Finite Group Databasebeta

← #15790274

Subgroups — #15790274

Order 3328.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718308C211yesmaximal, characteristic, complemented
4C2×#11718316C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic
6#13113106C211yesmaximal, characteristic, complemented
7#13113090C211yesmaximal, characteristic, complemented
8#13113090C211yesmaximal, characteristic, complemented
9#13113088C211yesmaximal, characteristic, complemented
10#13113079C211yesmaximal, characteristic
11#13113079C211yesmaximal, characteristic
12#13113073C211yesmaximal, characteristic
13#13113073C211yesmaximal, characteristic
14#13113070C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C2×#88178—24no—
28C2×#88178—24no—
29C2×#88178C418yescomplemented
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40#11718873—24no—
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718316—24no—
56#11718308—24no—
57#11718307—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—41no—
64C23×C4×C13—41no—
65C23×C4×C13C2×C414yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—41no—
85C22×Dic26—41no—
86C22×Dic26C2×C414yes—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4—41no—
90C2×C13×C22⋊C4—41no—
91C2×C13×C22⋊C4—41no—
92C2×C13×C22⋊C4Q814yescomplemented
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⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—41no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13C2×C414yes—
104C2×C22⋊Dic13C2×C414yes—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—41no—
112C2×C4⋊Dic13—41no—
113C2×C4⋊Dic13C2×C414yes—
114#88178—232no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—41no—
121C2×#6101—41no—
122C2×#6101—41no—
123C2×#6101C2×C414yes—
124C2×#6101C2×C414yes—
125C2×#6101D414yes—
126C2×#6101D414yes—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—41no—
131C2×C4×Dic13—41no—
132C2×C4×Dic13—41no—
133C13×#95—22no—
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—41no—
145#88071—41no—
146#88071—41no—
147#88071—41no—
148#88071—41no—
149#88071—41no—
150#88071D414yes—
151#14362—131nomaximal, Sylow
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×C13—21no—
164C24×C13C22×C412yes—
165C24×C13C2×Q812yes—
166C24×C13#4112yes—
167C24×C13C2411yescharacteristic
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—28no—
189C22×C4×C13—28no—
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×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—44no—
205C22×C4×C13—44no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13—44no—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×Q812yes—
215C22×C4×C13C2×Q812yes—
216C22×C4×C13#4112yes—
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—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13C22×C412yes—
264C22×Dic13C22×C412yes—
265C22×Dic13C22×C412yes—
266C22×Dic13C22×C412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×D412yes—
271C22×Dic13C2×D412yes—
272C22×Dic13C2×D412yes—
273C2×Dic26—28no—
274C2×Dic26—28no—
275C2×Dic26—44no—
276C2×Dic26—44no—
277C2×Dic26—44no—
278C2×Dic26—44no—
279C2×Dic26—44no—
280C13×C22⋊C4—44no—
281C13×C22⋊C4—44no—
282C22⋊Dic13—28no—
283C22⋊Dic13—28no—
284C22⋊Dic13—44no—
285C22⋊Dic13—44no—
286C4⋊Dic13—28no—
287C4⋊Dic13—44no—
288C4⋊Dic13—44no—
289#6101—28no—
290#6101—44no—
291#6101—44no—
292#6101C22⋊C4116yescomplemented
293C4×Dic13—44no—
294C4×Dic13—44no—
295C22×C22⋊Q8—131no—
296C2×#391—131no—
297C2×#389—131no—
298C2×#387—131no—
299C2×#380—131no—
300#1446—131no—
301#1441—131no—
302#1441—131no—
303#1441—131no—
304#1439—131no—
305#1439—131no—
306#1437—131no—
307#1437—131no—
308#1436—131no—
309C22⋊#95D1311yescharacteristic
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—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
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×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13C4×Q814yes—
345C23×C13C23×C411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×Q811yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
354C23×C13H(5,𝔽2)11yescharacteristic
355C23×C13H(5,𝔽2)11yescharacteristic
356C23×C132−1+411yescharacteristic
357C23×C132−1+411yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
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—22no—
377C2×C4×C13—22no—
378C2×C4×C13—416no—
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×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13C2×C22⋊C414yes—
402C2×C4×C13C4×D414yes—
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—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
