Finite Group Databasebeta

← #15784774

Subgroups — #15784774

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718609C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718310C211yesmaximal, characteristic, complemented
4C2×#11718310C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6C2×C22⋊C4×Dic13C211yesmaximal, characteristic
7C2×C22⋊C4×Dic13C211yesmaximal, characteristic
8#13113096C211yesmaximal, characteristic, complemented
9#13113088C211yesmaximal, characteristic, complemented
10#13113087C211yesmaximal, characteristic, complemented
11#13113086C211yesmaximal, characteristic, complemented
12#13113079C211yesmaximal, characteristic
13#13113079C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
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
51C4⋊C4×Dic13—24no—
52#11718609C418yescomplemented
53C22⋊C4×Dic13—24no—
54C22⋊C4×Dic13—24no—
55C22⋊C4×Dic13—24no—
56#11718310—24no—
57#11718310—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—22no—
70C23×Dic13—22no—
71C23×Dic13Q814yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4C2×C414yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13C2×C414yes—
100C2×C22⋊Dic13C2×C414yes—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13C2×C414yescomplemented
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101C2×C414yescomplemented
115C2×#6101C2×C414yescomplemented
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
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—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13D414yes—
132C2×C4×Dic13D414yes—
133C2×C4×Dic13D414yes—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071C2×C414yescomplemented
150C4×#396—131nomaximal, Sylow
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×Q812yes—
165C24×C13#4112yes—
166C24×C13C2411yescharacteristic
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×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13#4112yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
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×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—28no—
248C22×Dic13—28no—
249C22×Dic13—28no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13—44no—
253C22×Dic13—44no—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13C2×D412yes—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×Q812yes—
265C22×Dic13C2×Q812yes—
266C22×Dic13#4112yes—
267C22×Dic13#4112yes—
268C22×Dic13#4112yes—
269C22×Dic13#4112yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C13×C4⋊C4—28no—
273C13×C22⋊C4—28no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4—28no—
276C22⋊Dic13—28no—
277C22⋊Dic13—28no—
278C22⋊Dic13—28no—
279C4⋊Dic13—28no—
280#6101—28no—
281#6101—28no—
282#6101—28no—
283#6101—28no—
284C4×Dic13—28no—
285C4×Dic13—28no—
286C4×Dic13—28no—
287C4×Dic13—44no—
288C4×Dic13—44no—
289C4×Dic13—44no—
290C2×#396—131no—
291C2×C4×C4⋊C4—131no—
292C2×C4×C4⋊C4—131no—
293C2×C4×C4⋊C4—131no—
294C2×C4×C22⋊C4—131no—
295C2×C4×C22⋊C4—131no—
296C2×C4×C22⋊C4—131no—
297#1443—131no—
298#1441—131no—
299#1441—131no—
300#1441—131no—
301#1439—131no—
302#1439—131no—
303#1439D1311yescharacteristic
304C4×#95—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13C4×Q814yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13C4×D414yes—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—416no—
445C2×Dic13C4×D414yes—
446C2×Dic13C4×D414yes—
447C2×Dic13#12114yes—
448C2×Dic13#12114yes—
449C2×Dic13#12114yes—
450C2×Dic13C22⋊Q814yes—
451C2×Dic13C22⋊Q814yes—
452C2×Dic13C22⋊Q814yes—
453C2×Dic13#12614yes—
454C24×C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4C2×D1311yescharacteristic
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C22⋊C4C2×D1311yescharacteristic
465C22×C22⋊C4C2×D1311yescharacteristic
466C22×C22⋊C4C2×D1311yescharacteristic
467C22×C42—131no—
468C22×C42—131no—
