Finite Group Databasebeta

← #15879207

Subgroups — #15879207

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic
2D4×C4⋊Dic13C211yesmaximal, characteristic
3#13115806C211yesmaximal, characteristic, complemented
4#13115794C211yesmaximal, characteristic, complemented
5#13115270C211yesmaximal, characteristic, complemented
6#13115260C211yesmaximal, characteristic, complemented
7#13115144C211yesmaximal, characteristic, complemented
8#13115144C211yesmaximal, characteristic, complemented
9#13114931C211yesmaximal, characteristic, complemented
10#13114922C211yesmaximal, characteristic, complemented
11#13114841C211yesmaximal, characteristic, complemented
12#13114666C211yesmaximal, characteristic, complemented
13#13114557C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C2×C13×#552C211yesmaximal, characteristic
16C13×#552—24no—
17C13×#552C418yescomplemented
18C2×C13×#126—21no—
19C2×C13×#125—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×D4×Dic13—21no—
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33C23×#1055C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38#11718873C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718672—24no—
43#11718646—21no—
44#11718611—21no—
45#11718611—21no—
46#11718596C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×D4×C13D411yescharacteristic
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—21no—
68C23×Dic13—21no—
69C13×#126—28no—
70C13×#125—28no—
71C13×#125—22no—
72C13×#125C2×C414yescomplemented
73C13×#123—28no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8C2×C414yescomplemented
77C13×C22⋊Q8C2×C414yescomplemented
78C4×Q8×C13—22no—
79C4×Q8×C13C2×C414yescomplemented
80C4×D4×C13C2×C414yes—
81C4×D4×C13D414yes—
82C13×#117—22no—
83C13×#117—28no—
84C13×#117C2×C414yescomplemented
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4C2×C414yescomplemented
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C42×C13—21no—
103C2×C42×C13—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107D4×Dic13—44no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13—41no—
115C2×C4⋊Dic13—41no—
116C2×C4⋊Dic13C2311yescharacteristic
117C2×C4⋊Dic13C2311yescharacteristic
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4×Dic13—21no—
121C2×#6099—22no—
122C2×#6099—22no—
123C2×#6099—41no—
124C22×#1055—22no—
125C22×#1055—22no—
126C22×#1055—41no—
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131#88075—22no—
132#88075—22no—
133#88075—41no—
134#88075—41no—
135#88071—21no—
136#88071—21no—
137#88071—21no—
138C22⋊#1055—22no—
139C22⋊#1055—22no—
140C4⋊#1055—22no—
141#88043—22no—
142#22491—131nomaximal, Sylow
143C24×C13C2×D411yescharacteristic
144C24×C13C2×D411yescharacteristic
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13C22×C412yes—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13C22⋊C414yes—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—24no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—42no—
168C22×C4×C13—42no—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C22×C412yes—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2411yescharacteristic
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—42no—
183C22×Dic13—42no—
184C22×Dic13—42no—
185C22×Dic13—42no—
186C22×Dic13—81no—
187C22×Dic13—81no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—24no—
191C13×C4⋊C4—24no—
192C13×C4⋊C4—24no—
193C13×C4⋊C4—24no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4C22⋊C414yes—
198C13×C4⋊C4C22×C412yes—
199C13×C4⋊C4C22×C412yes—
200C13×C4⋊C4C22×C412yes—
201C13×C22⋊C4—24no—
202C13×C22⋊C4—24no—
203C13×C22⋊C4—24no—
204C13×C22⋊C4C22⋊C414yes—
205C13×C22⋊C4C22⋊C414yes—
206C42×C13—24no—
207C42×C13—24no—
208C42×C13C22×C412yes—
209C42×C13C2×D412yes—
210C22⋊Dic13—42no—
211C22⋊Dic13—42no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—21no—
216C4⋊Dic13—21no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—42no—
220C4⋊Dic13—42no—
221C4⋊Dic13—42no—
222C4⋊Dic13—81no—
223C4⋊Dic13#4112yes—
224C4×Dic13—42no—
225#6099—44no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—44no—
238C2×#1055#4112yes—
239C2×#552D1311yescharacteristic
240C2×#435—131no—
241D4×C4⋊C4—131no—
242#1992—131no—
243#1989—131no—
244#1894—131no—
245#1892—131no—
246#1872—131no—
247#1872—131no—
248#1825—131no—
249#1823—131no—
250#1803—131no—
251#1763—131no—
252#1736—131no—
