Finite Group Databasebeta

← C2×#13128748 #16771283

Subgroups — C2×#13128748 #16771283

Order 3328.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128748C2132yesmaximal, direct product factor
2C2×#11719273C212yesmaximal, complemented
3C2×#11719237C212yesmaximal, complemented
4C2×#11719395C212yesmaximal, complemented
5C2×#11719400C212yesmaximal, complemented
6C2×#11719235C212yesmaximal, complemented
7C2×#11719281C212yesmaximal, complemented
8C2×#11719338C212yesmaximal, complemented
9C2×#11719336C212yesmaximal, complemented
10C2×#11719348C212yesmaximal, complemented
11C2×#11719287C212yesmaximal, complemented
12C2×#11719334C212yesmaximal, complemented
13C2×#11719433C211yesmaximal, characteristic, complemented
14C2×#11719430C211yesmaximal, characteristic, complemented
15C2×#11719430C211yesmaximal, characteristic, complemented
16C2×#11719182C211yesmaximal, characteristic, complemented
17C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×#11719279C212yesmaximal, complemented
19C2×C4×#6127C211yesmaximal, characteristic, complemented
20C2×C13×#533C211yesmaximal, characteristic, complemented
21C22×#6131C2212yes—
22C22×#6131C2212yes—
23C22×Q8×D13C2212yes—
24C22×#6127C2211yescharacteristic
25C22×#6127C2212yes—
26C13×#533C22116yescomplemented
27C2×C13×C4⋊Q8C2211yescharacteristic
28C2×C13×C4⋊Q8C2211yescharacteristic
29C2×C13×#125C2212yes—
30C2×C13×C22⋊Q8C2212yes—
31C2×C13×C22⋊Q8C2212yes—
32C2×C4×Q8×C13C2212yes—
33C2×C4×Q8×C13C2212yes—
34C2×C13×#117C2212yes—
35C22×C42×C13C2211yescharacteristic
36C2×#88201C2212yes—
37C2×#88201C2212yes—
38C2×#88200C2212yes—
39C2×Q8×Dic13C2212yes—
40C2×#88198C2212yes—
41C2×#88184C2212yes—
42C2×#88184C2212yes—
43C2×C4×C22⋊D13C2211yescharacteristic
44C2×C4×C22⋊D13C2211yescharacteristic
45C2×C4×C22⋊D13C2211yescharacteristic
46C2×C4×C22⋊D13C2211yescharacteristic
47C2×#88180C2211yescharacteristic
48#11719433C22116yescomplemented
49#11719430C22116yescomplemented
50#11719430C22116yescomplemented
51D13×C4⋊Q8C22116yescomplemented
52#11719400C22132yescomplemented
53#11719395C22132yescomplemented
54#11719348C22132yescomplemented
55#11719338C22132yescomplemented
56#11719336C22132yescomplemented
57#11719334C22132yescomplemented
58#11719287C22132yescomplemented
59#11719281C22132yescomplemented
60#11719279C22132yescomplemented
61#11719273C22132yescomplemented
62#11719237C22132yescomplemented
63#11719235C22132yescomplemented
64C2×#88152C2214yes—
65C2×#88151C2214yes—
66C2×#88151C2212yes—
67C2×#88150C2214yes—
68C2×#88150C2214yes—
69C2×#88149C2212yes—
70C2×#88149C2212yes—
71C2×#88149C2214yes—
72C2×#88149C2212yes—
73C2×#88149C2212yes—
74C2×#88148C2214yes—
75C2×#88147C2212yes—
76C2×#88147C2214yes—
77C2×#88147C2212yes—
78C2×#88147C2212yes—
79C2×#88147C2212yes—
80C2×#88146C2212yes—
81C2×C4⋊C4×D13C2214yes—
82C2×C4⋊C4×D13C2212yes—
83C2×C4⋊C4×D13C2212yes—
84C2×#88144C2212yes—
85C2×#88142C2212yes—
86C2×#88142C2212yes—