469C22×C42—131no—
470C22×C42—131no—
471C22×C42—131no—
472C22×C42—131no—
473#396—138no—
474C4×C4⋊C4—264no—
475C4×C4⋊C4—264no—
476C4×C4⋊C4—264no—
477C4×C22⋊C4—264no—
478C4×C22⋊C4—264no—
479C4×C22⋊C4—264no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95C2×D1311yescharacteristic
494C2×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C2×C4×D411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13C2×C4×Q811yescharacteristic
515C22×C13C4×#4111yescharacteristic
516C22×C13C4×#4111yescharacteristic
517C22×C13C4×#4111yescharacteristic
518C22×C13C2×#12111yescharacteristic
519C22×C13C2×#12111yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×C22⋊Q811yescharacteristic
523C22×C13C2×C22⋊Q811yescharacteristic
524C22×C13#52511yescharacteristic
525C22×C13#52511yescharacteristic
526C22×C13#52511yescharacteristic
527C22×C13#52511yescharacteristic
528C22×C13#52511yescharacteristic
529C22×C13#52511yescharacteristic
530C22×C13C2×#12611yescharacteristic
531C22×C13#52911yescharacteristic
532C22×C13#52911yescharacteristic
533C22×C13#52911yescharacteristic
534C22×C13#52911yescharacteristic
535C22×C13#52911yescharacteristic
536C22×C13#52911yescharacteristic
537C22×C13#52911yescharacteristic
538C22×C13#52911yescharacteristic
539C22×C13#52911yescharacteristic
540C22×C13#53211yescharacteristic
541C22×C13#53211yescharacteristic
542C22×C13#53211yescharacteristic
543C22×C13#53311yescharacteristic
544C22×C13#53311yescharacteristic
545C22×C13#53311yescharacteristic
546C4×C13—24no—
547C4×C13—42no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552Dic13—24no—
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—42no—
559Dic13#39618yescomplemented
560C25C22×D1311yescharacteristic
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—134no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—262no—
573C23×C4—262no—
574C23×C4—262no—
575C23×C4—262no—
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—134no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—262no—
612C2×C22⋊C4—262no—
613C2×C22⋊C4—262no—
614C2×C22⋊C4—262no—
615C2×C22⋊C4—262no—
616C2×C22⋊C4—262no—
617C2×C22⋊C4C4×D1314yes—
618C2×C42—134no—
619C2×C42—134no—
620C2×C42—134no—
621C2×C42—262no—
622C2×C42—262no—
623C2×C42—262no—
624C2×C42—262no—
625C2×C42—262no—
626C2×C42—262no—
627C2×C42—262no—
628C2×C42—262no—
629C2×C42—262no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—262no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—134no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652C2×C13—44no—
653C2×C13C4×#12111yescharacteristic
654C2×C13C4×#12111yescharacteristic
655C2×C13C4×#12111yescharacteristic
656C2×C13C4×C22⋊Q811yescharacteristic
657C2×C13C4×C22⋊Q811yescharacteristic
658C2×C13C4×C22⋊Q811yescharacteristic
659C2×C13C4×#12611yescharacteristic
660C2×C13C2×#39611yescharacteristic
661C2×C13#239211yescharacteristic
662C2×C13#239211yescharacteristic
663C2×C13#239211yescharacteristic
664C2×C13#239611yescharacteristic
665C2×C13#239611yescharacteristic
666C2×C13#239611yescharacteristic
667C2×C13#240111yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×C4×D1312yes—
681C24#612912yes—
682C24Q8×D1312yes—
683C24C23×D1311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—132no—
732C22×C4—132no—
733C22×C4—132no—
734C22×C4—132no—
735C22×C4—132no—
736C22×C4—268no—
737C22×C4—268no—
738C22×C4—268no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—524no—
778C22×C4—524no—
779C22×C4—524no—
780C22×C4—524no—
781C22×C4C2×C4×D1312yes—
782C22×C4C2×C4×D1312yes—
783C22×C4D4×D1312yes—
784C22×C4D4×D1312yes—
785C22×C4D4×D1312yes—
786C22×C4#612912yes—
787C22×C4#612912yes—
788C22×C4#612912yes—
789C4⋊C4—28no—
790C4⋊C4—268no—
791C4⋊C4—268no—
792C4⋊C4—268no—
793C4⋊C4—268no—
794C4⋊C4—268no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—268no—
799C22⋊C4—268no—
800C22⋊C4—268no—
801C42—268no—
