Finite Group Databasebeta

← C2×#13128715 #16771355

Subgroups — C2×#13128715 #16771355

Order 3328.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128715C2132yesmaximal, direct product factor
2C2×#11719390C212yesmaximal, complemented
3C2×#11719274C212yesmaximal, complemented
4C2×#11719346C212yesmaximal, complemented
5C2×#11719238C212yesmaximal, complemented
6C2×#11719286C212yesmaximal, complemented
7C2×#11719234C212yesmaximal, complemented
8C2×#11719399C212yesmaximal, complemented
9C2×#11719344C212yesmaximal, complemented
10C2×#11719330C212yesmaximal, complemented
11C2×#11719288C212yesmaximal, complemented
12C2×#11719333C212yesmaximal
13C2×#11719175C211yesmaximal, characteristic, complemented
14C2×#11719433C211yesmaximal, characteristic, complemented
15C2×#11719433C211yesmaximal, characteristic, complemented
16C2×#11719433C211yesmaximal, characteristic, complemented
17C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×#11719277C212yesmaximal, complemented
19C2×C4×#6127C211yesmaximal, characteristic
20C2×C13×#533C211yesmaximal, characteristic, complemented
21C22×Q8×D13C2212yes—
22C22×#6127C2211yescharacteristic
23C13×#533C22116yescomplemented
24C2×C13×C4⋊Q8C2211yescharacteristic
25C2×C13×C4⋊Q8C2211yescharacteristic
26C2×C13×#125C2212yes—
27C2×C13×C22⋊Q8C2212yes—
28C2×C13×C22⋊Q8C2212yes—
29C2×C4×Q8×C13C2212yes—
30C2×C4×Q8×C13C2212yes—
31C2×C13×#117C2212yes—
32C22×C42×C13C2211yescharacteristic
33C2×#88200C2212yes—
34C2×#88200C2212yes—
35C2×#88200C2212yes—
36C2×Q8×Dic13C2212yes—
37C2×Q8×Dic13C2212yes—
38C2×Q8×Dic13C2212yes—
39C2×#88198C2212yes—
40C2×C4×C22⋊D13C2211yescharacteristic
41C2×C4×C22⋊D13C2211yescharacteristic
42C2×C4×C22⋊D13C2211yescharacteristic
43C2×C4×C22⋊D13C2211yescharacteristic
44C2×#88180C2211yescharacteristic
45C2×#88180C2212yes—
46C2×#88178C2212yes—
47C2×#88178C2212yes—
48#11719433C22116yescomplemented
49#11719433C22116yescomplemented
50#11719433C22116yescomplemented
51D13×C4⋊Q8C22116yescomplemented
52#11719399C22132yescomplemented
53#11719390C22132yescomplemented
54#11719346C22132yescomplemented
55#11719344C22132yescomplemented
56#11719333C22132yes—
57#11719330C22132yescomplemented
58#11719288C22132yescomplemented
59#11719286C22132yescomplemented
60#11719277C22132yescomplemented
61#11719274C22132yescomplemented
62#11719238C22132yescomplemented
63#11719234C22132yescomplemented
64C2×#88152C2214yes—
65C2×#88151C2212yes—
66C2×#88151C2212yes—
67C2×#88151C2212yes—
68C2×#88148C2214yes—
69C2×#88146C2214yes—
70C2×#88146C2212yes—
71C2×#88146C2212yes—
72C2×#88146C2212yes—
73C2×C4⋊C4×D13C2212yes—
74C2×C4⋊C4×D13C2212yes—
75C2×#88144C2212yes—
76C2×#88144C2214yes—
77C2×#88144C2212yes—
78C2×#88144C2212yes—
79C2×#88143C2214yes—
80C2×#88143C2214yes—
81C2×#88142C2212yes—
