Finite Group Databasebeta

← #16791595

Subgroups — #16791595

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719071C211yesmaximal, characteristic
2C2×#11719070C211yesmaximal, characteristic
3C2×C4×C4⋊#261C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×#261C211yesmaximal, characteristic
5#13130017C211yesmaximal, characteristic
6#13130017C211yesmaximal, characteristic
7#13130016C211yesmaximal, characteristic, complemented
8#13130016C211yesmaximal, characteristic, complemented
9#13130016C211yesmaximal, characteristic, complemented
10#13130015C211yesmaximal, characteristic, complemented
11#13130013C211yesmaximal, characteristic, complemented
12#13130012C211yesmaximal, characteristic, complemented
13#13130009C211yesmaximal, characteristic
14#95×#261C211yesmaximal, characteristic, complemented
15D13×#388C211yesmaximal, characteristic
16C24×#261C2211yescharacteristic
17C22×C22⋊#261C2211yescharacteristic
18C22×C22⋊#261C2211yescharacteristic
19C22×C22⋊#261C2211yescharacteristic
20C22×C4⋊#261C2211yescharacteristic
21C22×C4⋊#261C2211yescharacteristic
22C22×C4⋊#261C2211yescharacteristic
23C22×C4×#261C2211yescharacteristic
24C22×C4×#261C2211yescharacteristic
25C22×C4×#261C2211yescharacteristic
26C22×C4×#261C2211yescharacteristic
27C22×C4×#261C2211yescharacteristic
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×C22⋊C4×D13C2211yescharacteristic
30C2×C22⋊C4×D13C2211yescharacteristic
31C2×C22⋊C4×D13C2211yescharacteristic
32C2×C42×D13C2211yescharacteristic
33C2×(C2×#261)⋊C4C2211yescharacteristic
34C2×(C2×#261)⋊C4C2211yescharacteristic
35C2×(C2×#261)⋊C4C2211yescharacteristic
36C2×(C2×#261)⋊C4C2211yescharacteristic
37C2×(C2×#261)⋊C4C2211yescharacteristic
38C2×(C2×#261)⋊C4C2211yescharacteristic
39C2×(C2×#261)⋊C4C2211yescharacteristic
40C2×(C2×#261)⋊C4C2211yescharacteristic
41C2×(C2×#261)⋊C4C2211yescharacteristic
42C2×(C2×#261)⋊C4C2211yescharacteristic
43C2×(C2×#261)⋊C4C2211yescharacteristic
44C2×(C2×#261)⋊C4C2211yescharacteristic
45C2×(C2×#261)⋊C4C2211yescharacteristic
46C2×(C2×#261)⋊C4C2211yescharacteristic
47C2×(C2×#261)⋊C4C2211yescharacteristic
48C2×(C2×#261)⋊C4C2211yescharacteristic
49#11719071C418yescomplemented
50#11719070C418yescomplemented
51C22⋊C4×#261—24no—
52C4×C4⋊#261—24no—
53C13×#388C411yescharacteristic, complemented
54#11718651C411yescharacteristic, complemented
55#11718612C411yescharacteristic, complemented
56#11718606C411yescharacteristic, complemented
57#11718605C411yescharacteristic, complemented
58#11718601C411yescharacteristic, complemented
59#11718331C411yescharacteristic, complemented
60#11718330C411yescharacteristic, complemented
61D13×#95C2211yescharacteristic
62D13×#95C2211yescharacteristic
63C24×D13C2311yescharacteristic
64C23×#261—22no—
65C23×#261—22no—
66C23×#261—41no—
67C23×#261—41no—
68C23×#261—41no—
69C23×#261—41no—
70C23×#261C2×C414yes—
71C23×#261C2311yescharacteristic
72C23×#261C2311yescharacteristic
73C23×#261C2311yescharacteristic
74C23×#261C2311yescharacteristic
75C23×#261C2311yescharacteristic
76C23×#261C2311yescharacteristic
77C23×#261C2311yescharacteristic
78C23×#261C2311yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C22×C4×D13C2311yescharacteristic
81C22×C4×D13C2311yescharacteristic
82C22×C4×D13C2311yescharacteristic
83C22×C4×D13C2311yescharacteristic
84C22×C4×D13C2311yescharacteristic
85C2×C22⋊#261—22no—
86C2×C22⋊#261—22no—
