Finite Group Databasebeta

← #16735241

Subgroups — #16735241

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic
2#13126050C214yesmaximal, complemented
3#13126042C214yesmaximal, complemented
4#13125995C214yesmaximal, complemented
5#13125987C212yesmaximal, complemented
6#13125980C212yesmaximal, complemented
7#13125383C212yesmaximal, complemented
8#13125218C212yesmaximal, complemented
9#13124784C214yesmaximal
10#13124637C214yesmaximal, complemented
11#13123469C211yesmaximal, characteristic
12C2×C13×#533C211yesmaximal, characteristic
13C13×#533—21no—
14C13×#533—21no—
15C13×#533—21no—
16C13×#533—21no—
17C13×#533C2212yes—
18C13×#533C2212yes—
19C13×#533C2212yes—
20C13×#533C2212yes—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×#125C2212yes—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C4×Q8×C13—21no—
27C2×C4×Q8×C13—21no—
28C2×C13×#117C2212yes—
29C22×C42×C13C2211yescharacteristic
30C2×#88180—21no—
31C2×#88178—21no—
32C2×#88178C2212yes—
33#11719175—21no—
34#11719175—21no—
35#11719175—21no—
36#11719175—21no—
37#11719175C2212yes—
38#11719175C2212yes—
39#11719175C2212yes—
40#11719175C2212yes—
41C2×#88124—21no—
42C2×#88123C2211yescharacteristic
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26—21no—
45C2×C4×Dic26C2212yes—
46#11718868C2212yes—
47#11718755C2218yescomplemented
48#11718754C2214yescomplemented
49#11718754C2214yescomplemented
50#11718752C2218yescomplemented
51#11718740C2214yescomplemented
52#11718739C2214yescomplemented
53#11718730C2218yescomplemented
54#11718726C2218yescomplemented
55#11718724C22116yescomplemented
56#11718665C2218yes—
57#11718657C22116yes—
58#11718656C2218yes—
59#11718632C2218yes—
60#11718631C2218yes—
61#11718587C2212yes—
62#11718587C2212yes—
63#11718586C2212yes—
64#11718586C2212yes—
65#11718585C2212yes—
66C4×#6099C2212yes—
67C22×Q8×C13—21no—
68C22×Q8×C13—21no—
69C23×C4×C13D411yescharacteristic
70C23×C4×C13D411yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C22×Dic26—21no—
73C22×Dic26C2312yes—
74C13×C4⋊Q8—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8—21no—
78C13×C4⋊Q8C2312yes—
79C13×C4⋊Q8C2312yes—
80C13×C4⋊Q8C2312yes—
81C13×C4⋊Q8C2312yes—
82C13×#125—22no—
83C13×#125—22no—
84C13×#125C2314yes—
85C13×#125C2314yes—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C4×Q8×C13—22no—
95C4×Q8×C13—22no—
96C4×Q8×C13—22no—
97C4×Q8×C13—22no—
98C4×Q8×C13—22no—
99C4×Q8×C13—22no—
100C4×Q8×C13—22no—
101C4×Q8×C13—22no—
102C13×#117—22no—
103C13×#117—22no—
104C13×#117C2314yes—
105C13×#117C2314yes—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4C2312yes—
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C22⋊C4—22no—
113C2×C42×C13—22no—
114C2×C42×C13D411yescharacteristic
115C2×C42×C13D411yescharacteristic
116C2×C42×C13D411yescharacteristic
117C2×C42×C13D411yescharacteristic
118C2×C42×C13D411yescharacteristic
119C2×C42×C13D411yescharacteristic
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123C2×C42×C13C2311yescharacteristic