802C42—268no—
803C42—268no—
804C42—524no—
805C42—524no—
806C42—524no—
807C13C4×#39611yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23#8814114yes—
843C23C22×C4×D1311yescharacteristic
844C23C2×D4×D1311yescharacteristic
845C23C2×D4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23C2×#612911yescharacteristic
848C23C2×#612911yescharacteristic
849C23C2×#612911yescharacteristic
850C23C2×#612911yescharacteristic
851C23C2×Q8×D1311yescharacteristic
852C23#41×D1311yescharacteristic
853C23#41×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#41×D1311yescharacteristic
856C23#41×D1311yescharacteristic
857C23#41×D1311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—134no—
900C2×C4—134no—
901C2×C4—134no—
902C2×C4—134no—
903C2×C4—134no—
904C2×C4—134no—
905C2×C4—134no—
906C2×C4—134no—
907C2×C4—134no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—262no—
926C2×C4—262no—
927C2×C4—262no—
928C2×C4—262no—
929C2×C4—262no—
930C2×C4—262no—
931C2×C4—262no—
932C2×C4—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—5216no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4—521no—
956C2×C4#8813514yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×#8813511yescharacteristic
973C22C2×#8814111yescharacteristic
974C22#1171922711yescharacteristic
975C22C4×#612911yescharacteristic
976C22C4×#612911yescharacteristic
977C22C4×D4×D1311yescharacteristic
978C22C4×D4×D1311yescharacteristic
979C22#1171929111yescharacteristic
980C22#1171929111yescharacteristic
981C22#1171929111yescharacteristic
982C22#1171930111yescharacteristic
983C22#1171930511yescharacteristic
984C22#1171930511yescharacteristic
985C22D13×#12111yescharacteristic
986C22D13×#12111yescharacteristic
987C22D13×#12111yescharacteristic
988C22#1171931111yescharacteristic
989C22#1171931111yescharacteristic
990C22#1171932711yescharacteristic
991C22#1171932711yescharacteristic
992C22#1171932711yescharacteristic
993C22D13×C22⋊Q811yescharacteristic
994C22D13×C22⋊Q811yescharacteristic
995C22D13×C22⋊Q811yescharacteristic
996C22#1171935411yescharacteristic
997C22#1171935411yescharacteristic
998C22#1171935411yescharacteristic
999C22#1171935411yescharacteristic
1000C22#1171936111yescharacteristic
1001C22#1171937311yescharacteristic
1002C22#1171938511yescharacteristic
1003C22#1171938511yescharacteristic
1004C22D13×#12611yescharacteristic
1005C22#1171941111yescharacteristic
1006C22#1171942111yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—138no—
1014C4—264no—
1015C4—264no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—522no—
1020C4—522no—
1021C2—44no—
1022C2#1311734611yescharacteristic
1023C2#1311734811yescharacteristic
1024C2#1311735211yescharacteristic
1025C2#1311736411yescharacteristic
1026C2#1311736811yescharacteristic
1027C2#1311736811yescharacteristic
1028C2#1311739011yescharacteristic
1029C2D13×#39611yescharacteristic
1030C2#1311807111yescharacteristic
1031C2#1311807511yescharacteristic
1032C2#1311807911yescharacteristic
1033C2#1311810311yescharacteristic
1034C2#1311810511yescharacteristic
1035C2#1311811111yescharacteristic
1036C2#1311813311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13C4×#396
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic13C2semidirect
3. C2×#11718310C2semidirect
4. C2×#11718310C2semidirect
8. #13113096C2semidirect
9. #13113088C2semidirect
10. #13113087C2semidirect
11. #13113086C2semidirect
14. #95×Dic13C2semidirect
52. #11718609C4semidirect
103. C2×C4⋊Dic13C2×C4semidirect
114. C2×#6101C2×C4semidirect
115. C2×#6101C2×C4semidirect
149. #88071C2×C4semidirect
559. Dic13#396semidirect
807. C13C4×#396semidirect

Maximal subgroups

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

subgroupindex
C2×#117186092
C2×C4⋊C4×Dic132
C2×#117183102
C2×C22⋊C4×Dic132
#131130962
#131130882
#131130872
#131130862
#131130792
#95×Dic132
C13×#14392
C4×#39613