87C2×C22⋊#261—41no—
88C2×C22⋊#261—41no—
89C2×C22⋊#261—41no—
90C2×C22⋊#261—41no—
91C2×C22⋊#261C2×C414yes—
92C2×C22⋊#261C2×C414yes—
93C2×C22⋊#261C2×C414yes—
94C2×C4⋊#261—22no—
95C2×C4⋊#261—22no—
96C2×C4⋊#261—22no—
97C2×C4⋊#261—22no—
98C2×C4⋊#261—41no—
99C2×C4⋊#261—41no—
100C2×C4⋊#261C2×C414yes—
101C2×C4⋊#261C2×C414yes—
102C2×C4⋊#261C2×C414yescomplemented
103C2×C4×#261—22no—
104C2×C4×#261—22no—
105C2×C4×#261—22no—
106C2×C4×#261—41no—
107C2×C4×#261—41no—
108C2×C4×#261—41no—
109C2×C4×#261—41no—
110C2×C4×#261—41no—
111C2×C4×#261—41no—
112C2×C4×#261—41no—
113C2×C4×#261—41no—
114C2×C4×#261—41no—
115C2×C4×#261—41no—
116C2×C4×#261C2×C414yescomplemented
117C2×C4×#261D414yes—
118C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
119C2×C13×C22⋊C4C2×C411yescharacteristic
120C2×C13×C22⋊C4C2×C411yescharacteristic
121C2×C13×C22⋊C4C2×C411yescharacteristic
122C2×C42×C13C2×C411yescharacteristic, complemented
123C2×C22⋊Dic13C2×C411yescharacteristic
124C2×C22⋊Dic13C2×C411yescharacteristic
125C2×C22⋊Dic13C2×C411yescharacteristic
126C2×#6103C2×C411yescharacteristic
127C2×#6103C2×C411yescharacteristic
128C2×#6103C2×C411yescharacteristic
129C2×#6103C2×C411yescharacteristic
130C2×#6103C2×C411yescharacteristic
131C2×#6103C2×C411yescharacteristic
132C2×C4⋊Dic13C2×C411yescharacteristic, complemented
133C2×#6101C2×C411yescharacteristic, complemented
134C2×#6101C2×C411yescharacteristic, complemented
135C2×C4×Dic13C2×C411yescharacteristic, complemented
136C2×C4×Dic13C2×C411yescharacteristic, complemented
137C2×C4×Dic13C2×C411yescharacteristic, complemented
138C4⋊C4×D13—41no—
139C4⋊C4×D13—41no—
140C22⋊C4×D13—22no—
141C22⋊C4×D13—22no—
142C22⋊C4×D13—41no—
143C22⋊C4×D13—41no—
144C22⋊C4×D13C2×C414yes—
145C22⋊C4×D13C2×C414yes—
146C42×D13—22no—
147C42×D13—22no—
148(C2×#261)⋊C4—22no—
149(C2×#261)⋊C4—22no—
150(C2×#261)⋊C4—22no—
151(C2×#261)⋊C4—22no—
152(C2×#261)⋊C4—22no—
153(C2×#261)⋊C4—22no—
154(C2×#261)⋊C4—41no—
155(C2×#261)⋊C4—41no—
156(C2×#261)⋊C4—41no—
157(C2×#261)⋊C4—41no—
158(C2×#261)⋊C4—41no—
159(C2×#261)⋊C4—41no—
160(C2×#261)⋊C4C2×C414yes—
161(C2×#261)⋊C4C2×C414yes—
162(C2×#261)⋊C4C2×C414yescomplemented
163(C2×#261)⋊C4C2×C414yescomplemented
164C13×#95C2×C411yescharacteristic, complemented
165C13×#95C2×C411yescharacteristic, complemented
166#88071C2×C411yescharacteristic, complemented
167#88071C2×C411yescharacteristic, complemented
168#88071C2×C411yescharacteristic, complemented
169#88071C2×C411yescharacteristic, complemented
170#88071C2×C411yescharacteristic, complemented
171#88071C2×C411yescharacteristic, complemented
172#13789—131nomaximal, Sylow
173C24×C13C22×C411yescharacteristic
174C23×D13—21no—
175C23×D13—21no—
176C23×D13—21no—
177C23×D13—21no—
178C23×D13—21no—
179C23×D13—21no—
180C23×D13—21no—
181C23×D13—21no—
182C23×D13—21no—
183C23×D13—21no—
184C23×D13—21no—
185C23×D13—21no—
186C23×D13C22×C411yescharacteristic
187C23×D13C22×C412yes—
188C23×D13C22×C412yes—
189C23×D13C2411yescharacteristic
190C22×#261—21no—
191C22×#261—21no—
192C22×#261—21no—
193C22×#261—21no—
194C22×#261—21no—
195C22×#261—21no—
196C22×#261—21no—
197C22×#261—21no—
198C22×#261—21no—
199C22×#261—21no—
200C22×#261—21no—
201C22×#261—21no—
202C22×#261—21no—
203C22×#261—21no—
204C22×#261—21no—
205C22×#261—21no—
206C22×#261—21no—
207C22×#261—21no—
208C22×#261—21no—
209C22×#261—21no—
210C22×#261—21no—
211C22×#261—21no—
212C22×#261—21no—