87C2×#88141C2212yes—
88C2×#88139C2214yes—
89C2×#88138C2214yes—
90C2×#88138C2214yes—
91C2×#88137C2214yes—
92C2×#88130C2214yes—
93#11719182C22116yescomplemented
94C2×#88129C2214yes—
95C2×#88129C2212yes—
96C2×#88128C2211yescharacteristic
97C4×#6127C22116yescomplemented
98C2×C4×D52C2212yes—
99C2×C4×D52C2211yescharacteristic
100C2×C4×D52C2211yescharacteristic
101C2×C4×D52C2214yes—
102C2×C4×D52C2212yes—
103C2×#88126C2211yescharacteristic
104C2×#88126C2211yescharacteristic
105C2×#88126C2214yes—
106C2×C42×D13C2211yescharacteristic
107C2×C42×D13C2211yescharacteristic
108C2×#88123C2211yescharacteristic
109C2×C4×Dic26C2211yescharacteristic
110C2×C4×Dic26C2211yescharacteristic
111C22×Q8×C13C2312yes—
112C22×Q8×C13C2312yes—
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C23×C4×C13C2311yescharacteristic
116C22×C22⋊D13C2311yescharacteristic
117C22×C22⋊D13C2311yescharacteristic
118C22×C22⋊D13C2314yes—
119C2×#6131—216no—
120C2×#6131—48no—
121C2×#6131C23116yes—
122C2×#6131C23116yes—
123C2×Q8×D13—48no—
124C2×Q8×D13C23116yes—
125C2×#6127—28no—
126C2×#6127—48no—
127C2×#6127C2318yes—
128C2×#6127C23116yes—
129C22×D52C2311yescharacteristic
130C22×D52C2312yes—
131C22×D52C2312yes—
132C22×D52C2314yes—
133C22×D52C2312yes—
134C22×D52C2314yes—
135C22×C4×D13C2311yescharacteristic
136C22×C4×D13C2311yescharacteristic
137C22×C4×D13C2311yescharacteristic
138C22×C4×D13C2311yescharacteristic
139C22×C4×D13C2311yescharacteristic
140C22×C4×D13C2314yes—
141C22×C4×D13C2314yes—
142C22×C4×D13C2314yes—
143C22×C4×D13C2314yes—
144C22×C4×D13C2311yescharacteristic
145C22×Dic26C2311yescharacteristic
146C22×Dic26C2312yes—
147C22×Dic26C2314yes—
148C13×C4⋊Q8C2318yes—
149C13×C4⋊Q8C2318yes—
150C13×#125C23116yes—
151C13×C22⋊Q8C23116yes—
152C13×C22⋊Q8C23116yes—
153C4×Q8×C13C23116yes—
154C4×Q8×C13C23116yes—
155C13×#117C23116yes—
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2312yes—
160C2×C13×C4⋊C4C2314yes—
161C2×C13×C4⋊C4C2314yes—
162C2×C13×C22⋊C4C2314yes—
163C2×C42×C13C2311yescharacteristic
164C2×C42×C13C2311yescharacteristic
165C2×C42×C13C2311yescharacteristic
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2314yes—
168C2×C42×C13C2318yes—
169C2×C22⋊Dic13C2311yescharacteristic
170C2×C22⋊Dic13C2311yescharacteristic
171#88201C23116yes—
172#88201C23116yes—
173#88200C23116yes—
174Q8×Dic13C23116yes—
175#88198C23116yes—
176#88184C23116yes—
177#88184C23116yes—
178C4×C22⋊D13C2318yes—
179C4×C22⋊D13C2318yes—
180C4×C22⋊D13C2318yes—
181C4×C22⋊D13C2318yes—
182C2×#6103C2311yescharacteristic
183C2×#6103C2314yes—
184C2×#6103C2311yescharacteristic
185C2×#6103C2311yescharacteristic
186C2×#6103C2311yescharacteristic
187C2×#6103C2314yes—
188C2×#6103C2314yes—
189C2×#6103C2314yes—
190C2×#6103C2314yes—
191C2×#6103C2314yes—
192C2×#6103C2314yes—
193#88180C2318yes—
194C2×C4⋊Dic13C2311yescharacteristic
195C2×C4⋊Dic13C2311yescharacteristic
196C2×C4⋊Dic13C2312yes—