82C2×#88142C2212yes—
83C2×#88142C2214yes—
84C2×#88141C2212yes—
85C2×#88141C2214yes—
86C2×#88141C2212yes—
87C2×#88141C2212yes—
88C2×#88139C2214yes—
89C2×#88137C2214yes—
90C2×#88133C2214yes—
91C2×#88133C2214yes—
92C2×#88130C2214yes—
93C4×#6127C22116yes—
94C2×C4×D52C2211yescharacteristic
95C2×C4×D52C2211yescharacteristic
96C2×#88126C2211yescharacteristic
97C2×#88126C2211yescharacteristic
98C2×#88126C2214yes—
99C2×C42×D13C2211yescharacteristic
100C2×C42×D13C2211yescharacteristic
101#11719175C22116yescomplemented
102C2×#88124C2214yes—
103C2×#88124C2212yes—
104C2×#88123C2211yescharacteristic
105C2×#88123C2211yescharacteristic
106C2×C4×Dic26C2212yes—
107C2×C4×Dic26C2211yescharacteristic
108C2×C4×Dic26C2211yescharacteristic
109C2×C4×Dic26C2214yes—
110C2×C4×Dic26C2212yes—
111C22×Q8×C13C2312yes—
112C22×Q8×C13C2312yes—
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C23×C4×C13C2311yescharacteristic
116C22×C22⋊D13C2311yescharacteristic
117C22×C22⋊D13C2311yescharacteristic
118C2×Q8×D13—216no—
119C2×Q8×D13C23116yes—
120C2×#6127—28no—
121C2×#6127C2318yes—
122C22×D52C2311yescharacteristic
123C22×C4×D13C2311yescharacteristic
124C22×C4×D13C2311yescharacteristic
125C22×C4×D13C2311yescharacteristic
126C22×C4×D13C2311yescharacteristic
127C22×C4×D13C2311yescharacteristic
128C22×C4×D13C2314yes—
129C22×C4×D13C2311yescharacteristic
130C22×Dic26C2311yescharacteristic
131C22×Dic26C2312yes—
132C22×Dic26C2312yes—
133C22×Dic26C2314yes—
134C13×C4⋊Q8C2318yes—
135C13×C4⋊Q8C2318yes—
136C13×#125C23116yes—
137C13×C22⋊Q8C23116yes—
138C13×C22⋊Q8C23116yes—
139C4×Q8×C13C23116yes—
140C4×Q8×C13C23116yes—
141C13×#117C23116yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C13×C4⋊C4C2314yes—
144C2×C13×C4⋊C4C2312yes—
145C2×C13×C4⋊C4C2312yes—
146C2×C13×C4⋊C4C2314yes—
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C22⋊C4C2314yes—
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2311yescharacteristic
152C2×C42×C13C2314yes—
153C2×C42×C13C2311yescharacteristic
154C2×C42×C13C2318yes—
155C2×C22⋊Dic13C2311yescharacteristic
156C2×C22⋊Dic13C2311yescharacteristic
157C2×C22⋊Dic13C2314yes—
158#88200C23116yes—
159#88200C23116yes—
160#88200C23116yes—
161Q8×Dic13C23116yes—
162Q8×Dic13C23116yes—
163Q8×Dic13C23116yes—
164#88198C23116yes—
165C4×C22⋊D13C2318yes—
166C4×C22⋊D13C2318yes—
167C4×C22⋊D13C2318yes—
168C4×C22⋊D13C2318yes—
169C2×#6103C2311yescharacteristic
170C2×#6103C2311yescharacteristic
171C2×#6103C2311yescharacteristic
172C2×#6103C2311yescharacteristic
173C2×#6103C2314yes—
174C2×#6103C2314yes—
175C2×#6103C2314yes—
176#88180C23116yes—
177#88180C2318yes—
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2312yes—
180C2×C4⋊Dic13C2311yescharacteristic
181C2×C4⋊Dic13C2311yescharacteristic
182C2×C4⋊Dic13C2314yes—