213C22×#261—21no—
214C22×#261—21no—
215C22×#261—21no—
216C22×#261—21no—
217C22×#261—21no—
218C22×#261—21no—
219C22×#261—21no—
220C22×#261—21no—
221C22×#261—21no—
222C22×#261—21no—
223C22×#261—21no—
224C22×#261—21no—
225C22×#261—21no—
226C22×#261—21no—
227C22×#261—21no—
228C22×#261—21no—
229C22×#261—21no—
230C22×#261—21no—
231C22×#261—21no—
232C22×#261—21no—
233C22×#261—21no—
234C22×#261—28no—
235C22×#261—44no—
236C22×#261—44no—
237C22×#261—44no—
238C22×#261—44no—
239C22×#261—44no—
240C22×#261—44no—
241C22×#261C22×C412yes—
242C22×#261C22×C412yes—
243C22×#261C22×C412yes—
244C22×#261C22×C412yes—
245C22×#261C22×C412yes—
246C22×#261C22×C412yes—
247C22×#261C22×C412yes—
248C22×#261C22×C412yes—
249C22×#261C2×D412yes—
250C22×#261C2×D412yes—
251C22×#261#4112yes—
252C22×#261#4112yes—
253C22×C4×C13C22×C411yescharacteristic
254C22×C4×C13C22×C411yescharacteristic
255C22×C4×C13C22×C411yescharacteristic
256C22×C4×C13C22×C411yescharacteristic
257C22×C4×C13C22×C411yescharacteristic
258C22×C4×C13C22×C411yescharacteristic
259C22×Dic13C22×C411yescharacteristic
260C22×Dic13C22×C411yescharacteristic
261C22×Dic13C22×C411yescharacteristic
262C22×Dic13C22×C411yescharacteristic
263C22×Dic13C22×C411yescharacteristic
264C22×Dic13C22×C411yescharacteristic
265C2×C4×D13—21no—
266C2×C4×D13—21no—
267C2×C4×D13—21no—
268C2×C4×D13—21no—
269C2×C4×D13—21no—
270C2×C4×D13—21no—
271C2×C4×D13—21no—
272C2×C4×D13—21no—
273C2×C4×D13—21no—
274C2×C4×D13—21no—
275C2×C4×D13—21no—
276C2×C4×D13—21no—
277C2×C4×D13—21no—
278C2×C4×D13—21no—
279C2×C4×D13—21no—
280C2×C4×D13—21no—
281C2×C4×D13—21no—
282C2×C4×D13—21no—
283C2×C4×D13—21no—
284C2×C4×D13—21no—
285C2×C4×D13—21no—
286C2×C4×D13—21no—
287C2×C4×D13—21no—
288C2×C4×D13—21no—
289C2×C4×D13—21no—
290C2×C4×D13—21no—
291C2×C4×D13—21no—
292C2×C4×D13—21no—
293C2×C4×D13—21no—
294C2×C4×D13—21no—
295C2×C4×D13C22×C412yes—
296C2×C4×D13C22×C412yes—
297C2×C4×D13C22×C412yes—
298C2×C4×D13C22×C412yes—
299C2×C4×D13C2×D412yes—
300C2×C4×D13#4112yes—
301C22⋊#261—28no—
302C22⋊#261—44no—
303C22⋊#261—44no—
304C4⋊#261—28no—
305C4⋊#261—28no—
306C4⋊#261—44no—
307C4×#261—44no—
308C4×#261—44no—
309C4×#261—44no—
310C4×#261—44no—
311C4×#261—44no—
312C13×C4⋊C4—41no—
313C13×C22⋊C4—22no—
314C13×C22⋊C4—41no—
315C13×C22⋊C4C4214yescomplemented
316C42×C13—22no—
317C22⋊Dic13—22no—
318C22⋊Dic13—41no—
319C22⋊Dic13C4214yescomplemented
320#6103—22no—
321#6103—22no—
322#6103—41no—
323#6103—41no—
324#6103C4214yescomplemented
325#6103C4214yescomplemented
326C4⋊Dic13—41no—
327#6101—41no—
328#6101—41no—
329C4×Dic13—22no—
330C4×Dic13—22no—
331C4×Dic13—22no—
332C2×#388—131no—
333C2×#388—131no—
334C2×#385—131no—
335C2×C4×C4⋊C4—131no—
336C2×C4×C22⋊C4—131no—
337#1437—131no—
338#1437—131no—
339#1436—131no—
340#1436—131no—
341#1436—131no—
342#1436—131no—
343C4⋊#95—131no—
344#1434—131no—
345C22⋊#95—131no—
346C4×#95—131no—
347C23×C13—21no—
348C23×C13—21no—
349C23×C13—21no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—21no—
353C23×C13C2×C4212yes—
354C23×C13C23×C411yescharacteristic
355C22×D13—21no—
356C22×D13—21no—
357C22×D13—21no—
358C22×D13—21no—
359C22×D13—21no—
360C22×D13—21no—
361C22×D13—22no—
362C22×D13—22no—
363C22×D13—22no—
364C22×D13—22no—
365C22×D13—22no—
366C22×D13—22no—
367C22×D13—22no—
368C22×D13—22no—
369C22×D13—22no—
370C22×D13—22no—
371C22×D13—22no—
372C22×D13—22no—
373C22×D13—41no—
374C22×D13—41no—
375C22×D13—41no—
