no—
872C22×C4—138no—
873C22×C4—1316no—
874C22×C4—138no—
875C22×C4—134no—
876C22×C4—134no—
877C22×C4—132no—
878C22×C4—138no—
879C22×C4—1316no—
880C22×C4—138no—
881C22×C4—138no—
882C22×C4—138no—
883C22×C4—1316no—
884C22×C4—268no—
885C22×C4—2664no—
886C22×C4—268no—
887C22×C4—2616no—
888C22×C4—268no—
889C22×C4—2616no—
890C22×C4—268no—
891C22×C4—268no—
892C22×C4—528no—
893C22×C4—524no—
894C22×C4D4×D1318yes—
895C22×C4C23×D1314yes—
896C22×C4C23×D1314yes—
897C22×C4C23×D1318yes—
898C22×C4C23×D1314yes—
899C22×C4C23×D1314yes—
900C22×C4C23×D1314yes—
901C22×C4C23×D1312yes—
902C22×C4C23×D1312yes—
903C22×C4C23×D1312yes—
904C22×C4C23×D1311yescharacteristic
905C22×C4C23×D1311yescharacteristic
906C22×C4C23×D1314yes—
907C22×C4C23×D1311yescharacteristic
908C22×C4C23×D1311yescharacteristic
909C4⋊C4—138no—
910C4⋊C4—1316no—
911C4⋊C4—1316no—
912C4⋊C4—138no—
913C4⋊C4—1316no—
914C4⋊C4—1316no—
915C4⋊C4—1316no—
916C4⋊C4—1316no—
917C4⋊C4C23×D1314yes—
918C4⋊C4C23×D1318yes—
919C4⋊C4C23×D1314yes—
920C4⋊C4C23×D1318yes—
921C22⋊C4—1316no—
922C22⋊C4—1316no—
923C22⋊C4—1316no—
924C22⋊C4—1316no—
925C22⋊C4—1316no—
926C22⋊C4—1316no—
927C22⋊C4—1316no—
928C22⋊C4C23×D1318yes—
929C22⋊C4C23×D1318yes—
930C22⋊C4C23×D1318yes—
931C22⋊C4C23×D1318yes—
932C22⋊C4C23×D1318yes—
933C42—1316no—
934C42C23×D1318yes—
935C13C2×#348911yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—28no—
941C23—22no—
942C23—24no—
943C23—24no—
944C23—22no—
945C23—28no—
946C23—22no—
947C23—24no—
948C23—44no—
949C23—416no—
950C23—138no—
951C23—134no—
952C23—134no—
953C23—2616no—
954C23—264no—
955C23—264no—
956C23—264no—
957C23—264no—
958C23—2616no—
959C23—264no—
960C23—528no—
961C23—5232no—
962C23C2×D4×D1314yes—
963C23#8825714yescomplemented
964C23C24×D1312yes—
965C23C24×D1314yes—
966C23C24×D1312yes—
967C23C24×D1312yes—
968C23C24×D1311yescharacteristic
969Q8—28no—
970Q8—1316no—
971Q8—2632no—
972Q8—2616no—
973Q8—2616no—
974Q8—2616no—
975Q8—268no—
976D4—216no—
977D4—216no—
978D4—28no—
979D4—48no—
980D4—1332no—
981D4—1316no—
982D4—2616no—
983D4—2616no—
984D4—2616no—
985D4—2632no—
986D4—2616no—
987D4—268no—
988D4—5216no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—216no—
1000C2×C4—138no—
1001C2×C4—134no—
1002C2×C4—1332no—
1003C2×C4—138no—
1004C2×C4—138no—
1005C2×C4—134no—
1006C2×C4—2616no—
1007C2×C4—2616no—
1008C2×C4—2632no—
1009C2×C4—2616no—
1010C2×C4—2632no—
1011C2×C4—264no—
1012C2×C4—268no—
1013C2×C4—2616no—
1014C2×C4—268no—
1015C2×C4—2616no—
1016C2×C4—5216no—
1017C2×C4—528no—
1018C2×C4C2×D4×D1314yes—
1019C2×C4C2×D4×D1314yes—
1020C2×C4C2×D4×D13116yes—
1021C2×C4C24×D1314yes—
1022C2×C4C24×D1314yes—
1023C2×C4C24×D1314yes—
1024C2×C4C24×D1312yes—
1025C2×C4C24×D1312yes—