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2312yes—
185C2×C4⋊Dic13C2314yes—
186C2×C4⋊Dic13C2314yes—
187#88178C23116yes—
188#88178C23116yes—
189C2×#6101C2311yescharacteristic
190C2×#6101C2314yes—
191C2×#6101C2311yescharacteristic
192C2×#6101C2314yes—
193C2×#6101C2311yescharacteristic
194C2×#6101C2311yescharacteristic
195C2×#6101C2314yes—
196C2×#6101C2314yes—
197C2×#6101C2314yes—
198C2×#6101C2314yes—
199C2×#6101C2314yes—
200C2×C4×Dic13C2314yes—
201C2×C4×Dic13C2311yescharacteristic
202C2×C4×Dic13C2311yescharacteristic
203C2×C4×Dic13C2311yescharacteristic
204C2×C4×Dic13C2311yescharacteristic
205C2×C4×Dic13C2314yes—
206C2×C4×Dic13C2314yes—
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2311yescharacteristic
209C2×C4×Dic13C2314yes—
210#88152C23132yes—
211#88151C23116yes—
212#88151C23116yes—
213#88151C23116yes—
214#88148C23132yes—
215#88146C23116yes—
216#88146C23116yes—
217#88146C23116yes—
218#88146C23132yes—
219C4⋊C4×D13C23116yes—
220C4⋊C4×D13C23116yes—
221#88144C23116yes—
222#88144C23116yes—
223#88144C23116yes—
224#88144C23132yes—
225#88143C23132yes—
226#88143C23132yes—
227#88142C23116yes—
228#88142C23116yes—
229#88142C23132yes—
230#88141C23116yes—
231#88141C23116yes—
232#88141C23116yes—
233#88141C23132yes—
234#88139C23132yes—
235#88137C23132yes—
236#88133C23132yes—
237#88133C23132yes—
238#88130C23132yes—
239C4×D52C2318yes—
240C4×D52C2318yes—
241#88126C2318yes—
242#88126C2318yes—
243#88126C23132yes—
244C42×D13C2318yes—
245C42×D13C2318yes—
246#88124C23116yes—
247#88124C23132yes—
248#88123C2318yes—
249#88123C2318yes—
250C4×Dic26C23116yes—
251C4×Dic26C23116yes—
252C4×Dic26C2318yes—
253C4×Dic26C2318yes—
254C4×Dic26C23132yes—
255C2×#3509—131nomaximal, Sylow
256C24×C13C2411yescharacteristic
257C23×D13C2411yescharacteristic
258C23×D13C2411yescharacteristic
259C2×Q8×C13—28no—
260C2×Q8×C13—28no—
261C2×Q8×C13C2418yes—
262C2×Q8×C13C2418yes—
263C22×C4×C13—24no—
264C22×C4×C13—24no—
265C22×C4×C13—24no—
266C22×C4×C13C2411yescharacteristic
267C22×C4×C13C2414yes—
268C22×C4×C13C2414yes—
269C22×C4×C13C2411yescharacteristic
270C22×C4×C13C2411yescharacteristic
271C22×C4×C13C2414yes—
272C22×C4×C13C2414yes—
273C22×C4×C13C2414yes—
274C22×C4×C13C2411yescharacteristic
275C22×C4×C13C2411yescharacteristic
276C22×C4×C13C2411yescharacteristic
277C2×C22⋊D13—24no—
278C2×C22⋊D13—24no—
279C2×C22⋊D13C2414yes—
280C2×C22⋊D13C2414yes—
281C22×Dic13C2411yescharacteristic
282C22×Dic13C2411yescharacteristic
283C22×Dic13C2414yes—
284C22×Dic13C2411yescharacteristic
285C22×Dic13C2411yescharacteristic
286C22×Dic13C2411yescharacteristic
287C22×Dic13C2414yes—
288C22×Dic13C2411yescharacteristic
289Q8×D13—264no—
290#6127—232no—
291C2×D52—24no—
292C2×D52C2414yes—
293C2×C4×D13—216no—
294C2×C4×D13—24no—
295C2×C4×D13—24no—
296C2×C4×D13—24no—