197C2×C4⋊Dic13C2312yes—
198C2×C4⋊Dic13C2314yes—
199C2×#6101C2311yescharacteristic
200C2×#6101C2311yescharacteristic
201C2×#6101C2311yescharacteristic
202C2×#6101C2311yescharacteristic
203C2×#6101C2314yes—
204C2×#6101C2314yes—
205C2×#6101C2314yes—
206C2×C4×Dic13C2311yescharacteristic
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2311yescharacteristic
209C2×C4×Dic13C2311yescharacteristic
210C2×C4×Dic13C2311yescharacteristic
211C2×C4×Dic13C2311yescharacteristic
212C2×C4×Dic13C2314yes—
213#88152C23132yes—
214#88151C23116yes—
215#88151C23132yes—
216#88150C23132yes—
217#88150C23132yes—
218#88149C23116yes—
219#88149C23116yes—
220#88149C23116yes—
221#88149C23116yes—
222#88149C23132yes—
223#88148C23132yes—
224#88147C23116yes—
225#88147C23116yes—
226#88147C23116yes—
227#88147C23116yes—
228#88147C23132yes—
229#88146C23116yes—
230C4⋊C4×D13C23116yes—
231C4⋊C4×D13C23116yes—
232C4⋊C4×D13C23132yes—
233#88144C23116yes—
234#88142C23116yes—
235#88142C23116yes—
236#88141C23116yes—
237#88139C23132yes—
238#88138C23132yes—
239#88138C23132yes—
240#88137C23132yes—
241#88130C23132yes—
242#88129C23116yes—
243#88129C23132yes—
244#88128C2318yes—
245C4×D52C2318yes—
246C4×D52C2318yes—
247C4×D52C23116yes—
248C4×D52C23116yes—
249C4×D52C23132yes—
250#88126C2318yes—
251#88126C2318yes—
252#88126C23132yes—
253C42×D13C2318yes—
254C42×D13C2318yes—
255#88123C2318yes—
256C4×Dic26C2318yes—
257C4×Dic26C2318yes—
258C2×#3511—131nomaximal, Sylow
259C24×C13C2411yescharacteristic
260C23×D13C2414yes—
261C23×D13C2411yescharacteristic
262C23×D13C2411yescharacteristic
263C2×Q8×C13—28no—
264C2×Q8×C13—28no—
265C2×Q8×C13C2418yes—
266C2×Q8×C13C2418yes—
267C22×C4×C13—24no—
268C22×C4×C13—24no—
269C22×C4×C13—24no—
270C22×C4×C13C2414yes—
271C22×C4×C13C2411yescharacteristic
272C22×C4×C13C2411yescharacteristic
273C22×C4×C13C2414yes—
274C22×C4×C13C2411yescharacteristic
275C22×C4×C13C2414yes—
276C22×C4×C13C2414yes—
277C22×C4×C13C2414yes—
278C22×C4×C13C2411yescharacteristic
279C22×C4×C13C2411yescharacteristic
280C22×C4×C13C2411yescharacteristic
281C2×C22⋊D13—24no—
282C2×C22⋊D13—24no—
283C2×C22⋊D13—48no—
284C2×C22⋊D13C2414yes—
285C2×C22⋊D13C2414yes—
286C2×C22⋊D13C24116yes—
287C22×Dic13C2411yescharacteristic
288C22×Dic13C2411yescharacteristic
289C22×Dic13C2411yescharacteristic
290C22×Dic13C2411yescharacteristic
291C22×Dic13C2411yescharacteristic
292C22×Dic13C2414yes—
293C22×Dic13C2411yescharacteristic
294#6131—264no—
295#6131—432no—
296Q8×D13—432no—
297#6127—232no—
298#6127—432no—
299C2×D52—24no—
300C2×D52—216no—
301C2×D52—28no—
302C2×D52—28no—
303C2×D52—28no—
304C2×D52—48no—
305C2×D52C2414yes—
306C2×D52C2418yes—
307C2×D52C2418yes—
308C2×D52C24116yes—
309C2×D52C2418yes—
310C2×D52C24116yes—
311C2×C4×D13—24no—
312C2×C4×D13—24no—
313C2×C4×D13—24no—
314C2×C4×D13—24no—
315C2×C4×D13—24no—
316C2×C4×D13—216no—
317C2×C4×D13—48no—
318C2×C4×D13—48no—
319C2×C4×D13—48no—