253C2×#340—131no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13C2×C22⋊C412yes—
265C23×C13C2×C22⋊C412yes—
266C23×C13AGL(1,ℤ/8)12yes—
267C23×C13#13712yes—
268C23×C13C22×D411yescharacteristic
269Q8×C13—22no—
270Q8×C13—22no—
271Q8×C13—41no—
272Q8×C13—41no—
273D4×C13—28no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
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—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—48no—
303C2×C4×C13C2×C22⋊C412yes—
304C2×C4×C13C2×C22⋊C412yes—
305C2×C4×C13C2×C22⋊C412yes—
306C2×C4×C13C2×C22⋊C412yes—
307C2×C4×C13C23×C411yescharacteristic
308C2×C4×C13C22×D411yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13C2×#4111yescharacteristic
311C2×C4×C13H(5,𝔽2)11yescharacteristic
312C2×C4×C132−1+411yescharacteristic
313C2×Dic13—22no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—84no—
326C2×Dic13—84no—
327#1055—22no—
328#1055—41no—
329#1055—41no—
330#1055—41no—
331C22×M16—131no—
332C23×C8—131no—
333#552—24no—
334#552Dic1318yescomplemented
335C2×#126—21no—
336C2×#125—21no—
337C2×#125C2×D1311yescharacteristic
338C2×#123—21no—
339C2×C22⋊Q8C2×D1311yescharacteristic
340C2×C22⋊Q8C2×D1311yescharacteristic
341C2×C4×Q8C2×D1311yescharacteristic
342C2×C4×D4—261no—
343C2×C4×D4C2×D1311yescharacteristic
344C2×#117—21no—
345C2×#117C2×D1311yescharacteristic
346C22×C4⋊C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4C2×D1311yescharacteristic
349#435—264no—
350C2×C4⋊C8—131no—
351C2×#103—131no—
352C2×#103—131no—
353C2×#103—131no—
354C2×#103—131no—
355C2×C22⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×#97—131no—
358#389—261no—
359#385—261no—
360#385—261no—
361#384—131no—
362#380—131no—
363#380—131no—
364C4×C4⋊C4—131no—
365#340—131no—
366#340—131no—
367#340—131no—
368#340—131no—
369#340—131no—
370#340—131no—
371#340—131no—
372#340—131no—
373#340—131no—
374#340—131no—
375#340—131no—
376#340—131no—
377C22×C13—22no—
378C22×C13—22no—
379C22×C13—22no—
380C22×C13—22no—
381C22×C13—22no—
382C22×C13—22no—
383C22×C13—22no—
384C22×C13—22no—
385C22×C13—22no—
386C22×C13—41no—
387C22×C13—41no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13#41714yes—
391C22×C13C22×C22⋊C411yescharacteristic
392C22×C13#54611yescharacteristic
393C22×C13#54711yescharacteristic
394C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C13C2×#13711yescharacteristic
396C22×C13#57711yescharacteristic
397C22×C13#57811yescharacteristic
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—22no—
401C4×C13—22no—
402C4×C13—42no—
403C4×C13—42no—
404C4×C13—42no—
405C4×C13—42no—
406C4×C13C4×#4111yescharacteristic
407C4×C13#52011yescharacteristic
408C4×C13#54611yescharacteristic
409C4×C13#54711yescharacteristic
410Dic13—42no—
411Dic13—81no—
412Dic13—81no—
413Dic13—81no—
414C22×Q8C22×D1311yescharacteristic
415C22×D4C22⋊D1311yescharacteristic
416C23×C4—21no—
417C23×C4—261no—
418C23×C4—261no—
419C23×C4C22×D1311yescharacteristic
420C23×C4C22×D1311yescharacteristic
421C2×M16—262no—
422C2×M16—262no—
423C2×M16—521no—
424C22×C8—131no—
425C22×C8—131no—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8—262no—
429C22×C8—262no—
430C22×C8—521no—
431#126—28no—
432#125—28no—
433#125—22no—
434#125C2×Dic1314yescomplemented
435#123—28no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8C2×Dic1314yescomplemented
439C22⋊Q8C2×Dic1314yescomplemented
440C4×Q8—22no—
441C4×Q8C2×Dic1314yescomplemented
442C4×D4—524no—
443C4×D4C2×Dic1314yes—
444C4×D4C22⋊D1314yes—
445#117—22no—
446#117—28no—
447#117C2×Dic1314yescomplemented
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—261no—
462C2×C4⋊C4—261no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—521no—
466C2×C4⋊C4—521no—
467C2×C4⋊C4C2×Dic1314yescomplemented
468C2×C4⋊C4C22⋊D1311yescharacteristic
469C2×C4⋊C4C22×D1311yescharacteristic
470C2×C4⋊C4C22×D1311yescharacteristic
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4C22⋊D1311yescharacteristic
478C2×C22⋊C4C22⋊D1311yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—261no—
482C2×C42C22×D1311yescharacteristic
483C4⋊C8—262no—
484#103—262no—
485#103—262no—
486#103—521no—
487#103—521no—
488C22⋊C8—262no—
489C22⋊C8—262no—
490#97—262no—
491#95—261no—
492#95—261no—
493#95—261no—
494C2×C13—24no—
495C2×C13—42no—
496C2×C13#233911yescharacteristic
497C2×C13C2×#41711yescharacteristic
498C2×C13#289811yescharacteristic