297C2×C4×D13—24no—
298C2×C4×D13—24no—
299C2×C4×D13#4118yes—
300C2×C4×D13C2414yes—
301C2×C4×D13C2414yes—
302C2×C4×D13C2414yes—
303C2×C4×D13C2414yes—
304C2×C4×D13C2414yes—
305C2×C4×D13C24116yes—
306C2×C4×D13C2414yes—
307C2×Dic26—28no—
308C2×Dic26—28no—
309C2×Dic26—24no—
310C2×Dic26—216no—
311C2×Dic26C2414yes—
312C2×Dic26C2418yes—
313C2×Dic26C2418yes—
314C2×Dic26C24116yes—
315C13×C4⋊C4C2418yes—
316C13×C4⋊C4C24116yes—
317C13×C4⋊C4C2418yes—
318C13×C4⋊C4C2418yes—
319C13×C4⋊C4C24116yes—
320C13×C4⋊C4C2418yes—
321C13×C22⋊C4C24116yes—
322C42×C13C2414yes—
323C42×C13C2414yes—
324C42×C13C2414yes—
325C42×C13C24116yes—
326C42×C13C2414yes—
327C22⋊Dic13C2414yes—
328C22⋊Dic13C2414yes—
329C22⋊Dic13C24116yes—
330#6103C2414yes—
331#6103C2414yes—
332#6103C2414yes—
333#6103C2414yes—
334#6103C24116yes—
335#6103C24116yes—
336#6103C24116yes—
337C4⋊Dic13C2418yes—
338C4⋊Dic13C2418yes—
339C4⋊Dic13C2414yes—
340C4⋊Dic13C2414yes—
341C4⋊Dic13C24116yes—
342C4⋊Dic13C2418yes—
343C4⋊Dic13C2418yes—
344C4⋊Dic13C24116yes—
345C4⋊Dic13C24116yes—
346#6101C2414yes—
347#6101C24116yes—
348#6101C2414yes—
349#6101C24116yes—
350#6101C2414yes—
351#6101C2414yes—
352#6101C24116yes—
353#6101C24116yes—
354#6101C24116yes—
355#6101C24116yes—
356#6101C24116yes—
357C4×Dic13C24116yes—
358C4×Dic13C2414yes—
359C4×Dic13C2414yes—
360C4×Dic13C2414yes—
361C4×Dic13C2414yes—
362C4×Dic13C24116yes—
363C4×Dic13C24116yes—
364C4×Dic13C2414yes—
365C4×Dic13C2414yes—
366C4×Dic13C24116yes—
367#3509—1332no—
368C2×#557—132no—
369C2×#557—132no—
370C2×#556—132no—
371C2×#556—132no—
372C2×#552—132no—
373C2×#552—132no—
374C2×#552—132no—
375C2×#552—132no—
376C2×#541—132no—
377C2×#541—132no—
378C2×#536—132no—
379C2×#533—131no—
380C2×#533—131no—
381C2×#533—131no—
382C2×#533—131no—
383C2×#533D1311yescharacteristic, complemented
384C22×C4⋊Q8—131no—
385C2×#519—132no—
386C2×C4×#41—131no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13C2512yes—
391C23×C13C2511yescharacteristic
392C22×D13—22no—
393C22×D13—22no—
394C22×D13—22no—
395C22×D13—22no—
396C22×D13—22no—
397C22×D13C2×#4114yes—
398C22×D13C2512yes—
399C22×D13C2512yes—
400Q8×C13—216no—
401Q8×C13—216no—
402C2×C4×C13—28no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—28no—
407C2×C4×C13—28no—
408C2×C4×C13—28no—
409C2×C4×C13—28no—
410C2×C4×C13C2×#4114yes—
411C2×C4×C132−1+414yes—
412C2×C4×C132−1+414yes—
413C2×C4×C13C2512yes—
414C2×C4×C13C2518yes—
415C2×C4×C13C2518yes—
416C2×C4×C13C2512yes—
417C2×C4×C13C2512yes—
418C2×C4×C13C2512yes—
419C2×C4×C13C2512yes—
420C2×C4×C13C2512yes—
421C22⋊D13—28no—
422C22⋊D13—28no—
423C2×Dic13—28no—
424C2×Dic13—22no—
425C2×Dic13—28no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13C2×#4114yes—
431C2×Dic13C2512yes—
432C2×Dic13C2512yes—
433C2×Dic13C2518yes—
434C2×Dic13C2512yes—
435C2×Dic13C2512yes—