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—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13C2×C22⋊C414yes—
458C2×Dic13C2×C22⋊C414yes—
459Dic26—416no—
460C23×Q8—131no—
461C24×C4C2×D1311yescharacteristic
462C2×C22⋊Q8—138no—
463C2×C22⋊Q8—264no—
464C2×C22⋊Q8—264no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4—131no—
470C22×C4⋊C4—131no—
471C22×C4⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4—131no—
474C22×C22⋊C4—131no—
475C22×C22⋊C4—131no—
476C22×C22⋊C4C2×D1311yescharacteristic
477C22×C22⋊C4C2×D1311yescharacteristic
478C22×C42—131no—
479C22×C42—131no—
480#391—264no—
481#389—264no—
482#387—264no—
483#380—264no—
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×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95C2×D1311yescharacteristic
499C2×#95C2×D1311yescharacteristic
500C2×#95C2×D1311yescharacteristic
501C2×#95C2×D1311yescharacteristic
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13C22×C22⋊C411yescharacteristic
518C22×C13C2×C4×D411yescharacteristic
519C22×C13C2×C4×Q811yescharacteristic
520C22×C13#51811yescharacteristic
521C22×C13#51911yescharacteristic
522C22×C13#52011yescharacteristic
523C22×C13#52011yescharacteristic
524C22×C13#53511yescharacteristic
525C22×C13#53611yescharacteristic
526C22×C13#53611yescharacteristic
527C22×C13#53711yescharacteristic
528C22×C13#53711yescharacteristic
529C22×C13#53711yescharacteristic
530C22×C13#53811yescharacteristic
531C22×C13#53911yescharacteristic
532C22×C13#54111yescharacteristic
533C22×C13#54211yescharacteristic
534C22×C13#54311yescharacteristic
535C22×C13#54411yescharacteristic
536C22×C13D4211yescharacteristic
537C22×C13D4211yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54611yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13D4×Q811yescharacteristic
544C22×C13D4×Q811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13#55211yescharacteristic
547C22×C13#55411yescharacteristic
548C22×C13#56211yescharacteristic
549C22×C13#56211yescharacteristic
550C22×C13#56311yescharacteristic
551C22×C13#56311yescharacteristic
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—81no—
557C4×C13—81no—
558Dic13—24no—
559Dic13—24no—
560Dic13—42no—
561Dic13—42no—
562Dic13—42no—
563Dic13—42no—
564Dic13—81no—
565Dic13—81no—
566C25C22×D1311yescharacteristic
567C22×Q8—134no—
568C22×Q8—262no—
569C22×Q8—262no—
570C22×Q8—262no—
571C22×Q8—262no—
572C22×Q8—521no—
573C22×Q8—521no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4—131no—
581C23×C4—131no—
582C23×C4—131no—
583C23×C4—131no—
584C23×C4—131no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—131no—
588C23×C4C4×D1314yes—
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C22⋊Q8—2632no—
596C2×C4⋊C4—134no—
597C2×C4⋊C4—134no—
598C2×C4⋊C4—134no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—134no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—262no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—262no—
609C2×C4⋊C4—262no—
610C2×C4⋊C4—262no—
611C2×C4⋊C4—262no—
612C2×C4⋊C4—521no—
613C2×C4⋊C4—521no—
614C2×C4⋊C4—521no—
615C2×C4⋊C4—521no—
616C2×C4⋊C4—521no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—134no—
623C2×C22⋊C4—134no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—262no—
628C2×C22⋊C4—262no—
629C2×C22⋊C4—262no—
630C2×C22⋊C4—262no—
631C2×C22⋊C4—262no—
632C2×C22⋊C4—521no—
633C2×C22⋊C4—521no—
634C2×C22⋊C4Dic2614yescomplemented
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638C2×C42—521no—
639C2×C42—521no—
640C2×C42—521no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—134no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—521no—
654#95—521no—
655#95—521no—
656#95—521no—
657#95—521no—
658#95—521no—
659C2×C13—44no—
660C2×C13#231111yescharacteristic
661C2×C13#232311yescharacteristic
662C2×C13#232911yescharacteristic
663C2×C13D4×C22⋊C411yescharacteristic
664C2×C13Q8×C22⋊C411yescharacteristic
665C2×C13#236011yescharacteristic
666C2×C13#237811yescharacteristic
667C2×C13#267611yescharacteristic
668C2×C13#267711yescharacteristic
669C2×C13#268111yescharacteristic
670C2×C13#268311yescharacteristic
671C2×C13#269011yescharacteristic
672C2×C13#269211yescharacteristic
673C2×C13#270211yescharacteristic
674C2×C13#270411yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×Dic2612yes—
688C24C2×C4×D1312yes—
689C24#612712yes—
690C24C23×D1311yescharacteristic
691C2×Q8—268no—
692C2×Q8—268no—
693C2×Q8—524no—
694C2×Q8—524no—
695C2×Q8—524no—
696C2×Q8—524no—
697C2×Q8—524no—
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—28no—