124C2×C42×C13C2311yescharacteristic
125C2×C42×C13C2311yescharacteristic
126C2×C22⋊Dic13—22no—
127#88180—22no—
128#88180—22no—
129#88180—22no—
130#88180—22no—
131C2×C4⋊Dic13—21no—
132C2×C4⋊Dic13—21no—
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13C2312yes—
135#88178—22no—
136#88178—22no—
137#88178—22no—
138#88178—22no—
139#88178—22no—
140#88178—22no—
141#88178C2314yes—
142#88178C2314yes—
143C2×#6101—22no—
144C2×#6101—22no—
145C2×C4×Dic13—22no—
146C2×#6099C2314yes—
147#88124—22no—
148#88124—22no—
149#88124—22no—
150#88124—22no—
151#88123—21no—
152#88123—21no—
153#88123—21no—
154#88123—21no—
155#88123C2312yes—
156#88123C2312yes—
157#88123C2312yes—
158#88123C2312yes—
159C4×Dic26—22no—
160C4×Dic26—22no—
161C4×Dic26—22no—
162C4×Dic26—22no—
163C4×Dic26—22no—
164C4×Dic26—22no—
165C4×Dic26C2314yes—
166C4×Dic26C2314yes—
167C22⋊#1055C2314yes—
168C22⋊#1055C2314yes—
169#88050C23116yes—
170#88050C23116yes—
171#88048C23116yes—
172#88047C23116yes—
173C4⋊#1055C2314yes—
174C4⋊#1055C2314yes—
175#88043C2314yes—
176C4×#1055C2314yes—
177#60865—131nomaximal, Sylow
178C24×C13C2×D411yescharacteristic
179C2×Q8×C13—22no—
180C2×Q8×C13—22no—
181C2×Q8×C13—22no—
182C2×Q8×C13—22no—
183C2×Q8×C13—44no—
184C2×Q8×C13—44no—
185C22×C4×C13—24no—
186C22×C4×C13—24no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—42no—
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2411yescharacteristic
206C22×C4×C13C2411yescharacteristic
207C22×C4×C13C2411yescharacteristic
208C22×Dic13—22no—
209C22×Dic13—22no—
210C2×Dic26—28no—
211C2×Dic26—22no—
212C2×Dic26—22no—
213C2×Dic26—22no—
214C2×Dic26—44no—
215C2×Dic26C2414yes—
216C13×C4⋊C4—24no—
217C13×C4⋊C4—24no—
218C13×C4⋊C4—24no—
219C13×C4⋊C4—24no—
220C13×C4⋊C4—22no—
221C13×C4⋊C4—22no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—22no—
224C13×C4⋊C4—22no—
225C13×C4⋊C4—22no—
226C13×C4⋊C4C2414yes—
227C13×C4⋊C4C2414yes—
228C13×C22⋊C4—24no—
229C13×C22⋊C4—24no—
230C42×C13—24no—
231C42×C13—24no—
232C42×C13C2×D411yescharacteristic
233C42×C13C2×D411yescharacteristic
234C42×C13C2×D411yescharacteristic
235C42×C13C2×D411yescharacteristic
236C42×C13C2×D411yescharacteristic
237C42×C13C2×D411yescharacteristic
238C42×C13C2×D411yescharacteristic
239C42×C13C2×D411yescharacteristic
240C42×C13C2×D411yescharacteristic
241C42×C13C2×D411yescharacteristic
242C42×C13C2×D411yescharacteristic
243C42×C13C2×D411yescharacteristic
244C42×C13C2411yescharacteristic
245C42×C13C2411yescharacteristic
246C42×C13C2411yescharacteristic
247C42×C13C2411yescharacteristic
248C22⋊Dic13—24no—
249C22⋊Dic13—24no—
250C4⋊Dic13—22no—
251C4⋊Dic13—22no—
252C4⋊Dic13—22no—
253C4⋊Dic13—22no—
254C4⋊Dic13—22no—
255C4⋊Dic13—22no—
256C4⋊Dic13—22no—
257C4⋊Dic13C2414yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262C4×Dic13—24no—
263C4×Dic13—24no—
264#6099—28no—
265C2×#1055C2418yes—
266C2×#533—131no—
267C2×#533D1311yescharacteristic
268#3237—134no—
269#3236—134no—
270#3231—134no—
271#3230—132no—
272#3229—132no—