376C22×D13—41no—
377C22×D13—41no—
378C22×D13—41no—
379C22×D13—41no—
380C22×D13—41no—
381C22×D13—41no—
382C22×D13—41no—
383C22×D13—41no—
384C22×D13—41no—
385C22×D13—41no—
386C22×D13—41no—
387C22×D13—41no—
388C22×D13—41no—
389C22×D13C2×C4212yes—
390C22×D13C23×C411yescharacteristic
391C22×D13C23×C411yescharacteristic
392C22×D13C22×D411yescharacteristic
393C22×D13C2×#4111yescharacteristic
394C22×D13C2×#4111yescharacteristic
395C22×D13C2×#4111yescharacteristic
396C22×D13H(5,𝔽2)11yescharacteristic
397C22×D13H(5,𝔽2)11yescharacteristic
398C22×D13H(5,𝔽2)11yescharacteristic
399C22×D13H(5,𝔽2)11yescharacteristic
400C22×D13H(5,𝔽2)11yescharacteristic
401C22×D132−1+411yescharacteristic
402C22×D132−1+411yescharacteristic
403C22×D132−1+411yescharacteristic
404C2×#261—22no—
405C2×#261—22no—
406C2×#261—22no—
407C2×#261—22no—
408C2×#261—22no—
409C2×#261—22no—
410C2×#261—22no—
411C2×#261—22no—
412C2×#261—22no—
413C2×#261—22no—
414C2×#261—22no—
415C2×#261—22no—
416C2×#261—22no—
417C2×#261—22no—
418C2×#261—22no—
419C2×#261—22no—
420C2×#261—22no—
421C2×#261—22no—
422C2×#261—22no—
423C2×#261—22no—
424C2×#261—22no—
425C2×#261—22no—
426C2×#261—22no—
427C2×#261—22no—
428C2×#261—22no—
429C2×#261—22no—
430C2×#261—22no—
431C2×#261—22no—
432C2×#261—22no—
433C2×#261—22no—
434C2×#261—416no—
435C2×#261—41no—
436C2×#261—41no—
437C2×#261—41no—
438C2×#261—41no—
439C2×#261—41no—
440C2×#261—41no—
441C2×#261—41no—
442C2×#261—41no—
443C2×#261—41no—
444C2×#261—41no—
445C2×#261—41no—
446C2×#261—41no—
447C2×#261—41no—
448C2×#261—41no—
449C2×#261—41no—
450C2×#261—41no—
451C2×#261—41no—
452C2×#261—41no—
453C2×#261—41no—
454C2×#261—41no—
455C2×#261—41no—
456C2×#261—41no—
457C2×#261—41no—
458C2×#261—41no—
459C2×#261C4×D414yes—
460C2×#261C4×D414yes—
461C2×C4×C13—21no—
462C2×C4×C13—21no—
463C2×C4×C13—21no—
464C2×C4×C13—21no—
465C2×C4×C13—21no—
466C2×C4×C13—21no—
467C2×C4×C13—21no—
468C2×C4×C13—21no—
469C2×C4×C13—21no—
470C2×C4×C13—21no—
471C2×C4×C13—21no—
472C2×C4×C13—21no—
473C2×C4×C13—21no—
474C2×C4×C13—21no—
475C2×C4×C13—21no—
476C2×C4×C13C2×C4212yes—
477C2×C4×C13C2×C4212yes—
478C2×C4×C13C4×D412yes—
479C2×Dic13—21no—
480C2×Dic13—21no—
481C2×Dic13—21no—
482C2×Dic13—21no—
483C2×Dic13—21no—
484C2×Dic13—21no—
485C2×Dic13—21no—
486C2×Dic13—21no—
487C2×Dic13—21no—
488C2×Dic13—21no—
489C2×Dic13—21no—
490C2×Dic13—21no—
491C2×Dic13—21no—
492C2×Dic13—21no—
493C2×Dic13—21no—
494C2×Dic13C2×C4212yes—
495C2×Dic13C2×C4212yes—
496C2×Dic13C4×D412yes—
497C4×D13—22no—
498C4×D13—22no—
499C4×D13—22no—
500C4×D13—22no—
501C4×D13—22no—
502C4×D13—22no—
503C4×D13—22no—
504C4×D13—22no—
505C4×D13—22no—
506C4×D13—22no—
507C4×D13—22no—
508C4×D13—22no—
509C4×D13—41no—
510C4×D13—41no—
511C4×D13—41no—
512C4×D13—41no—
513C4×D13—41no—
514C4×D13—41no—
515C4×D13—41no—
516C4×D13—41no—
517C4×D13—41no—
518C4×D13—41no—
519C4×D13—41no—
520C4×D13—41no—
521C24×C4—131no—
522C22×C4⋊C4—131no—
523C22×C4⋊C4—131no—
524C22×C4⋊C4—131no—
525C22×C4⋊C4—131no—
526C22×C22⋊C4—131no—
527C22×C22⋊C4—131no—
528C22×C22⋊C4—131no—
529C22×C22⋊C4—131no—
530C22×C22⋊C4—131no—
531C22×C22⋊C4—131no—
532C22×C42—131no—
533C22×C42—131no—
534C22×C42—131no—
535C22×C42—131no—
536C22×C42—131no—
537C22×C42—131no—
538#388—138no—
539#388—131no—
540#388—131no—
541#388—131no—
542#388—131no—
543#388—131no—
544#388—131no—
545#388—131no—
546#388#26111yescharacteristic, complemented
547#385—138no—
548C4×C4⋊C4—264no—