1026C2×C4C24×D1312yes—
1027C2×C4C24×D1312yes—
1028C22—28no—
1029C22—28no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—24no—
1036C22—24no—
1037C22—22no—
1038C22—22no—
1039C22—24no—
1040C22—416no—
1041C22—48no—
1042C22—44no—
1043C22—138no—
1044C22—2616no—
1045C22—264no—
1046C22—264no—
1047C22—264no—
1048C22—264no—
1049C22—264no—
1050C22—5232no—
1051C22—528no—
1052C22C22×D4×D1314yes—
1053C22C22×D4×D1312yes—
1054C22C2×#8825712yes—
1055C22C2×#8825714yescomplemented
1056C22#1171964812yes—
1057C22C25×D1311yescharacteristic
1058C4—22no—
1059C4—22no—
1060C4—24no—
1061C4—24no—
1062C4—24no—
1063C4—138no—
1064C4—264no—
1065C4—268no—
1066C4—268no—
1067C4C22×D4×D1314yes—
1068C4C22×D4×D1314yes—
1069C2—24no—
1070C2—24no—
1071C2—42no—
1072C2—44no—
1073C2—268no—
1074C2—524no—
1075C2#1312850814yesdirect product factor
1076C2C23×D4×D1311yescharacteristic
1077C2C22×#8825711yescharacteristic
1078C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#525C2
socleC23×C13C25
hypercenterC2×#525D13
hypocenterC13C2×#3489
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#88257C2semidirect
2. C23×#6127C2semidirect
3. #13128508C2direct (N × H)
4. C2×D4×Dic26C2semidirect
5. C2×#11719257C2semidirect
6. C2×#11719256C2semidirect
7. C2×#11719360C2semidirect
8. C2×#11719255C2semidirect
9. C2×#11719296C2semidirect
10. C2×#11719313C2semidirect
11. C2×#11719538C2semidirect
12. C2×#11719231C2semidirect
13. C2×#11719333C2semidirect
14. C2×#11719311C2semidirect
15. C22×#88178C2semidirect
16. C2×D13×C22⋊Q8C2semidirect
17. C2×#11719228C2semidirect
18. C2×C13×#525C2semidirect
19. C22×C13×#41C22semidirect
23. C2×#88257C22semidirect
24. C22×Q8×D13C22semidirect
25. C22×#6129C22semidirect
26. C22×#6129C22semidirect
34. C22×#6127C22semidirect
35. C22×#6127C22semidirect
39. C23×Dic26C22semidirect
40. C23×Dic26C22semidirect
41. C13×#525C22semidirect
42. C2×C13×#123C22semidirect
44. C2×C13×C22⋊Q8C22semidirect
46. C2×C13×#121C22semidirect
49. C2×C4×D4×C13C22semidirect
50. C2×C13×#117C22semidirect
52. #11719538C22semidirect
53. C2×#88200C22semidirect
54. C2×#88193C22semidirect
55. C2×#88193C22semidirect
56. C2×#88192C22semidirect
57. C2×#88192C22semidirect
60. C2×#88184C22semidirect
61. C22×C4⋊Dic13C22semidirect
64. C2×#88178C22semidirect
65. C2×#88178C22semidirect
66. C2×#88178C22semidirect
67. C2×#88178C22semidirect
68. C22×#6101C22semidirect
69. #11719360C22semidirect
70. #11719333C22semidirect
71. D13×C22⋊Q8C22semidirect
72. #11719313C22semidirect
73. #11719311C22semidirect
74. #11719296C22semidirect
75. #11719257C22semidirect
76. #11719256C22semidirect
77. #11719255C22semidirect
78. D4×Dic26C22semidirect
79. #11719231C22semidirect