499C2×C13#331011yescharacteristic
500C2×C13#331211yescharacteristic
501C2×C13#334311yescharacteristic
502C2×C13#334411yescharacteristic
503C24C2×C22⋊D1311yescharacteristic
504C24C2×C22⋊D1311yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C22×Dic1312yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4C22⋊Dic1314yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—261no—
530C22×C4—261no—
531C22×C4—261no—
532C22×C4—261no—
533C22×C4—522no—
534C22×C4—522no—
535C22×C4—522no—
536C22×C4—522no—
537C22×C4—1041no—
538C22×C4—1041no—
539C22×C4C22×Dic1312yes—
540C22×C4C22×Dic1312yes—
541C22×C4C2×C22⋊D1311yescharacteristic
542C22×C4C2×C22⋊D1311yescharacteristic
543C22×C4C2×C22⋊D1311yescharacteristic
544C22×C4C2×C22⋊D1311yescharacteristic
545C22×C4C2×C22⋊D1312yes—
546C22×C4C2×C22⋊D1312yes—
547C22×C4C23×D1311yescharacteristic
548M16—524no—
549C2×C8—132no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—261no—
561C2×C8—524no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—132no—
572C4⋊C4—261no—
573C4⋊C4—261no—
574C4⋊C4—261no—
575C4⋊C4—261no—
576C4⋊C4—261no—
577C4⋊C4—261no—
578C4⋊C4—261no—
579C4⋊C4—522no—
580C4⋊C4—522no—
581C4⋊C4—522no—
582C4⋊C4—1041no—
583C4⋊C4C22⋊Dic1314yes—
584C4⋊C4C22×Dic1312yes—
585C4⋊C4C22×Dic1312yes—
586C4⋊C4C22×Dic1312yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—522no—
591C22⋊C4—522no—
592C22⋊C4C22⋊Dic1314yes—
593C22⋊C4C22⋊Dic1314yes—
594C42—24no—
595C42—24no—
596C42—522no—
597C42C22×Dic1312yes—
598C42C2×C22⋊D1312yes—
599C13#2249111yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23#8820312yes—
611C23#8820512yes—
612C23C2×C22⋊Dic1312yes—
613C23C2×C22⋊Dic1312yes—
614C23C22×C22⋊D1311yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
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—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—48no—
649C2×C4—262no—
650C2×C4—521no—
651C2×C4—521no—
652C2×C4—521no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4—521no—
657C2×C4—521no—
658C2×C4—521no—
659C2×C4—521no—
660C2×C4—521no—
661C2×C4—1044no—
662C2×C4—1044no—
663C2×C4C2×C22⋊Dic1312yes—
664C2×C4C2×C22⋊Dic1312yes—
665C2×C4C2×C22⋊Dic1312yes—
666C2×C4C2×C22⋊Dic1312yes—
667C2×C4#41×D1311yescharacteristic
668C2×C4#41×D1311yescharacteristic
669C2×C4#8825611yescharacteristic
670C2×C4#8825711yescharacteristic
671C2×C4C23×Dic1311yescharacteristic
672C2×C4C22×C22⋊D1311yescharacteristic
673C8—262no—
674C8—521no—
675C8—521no—
676C8—521no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1171889314yes—
691C22C2×#8820311yescharacteristic
692C22C2×#8820511yescharacteristic
693C22#1171952911yescharacteristic
694C22#1171953411yescharacteristic
695C22#1171954211yescharacteristic
696C22#1171954311yescharacteristic
697C22C22×C22⋊Dic1311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—522no—
707C4—1041no—
708C4—1041no—
709C4—1041no—
710C4#1171952911yescharacteristic
711C4#41×Dic1311yescharacteristic
712C4#1171953211yescharacteristic
713C4#1171953411yescharacteristic
714C2—24no—
715C2—42no—
716C2#1311766611yescharacteristic
717C2C2×#1171889311yescharacteristic
718C2#1312336911yescharacteristic
719C2#1312685111yescharacteristic
720C2#1312688111yescharacteristic
721C2#1312727611yescharacteristic
722C2#1312729111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenterC2×#552D13
hypocenterC13#22491
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #13115806C2semidirect
4. #13115794C2semidirect
5. #13115270C2semidirect
6. #13115260C2semidirect
7. #13115144C2semidirect
8. #13115144C2semidirect
9. #13114931C2semidirect
10. #13114922C2semidirect
11. #13114841C2semidirect
12. #13114666C2semidirect
13. #13114557C2semidirect
14. C2×#11718121C2semidirect
17. C13×#552C4semidirect
72. C13×#125C2×C4semidirect
76. C13×C22⋊Q8C2×C4semidirect
77. C13×C22⋊Q8C2×C4semidirect
79. C4×Q8×C13C2×C4semidirect
84. C13×#117C2×C4semidirect
92. C2×C13×C4⋊C4C2×C4semidirect
334. #552Dic13semidirect
434. #125C2×Dic13semidirect
438. C22⋊Q8C2×Dic13semidirect
439. C22⋊Q8C2×Dic13semidirect
441. C4×Q8C2×Dic13semidirect
447. #117C2×Dic13semidirect
467. C2×C4⋊C4C2×Dic13semidirect
599. C13#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
D4×C4⋊Dic132
#131158062
#131157942
#131152702
#131152602
#131151442
#131149312
#131149222
#131148412
#131146662
#131145572
C2×#117181212
C2×C13×#5522
#2249113