273#3165—132no—
274#3139—132no—
275#3095—134no—
276#3078—134no—
277#2920—131no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—41no—
281C23×C13C22×D411yescharacteristic
282C23×C13C22×D411yescharacteristic
283C23×C13C22×D411yescharacteristic
284Q8×C13—44no—
285Q8×C13—44no—
286Q8×C13—44no—
287Q8×C13—44no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—24no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—44no—
307C2×C4×C13—44no—
308C2×C4×C13#13714yes—
309C2×C4×C13C22×D411yescharacteristic
310C2×C4×C13C22×D411yescharacteristic
311C2×C4×C13C22×D411yescharacteristic
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C22×D411yescharacteristic
314C2×C4×C13C22×D411yescharacteristic
315C2×C4×C13C22×D411yescharacteristic
316C2×C4×C13C22×D411yescharacteristic
317C2×C4×C13C22×D411yescharacteristic
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C132−1+414yes—
321C2×C4×C13C2511yescharacteristic
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326Dic26—28no—
327Dic26—44no—
328Dic26—44no—
329Dic26—44no—
330#1055—28no—
331#533—21no—
332#533—21no—
333#533—21no—
334#533—21no—
335#533—132no—
336#533—132no—
337#533—132no—
338#533—132no—
339#533—261no—
340#533—261no—
341#533—261no—
342#533—261no—
343#533C2×D1312yes—
344#533C2×D1312yes—
345#533C2×D1312yes—
346#533C2×D1312yes—
347C2×C4⋊Q8—131no—
348C2×C4⋊Q8—131no—
349C2×C4⋊Q8C2×D1311yescharacteristic
350C2×C4⋊Q8C2×D1311yescharacteristic
351C2×#125—261no—
352C2×#125C2×D1312yes—
353C2×C22⋊Q8—21no—
354C2×C22⋊Q8—21no—
355C2×C22⋊Q8—132no—
356C2×C22⋊Q8—261no—
357C2×C4×Q8—21no—
358C2×C4×Q8—21no—
359C2×C4×Q8—132no—
360C2×C4×Q8—261no—
361C2×#117—261no—
362C2×#117C2×D1312yes—
363C22×C42C2×D1311yescharacteristic
364#501—138no—
365#500—134no—
366#498—134no—
367#491—138no—
368#487—134no—
369#487—134no—
370#485—1316no—
371#484—138no—
372#483—138no—
373#479—1316no—
374#477—138no—
375#475—138no—
376#432—132no—
377#432—132no—
378#431—132no—
379#431—132no—
380#428—138no—
381#423—132no—
382#419—138no—
383#407—132no—
384C4×M16—132no—
385C22×C13—21no—
386C22×C13—21no—
387C22×C13—21no—
388C22×C13—21no—
389C22×C13—21no—
390C22×C13—21no—
391C22×C13—21no—
392C22×C13—44no—
393C22×C13#53612yes—
394C22×C13C2×#13712yes—
395C22×C13C23×D411yescharacteristic
396C4×C13—21no—
397C4×C13—21no—
398C4×C13—21no—
399C4×C13—21no—
400C4×C13—21no—
401C4×C13—21no—
402C4×C13—21no—
403C4×C13—44no—
404C4×C13—44no—
405C4×C13#53612yes—
406C4×C13C2×#13712yes—
407C4×C13C2×#13712yes—
408C4×C13#57512yes—
409C4×C13C2×2−1+412yes—
410Dic13—44no—
411Dic13—44no—
412C22×Q8—21no—
413C22×Q8—21no—
414C22×Q8—132no—
415C22×Q8—261no—
416C23×C4C22⋊D1311yescharacteristic
417C23×C4C22⋊D1311yescharacteristic
418C23×C4C22×D1311yescharacteristic
419C2×M16—134no—
420C4⋊Q8—21no—
421C4⋊Q8—21no—
422C4⋊Q8—21no—
423C4⋊Q8—21no—
424C4⋊Q8—132no—
425C4⋊Q8—132no—
426C4⋊Q8—132no—
427C4⋊Q8—132no—
428C4⋊Q8—261no—
429C4⋊Q8—261no—
430C4⋊Q8—261no—
431C4⋊Q8—261no—
432C4⋊Q8C22×D1312yes—
433C4⋊Q8C22×D1312yes—