320C2×C4×D13#4118yescomplemented
321C2×C4×D13C2414yes—
322C2×C4×D13C2414yes—
323C2×C4×D13C2414yes—
324C2×C4×D13C2414yes—
325C2×C4×D13C2414yes—
326C2×C4×D13C24116yes—
327C2×C4×D13C24116yes—
328C2×C4×D13C24116yes—
329C2×C4×D13C24116yes—
330C2×C4×D13C2414yes—
331C2×Dic26—28no—
332C2×Dic26—24no—
333C2×Dic26—48no—
334C2×Dic26C2414yes—
335C2×Dic26C2418yes—
336C2×Dic26C24116yes—
337C13×C4⋊C4C2418yes—
338C13×C4⋊C4C2418yes—
339C13×C4⋊C4C2418yes—
340C13×C4⋊C4C2418yes—
341C13×C4⋊C4C24116yes—
342C13×C4⋊C4C24116yes—
343C13×C22⋊C4C24116yes—
344C42×C13C2414yes—
345C42×C13C2414yes—
346C42×C13C2414yes—
347C42×C13C2414yes—
348C42×C13C24116yes—
349C22⋊Dic13C2414yes—
350C22⋊Dic13C2414yes—
351#6103C2414yes—
352#6103C24116yes—
353#6103C2414yes—
354#6103C2414yes—
355#6103C2414yes—
356#6103C24116yes—
357#6103C24116yes—
358#6103C24116yes—
359#6103C24116yes—
360#6103C24116yes—
361#6103C24116yes—
362C4⋊Dic13C2414yes—
363C4⋊Dic13C2414yes—
364C4⋊Dic13C2418yes—
365C4⋊Dic13C2418yes—
366C4⋊Dic13C24116yes—
367#6101C2414yes—
368#6101C2414yes—
369#6101C2414yes—
370#6101C2414yes—
371#6101C24116yes—
372#6101C24116yes—
373#6101C24116yes—
374C4×Dic13C2414yes—
375C4×Dic13C2414yes—
376C4×Dic13C2414yes—
377C4×Dic13C2414yes—
378C4×Dic13C2414yes—
379C4×Dic13C2414yes—
380C4×Dic13C24116yes—
381#3511—1332no—
382C2×#556—132no—
383C2×#555—132no—
384C2×#554—132no—
385C2×#553—132no—
386C2×#553—132no—
387C2×#548—132no—
388C2×#548—132no—
389C2×#547—132no—
390C2×#542—132no—
391C2×#542—132no—
392C2×#537—132no—
393C2×#533—131no—
394C2×#533D1311yescharacteristic, complemented
395C2×#532—131no—
396C2×#532—131no—
397C2×#532—131no—
398C22×C4⋊Q8—131no—
399C2×#520—132no—
400C2×C4×#41—131no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13C2512yes—
405C23×C13C2511yescharacteristic
406C22×D13—22no—
407C22×D13—22no—
408C22×D13—28no—
409C22×D13—22no—
410C22×D13—22no—
411C22×D13—28no—
412C22×D13—22no—
413C22×D13—28no—
414C22×D13C2×#4114yes—
415C22×D13C2518yes—
416C22×D13C2512yes—
417C22×D13C2512yes—
418Q8×C13—216no—
419Q8×C13—216no—
420C2×C4×C13—22no—
421C2×C4×C13—28no—
422C2×C4×C13—28no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—28no—
426C2×C4×C13—28no—
427C2×C4×C13—28no—
428C2×C4×C13C2×#4114yes—
429C2×C4×C13H(5,𝔽2)14yes—
430C2×C4×C132−1+414yes—
431C2×C4×C13C2518yes—
432C2×C4×C13C2512yes—
433C2×C4×C13C2512yes—
434C2×C4×C13C2518yes—
435C2×C4×C13C2512yes—
436C2×C4×C13C2512yes—
437C2×C4×C13C2512yes—
438C2×C4×C13C2512yes—
439C22⋊D13—28no—
440C22⋊D13—28no—
441C22⋊D13—416no—
442C2×Dic13—22no—
443C2×Dic13—28no—
444C2×Dic13—22no—
445C2×Dic13—22no—
446C2×Dic13—22no—
447C2×Dic13—22no—
448C2×Dic13C2×#4114yes—
449C2×Dic13C2512yes—
450C2×Dic13C2512yes—
451C2×Dic13C2512yes—
452C2×Dic13C2512yes—
453C2×Dic13C2512yes—
454C2×Dic13C2518yes—
455C2×Dic13C2512yes—
456D52—28no—
457D52—232no—
458D52—216no—
459D52—216no—
460D52—216no—
461D52—416no—
462C4×D13—28no—
463C4×D13—28no—
464C4×D13—28no—