436C2×Dic13C2512yes—
437C2×Dic13C2518yes—
438C2×Dic13C2512yes—
439D52—28no—
440C4×D13—232no—
441C4×D13—28no—
442C4×D13—28no—
443C4×D13—28no—
444C4×D13—28no—
445C4×D13—28no—
446C4×D13C2×#41116yes—
447Dic26—216no—
448Dic26—216no—
449Dic26—28no—
450Dic26—232no—
451C22×#41—131no—
452C23×Q8—132no—
453#557—1332no—
454#557—1332no—
455#556—1332no—
456#556—1332no—
457#552—1332no—
458#552—1332no—
459#552—1332no—
460#552—1332no—
461#541—1332no—
462#541—1332no—
463#536—1332no—
464#533—1316no—
465#533—1316no—
466#533—1316no—
467#533—1316no—
468#533C2×D13116yescomplemented
469C2×C4⋊Q8—132no—
470C2×C4⋊Q8—1316no—
471C2×C4⋊Q8—132no—
472C2×C4⋊Q8—132no—
473C2×C4⋊Q8—134no—
474C2×C4⋊Q8—131no—
475C2×C4⋊Q8—131no—
476C2×C4⋊Q8C2×D1311yescharacteristic
477C2×C4⋊Q8C2×D1311yescharacteristic
478C2×#126—134no—
479C2×#126—134no—
480C2×#126—134no—
481C2×#126—134no—
482C2×#125—134no—
483C2×#125—134no—
484C2×#125—132no—
485C2×#125—132no—
486C2×#125—132no—
487C2×#125—134no—
488C2×#125—132no—
489C2×#125—134no—
490C2×#125C2×D1312yes—
491C2×#124—134no—
492C2×#123—134no—
493C2×#123—134no—
494C2×C22⋊Q8—132no—
495C2×C22⋊Q8—132no—
496C2×C22⋊Q8—132no—
497C2×C22⋊Q8—132no—
498C2×C22⋊Q8—132no—
499C2×C22⋊Q8—132no—
500C2×C22⋊Q8—132no—
501C2×C22⋊Q8—132no—
502C2×C22⋊Q8C2×D1312yes—
503C2×C22⋊Q8C2×D1312yes—
504#519—1332no—
505C4×#41—1316no—
506C2×C4×Q8—132no—
507C2×C4×Q8—132no—
508C2×C4×Q8—132no—
509C2×C4×Q8—132no—
510C2×C4×Q8—134no—
511C2×C4×Q8—132no—
512C2×C4×Q8—132no—
513C2×C4×Q8—131no—
514C2×C4×Q8—131no—
515C2×C4×Q8—132no—
516C2×C4×Q8—134no—
517C2×C4×Q8—132no—
518C2×C4×Q8C2×D1312yes—
519C2×C4×Q8C2×D1312yes—
520C2×C4×D4—131no—
521C2×C4×D4—131no—
522C2×C4×D4—131no—
523C2×C4×D4—131no—
524C2×C4×D4—131no—
525C2×C4×D4—131no—
526C2×#117—131no—
527C2×#117—132no—
528C2×#117—132no—
529C2×#117—134no—
530C2×#117—132no—
531C2×#117—132no—
532C2×#117—131no—
533C2×#117—131no—
534C2×#117—134no—
535C2×#117C2×D1312yes—
536C22×C4⋊C4—132no—
537C22×C4⋊C4—132no—
538C22×C42—131no—
539C22×C42—131no—
540C22×C42C2×D1311yescharacteristic
541C22×C13—22no—
542C22×C13—22no—
543C22×C13—22no—
544C22×C13—44no—
545C22×C13C22×#4112yes—
546C22×C13C2×2−1+412yes—
547C22×C13C2×2−1+412yes—
548C22×C13C2611yescharacteristic
549C2×D13—22no—
550C2×D13—22no—
551C2×D13—28no—
552C2×D13—22no—
553C2×D13—22no—
554C2×D13—22no—
555C2×D13—44no—
556C2×D13C22×#4114yes—
557C4×C13—28no—
558C4×C13—22no—
559C4×C13—22no—
560C4×C13—22no—
561C4×C13—28no—
562C4×C13C22×#4114yes—
563C4×C13C2×2−1+414yes—
564C4×C13C2×2−1+414yes—
565Dic13—28no—
566Dic13—22no—
567Dic13—28no—
568Dic13—22no—
569Dic13—22no—
570Dic13—22no—
571Dic13—22no—
572Dic13C22×#4114yes—
573C2×#41—138no—
574C2×#41—268no—
575C22×Q8—1316no—
576C22×Q8—132no—
577C22×Q8—132no—
578C22×Q8—134no—
579C22×Q8—131no—
580C22×Q8—2616no—