719C22×C4—28no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—132no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—132no—
743C22×C4—132no—
744C22×C4—132no—
745C22×C4—132no—
746C22×C4—132no—
747C22×C4—132no—
748C22×C4—132no—
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—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4C2×Dic2612yes—
796C22×C4C2×Dic2612yes—
797C22×C4C2×C4×D1312yes—
798C22×C4C2×C4×D1312yes—
799C22×C4D4×D1312yes—
800C22×C4D4×D1312yes—
801C22×C4D4×D1312yes—
802C22×C4#612912yes—
803C4⋊C4—1316no—
804C4⋊C4—268no—
805C4⋊C4—268no—
806C4⋊C4—524no—
807C4⋊C4—524no—
808C4⋊C4—524no—
809C4⋊C4—524no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—268no—
813C22⋊C4—268no—
814C22⋊C4—524no—
815C22⋊C4—524no—
816C42—524no—
817C42—524no—
818C13#1436211yescharacteristic, complemented, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23C4×Dic2614yes—
854C23C22×Dic2611yescharacteristic
855C23C22×C4×D1311yescharacteristic
856C23C2×#612711yescharacteristic
857C23C2×D4×D1311yescharacteristic
858C23C2×D4×D1311yescharacteristic
859C23C2×D4×D1311yescharacteristic
860C23C2×#612911yescharacteristic
861C23#8825111yescharacteristic
862C23#8825111yescharacteristic
863C23#8825111yescharacteristic
864C23#8825411yescharacteristic
865C23#8825611yescharacteristic
866C23#8825711yescharacteristic
867C23#8825711yescharacteristic
868C23#8825711yescharacteristic
869Q8—5216no—
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—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—416no—
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—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—134no—
912C2×C4—134no—
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—262no—
936C2×C4—262no—
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—521no—
957C2×C4—521no—
958C2×C4—521no—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4C22⋊C4×D1314yes—
968C2×C4#8813514yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×C4×Dic2611yescharacteristic
985C22#1171918811yescharacteristic
986C22C2×C22⋊C4×D1311yescharacteristic
987C22C2×#8813511yescharacteristic
988C22#1171919111yescharacteristic
989C22#1171919911yescharacteristic
990C22#1171920511yescharacteristic
991C22#1171920911yescharacteristic
992C22#1171922011yescharacteristic
993C22#1171922111yescharacteristic
994C22#1171922811yescharacteristic
995C22D4×Dic2611yescharacteristic
996C22D4×Dic2611yescharacteristic
997C22D4×Dic2611yescharacteristic
998C22#1171924611yescharacteristic
999C22#1171924811yescharacteristic
1000C22#1171925511yescharacteristic
1001C22#1171925711yescharacteristic
1002C22#1171925711yescharacteristic
1003C22#1171929511yescharacteristic
1004C22#1171929511yescharacteristic
1005C22#1171929611yescharacteristic
1006C22#1171929611yescharacteristic
1007C22#1171930811yescharacteristic
1008C22#1171931211yescharacteristic
1009C22#1171931311yescharacteristic
1010C22#1171931311yescharacteristic
1011C22#1171933011yescharacteristic
1012C22#1171933311yescharacteristic
1013C22#1171933311yescharacteristic
1014C22#1171933411yescharacteristic
1015C22#1171935611yescharacteristic
1016C22#1171935611yescharacteristic
1017C22#1171937211yescharacteristic
1018C22#1171937211yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C4—264no—
1026C4—264no—
1027C4—522no—
1028C4—522no—
1029C4—522no—
1030C4—522no—
1031C4—1041no—
1032C4—1041no—
1033C2—44no—
1034C2#1311742511yescharacteristic
1035C2#1311751411yescharacteristic
1036C2#1311756911yescharacteristic
1037C2#1311765211yescharacteristic
1038C2C22⋊C4×Dic2611yescharacteristic
1039C2#1311783911yescharacteristic
1040C2#1311800411yescharacteristic
1041C2#1312114111yescharacteristic
1042C2#1312115111yescharacteristic
1043C2#1312118911yescharacteristic
1044C2#1312120911yescharacteristic
1045C2#1312130611yescharacteristic
1046C2#1312133611yescharacteristic
1047C2#1312146811yescharacteristic
1048C2#1312149811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14362
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
3. C2×#11718308C2semidirect
4. C2×#11718316C2semidirect
6. #13113106C2semidirect
7. #13113090C2semidirect
8. #13113090C2semidirect
9. #13113088C2semidirect
14. #13113070C2semidirect
29. C2×#88178C4semidirect
92. C2×C13×C22⋊C4Q8semidirect
292. #6101C22⋊C4semidirect
634. C2×C22⋊C4Dic26semidirect
818. C13#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#881782
C2×#117183072
C2×#117183082
C2×#117183162
C2×#117188732
#131131062
#131130902
#131130882
#131130792
#131130732
#131130702
C13×C22⋊#952
#1436213