549C4×C22⋊C4—264no—
550C2×#95—131no—
551C2×#95—131no—
552C2×#95—131no—
553C2×#95—131no—
554C2×#95—131no—
555C2×#95—131no—
556C2×#95—131no—
557C2×#95—131no—
558C2×#95—131no—
559C2×#95—131no—
560C2×#95—131no—
561C2×#95—131no—
562C2×#95—131no—
563C2×#95—131no—
564C2×#95—131no—
565C2×#95—131no—
566C2×#95—131no—
567C2×#95—131no—
568C22×C13—22no—
569C22×C13—22no—
570C22×C13—22no—
571C22×C13—41no—
572C22×C13—41no—
573C22×C13—41no—
574C22×C13—41no—
575C22×C13C22×C4211yescharacteristic
576C22×C13C2×C4×D411yescharacteristic
577C22×C13C4×#4111yescharacteristic
578C22×C13#51811yescharacteristic
579C22×C13#52011yescharacteristic
580C22×C13#52011yescharacteristic
581C22×C13#52011yescharacteristic
582C2×D13—22no—
583C2×D13—22no—
584C2×D13—22no—
585C2×D13—41no—
586C2×D13—41no—
587C2×D13—41no—
588C2×D13—41no—
589C2×D13—42no—
590C2×D13—42no—
591C2×D13—42no—
592C2×D13—42no—
593C2×D13—42no—
594C2×D13—42no—
595C2×D13—42no—
596C2×D13—42no—
597C2×D13C2×C4×D411yescharacteristic
598C2×D13C2×C4×D411yescharacteristic
599C2×D13C4×#4111yescharacteristic
600C2×D13C4×#4111yescharacteristic
601C2×D13#51811yescharacteristic
602C2×D13#51811yescharacteristic
603C2×D13#51811yescharacteristic
604C2×D13#51911yescharacteristic
605C2×D13#52011yescharacteristic
606C2×D13#52011yescharacteristic
607C2×D13#52011yescharacteristic
608C2×D13#52011yescharacteristic
609C2×D13#53411yescharacteristic
610C2×D13#53511yescharacteristic
611C2×D13#53611yescharacteristic
612C2×D13#53711yescharacteristic
613C2×D13#53811yescharacteristic
614C2×D13#53811yescharacteristic
615C2×D13#53811yescharacteristic
616C2×D13#53911yescharacteristic
617C2×D13#53911yescharacteristic
618C2×D13#53911yescharacteristic
619C2×D13#54011yescharacteristic
620C2×D13#54111yescharacteristic
621C2×D13#54211yescharacteristic
622C2×D13#54211yescharacteristic
623C2×D13#54211yescharacteristic
624C2×D13#54211yescharacteristic
625#261—24no—
626#261—24no—
627#261—42no—
628#261—42no—
629#261—42no—
630#261—42no—
631#261—42no—
632#261—42no—
633C4×C13—22no—
634C4×C13—22no—
635C4×C13—22no—
636C4×C13—41no—
637C4×C13—41no—
638C4×C13—41no—
639Dic13—22no—
640Dic13—22no—
641Dic13—22no—
642Dic13—41no—
643Dic13—41no—
644Dic13—41no—
645C25—131no—
646C23×C4—131no—
647C23×C4—131no—
648C23×C4—131no—
649C23×C4—131no—
650C23×C4—131no—
651C23×C4—131no—
652C23×C4—131no—
653C23×C4—131no—
654C23×C4—131no—
655C23×C4—131no—
656C23×C4—131no—
657C23×C4—134no—
658C23×C4—131no—
659C23×C4—131no—
660C23×C4—131no—
661C23×C4—262no—
662C23×C4—262no—
663C23×C4—521no—
664C23×C4—521no—
665C23×C4—521no—
666C23×C4—521no—
667C2×C4⋊C4—134no—
668C2×C4⋊C4—134no—
669C2×C4⋊C4—134no—
670C2×C4⋊C4—131no—
671C2×C4⋊C4—131no—
672C2×C4⋊C4—131no—
673C2×C4⋊C4—262no—
674C2×C4⋊C4—262no—
675C2×C4⋊C4—262no—
676C2×C4⋊C4—262no—
677C2×C4⋊C4—521no—
678C2×C4⋊C4—521no—
679C2×C4⋊C4—521no—
680C2×C4⋊C4—521no—
681C2×C4⋊C4C2×#26111yescharacteristic, complemented
682C2×C22⋊C4—131no—
683C2×C22⋊C4—131no—
684C2×C22⋊C4—131no—
685C2×C22⋊C4—134no—
686C2×C22⋊C4—134no—
687C2×C22⋊C4—134no—
688C2×C22⋊C4—131no—
689C2×C22⋊C4—131no—
690C2×C22⋊C4—131no—
691C2×C22⋊C4—134no—
692C2×C22⋊C4—134no—
693C2×C22⋊C4—131no—
694C2×C22⋊C4—131no—
695C2×C22⋊C4—131no—
696C2×C22⋊C4—262no—
697C2×C22⋊C4—262no—
698C2×C22⋊C4—262no—
699C2×C22⋊C4—262no—
700C2×C22⋊C4—521no—
701C2×C22⋊C4—521no—
702C2×C22⋊C4—521no—
703C2×C22⋊C4—521no—
704C2×C22⋊C4—521no—
705C2×C22⋊C4—521no—