465C4×D13—28no—
466C4×D13—28no—
467C4×D13—232no—
468C4×D13—416no—
469C4×D13—416no—
470C4×D13—416no—
471C4×D13C2×#41116yescomplemented
472Dic26—216no—
473Dic26—28no—
474Dic26—416no—
475C22×#41—132no—
476C22×#41—132no—
477C22×#41—131no—
478C22×#41—132no—
479C23×Q8—132no—
480#556—1332no—
481#555—1332no—
482#554—1332no—
483#553—1332no—
484#553—1332no—
485#548—1332no—
486#548—1332no—
487#547—1332no—
488#542—1332no—
489#542—1332no—
490#537—1332no—
491#533—1316no—
492#533C2×D13116yescomplemented
493#532—1316no—
494#532—1316no—
495#532—1316no—
496C2×C4⋊Q8—132no—
497C2×C4⋊Q8—1316no—
498C2×C4⋊Q8—132no—
499C2×C4⋊Q8—132no—
500C2×C4⋊Q8—131no—
501C2×C4⋊Q8C2×D1311yescharacteristic
502C2×C4⋊Q8C2×D1311yescharacteristic
503C2×#127—131no—
504C2×#126—134no—
505C2×#126—134no—
506C2×#125—132no—
507C2×#125C2×D1312yes—
508C2×#124—132no—
509C2×#124—132no—
510C2×#124—134no—
511C2×#124—132no—
512C2×#124—134no—
513C2×#123—134no—
514C2×#123—134no—
515C2×C22⋊Q8—132no—
516C2×C22⋊Q8—134no—
517C2×C22⋊Q8—134no—
518C2×C22⋊Q8—132no—
519C2×C22⋊Q8—134no—
520C2×C22⋊Q8C2×D1312yes—
521C2×C22⋊Q8C2×D1312yes—
522C2×#121—132no—
523C2×#121—132no—
524C2×#121—132no—
525C2×#121—132no—
526C2×#121—132no—
527C2×#121—132no—
528C2×#121—134no—
529C2×#121—134no—
530C2×#121—134no—
531#520—1332no—
532C4×#41—1316no—
533C2×C4×Q8—132no—
534C2×C4×Q8—132no—
535C2×C4×Q8—131no—
536C2×C4×Q8—131no—
537C2×C4×Q8C2×D1312yes—
538C2×C4×Q8C2×D1312yes—
539C2×C4×D4—131no—
540C2×C4×D4—131no—
541C2×C4×D4—131no—
542C2×C4×D4—131no—
543C2×C4×D4—132no—
544C2×C4×D4—134no—
545C2×C4×D4—132no—
546C2×C4×D4—132no—
547C2×C4×D4—132no—
548C2×C4×D4—131no—
549C2×C4×D4—131no—
550C2×C4×D4—132no—
551C2×C4×D4—134no—
552C2×C4×D4—132no—
553C2×#117—131no—
554C2×#117—132no—
555C2×#117—131no—
556C2×#117—131no—
557C2×#117—134no—
558C2×#117C2×D1312yes—
559C22×C4⋊C4—132no—
560C22×C4⋊C4—134no—
561C22×C4⋊C4—132no—
562C22×C42—131no—
563C22×C42—131no—
564C22×C42C2×D1311yescharacteristic
565C22×C13—22no—
566C22×C13—22no—
567C22×C13—22no—
568C22×C13—44no—
569C22×C13C22×#4112yes—
570C22×C13C2×H(5,𝔽2)12yes—
571C22×C13C2×2−1+412yes—
572C22×C13C2611yescharacteristic
573C2×D13—22no—
574C2×D13—22no—
575C2×D13—28no—
576C2×D13—28no—
577C2×D13—22no—
578C2×D13—22no—
579C2×D13—28no—
580C2×D13—22no—
581C2×D13—28no—
582C2×D13—416no—
583C2×D13—44no—
584C2×D13C22×#4114yes—
585C4×C13—22no—
586C4×C13—28no—
587C4×C13—28no—
588C4×C13—22no—
589C4×C13—22no—
590C4×C13C22×#4114yes—
591C4×C13C2×H(5,𝔽2)14yes—
592C4×C13C2×2−1+414yes—
593Dic13—22no—
594Dic13—28no—
595Dic13—22no—
596Dic13—22no—
597Dic13—22no—
598Dic13—22no—
599Dic13C22×#4114yes—
600C2×#41—1316no—
601C2×#41—1316no—
602C2×#41—138no—
603C2×#41—1316no—
604C2×#41—268no—
605C2×#41—2616no—
606C2×#41—528no—
607C2×#41—528no—
608C22×Q8—1316no—
609C22×Q8—131no—
610C22×Q8—132no—
611C22×Q8—134no—
612C22×Q8—528no—
613C22×Q8C22×D1312yes—
614C22×Q8C22×D1312yes—
615C22×D4—131no—
616C22×D4—131no—