581C22×Q8C22×D1312yes—
582C22×Q8C22×D1312yes—
583C22×D4—131no—
584C22×D4—131no—
585C22×D4—131no—
586C23×C4—131no—
587C23×C4—134no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—131no—
591C23×C4—131no—
592C23×C4—131no—
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C23×C4C22×D1311yescharacteristic
596C4⋊Q8—1316no—
597C4⋊Q8—1316no—
598C4⋊Q8—1316no—
599C4⋊Q8—1332no—
600C4⋊Q8—138no—
601C4⋊Q8—138no—
602C4⋊Q8C22×D1318yes—
603C4⋊Q8C22×D1318yes—
604#126—1332no—
605#126—1332no—
606#126—1332no—
607#126—1332no—
608#125—1316no—
609#125—1316no—
610#125—1316no—
611#125—1332no—
612#125—1332no—
613#125—1332no—
614#125—1316no—
615#125—1332no—
616#125C22×D13116yes—
617#124—1332no—
618#123—1332no—
619#123—1332no—
620C22⋊Q8—1316no—
621C22⋊Q8—1316no—
622C22⋊Q8—1316no—
623C22⋊Q8—1316no—
624C22⋊Q8—1316no—
625C22⋊Q8—1316no—
626C22⋊Q8—1316no—
627C22⋊Q8—1316no—
628C22⋊Q8C22×D13116yes—
629C22⋊Q8C22×D13116yes—
630C4×Q8—1316no—
631C4×Q8—1316no—
632C4×Q8—1316no—
633C4×Q8—1316no—
634C4×Q8—1332no—
635C4×Q8—1316no—
636C4×Q8—1316no—
637C4×Q8—138no—
638C4×Q8—138no—
639C4×Q8—1316no—
640C4×Q8—1332no—
641C4×Q8—1316no—
642C4×Q8C22×D13116yes—
643C4×Q8C22×D13116yes—
644C4×D4—138no—
645C4×D4—138no—
646C4×D4—138no—
647C4×D4—138no—
648C4×D4—138no—
649C4×D4—138no—
650#117—138no—
651#117—1316no—
652#117—1316no—
653#117—1332no—
654#117—1316no—
655#117—1316no—
656#117—138no—
657#117—138no—
658#117—1332no—
659#117C22×D13116yes—
660C2×C4⋊C4—132no—
661C2×C4⋊C4—132no—
662C2×C4⋊C4—134no—
663C2×C4⋊C4—134no—
664C2×C4⋊C4—132no—
665C2×C4⋊C4—131no—
666C2×C4⋊C4—131no—
667C2×C4⋊C4—131no—
668C2×C4⋊C4—131no—
669C2×C4⋊C4—131no—
670C2×C4⋊C4—131no—
671C2×C4⋊C4—132no—
672C2×C4⋊C4—134no—
673C2×C4⋊C4—134no—
674C2×C4⋊C4—134no—
675C2×C4⋊C4—134no—
676C2×C4⋊C4—134no—
677C2×C4⋊C4—134no—
678C2×C4⋊C4—134no—
679C2×C4⋊C4—134no—
680C2×C4⋊C4—1316no—
681C2×C4⋊C4—1316no—
682C2×C4⋊C4C22×D1312yes—
683C2×C4⋊C4C22×D1312yes—
684C2×C4⋊C4C22×D1312yes—
685C2×C4⋊C4C22×D1312yes—
686C2×C4⋊C4C22×D1314yes—
687C2×C4⋊C4C22×D1314yes—
688C2×C22⋊C4—131no—
689C2×C22⋊C4—131no—
690C2×C22⋊C4—134no—
691C2×C22⋊C4—131no—
692C2×C22⋊C4—131no—
693C2×C22⋊C4—134no—
694C2×C22⋊C4—131no—
695C2×C22⋊C4—131no—
696C2×C22⋊C4—134no—
697C2×C22⋊C4—134no—
698C2×C22⋊C4C22×D1314yes—
699C2×C42—131no—
700C2×C42—134no—
701C2×C42—134no—
702C2×C42—134no—
703C2×C42—131no—
704C2×C42—134no—
705C2×C42—131no—
706C2×C42—131no—
707C2×C42—131no—
708C2×C42—131no—
709C2×C42—138no—
710C2×C42—138no—
711C2×C42C22×D1311yescharacteristic
712C2×C42C22×D1314yes—
713C2×C42C22×D1311yescharacteristic
714C2×C42C22×D1311yescharacteristic
715C2×C42C22×D1318yes—
716C2×C42C22×D1311yescharacteristic
717C2×C13—42no—
718C2×C13#350914yescomplemented
719C2×C13C23×#4111yescharacteristic
720C2×C13C22×2−1+411yescharacteristic