434C4⋊Q8C22×D1312yes—
435C4⋊Q8C22×D1312yes—
436#125—22no—
437#125—22no—
438#125—262no—
439#125—262no—
440#125—262no—
441#125—262no—
442#125C22×D1314yes—
443#125C22×D1314yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—134no—
453C22⋊Q8—134no—
454C22⋊Q8—262no—
455C22⋊Q8—262no—
456C22⋊Q8—262no—
457C22⋊Q8—262no—
458C22⋊Q8—262no—
459C22⋊Q8—262no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—134no—
469C4×Q8—134no—
470C4×Q8—262no—
471C4×Q8—262no—
472C4×Q8—262no—
473C4×Q8—262no—
474C4×Q8—262no—
475C4×Q8—262no—
476#117—22no—
477#117—22no—
478#117—262no—
479#117—262no—
480#117—262no—
481#117—262no—
482#117C22×D1314yes—
483#117C22×D1314yes—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—132no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4C22×D1312yes—
495C2×C4⋊C4C22×D1312yes—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—262no—
498C2×C42—22no—
499C2×C42—262no—
500C2×C42C22⋊D1311yescharacteristic
501C2×C42C22⋊D1311yescharacteristic
502C2×C42C22⋊D1311yescharacteristic
503C2×C42C22⋊D1311yescharacteristic
504C2×C42C22⋊D1311yescharacteristic
505C2×C42C22⋊D1311yescharacteristic
506C2×C42C22×D1311yescharacteristic
507C2×C42C22×D1311yescharacteristic
508C2×C42C22×D1311yescharacteristic
509C2×C42C22×D1311yescharacteristic
510C2×C42C22×D1311yescharacteristic
511C2×C42C22×D1311yescharacteristic
512#107—1316no—
513#106—1316no—
514C4⋊C8—134no—
515C4⋊C8—134no—
516#103—1316no—
517#103—1316no—
518C22⋊C8—134no—
519C22⋊C8—134no—
520#97—134no—
521C4×C8—134no—
522C2×C13—22no—
523C2×C13—22no—
524C2×C13—41no—
525C2×C13C2×#53611yescharacteristic
526C2×C13C22×#13711yescharacteristic
527C2×C13C2×#57511yescharacteristic
528C24C2×C22⋊D1311yescharacteristic
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—134no—
536C2×Q8—262no—
537C2×Q8—262no—
538C2×Q8—262no—
539C2×Q8—268no—
540C2×Q8—524no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—42no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4C2×C22⋊D1311yescharacteristic
549C22×C4C2×C22⋊D1311yescharacteristic
550C22×C4C2×C22⋊D1311yescharacteristic
551C22×C4C2×C22⋊D1311yescharacteristic
552C22×C4C2×C22⋊D1311yescharacteristic
553C22×C4C2×C22⋊D1311yescharacteristic
554C22×C4C2×C22⋊D1311yescharacteristic
555C22×C4C2×C22⋊D1311yescharacteristic
556C22×C4C2×C22⋊D1311yescharacteristic
557C22×C4C2×C22⋊D1311yescharacteristic
558C22×C4C2×C22⋊D1311yescharacteristic
559C22×C4C2×C22⋊D1311yescharacteristic
560C22×C4C2×C22⋊D1311yescharacteristic
561C22×C4C2×C22⋊D1311yescharacteristic
562C22×C4C2×C22⋊D1311yescharacteristic
563C22×C4C23×D1311yescharacteristic
564C22×C4C23×D1311yescharacteristic
565C22×C4C23×D1311yescharacteristic
566M16—268no—
567C2×C8—138no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—134no—
579C4⋊C4—262no—
580C4⋊C4—262no—
581C4⋊C4—262no—
582C4⋊C4—262no—
583C4⋊C4—262no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—264no—
588C4⋊C4—262no—
589C4⋊C4—262no—
590C4⋊C4C23×D1314yes—