617C22×D4—134no—
618C22×D4—132no—
619C22×D4—134no—
620C22×D4—131no—
621C22×D4—132no—
622C22×D4—132no—
623C22×D4—134no—
624C23×C4—131no—
625C23×C4—131no—
626C23×C4—134no—
627C23×C4—131no—
628C23×C4—131no—
629C23×C4—131no—
630C23×C4—131no—
631C23×C4—134no—
632C23×C4—134no—
633C23×C4—134no—
634C23×C4C22×D1311yescharacteristic
635C23×C4C22×D1311yescharacteristic
636C23×C4C22×D1311yescharacteristic
637C4⋊Q8—1316no—
638C4⋊Q8—1316no—
639C4⋊Q8—1316no—
640C4⋊Q8—138no—
641C4⋊Q8C22×D1318yes—
642C4⋊Q8C22×D1318yes—
643#127—138no—
644#126—1332no—
645#126—1332no—
646#125—1316no—
647#125C22×D13116yes—
648#124—1316no—
649#124—1316no—
650#124—1332no—
651#124—1316no—
652#124—1332no—
653#123—1332no—
654#123—1332no—
655C22⋊Q8—1316no—
656C22⋊Q8—1316no—
657C22⋊Q8—1332no—
658C22⋊Q8—1332no—
659C22⋊Q8—1332no—
660C22⋊Q8C22×D13116yes—
661C22⋊Q8C22×D13116yes—
662#121—1316no—
663#121—1316no—
664#121—1316no—
665#121—1316no—
666#121—1316no—
667#121—1316no—
668#121—1332no—
669#121—1332no—
670#121—1332no—
671C4×Q8—1316no—
672C4×Q8—1316no—
673C4×Q8—138no—
674C4×Q8—138no—
675C4×Q8C22×D13116yes—
676C4×Q8C22×D13116yes—
677C4×D4—138no—
678C4×D4—138no—
679C4×D4—138no—
680C4×D4—138no—
681C4×D4—1316no—
682C4×D4—1332no—
683C4×D4—1316no—
684C4×D4—1316no—
685C4×D4—1316no—
686C4×D4—138no—
687C4×D4—138no—
688C4×D4—1316no—
689C4×D4—1332no—
690C4×D4—1316no—
691#117—138no—
692#117—1316no—
693#117—138no—
694#117—138no—
695#117—1332no—
696#117C22×D13116yes—
697C2×C4⋊C4—131no—
698C2×C4⋊C4—134no—
699C2×C4⋊C4—132no—
700C2×C4⋊C4—132no—
701C2×C4⋊C4—134no—
702C2×C4⋊C4—134no—
703C2×C4⋊C4—131no—
704C2×C4⋊C4—131no—
705C2×C4⋊C4—131no—
706C2×C4⋊C4—131no—
707C2×C4⋊C4—131no—
708C2×C4⋊C4—134no—
709C2×C4⋊C4—1316no—
710C2×C4⋊C4—1332no—
711C2×C4⋊C4—1316no—
712C2×C4⋊C4C22×D1312yes—
713C2×C4⋊C4C22×D1312yes—
714C2×C4⋊C4C22×D1314yes—
715C2×C4⋊C4C22×D1312yes—
716C2×C4⋊C4C22×D1312yes—
717C2×C4⋊C4C22×D1314yes—
718C2×C22⋊C4—131no—
719C2×C22⋊C4—131no—
720C2×C22⋊C4—131no—
721C2×C22⋊C4—131no—
722C2×C22⋊C4—134no—
723C2×C22⋊C4—134no—
724C2×C22⋊C4—131no—
725C2×C22⋊C4—131no—
726C2×C22⋊C4—134no—
727C2×C22⋊C4—134no—
728C2×C22⋊C4—134no—
729C2×C22⋊C4—134no—
730C2×C22⋊C4—134no—
731C2×C22⋊C4C22×D1314yes—
732C2×C42—131no—
733C2×C42—134no—
734C2×C42—131no—
735C2×C42—131no—
736C2×C42—131no—
737C2×C42—131no—
738C2×C42—131no—
739C2×C42—138no—
740C2×C42—138no—
741C2×C42C22×D1311yescharacteristic
742C2×C42C22×D1314yes—
743C2×C42C22×D1311yescharacteristic
744C2×C42C22×D1311yescharacteristic
745C2×C42C22×D1318yes—
746C2×C42C22×D1311yescharacteristic
747C2×C13—42no—
748C2×C13#351114yescomplemented
749C2×C13C23×#4111yescharacteristic
750C2×C13C22×H(5,𝔽2)11yescharacteristic
751C2×C13C22×2−1+411yescharacteristic
752D13—24no—
753D13—48no—
754D13—42no—
755C24—131no—
756C24—131no—
757C24—134no—
758C24C23×D1311yescharacteristic
759#41—2632no—
760#41—2664no—
761#41—5232no—
762#41—5232no—
763C2×Q8—28no—
764C2×Q8—28no—
