Finite Group Databasebeta

← #15786649

Subgroups — #15786649

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718308C211yesmaximal, characteristic
3C2×#11718308C211yesmaximal, characteristic
4C2×#11718308C211yesmaximal, characteristic
5C2×#11718633C211yesmaximal, characteristic
6C2×C4⋊C4×Dic13C211yesmaximal, characteristic
7C2×#11718310C211yesmaximal, characteristic
8#13113092C211yesmaximal, characteristic
9#13113091C211yesmaximal, characteristic
10#13113086C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic
12#13113067C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic
14#13113064C211yesmaximal, characteristic
15C13×#1441C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718646—24no—
52C4⋊C4×Dic13—24no—
53#11718633C418yescomplemented
54#11718310—24no—
55#11718308—24no—
56#11718308—24no—
57#11718308—24no—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4C2×C414yes—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13D414yes—
88C2×#6101—22no—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—41no—
103C2×#6101C2×C414yes—
104C2×#6101C2×C414yes—
105C2×#6101C2×C414yes—
106C2×#6101D414yes—
107C2×#6101Q814yes—
108C2×#6101Q814yes—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13C2×C414yes—
123C2×C4×Dic13D414yes—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—41no—
139#88071—41no—
140#88071C2×C414yes—
141#88071C2×C414yes—
142#14046—131nomaximal, Sylow
143C24×C13C2411yescharacteristic
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
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—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13C22×C412yes—
184C22×C4×C13C22×C412yes—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C2×D412yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×Q812yes—
190C22×C4×C13C2×Q812yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13C22×C412yes—
233C22×Dic13C22×C412yes—
234C22×Dic13C22×C412yes—
235C22×Dic13C22×C412yes—
236C22×Dic13C2×D412yes—
237C22×Dic13C2×D412yes—
238C22×Dic13C2×D412yes—
239C22×Dic13C2×D412yes—
240C22×Dic13C2×D412yes—
241C22×Dic13C2×D412yes—
242C22×Dic13C2×Q812yes—
243C22×Dic13C2×Q812yes—
244C22×Dic13C2×Q812yes—
245C22×Dic13C2×Q812yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—28no—
250C13×C4⋊C4—28no—
251C4⋊Dic13—28no—
252C4⋊Dic13—44no—
253C4⋊Dic13—44no—
254#6101—28no—
255#6101—28no—
256#6101—28no—
257#6101—44no—
258#6101—44no—
259#6101—44no—
260#6101C4⋊C4116yescomplemented
261C4×Dic13—28no—
262C4×Dic13—28no—
263C4×Dic13—44no—
264C4×Dic13—44no—
265C4×Dic13—44no—
266C2×#389—131no—
267C2×#389—131no—
268C2×#389—131no—
269C2×#389—131no—
270C2×#389—131no—
271C2×C4×C4⋊C4—131no—
272C2×C4×C4⋊C4—131no—
273#1442—131no—
274#1442—131no—
275#1441—131no—
276#1441D1311yescharacteristic
277#1436—131no—
278#1436—131no—
279C4⋊#95—131no—
280C4⋊#95—131no—
281C23×C13C23×C411yescharacteristic
282C23×C13C22×D411yescharacteristic
283C23×C13C22×D411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C22×Q811yescharacteristic
286C23×C13C22×Q811yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13C2×#4111yescharacteristic
291C23×C13C2×#4111yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C132−1+411yescharacteristic
294C23×C132−1+411yescharacteristic
295C23×C132−1+411yescharacteristic
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13C2×C4⋊C414yes—
344C2×C4×C13C4×D414yes—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13C2×C4⋊C414yes—
393C2×Dic13C2×C4⋊C414yes—
394C2×Dic13C4×D414yes—
395C2×Dic13C4×Q814yes—
396C2×Dic13#12114yes—
397C2×Dic13#12114yes—
398C2×Dic13C22⋊Q814yes—
399C2×Dic13#12514yes—
400C2×Dic13C4⋊Q814yes—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4C2×D1311yescharacteristic
412C22×C4⋊C4C2×D1311yescharacteristic
413C22×C42—131no—
414C22×C42—131no—
415C22×C42—131no—
416C22×C42—131no—
417C22×C42—131no—
418#389—138no—
419#389—264no—
420#389—264no—
421#389—264no—