591C4⋊C4C23×D1314yes—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—264no—
595C22⋊C4—264no—
596C42—24no—
597C42—24no—
598C42—264no—
599C42—264no—
600C42C2×C22⋊D1311yescharacteristic
601C42C2×C22⋊D1311yescharacteristic
602C42C2×C22⋊D1311yescharacteristic
603C42C2×C22⋊D1311yescharacteristic
604C42C2×C22⋊D1311yescharacteristic
605C42C2×C22⋊D1311yescharacteristic
606C42C2×C22⋊D1311yescharacteristic
607C42C2×C22⋊D1311yescharacteristic
608C42C2×C22⋊D1311yescharacteristic
609C42C2×C22⋊D1311yescharacteristic
610C42C2×C22⋊D1311yescharacteristic
611C42C2×C22⋊D1311yescharacteristic
612C42C23×D1311yescharacteristic
613C42C23×D1311yescharacteristic
614C42C23×D1311yescharacteristic
615C42C23×D1311yescharacteristic
616C13#6086511yescharacteristic, complemented, Sylow
617C23—22no—
618C23—22no—
619C23—41no—
620C23C22×C22⋊D1311yescharacteristic
621C23C22×C22⋊D1311yescharacteristic
622C23C22×C22⋊D1311yescharacteristic
623Q8—44no—
624Q8—44no—
625Q8—44no—
626Q8—44no—
627Q8—268no—
628Q8—524no—
629Q8—524no—
630Q8—524no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—264no—
652C2×C4—264no—
653C2×C4—524no—
654C2×C4—524no—
655C2×C4#8820514yes—
656C2×C4#8825414yes—
657C2×C4C22×C22⋊D1311yescharacteristic
658C2×C4C22×C22⋊D1311yescharacteristic
659C2×C4C22×C22⋊D1311yescharacteristic
660C2×C4C22×C22⋊D1311yescharacteristic
661C2×C4C22×C22⋊D1311yescharacteristic
662C2×C4C22×C22⋊D1311yescharacteristic
663C2×C4C22×C22⋊D1311yescharacteristic
664C2×C4C22×C22⋊D1311yescharacteristic
665C2×C4C22×C22⋊D1311yescharacteristic
666C2×C4C22×C22⋊D1311yescharacteristic
667C2×C4C22×C22⋊D1311yescharacteristic
668C2×C4C24×D1311yescharacteristic
669C8—268no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—44no—
678C22#1171952112yes—
679C22C2×#8820512yes—
680C22C23×C22⋊D1311yescharacteristic
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—44no—
689C4—44no—
690C4—524no—
691C4—524no—
692C4#1171952112yes—
693C4#1171952712yes—
694C4C2×#8820512yes—
695C4C2×#8820512yes—
696C4C2×#8825412yes—
697C2—22no—
698C2—22no—
699C2—41no—
700C2C2×#1171952111yescharacteristic
701C2C22×#8820511yescharacteristic
702C2C2×#1171952711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#533C2
socleC22×C13C23×D4
prime radicalC24×C13C2×D4
hypercenterC2×#533D13
hypocenterC13#60865
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13126050C2semidirect
3. #13126042C2semidirect
4. #13125995C2semidirect
5. #13125987C2semidirect
6. #13125980C2semidirect
7. #13125383C2semidirect
8. #13125218C2semidirect
10. #13124637C2semidirect
47. #11718755C22semidirect
48. #11718754C22semidirect
49. #11718754C22semidirect
50. #11718752C22semidirect
51. #11718740C22semidirect
52. #11718739C22semidirect
53. #11718730C22semidirect
54. #11718726C22semidirect
55. #11718724C22semidirect
616. C13#60865semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
#131260502
#131260422
#131259952
#131259872
#131259802
#131253832
#131252182
#131247842
#131246372
#131234692
C2×C13×#5332
#6086513