706C2×C22⋊C4C2×#26111yescharacteristic
707C2×C22⋊C4C2×#26111yescharacteristic
708C2×C22⋊C4C2×#26111yescharacteristic
709C2×C42—131no—
710C2×C42—131no—
711C2×C42—131no—
712C2×C42—134no—
713C2×C42—134no—
714C2×C42—262no—
715C2×C42—262no—
716C2×C42—262no—
717C2×C42—262no—
718C2×C42—262no—
719C2×C42—521no—
720C2×C42—521no—
721C2×C42—521no—
722C2×C42—521no—
723C2×C42—521no—
724C2×C42—521no—
725C2×C42—521no—
726C2×C42—521no—
727C2×C42—521no—
728C2×C42—521no—
729C2×C42C2×#26111yescharacteristic, complemented
730#95—134no—
731#95—134no—
732#95—134no—
733#95—134no—
734#95—131no—
735#95—131no—
736#95—131no—
737#95—131no—
738#95—131no—
739#95—131no—
740#95—262no—
741#95—262no—
742#95—262no—
743#95—262no—
744#95—262no—
745#95—262no—
746#95—521no—
747#95—521no—
748#95—521no—
749#95—521no—
750#95—521no—
751#95—521no—
752#95C2×#26111yescharacteristic, complemented
753#95C2×#26111yescharacteristic, complemented
754C2×C13—42no—
755C2×C13C42×D411yescharacteristic
756C2×C13#227411yescharacteristic
757C2×C13#227511yescharacteristic
758C2×C13#232211yescharacteristic
759C2×C13#232411yescharacteristic
760C2×C13#233411yescharacteristic
761C2×C13#233711yescharacteristic
762D13—42no—
763D13#232111yescharacteristic
764D13#232311yescharacteristic
765D13#232511yescharacteristic
766D13#232611yescharacteristic
767D13#233211yescharacteristic
768D13#233411yescharacteristic
769D13#233511yescharacteristic
770D13#233511yescharacteristic
771C24—131no—
772C24—132no—
773C24—132no—
774C24—131no—
775C24—261no—
776C24—261no—
777C24—261no—
778C24—261no—
779C24—261no—
780C24—261no—
781C24—261no—
782C24—261no—
783C24—261no—
784C24—261no—
785C24—261no—
786C24—261no—
787C24C22×#26111yescharacteristic
788C22×C4—132no—
789C22×C4—132no—
790C22×C4—132no—
791C22×C4—132no—
792C22×C4—132no—
793C22×C4—132no—
794C22×C4—131no—
795C22×C4—131no—
796C22×C4—131no—
797C22×C4—132no—
798C22×C4—132no—
799C22×C4—132no—
800C22×C4—132no—
801C22×C4—132no—
802C22×C4—132no—
803C22×C4—132no—
804C22×C4—132no—
805C22×C4—132no—
806C22×C4—132no—
807C22×C4—132no—
808C22×C4—132no—
809C22×C4—131no—
810C22×C4—131no—
811C22×C4—131no—
812C22×C4—261no—
813C22×C4—261no—
814C22×C4—261no—
815C22×C4—261no—
816C22×C4—261no—
817C22×C4—261no—
818C22×C4—261no—
819C22×C4—261no—
820C22×C4—261no—
821C22×C4—261no—
822C22×C4—261no—
823C22×C4—261no—
824C22×C4—261no—
825C22×C4—261no—
826C22×C4—261no—
827C22×C4—261no—
828C22×C4—261no—
829C22×C4—261no—
830C22×C4—261no—
831C22×C4—261no—
832C22×C4—261no—
833C22×C4—261no—
834C22×C4—261no—
835C22×C4—261no—
836C22×C4—261no—
837C22×C4—261no—
838C22×C4—261no—
839C22×C4—261no—
840C22×C4—261no—
841C22×C4—261no—
842C22×C4—268no—
843C22×C4—261no—
844C22×C4—261no—
845C22×C4—261no—
846C22×C4—261no—
847C22×C4—261no—
848C22×C4—261no—
849C22×C4—261no—
850C22×C4—261no—
851C22×C4—261no—
852C22×C4—261no—
853C22×C4—261no—
854C22×C4—261no—
855C22×C4—261no—
856C22×C4—261no—
857C22×C4—261no—
858C22×C4—261no—
859C22×C4—261no—
860C22×C4—261no—
861C22×C4—261no—
862C22×C4—261no—
863C22×C4—261no—
864C22×C4—261no—
865C22×C4—261no—
866C22×C4—261no—
867C22×C4—261no—
868C22×C4—261no—
869C22×C4—261no—
870C22×C4—261no—
871C22×C4—261no—
872C22×C4—261no—
873C22×C4—261no—
874C22×C4—261no—
875C22×C4—261no—
876C22×C4—261no—
877C22×C4—261no—
878C22×C4—261no—
879C22×C4—261no—
880C22×C4—261no—
881C22×C4—261no—
882C22×C4—261no—
883C22×C4—261no—
884C22×C4—261no—