422#389—264no—
423C4×C4⋊C4—264no—
424C4×C4⋊C4—264no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95—131no—
429C2×#95—131no—
430C2×#95—131no—
431C2×#95—131no—
432C2×#95—131no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95C2×D1311yescharacteristic
439C2×#95C2×D1311yescharacteristic
440C2×#95C2×D1311yescharacteristic
441C2×#95C2×D1311yescharacteristic
442C2×#95C2×D1311yescharacteristic
443C22×C13C22×C4⋊C411yescharacteristic
444C22×C13C2×C4×D411yescharacteristic
445C22×C13C2×C4×D411yescharacteristic
446C22×C13C2×C4×Q811yescharacteristic
447C22×C13C4×#4111yescharacteristic
448C22×C13#51911yescharacteristic
449C22×C13#52011yescharacteristic
450C22×C13C2×#12111yescharacteristic
451C22×C13C2×#12111yescharacteristic
452C22×C13C2×C22⋊Q811yescharacteristic
453C22×C13#52511yescharacteristic
454C22×C13C2×#12511yescharacteristic
455C22×C13#52911yescharacteristic
456C22×C13C2×C4⋊Q811yescharacteristic
457C22×C13#53211yescharacteristic
458C22×C13#53611yescharacteristic
459C22×C13#53711yescharacteristic
460C22×C13#54111yescharacteristic
461C22×C13#54211yescharacteristic
462C22×C13D4211yescharacteristic
463C22×C13#54711yescharacteristic
464C22×C13#54711yescharacteristic
465C22×C13#54811yescharacteristic
466C22×C13#54811yescharacteristic
467C22×C13D4×Q811yescharacteristic
468C22×C13D4×Q811yescharacteristic
469C22×C13#55211yescharacteristic
470C22×C13#55311yescharacteristic
471C22×C13#55411yescharacteristic
472C22×C13#55411yescharacteristic
473C22×C13#55611yescharacteristic
474C22×C13#55711yescharacteristic
475C22×C13#55711yescharacteristic
476C22×C13#55711yescharacteristic
477C22×C13#55711yescharacteristic
478C4×C13—24no—
479C4×C13—24no—
480C4×C13—42no—
481C4×C13—42no—
482C4×C13—42no—
483C4×C13—42no—
484C4×C13—81no—
485Dic13—24no—
486Dic13—24no—
487Dic13—42no—
488Dic13—42no—
489Dic13—42no—
490Dic13—42no—
491Dic13—81no—
492Dic13#38918yescomplemented
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4—131no—
499C23×C4—131no—
500C23×C4—131no—
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—262no—
521C2×C4⋊C4—262no—
522C2×C4⋊C4—262no—
523C2×C4⋊C4—262no—
524C2×C4⋊C4—262no—
525C2×C4⋊C4—262no—
526C2×C4⋊C4—262no—
527C2×C4⋊C4—262no—
528C2×C4⋊C4—262no—
529C2×C4⋊C4—262no—
530C2×C4⋊C4—262no—
531C2×C4⋊C4—262no—
532C2×C4⋊C4—262no—
533C2×C4⋊C4—262no—
534C2×C4⋊C4—262no—
535C2×C4⋊C4—262no—
536C2×C4⋊C4—262no—
537C2×C4⋊C4—262no—
538C2×C4⋊C4—262no—
539C2×C4⋊C4—262no—
540C2×C4⋊C4—262no—
541C2×C4⋊C4—521no—
542C2×C4⋊C4—521no—
543C2×C4⋊C4C4×D1314yes—
544C2×C42—134no—
545C2×C42—134no—
546C2×C42—262no—
547C2×C42—262no—
548C2×C42—262no—
549C2×C42—262no—
550C2×C42—262no—
551C2×C42—262no—
552C2×C42—262no—
553C2×C42—262no—
554C2×C42—262no—
555C2×C42—262no—
556C2×C42—262no—
557C2×C42—521no—
558C2×C42—521no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—134no—
565#95—134no—
566#95—262no—
567#95—262no—
568#95—262no—
569#95—262no—
570#95—262no—
571#95—262no—
572#95—262no—
573#95—262no—
574#95—262no—
575#95—521no—
576#95—521no—
577C2×C13C2×#38911yescharacteristic
578C2×C13C4×#12111yescharacteristic
579C2×C13#232311yescharacteristic
580C2×C13D4×C4⋊C411yescharacteristic
581C2×C13#235111yescharacteristic
582C2×C13#236511yescharacteristic
583C2×C13#237011yescharacteristic
584C2×C13#241511yescharacteristic
585C2×C13#241611yescharacteristic
586C2×C13#245211yescharacteristic
587C2×C13#245311yescharacteristic
588C2×C13#250611yescharacteristic
589C2×C13#250911yescharacteristic
590C2×C13#254611yescharacteristic
591C2×C13#258411yescharacteristic
592C24C23×D1311yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—132no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—132no—
642C22×C4—132no—
643C22×C4—132no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4C2×C4×D1312yes—
689C22×C4C2×C4×D1312yes—
690C22×C4C2×C4×D1312yes—
691C22×C4D4×D1312yes—
692C22×C4D4×D1312yes—
693C22×C4D4×D1312yes—
694C22×C4#612912yes—
