Finite Group Databasebeta

← #15786138

Subgroups — #15786138

Order 3328.

1614 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718589C211yesmaximal, characteristic
2C2×#11718308C211yesmaximal, characteristic
3C2×#11718308C211yesmaximal, characteristic
4C2×#11718308C211yesmaximal, characteristic
5C2×#11718308C211yesmaximal, characteristic
6C2×#11718637C211yesmaximal, characteristic
7C2×C4×#6101C211yesmaximal, characteristic
8#13113101C211yesmaximal, characteristic
9#13113099C211yesmaximal, characteristic
10#13113088C211yesmaximal, characteristic
11#13113087C211yesmaximal, characteristic
12#13113070C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718637—24no—
52C4×#6101—24no—
53#11718589—24no—
54#11718308—24no—
55#11718308—24no—
56#11718308—24no—
57#11718308C418yescomplemented
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—41no—
76C2×C42×C13—22no—
77C2×C42×C13—22no—
78C2×C42×C13—41no—
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—22no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13—41no—
89C2×C4⋊Dic13—41no—
90C2×C4⋊Dic13C2×C414yes—
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—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101—41no—
112C2×#6101C2×C414yes—
113C2×#6101C2×C414yes—
114C2×#6101C2×C414yes—
115C2×#6101D414yes—
116C2×#6101D414yes—
117C2×#6101Q814yes—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—41no—
128C2×C4×Dic13C2×C414yes—
129C2×C4×Dic13Q814yes—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95C2×C414yes—
134C13×#95Q814yes—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—41no—
143#88071—41no—
144#88071C2×C414yes—
145#88071D414yes—
146#14005—131nomaximal, Sylow
147C24×C13C2411yescharacteristic
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×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×Q812yes—
192C22×C4×C13C2×Q812yes—
193C22×C4×C13C2×Q812yes—
194C22×C4×C13C2×Q812yes—
195C22×C4×C13C2×Q812yes—
196C22×C4×C13#4112yes—
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×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13C22×C412yes—
237C22×Dic13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13C22×C412yes—
240C22×Dic13C2×D412yes—
241C22×Dic13C2×D412yes—
242C22×Dic13C2×D412yes—
243C22×Dic13C2×D412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13C2×D412yes—
246C22×Dic13C2×Q812yes—
247C22×Dic13C2×Q812yes—
248C22×Dic13C2×Q812yes—
249C22×Dic13C2×Q812yes—
250C22×Dic13#4112yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C13×C4⋊C4—44no—
254C42×C13—44no—
255C4⋊Dic13—28no—
256C4⋊Dic13—44no—
257C4⋊Dic13—44no—
258C4⋊Dic13—44no—
259#6101—28no—
260#6101—28no—
261#6101—28no—
262#6101—44no—
263#6101—44no—
264#6101—44no—
265#6101—44no—
266#6101—44no—
267#6101C4⋊C4116yescomplemented
268C4×Dic13—28no—
269C4×Dic13—28no—
270C4×Dic13—44no—
271C4×Dic13—44no—
272C2×#389—131no—
273C2×#389—131no—
274C2×#389—131no—
275C2×#389—131no—
276C2×#389—131no—
277C2×#384—131no—
278C2×C4×C4⋊C4—131no—
279#1444—131no—
280#1444—131no—
281#1441—131no—
282#1441—131no—
283#1436—131no—
284#1436D1311yescharacteristic
285C4⋊#95—131no—
286C4×#95—131no—
287C23×C13C23×C411yescharacteristic
288C23×C13C22×D411yescharacteristic
289C23×C13C22×D411yescharacteristic
290C23×C13C22×D411yescharacteristic
291C23×C13C22×Q811yescharacteristic
292C23×C13C22×Q811yescharacteristic
293C23×C13C22×Q811yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13H(5,𝔽2)11yescharacteristic
299C23×C13H(5,𝔽2)11yescharacteristic
300C23×C132−1+411yescharacteristic
301C23×C132−1+411yescharacteristic
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—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
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×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13C2×C4⋊C414yes—
349C2×C4×C13C4×Q814yes—
350C2×C4×C13C4⋊Q814yes—
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—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
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×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13C2×C4⋊C414yes—
399C2×Dic13C2×C4⋊C414yes—
400C2×Dic13C4×D414yes—
401C2×Dic13C4×D414yes—
402C2×Dic13C4×Q814yes—
403C2×Dic13#12114yes—
404C2×Dic13C22⋊Q814yes—
405C2×Dic13#12514yes—
406C2×Dic13C4⋊Q814yes—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4—131no—