885C22×C4—261no—
886C22×C4—261no—
887C22×C4—524no—
888C22×C4—524no—
889C22×C4—524no—
890C22×C4—524no—
891C22×C4—524no—
892C22×C4—524no—
893C22×C4C22×#26111yescharacteristic
894C22×C4C22×#26111yescharacteristic
895C22×C4C22×#26111yescharacteristic
896C22×C4C22×#26111yescharacteristic
897C22×C4C22×#26111yescharacteristic
898C22×C4C22×#26111yescharacteristic
899C4⋊C4—41no—
900C4⋊C4—268no—
901C4⋊C4—268no—
902C4⋊C4—521no—
903C4⋊C4—521no—
904C4⋊C4—521no—
905C4⋊C4—524no—
906C22⋊C4—22no—
907C22⋊C4—41no—
908C22⋊C4—134no—
909C22⋊C4—134no—
910C22⋊C4—134no—
911C22⋊C4—262no—
912C22⋊C4—262no—
913C22⋊C4—268no—
914C22⋊C4—262no—
915C22⋊C4—521no—
916C22⋊C4—521no—
917C22⋊C4—521no—
918C22⋊C4—524no—
919C22⋊C4—524no—
920C22⋊C4C4×#26114yescomplemented
921C42—22no—
922C42—262no—
923C42—262no—
924C42—262no—
925C42—524no—
926C42—524no—
927C42—524no—
928C42—524no—
929C42—524no—
930C13#1378911yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—131no—
938C23—131no—
939C23—131no—
940C23—131no—
941C23—131no—
942C23—131no—
943C23—131no—
944C23—131no—
945C23—131no—
946C23—131no—
947C23—131no—
948C23—131no—
949C23—131no—
950C23—131no—
951C23—132no—
952C23—262no—
953C23—262no—
954C23—262no—
955C23—262no—
956C23—262no—
957C23—262no—
958C23—262no—
959C23—262no—
960C23—262no—
961C23—262no—
962C23—262no—
963C23—262no—
964C23—261no—
965C23—261no—
966C23—261no—
967C23—261no—
968C23—261no—
969C23—261no—
970C23—521no—
971C23—521no—
972C23—521no—
973C23—521no—
974C23—521no—
975C23—521no—
976C23—521no—
977C23—521no—
978C23—521no—
979C23—521no—
980C23—521no—
981C23—521no—
982C23—521no—
983C23—521no—
984C23—521no—
985C23—521no—
986C23C2×C4×#26112yes—
987C23C23×#26111yescharacteristic
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—134no—
1004C2×C4—134no—
1005C2×C4—132no—
1006C2×C4—132no—
1007C2×C4—132no—
1008C2×C4—262no—
1009C2×C4—262no—
1010C2×C4—262no—
1011C2×C4—262no—
1012C2×C4—262no—
1013C2×C4—262no—
1014C2×C4—262no—
1015C2×C4—262no—
1016C2×C4—262no—
1017C2×C4—262no—
1018C2×C4—262no—
1019C2×C4—262no—
1020C2×C4—262no—
1021C2×C4—262no—
1022C2×C4—262no—
1023C2×C4—262no—
1024C2×C4—262no—
1025C2×C4—262no—
1026C2×C4—262no—
1027C2×C4—262no—
1028C2×C4—262no—
1029C2×C4—262no—
1030C2×C4—262no—
1031C2×C4—262no—
1032C2×C4—261no—
1033C2×C4—261no—
1034C2×C4—261no—
1035C2×C4—261no—
1036C2×C4—261no—
1037C2×C4—261no—
1038C2×C4—262no—
1039C2×C4—262no—
1040C2×C4—262no—
1041C2×C4—262no—
1042C2×C4—262no—
1043C2×C4—262no—
1044C2×C4—262no—
1045C2×C4—262no—
1046C2×C4—262no—
1047C2×C4—262no—
1048C2×C4—262no—
1049C2×C4—262no—
1050C2×C4—262no—
1051C2×C4—262no—
1052C2×C4—262no—
1053C2×C4—262no—
1054C2×C4—262no—
1055C2×C4—262no—
1056C2×C4—261no—
1057C2×C4—261no—
1058C2×C4—261no—
1059C2×C4—261no—
1060C2×C4—261no—
1061C2×C4—261no—
1062C2×C4—261no—
1063C2×C4—261no—
1064C2×C4—261no—
1065C2×C4—521no—
1066C2×C4—521no—
1067C2×C4—521no—
1068C2×C4—521no—
1069C2×C4—521no—
1070C2×C4—521no—
1071C2×C4—521no—
1072C2×C4—521no—
1073C2×C4—521no—
1074C2×C4—521no—
1075C2×C4—521no—
1076C2×C4—521no—
1077C2×C4—5216no—
1078C2×C4—521no—
1079C2×C4—521no—
1080C2×C4—521no—
1081C2×C4—521no—
1082C2×C4—521no—
1083C2×C4—521no—
1084C2×C4—521no—
1085C2×C4—521no—
1086C2×C4—521no—
1087C2×C4—521no—
1088C2×C4—521no—
1089C2×C4—521no—
1090C2×C4—521no—
1091C2×C4—521no—
1092C2×C4—521no—
1093C2×C4—521no—
1094C2×C4—521no—
1095C2×C4—521no—
1096C2×C4—521no—
1097C2×C4—521no—
1098C2×C4—521no—