765C2×Q8—134no—
766C2×Q8—138no—
767C2×Q8—1316no—
768C2×Q8—264no—
769C2×Q8—268no—
770C2×Q8—528no—
771C2×Q8—5232no—
772C2×Q8C23×D1318yes—
773C2×Q8C23×D1318yes—
774C2×D4—134no—
775C2×D4—134no—
776C2×D4—1316no—
777C2×D4—138no—
778C2×D4—1316no—
779C2×D4—134no—
780C2×D4—138no—
781C2×D4—138no—
782C2×D4—1316no—
783C2×D4—264no—
784C2×D4—2616no—
785C2×D4—264no—
786C2×D4—264no—
787C2×D4—268no—
788C2×D4—268no—
789C2×D4—268no—
790C2×D4—528no—
791C2×D4—528no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—131no—
796C22×C4—138no—
797C22×C4—134no—
798C22×C4—131no—
799C22×C4—131no—
800C22×C4—131no—
801C22×C4—131no—
802C22×C4—131no—
803C22×C4—134no—
804C22×C4—134no—
805C22×C4—134no—
806C22×C4—134no—
807C22×C4—134no—
808C22×C4—134no—
809C22×C4—1316no—
810C22×C4—1316no—
811C22×C4—1316no—
812C22×C4—1316no—
813C22×C4—2616no—
814C22×C4—264no—
815C22×C4—264no—
816C22×C4—264no—
817C22×C4—264no—
818C22×C4—264no—
819C22×C4—528no—
820C22×C4—528no—
821C22×C4—528no—
822C22×C4C23×D1314yes—
823C22×C4C23×D1314yes—
824C22×C4C23×D1314yes—
825C22×C4C23×D1314yes—
826C22×C4C23×D1311yescharacteristic
827C22×C4C23×D1311yescharacteristic
828C22×C4C23×D1311yescharacteristic
829C22×C4C23×D1314yes—
830C22×C4C23×D1311yescharacteristic
831C22×C4C23×D1311yescharacteristic
832C22×C4C23×D1311yescharacteristic
833C4⋊C4—134no—
834C4⋊C4—1316no—
835C4⋊C4—138no—
836C4⋊C4—138no—
837C4⋊C4—1316no—
838C4⋊C4—1316no—
839C4⋊C4—134no—
840C4⋊C4—134no—
841C4⋊C4—134no—
842C4⋊C4—134no—
843C4⋊C4—134no—
844C4⋊C4—1316no—
845C4⋊C4C23×D1318yes—
846C4⋊C4C23×D1318yes—
847C4⋊C4C23×D13116yes—
848C4⋊C4C23×D1318yes—
849C4⋊C4C23×D1318yes—
850C4⋊C4C23×D13116yes—
851C22⋊C4—134no—
852C22⋊C4—134no—
853C22⋊C4—134no—
854C22⋊C4—134no—
855C22⋊C4—1316no—
856C22⋊C4—1316no—
857C22⋊C4—134no—
858C22⋊C4—134no—
859C22⋊C4—1316no—
860C22⋊C4—1316no—
861C22⋊C4—1316no—
862C22⋊C4—1316no—
863C22⋊C4—1316no—
864C22⋊C4C23×D13116yes—
865C42—134no—
866C42—134no—
867C42—134no—
868C42—134no—
869C42—134no—
870C42—134no—
871C42—1316no—
872C42C23×D1314yes—
873C42C23×D1314yes—
874C42C23×D1314yes—
875C42C23×D1314yes—
876C42C23×D13116yes—
877C13C2×#351111yescharacteristic, complemented, Sylow
878C23—22no—
879C23—22no—
880C23—22no—
881C23—134no—
882C23—132no—
883C23—132no—
884C23—138no—
885C23—262no—
886C23—262no—
887C23—262no—
888C23—268no—
889C23—268no—
890C23—262no—
891C23—262no—
892C23—268no—
893C23C24×D1312yes—
894C23C24×D1311yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—268no—
898Q8—2616no—
899Q8—5216no—
900D4—268no—
901D4—2632no—
902D4—268no—
903D4—268no—
904D4—2616no—
905D4—2616no—
906D4—2616no—
907D4—5216no—
908D4—5216no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—134no—
918C2×C4—132no—
919C2×C4—1316no—
920C2×C4—132no—
921C2×C4—132no—
922C2×C4—132no—
923C2×C4—132no—
924C2×C4—132no—
925C2×C4—138no—
926C2×C4—2632no—
927C2×C4—262no—
928C2×C4—262no—
929C2×C4—262no—
930C2×C4—262no—
931C2×C4—262no—