721C2×C13C22×2−1+411yescharacteristic
722D13—24no—
723D13—42no—
724C24—131no—
725C24—131no—
726C24C23×D1311yescharacteristic
727#41—2632no—
728C2×Q8—28no—
729C2×Q8—28no—
730C2×Q8—138no—
731C2×Q8—138no—
732C2×Q8—1316no—
733C2×Q8—134no—
734C2×Q8—2616no—
735C2×Q8—264no—
736C2×Q8—2664no—
737C2×Q8—268no—
738C2×Q8—268no—
739C2×Q8C23×D1318yes—
740C2×Q8C23×D1318yes—
741C2×D4—134no—
742C2×D4—134no—
743C2×D4—134no—
744C2×D4—264no—
745C2×D4—264no—
746C2×D4—264no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—131no—
751C22×C4—138no—
752C22×C4—134no—
753C22×C4—131no—
754C22×C4—131no—
755C22×C4—134no—
756C22×C4—131no—
757C22×C4—131no—
758C22×C4—134no—
759C22×C4—131no—
760C22×C4—134no—
761C22×C4—134no—
762C22×C4—134no—
763C22×C4—134no—
764C22×C4—134no—
765C22×C4—1316no—
766C22×C4—2616no—
767C22×C4—264no—
768C22×C4—264no—
769C22×C4—264no—
770C22×C4—264no—
771C22×C4—264no—
772C22×C4C23×D1314yes—
773C22×C4C23×D1314yes—
774C22×C4C23×D1314yes—
775C22×C4C23×D1311yescharacteristic
776C22×C4C23×D1314yes—
777C22×C4C23×D1314yes—
778C22×C4C23×D1311yescharacteristic
779C22×C4C23×D1311yescharacteristic
780C22×C4C23×D1311yescharacteristic
781C22×C4C23×D1311yescharacteristic
782C22×C4C23×D1311yescharacteristic
783C4⋊C4—138no—
784C4⋊C4—138no—
785C4⋊C4—1316no—
786C4⋊C4—1316no—
787C4⋊C4—138no—
788C4⋊C4—134no—
789C4⋊C4—134no—
790C4⋊C4—134no—
791C4⋊C4—134no—
792C4⋊C4—134no—
793C4⋊C4—134no—
794C4⋊C4—138no—
795C4⋊C4—1316no—
796C4⋊C4—1316no—
797C4⋊C4—1316no—
798C4⋊C4—1316no—
799C4⋊C4—1316no—
800C4⋊C4—1316no—
801C4⋊C4—1316no—
802C4⋊C4—1316no—
803C4⋊C4C23×D1318yes—
804C4⋊C4C23×D1318yes—
805C4⋊C4C23×D1318yes—
806C4⋊C4C23×D1318yes—
807C4⋊C4C23×D13116yes—
808C4⋊C4C23×D13116yes—
809C22⋊C4—134no—
810C22⋊C4—134no—
811C22⋊C4—1316no—
812C22⋊C4—134no—
813C22⋊C4—134no—
814C22⋊C4—1316no—
815C22⋊C4—134no—
816C22⋊C4—134no—
817C22⋊C4—1316no—
818C22⋊C4—1316no—
819C22⋊C4C23×D13116yes—
820C42—134no—
821C42—134no—
822C42—134no—
823C42—134no—
824C42—134no—
825C42—134no—
826C42—1316no—
827C42—1316no—
828C42—1316no—
829C42—1316no—
830C42C23×D1314yes—
831C42C23×D1314yes—
832C42C23×D1314yes—
833C42C23×D1314yes—
834C42C23×D13116yes—
835C13C2×#350911yescharacteristic, complemented, Sylow
836C23—22no—
837C23—22no—
838C23—22no—
839C23—134no—
840C23—132no—
841C23—132no—
842C23—262no—
843C23—262no—
844C23—262no—
845C23—262no—
846C23—262no—
847C23C24×D1312yes—
848C23C24×D1311yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—2632no—
852Q8—268no—
853Q8—2616no—
854Q8—2616no—
855D4—268no—
856D4—268no—
857D4—268no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—22no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—134no—
867C2×C4—132no—
868C2×C4—1316no—
869C2×C4—132no—
870C2×C4—132no—
871C2×C4—138no—
872C2×C4—132no—
873C2×C4—132no—
874C2×C4—138no—
875C2×C4—132no—