695C22×C4#612912yes—
696C22×C4Q8×D1312yes—
697C22×C4Q8×D1312yes—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—1316no—
701C4⋊C4—268no—
702C4⋊C4—268no—
703C4⋊C4—268no—
704C4⋊C4—268no—
705C4⋊C4—524no—
706C4⋊C4—524no—
707C4⋊C4—524no—
708C4⋊C4—524no—
709C4⋊C4—524no—
710C42—268no—
711C42—268no—
712C42—524no—
713C42—524no—
714C42—524no—
715C13#1404611yescharacteristic, complemented, Sylow
716C23C22×C4×D1311yescharacteristic
717C23C2×D4×D1311yescharacteristic
718C23C2×D4×D1311yescharacteristic
719C23C2×D4×D1311yescharacteristic
720C23C2×#612911yescharacteristic
721C23C2×#612911yescharacteristic
722C23C2×Q8×D1311yescharacteristic
723C23C2×Q8×D1311yescharacteristic
724C23#8825411yescharacteristic
725C23#41×D1311yescharacteristic
726C23#41×D1311yescharacteristic
727C23#41×D1311yescharacteristic
728C23#8825611yescharacteristic
729C23#8825711yescharacteristic
730C23#8825711yescharacteristic
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—134no—
779C2×C4—134no—
780C2×C4—134no—
781C2×C4—134no—
782C2×C4—134no—
783C2×C4—134no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—134no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—521no—
812C2×C4—521no—
813C2×C4—521no—
814C2×C4—521no—
815C2×C4—521no—
816C2×C4—521no—
817C2×C4—521no—
818C2×C4—521no—
819C2×C4—521no—
820C2×C4—521no—
821C2×C4—521no—
822C2×C4—521no—
823C2×C4—521no—
824C2×C4—521no—
825C2×C4—521no—
826C2×C4—521no—
827C2×C4—521no—
828C2×C4—521no—
829C2×C4—521no—
830C2×C4—521no—
831C2×C4—521no—
832C2×C4—521no—
833C2×C4—521no—
834C2×C4#8813514yes—
835C2×C4C4⋊C4×D1314yes—
836C22C2×#8813511yescharacteristic
837C22C2×C4⋊C4×D1311yescharacteristic
838C22#1171922811yescharacteristic
839C22C4×#612911yescharacteristic
840C22C4×D4×D1311yescharacteristic
841C22C4×Q8×D1311yescharacteristic
842C22#1171927711yescharacteristic
843C22#1171929111yescharacteristic
844C22#1171930111yescharacteristic
845C22#1171930311yescharacteristic
846C22D13×#12111yescharacteristic
847C22D13×#12111yescharacteristic
848C22#1171931411yescharacteristic
849C22#1171931611yescharacteristic
850C22D13×C22⋊Q811yescharacteristic
851C22#1171933411yescharacteristic
852C22#1171933611yescharacteristic
853C22#1171933711yescharacteristic
854C22#1171933711yescharacteristic
855C22#1171933811yescharacteristic
856C22#1171934011yescharacteristic
857C22#1171934011yescharacteristic
858C22#1171935311yescharacteristic
859C22#1171935411yescharacteristic
860C22#1171935511yescharacteristic
861C22#1171937611yescharacteristic
862C22#1171939011yescharacteristic
863C22#1171939011yescharacteristic
864C22D13×#12511yescharacteristic
865C22#1171940111yescharacteristic
866C22#1171941411yescharacteristic
867C22#1171941511yescharacteristic
868C22#1171942611yescharacteristic
869C22#1171942611yescharacteristic
870C22D13×C4⋊Q811yescharacteristic
871C4—24no—
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—81no—
878C4—138no—
879C4—264no—
880C4—264no—
881C4—522no—
882C4—522no—
883C4—522no—
884C4—522no—
885C4—1041no—
886C2D13×#38911yescharacteristic
887C2#1311734611yescharacteristic
888C2#1311751711yescharacteristic
889C2#1311773211yescharacteristic
890C2#1311775511yescharacteristic
891C2#1311789311yescharacteristic
892C2#1311792911yescharacteristic
893C2#1311825811yescharacteristic
894C2#1311827111yescharacteristic
895C2#1311867911yescharacteristic
896C2#1311869211yescharacteristic
897C2#1311934511yescharacteristic
898C2#1311938011yescharacteristic
899C2#1311982011yescharacteristic
900C2#1312021811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14046
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
53. #11718633C4semidirect
260. #6101C4⋊C4semidirect
492. Dic13#389semidirect
715. C13#14046semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117183082
C2×#117186332
C2×C4⋊C4×Dic132
C2×#117183102
#131130922
#131130912
#131130862
#131130702
#131130672
#131130642
C13×#14412
#1404613