1099C2×C4—521no—
1100C2×C4—521no—
1101C2×C4—521no—
1102C2×C4C2×C4×#26112yes—
1103C2×C4C2×C4×#26112yes—
1104C2×C4D4×#26112yes—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—131no—
1113C22—131no—
1114C22—131no—
1115C22—131no—
1116C22—131no—
1117C22—131no—
1118C22—131no—
1119C22—131no—
1120C22—131no—
1121C22—131no—
1122C22—131no—
1123C22—131no—
1124C22—131no—
1125C22—131no—
1126C22—131no—
1127C22—131no—
1128C22—131no—
1129C22—131no—
1130C22—131no—
1131C22—131no—
1132C22—131no—
1133C22—131no—
1134C22—131no—
1135C22—131no—
1136C22—131no—
1137C22—131no—
1138C22—131no—
1139C22—131no—
1140C22—262no—
1141C22—262no—
1142C22—262no—
1143C22—522no—
1144C22—522no—
1145C22—522no—
1146C22—522no—
1147C22—522no—
1148C22—522no—
1149C22—522no—
1150C22—522no—
1151C22—521no—
1152C22—521no—
1153C22—521no—
1154C22—521no—
1155C22C22×C4×#26111yescharacteristic
1156C22C2×D4×#26111yescharacteristic
1157C22#1171962311yescharacteristic
1158C22#41×#26111yescharacteristic
1159C22#1171963111yescharacteristic
1160C22#1171963111yescharacteristic
1161C22#1171963111yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—264no—
1169C4—264no—
1170C4—262no—
1171C4—262no—
1172C4—262no—
1173C4—522no—
1174C4—522no—
1175C4—522no—
1176C4—522no—
1177C4—522no—
1178C4—522no—
1179C4—521no—
1180C4—521no—
1181C4—521no—
1182C2—42no—
1183C2—131no—
1184C2—131no—
1185C2—131no—
1186C2—131no—
1187C2—131no—
1188C2—131no—
1189C2—131no—
1190C2—131no—
1191C2—522no—
1192C2C4×D4×#26111yescharacteristic
1193C2#1313127311yescharacteristic
1194C2#1313127511yescharacteristic
1195C2#1313132211yescharacteristic
1196C2#1313132411yescharacteristic
1197C2#1313133411yescharacteristic
1198C2#1313133711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenter#388#261
hypocenterC13#13789
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊#261C2semidirect
7. #13130016C2semidirect
8. #13130016C2semidirect
9. #13130016C2semidirect
10. #13130015C2semidirect
11. #13130013C2semidirect
12. #13130012C2semidirect
14. #95×#261C2semidirect
49. #11719071C4semidirect
50. #11719070C4semidirect
53. C13×#388C4semidirect
54. #11718651C4semidirect
55. #11718612C4semidirect
56. #11718606C4semidirect
57. #11718605C4semidirect
58. #11718601C4semidirect
59. #11718331C4semidirect
60. #11718330C4semidirect
102. C2×C4⋊#261C2×C4semidirect
116. C2×C4×#261C2×C4semidirect
118. C2×C13×C4⋊C4C2×C4semidirect
122. C2×C42×C13C2×C4semidirect
132. C2×C4⋊Dic13C2×C4semidirect
133. C2×#6101C2×C4semidirect
134. C2×#6101C2×C4semidirect
135. C2×C4×Dic13C2×C4semidirect
136. C2×C4×Dic13C2×C4semidirect
137. C2×C4×Dic13C2×C4semidirect
162. (C2×#261)⋊C4C2×C4semidirect
163. (C2×#261)⋊C4C2×C4semidirect
164. C13×#95C2×C4semidirect
165. C13×#95C2×C4semidirect
166. #88071C2×C4semidirect
167. #88071C2×C4semidirect
168. #88071C2×C4semidirect
169. #88071C2×C4semidirect
170. #88071C2×C4semidirect
171. #88071C2×C4semidirect
315. C13×C22⋊C4C42semidirect
319. C22⋊Dic13C42semidirect
324. #6103C42semidirect
325. #6103C42semidirect
546. #388#261semidirect
681. C2×C4⋊C4C2×#261semidirect
729. C2×C42C2×#261semidirect
752. #95C2×#261semidirect
753. #95C2×#261semidirect
920. C22⋊C4C4×#261semidirect
930. C13#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#117190712
C2×#117190702
C2×C4×C4⋊#2612
C2×C22⋊C4×#2612
#131300172
#131300162
#131300152
#131300132
#131300122
#131300092
#95×#2612
D13×#3882
#1378913