876C2×C4—2632no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—268no—
880C2×C4—262no—
881C2×C4—268no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—268no—
885C2×C4—268no—
886C2×C4—268no—
887C2×C4—268no—
888C2×C4—268no—
889C2×C4#8825414yes—
890C2×C4#41×D1314yes—
891C2×C4#8825714yes—
892C2×C4C24×D1312yes—
893C2×C4C24×D1318yes—
894C2×C4C24×D1318yes—
895C2×C4C24×D1312yes—
896C2×C4C24×D1312yes—
897C2×C4C24×D1312yes—
898C2×C4C24×D1312yes—
899C2×C4C24×D1312yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—134no—
905C22—268no—
906C22—262no—
907C22—262no—
908C22—262no—
909C22—262no—
910C22—262no—
911C22—524no—
912C22C2×#8825412yes—
913C22C2×#41×D1312yes—
914C22C2×#8825712yes—
915C22C25×D1311yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—134no—
922C4—262no—
923C4—268no—
924C4—262no—
925C4—262no—
926C4—262no—
927C4—262no—
928C4—268no—
929C4C2×#8825414yes—
930C4C2×#41×D1314yes—
931C4C2×#8825714yes—
932C2—42no—
933C2—264no—
934C2—522no—
935C2#1312871514yesdirect product factor
936C2C22×#41×D1311yescharacteristic
937C2C22×#8825711yescharacteristic
938C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#533C2
socleC23×C13C25
prime radicalC22×#6127C22
hypercenterC2×#533D13
hypocenterC13C2×#3509
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13128715C2direct (N × H)
2. C2×#11719390C2semidirect
3. C2×#11719274C2semidirect
4. C2×#11719346C2semidirect
5. C2×#11719238C2semidirect
6. C2×#11719286C2semidirect
7. C2×#11719234C2semidirect
8. C2×#11719399C2semidirect
9. C2×#11719344C2semidirect
10. C2×#11719330C2semidirect
11. C2×#11719288C2semidirect
13. C2×#11719175C2semidirect
14. C2×#11719433C2semidirect
15. C2×#11719433C2semidirect
16. C2×#11719433C2semidirect
17. C2×D13×C4⋊Q8C2semidirect
18. C2×#11719277C2semidirect
20. C2×C13×#533C2semidirect
23. C13×#533C22semidirect
48. #11719433C22semidirect
49. #11719433C22semidirect
50. #11719433C22semidirect
51. D13×C4⋊Q8C22semidirect
52. #11719399C22semidirect
53. #11719390C22semidirect
54. #11719346C22semidirect
55. #11719344C22semidirect
57. #11719330C22semidirect
58. #11719288C22semidirect
59. #11719286C22semidirect
60. #11719277C22semidirect
61. #11719274C22semidirect
62. #11719238C22semidirect
63. #11719234C22semidirect
101. #11719175C22semidirect
383. C2×#533D13semidirect
468. #533C2×D13semidirect
718. C2×C13#3509semidirect
835. C13C2×#3509semidirect
935. C2#13128715direct (N × H)

Maximal subgroups

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

subgroupindex
#131287152
C2×#117193902
C2×#117192742
C2×#117193462
C2×#117192382
C2×#117192862
C2×#117192342
C2×#117193992
C2×#117193442
C2×#117193302
C2×#117192882
C2×#117193332
C2×#117191752
C2×#117194332
C2×D13×C4⋊Q82
C2×#117192772
C2×C4×#61272
C2×C13×#5332
C2×#350913