932C2×C4—268no—
933C2×C4—268no—
934C2×C4—268no—
935C2×C4—268no—
936C2×C4—268no—
937C2×C4—268no—
938C2×C4—5216no—
939C2×C4—5216no—
940C2×C4—5216no—
941C2×C4#8825414yes—
942C2×C4#41×D1314yes—
943C2×C4#8825614yes—
944C2×C4C24×D1318yes—
945C2×C4C24×D1312yes—
946C2×C4C24×D1312yes—
947C2×C4C24×D1312yes—
948C2×C4C24×D1318yes—
949C2×C4C24×D1312yes—
950C2×C4C24×D1312yes—
951C2×C4C24×D1312yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—134no—
957C22—268no—
958C22—262no—
959C22—262no—
960C22—268no—
961C22—262no—
962C22—262no—
963C22—268no—
964C22—262no—
965C22—268no—
966C22—524no—
967C22—5216no—
968C22C2×#8825412yes—
969C22C2×#41×D1312yes—
970C22C2×#8825612yes—
971C22C25×D1311yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—134no—
978C4—262no—
979C4—262no—
980C4—262no—
981C4—268no—
982C4—262no—
983C4—262no—
984C4C2×#8825414yes—
985C4C2×#41×D1314yes—
986C4C2×#8825614yes—
987C2—42no—
988C2—264no—
989C2—522no—
990C2—528no—
991C2#1312874814yesdirect product factor
992C2C22×#41×D1311yescharacteristic
993C2C22×#8825611yescharacteristic
994C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#533C2
socleC23×C13C25
hypercenterC2×#533D13
hypocenterC13C2×#3511
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13128748C2direct (N × H)
2. C2×#11719273C2semidirect
3. C2×#11719237C2semidirect
4. C2×#11719395C2semidirect
5. C2×#11719400C2semidirect
6. C2×#11719235C2semidirect
7. C2×#11719281C2semidirect
8. C2×#11719338C2semidirect
9. C2×#11719336C2semidirect
10. C2×#11719348C2semidirect
11. C2×#11719287C2semidirect
12. C2×#11719334C2semidirect
13. C2×#11719433C2semidirect
14. C2×#11719430C2semidirect
15. C2×#11719430C2semidirect
16. C2×#11719182C2semidirect
17. C2×D13×C4⋊Q8C2semidirect
18. C2×#11719279C2semidirect
19. C2×C4×#6127C2semidirect
20. C2×C13×#533C2semidirect
26. C13×#533C22semidirect
48. #11719433C22semidirect
49. #11719430C22semidirect
50. #11719430C22semidirect
51. D13×C4⋊Q8C22semidirect
52. #11719400C22semidirect
53. #11719395C22semidirect
54. #11719348C22semidirect
55. #11719338C22semidirect
56. #11719336C22semidirect
57. #11719334C22semidirect
58. #11719287C22semidirect
59. #11719281C22semidirect
60. #11719279C22semidirect
61. #11719273C22semidirect
62. #11719237C22semidirect
63. #11719235C22semidirect
93. #11719182C22semidirect
97. C4×#6127C22semidirect
320. C2×C4×D13#41semidirect
394. C2×#533D13semidirect
471. C4×D13C2×#41semidirect
492. #533C2×D13semidirect
748. C2×C13#3511semidirect
877. C13C2×#3511semidirect
991. C2#13128748direct (N × H)

Maximal subgroups

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

subgroupindex
#131287482
C2×#117192732
C2×#117192372
C2×#117193952
C2×#117194002
C2×#117192352
C2×#117192812
C2×#117193382
C2×#117193362
C2×#117193482
C2×#117192872
C2×#117193342
C2×#117194332
C2×#117194302
C2×#117191822
C2×D13×C4⋊Q82
C2×#117192792
C2×C4×#61272
C2×C13×#5332
C2×#351113