80. #11719228C22semidirect
81. C2×#88151C22semidirect
82. C2×#88151C22semidirect
83. C2×#88150C22semidirect
84. C2×#88148C22semidirect
85. C2×#88146C22semidirect
86. C2×C4⋊C4×D13C22semidirect
87. C2×C4⋊C4×D13C22semidirect
88. C2×#88142C22semidirect
89. C2×#88140C22semidirect
90. C2×#88139C22semidirect
91. C2×#88138C22semidirect
92. C2×#88137C22semidirect
93. C2×#88137C22semidirect
94. C2×#88135C22semidirect
95. C2×#88135C22semidirect
98. C2×#88132C22semidirect
99. C2×#88129C22semidirect
100. C2×C4×D52C22semidirect
101. C2×#88123C22semidirect
102. C2×C4×Dic26C22semidirect
106. C2×C13×#41C23semidirect
135. C2×Q8×D13C23semidirect
138. C2×#6129C23semidirect
139. C2×#6129C23semidirect
147. C2×#6127D4semidirect
154. C2×#6127C23semidirect
178. C22×Dic26C23semidirect
179. C22×Dic26C23semidirect
180. C13×#123C23semidirect
182. C13×C22⋊Q8C23semidirect
184. C13×#121C23semidirect
187. C4×D4×C13C23semidirect
188. C13×#117C23semidirect
203. #88200C23semidirect
204. #88193C23semidirect
205. #88193C23semidirect
206. #88192C23semidirect
207. #88192C23semidirect
210. #88184C23semidirect
219. C2×C4⋊Dic13C23semidirect
222. #88178C23semidirect
223. #88178C23semidirect
224. #88178C23semidirect
229. C2×#6101C23semidirect
231. #88151C23semidirect
232. #88151C23semidirect
233. #88150C23semidirect
234. #88148C23semidirect
235. #88146C23semidirect
236. C4⋊C4×D13C23semidirect
237. C4⋊C4×D13C23semidirect
238. #88142C23semidirect
239. #88140C23semidirect
240. #88139C23semidirect
241. #88138C23semidirect
242. #88137C23semidirect
243. #88137C23semidirect
244. #88135C23semidirect
245. #88135C23semidirect
248. #88132C23semidirect
249. #88129C23semidirect
250. C4×D52C23semidirect
251. #88123C23semidirect
252. C4×Dic26C23semidirect
335. #6127C2×D4semidirect
411. C2×#525D13semidirect
430. C23×C132−1+4semidirect
520. C22×#41C2×D13semidirect
544. #525C2×D13semidirect
549. C2×#123C2×D13semidirect
564. C2×C22⋊Q8C2×D13semidirect
572. C2×#121C2×D13semidirect
582. C2×C4×D4C2×D13semidirect
584. C2×#117C2×D13semidirect
609. C22×C13C2×2−1+4semidirect
655. C2×#41C22×D13semidirect
717. #123C22×D13semidirect
730. C22⋊Q8C22×D13semidirect
738. #121C22×D13semidirect
747. C4×D4C22×D13semidirect
749. #117C22×D13semidirect
786. C2×C13#3489semidirect
935. C13C2×#3489semidirect
963. C23#88257semidirect
1055. C22C2×#88257semidirect
1075. C2#13128508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882572
C23×#61272
#131285082
C2×D4×Dic262
C2×#117192572
C2×#117192562
C2×#117193602
C2×#117192552
C2×#117192962
C2×#117193132
C2×#117195382
C2×#117192312
C2×#117193332
C2×#117193112
C22×#881782
C2×D13×C22⋊Q82
C2×#117192282
C2×C13×#5252
C2×#348913