412C22×C4⋊C4—131no—
413C22×C4⋊C4—131no—
414C22×C4⋊C4—131no—
415C22×C4⋊C4—131no—
416C22×C4⋊C4—131no—
417C22×C4⋊C4—131no—
418C22×C4⋊C4—131no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424C22×C42—131no—
425C22×C42C2×D1311yescharacteristic
426#389—138no—
427#389—264no—
428#389—264no—
429#389—264no—
430#389—264no—
431#384—264no—
432C4×C4⋊C4—264no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95C2×D1311yescharacteristic
445C2×#95C2×D1311yescharacteristic
446C2×#95C2×D1311yescharacteristic
447C2×#95C2×D1311yescharacteristic
448C2×#95C2×D1311yescharacteristic
449C22×C13C22×C4⋊C411yescharacteristic
450C22×C13C2×C4×D411yescharacteristic
451C22×C13C2×C4×D411yescharacteristic
452C22×C13C2×C4×Q811yescharacteristic
453C22×C13C2×C4×Q811yescharacteristic
454C22×C13#52011yescharacteristic
455C22×C13#52011yescharacteristic
456C22×C13C2×#12111yescharacteristic
457C22×C13C2×C22⋊Q811yescharacteristic
458C22×C13C2×#12511yescharacteristic
459C22×C13C2×C4⋊Q811yescharacteristic
460C22×C13C2×C4⋊Q811yescharacteristic
461C22×C13#53211yescharacteristic
462C22×C13#53311yescharacteristic
463C22×C13#53311yescharacteristic
464C22×C13#54011yescharacteristic
465C22×C13#54111yescharacteristic
466C22×C13#54411yescharacteristic
467C22×C13#54411yescharacteristic
468C22×C13D4211yescharacteristic
469C22×C13D4211yescharacteristic
470C22×C13#54611yescharacteristic
471C22×C13#54711yescharacteristic
472C22×C13#54711yescharacteristic
473C22×C13#54811yescharacteristic
474C22×C13D4×Q811yescharacteristic
475C22×C13D4×Q811yescharacteristic
476C22×C13D4×Q811yescharacteristic
477C22×C13#55011yescharacteristic
478C22×C13#55211yescharacteristic
479C22×C13#55311yescharacteristic
480C22×C13#55411yescharacteristic
481C22×C13#55411yescharacteristic
482C22×C13#55711yescharacteristic
483C22×C13Q8211yescharacteristic
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—24no—
487C4×C13—42no—
488C4×C13—42no—
489C4×C13—42no—
490C4×C13—81no—
491Dic13—24no—
492Dic13—24no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497Dic13—81no—
498Dic13#38918yescomplemented
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—131no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—131no—
506C23×C4—131no—
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
510C23×C4C22×D1311yescharacteristic
511C23×C4C22×D1311yescharacteristic
512C23×C4C22×D1311yescharacteristic
513C23×C4C22×D1311yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—134no—
521C2×C4⋊C4—134no—
522C2×C4⋊C4—134no—
523C2×C4⋊C4—134no—
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—262no—
542C2×C4⋊C4—262no—
543C2×C4⋊C4—262no—
544C2×C4⋊C4—262no—
545C2×C4⋊C4—262no—
546C2×C4⋊C4—262no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—262no—
549C2×C4⋊C4—521no—
550C2×C4⋊C4—521no—
551C2×C4⋊C4—521no—
552C2×C4⋊C4—521no—
553C2×C4⋊C4—521no—
554C2×C4⋊C4—521no—
555C2×C4⋊C4—521no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—41no—
559C2×C42—134no—
560C2×C42—134no—
561C2×C42—262no—
562C2×C42—262no—
563C2×C42—262no—
564C2×C42—262no—
565C2×C42—262no—
566C2×C42—262no—
567C2×C42—262no—
568C2×C42—262no—
569C2×C42—262no—
570C2×C42—521no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—134no—
575#95—134no—
576#95—262no—
577#95—262no—
578#95—262no—
579#95—262no—
580#95—262no—
581#95—262no—
582#95—262no—
583#95—521no—
584#95—521no—
585#95Dic2614yes—
586#95C4×D1314yes—
587C2×C13C2×#38911yescharacteristic
588C2×C13C4×C4⋊Q811yescharacteristic
589C2×C13#233011yescharacteristic
590C2×C13D4×C4⋊C411yescharacteristic
591C2×C13Q8×C4⋊C411yescharacteristic
592C2×C13#236011yescharacteristic
593C2×C13#236111yescharacteristic
594C2×C13#242811yescharacteristic
595C2×C13#242911yescharacteristic
596C2×C13#244011yescharacteristic
597C2×C13#244111yescharacteristic
598C2×C13#250611yescharacteristic
599C2×C13#250711yescharacteristic
600C2×C13#255011yescharacteristic
601C2×C13#255111yescharacteristic
602C24C23×D1311yescharacteristic
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—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
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—132no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
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×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4C2×Dic2612yes—
697C22×C4C2×Dic2612yes—
698C22×C4C2×Dic2612yes—
699C22×C4C2×C4×D1312yes—
700C22×C4C2×C4×D1312yes—
701C22×C4C2×C4×D1312yes—
702C22×C4#612712yes—
703C22×C4D4×D1312yes—
704C22×C4D4×D1312yes—
705C22×C4D4×D1312yes—
706C22×C4Q8×D1312yes—
707C22×C4Q8×D1312yes—
708C4⋊C4—44no—
709C4⋊C4—1316no—
710C4⋊C4—268no—
711C4⋊C4—268no—
712C4⋊C4—268no—
713C4⋊C4—268no—
714C4⋊C4—524no—
715C4⋊C4—524no—
716C4⋊C4—524no—
717C4⋊C4—524no—
718C4⋊C4—524no—
719C4⋊C4—524no—
720C4⋊C4—524no—
721C4⋊C4—524no—
722C42—44no—
723C42—268no—
724C42—268no—
725C42—524no—
726C42—524no—
727C13#1400511yescharacteristic, complemented, Sylow
728C23C22×Dic2611yescharacteristic
729C23C22×C4×D1311yescharacteristic
730C23C2×#612711yescharacteristic
731C23C2×D4×D1311yescharacteristic
732C23C2×D4×D1311yescharacteristic
733C23C2×D4×D1311yescharacteristic
734C23#8825111yescharacteristic
735C23C2×Q8×D1311yescharacteristic
736C23C2×Q8×D1311yescharacteristic
737C23#41×D1311yescharacteristic
738C23#41×D1311yescharacteristic
739C23#41×D1311yescharacteristic
740C23#8825611yescharacteristic
741C23#8825711yescharacteristic
742C23#8825711yescharacteristic
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—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
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—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—134no—
790C2×C4—134no—
791C2×C4—134no—
792C2×C4—134no—
793C2×C4—134no—
794C2×C4—134no—
795C2×C4—134no—
796C2×C4—134no—
797C2×C4—134no—
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—262no—
812C2×C4—262no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
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—521no—
835C2×C4—521no—
836C2×C4—521no—
837C2×C4—521no—
838C2×C4—521no—
839C2×C4—521no—
840C2×C4—521no—
841C2×C4—521no—
842C2×C4—521no—
843C2×C4—521no—
844C2×C4—521no—
845C2×C4C4×Dic2614yes—
846C2×C4#8814214yes—
847C2×C4C4⋊C4×D1314yes—
848C22C2×C4×Dic2611yescharacteristic
849C22#1171919511yescharacteristic
850C22C2×#8814211yescharacteristic
851C22C2×C4⋊C4×D1311yescharacteristic
852C22#1171922211yescharacteristic
853C22#1171922811yescharacteristic
854C22#1171923611yescharacteristic
855C22D4×Dic2611yescharacteristic
856C22D4×Dic2611yescharacteristic
857C22#1171924411yescharacteristic
858C22C4×D4×D1311yescharacteristic
859C22C4×D4×D1311yescharacteristic
860C22#1171925111yescharacteristic
861C22#1171925311yescharacteristic
862C22#1171925811yescharacteristic
863C22Q8×Dic2611yescharacteristic
864C22#1171927211yescharacteristic
865C22C4×Q8×D1311yescharacteristic
866C22#1171928311yescharacteristic
867C22#1171929511yescharacteristic
868C22D13×#12111yescharacteristic
869C22#1171931411yescharacteristic
870C22#1171932811yescharacteristic
871C22D13×C22⋊Q811yescharacteristic
872C22#1171933711yescharacteristic
873C22#1171934111yescharacteristic
874C22#1171936011yescharacteristic
875C22#1171936011yescharacteristic
876C22#1171936811yescharacteristic
877C22#1171938211yescharacteristic
878C22D13×#12511yescharacteristic
879C22#1171939411yescharacteristic
880C22#1171940611yescharacteristic
881C22#1171941411yescharacteristic
882C22D13×C4⋊Q811yescharacteristic
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—81no—
890C4—138no—
891C4—264no—
892C4—264no—
893C4—522no—
894C4—522no—
895C4—522no—
896C4—522no—
897C4—1041no—
898C2D13×#38911yescharacteristic
899C2C4×#8814211yescharacteristic
900C2#1311757211yescharacteristic
901C2#1311773411yescharacteristic
902C2C4⋊C4×Dic2611yescharacteristic
903C2#1311784211yescharacteristic
904C2#1311784911yescharacteristic
905C2#1311842311yescharacteristic
906C2#1311843211yescharacteristic
907C2#1311853711yescharacteristic
908C2#1311854811yescharacteristic
909C2#1311934911yescharacteristic
910C2#1311936211yescharacteristic
911C2#1311985411yescharacteristic
912C2#1311986411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1436D13
hypocenterC13#14005
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
57. #11718308C4semidirect
267. #6101C4⋊C4semidirect
498. Dic13#389semidirect
727. C13#14005semidirect

Maximal subgroups

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

subgroupindex
C2×#117185892
C2×#117183082
C2×#117186372
C2×C4×#61012
#131131012
#131130992
#131130882
#131130872
#131130702
#131130642
#95×Dic132
C13×#14362
#1400513