Finite Group Databasebeta

← #15867389

Subgroups — #15867389

Order 3328.

1162 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719283C211yesmaximal, characteristic
2C2×#11718500C211yesmaximal, characteristic
3C2×#11718350C211yesmaximal, characteristic
4#13115777C211yesmaximal, characteristic, complemented
5#13115775C211yesmaximal, characteristic, complemented
6#13115774C211yesmaximal, characteristic, complemented
7#13115774C211yesmaximal, characteristic, complemented
8#13115772C211yesmaximal, characteristic, complemented
9#13115770C211yesmaximal, characteristic, complemented
10#13115770C211yesmaximal, characteristic, complemented
11#13114531C211yesmaximal, characteristic
12#13114531C211yesmaximal, characteristic
13#13114528C211yesmaximal, characteristic
14D13×#336C211yesmaximal, characteristic
15C13×#1984C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200C411yescharacteristic
18C2×#88198C411yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×#6094C2211yescharacteristic
21C22×C8×D13C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23#11719283—24no—
24#11719283—24no—
25C2×#88151C411yescharacteristic
26C2×#88150C411yescharacteristic
27C2×#88150C411yescharacteristic
28C2×#88143C411yescharacteristic
29C2×#88143C411yescharacteristic
30C2×#88142C411yescharacteristic
31C2×#88126C2211yescharacteristic
32C2×#88126C2211yescharacteristic
33C2×C42×D13C2211yescharacteristic
34C2×C4×Dic26C2211yescharacteristic
35C2×C4×Dic26C2211yescharacteristic
36C2×C4×Dic26C2211yescharacteristic
37C2×C13×C4⋊C8C2211yescharacteristic
38C2×C4×C8×C13C2211yescharacteristic
39C2×#88055C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×#88054C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718500—24no—
46#11718350—24no—
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13C2×C411yescharacteristic
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2×C411yescharacteristic
66C22×C4×D13C2311yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C22×Dic26C2×C411yescharacteristic
69C22×Dic26C2×C411yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C4×Q8×C13—22no—
75C4×Q8×C13—22no—
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82#88200—24no—
83#88198—24no—
84C2×#6103C2×C411yescharacteristic
85C2×#6103C2×C411yescharacteristic
86C2×#6103C2×C411yescharacteristic
87C2×#6103C2×C411yescharacteristic
88C2×C4⋊Dic13C2×C411yescharacteristic
89C2×C4⋊Dic13C2×C411yescharacteristic
90C2×C4⋊Dic13C2×C411yescharacteristic
91C2×#6101C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×C4×Dic13C2×C411yescharacteristic
102C2×C4×Dic13C2×C411yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C2×#6094—22no—
111C2×#6094—22no—
112C2×#6094—22no—
113C2×#6094—22no—
114C2×#6094—22no—
115C2×#6094Q814yescomplemented
116C2×C8×D13—22no—
117C2×C8×D13—22no—
118C2×C8×D13—22no—
119C2×C8×D13—22no—
120C2×C8×D13—22no—
121C2×C8×D13Q814yescomplemented
122#88151—24no—
123#88150—24no—
124#88150—24no—
125#88143—24no—
126#88143—24no—
127#88142—24no—
128#88126—22no—
129#88126—22no—
130#88126D414yes—
131#88126D414yes—
132C42×D13—22no—
133C42×D13—22no—
134C4×Dic26—22no—
135C4×Dic26—22no—
136C4×Dic26—22no—
137C4×Dic26—22no—
138C4×Dic26—22no—
139C4×Dic26—22no—
140C13×C4⋊C8—22no—
141C4×C8×C13—22no—
142#88055—22no—
143#88054—22no—
144#88054—22no—
145C8×Dic13—22no—
146C4⋊#1055—22no—
147#88043—22no—
148#21304—131nomaximal, Sylow
149C23×D13C22×C411yescharacteristic
150C2×Q8×C13—22no—
151C2×Q8×C13—22no—
152C2×Q8×C13—41no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—41no—
172C2×C4×D13—41no—
173C2×C4×D13C2×D412yes—
174C2×C4×D13C2×D412yes—
175C2×C4×D13C2×Q812yes—
176C2×C4×D13C2×Q812yes—
177C2×C4×D13#4112yes—
178C2×C4×D13#4112yes—
179C2×Dic26—22no—
180C2×Dic26—22no—
181C2×Dic26—22no—
182C2×Dic26—22no—
183C2×Dic26—22no—
184C2×Dic26—22no—
185C2×Dic26—41no—
186C2×Dic26—41no—
187C2×Dic26—41no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13—21no—
193C2×C8×C13—21no—
194C2×C8×C13—21no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13C2×Q812yes—
199C2×C8×C13C2×Q812yes—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C42×C13C2×D412yes—
208C42×C13C2×D412yes—
209#6103—22no—
210#6103—22no—
211#6103C22⋊C414yes—
212#6103C22⋊C414yes—
213C4⋊Dic13—22no—
214C4⋊Dic13—22no—
215C4⋊Dic13—22no—
216#6101—22no—
217#6101—22no—
218#6101—22no—
219#6101—22no—
220#6101—22no—
221#6101—22no—
222#6101—22no—
223#6101—22no—
224#6101C22⋊C414yes—
225#6101C22⋊C414yes—
226C4×Dic13—21no—
227C4×Dic13—21no—
228C4×Dic13—21no—
229C4×Dic13—21no—
230C4×Dic13—22no—
231C4×Dic13—22no—
232C4×Dic13C2×D412yes—
233C4×Dic13C2×D412yes—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055C2×Q812yes—
245C2×#1055C2×Q812yes—
246#6094—28no—
247#6094—44no—
248C8×D13—28no—
249C8×D13—44no—
250C2×#533—131no—
251C2×#424—131no—
252C2×#405—131no—
253#1985—131no—
254#1985—131no—
255#1985—131no—
256#1985—131no—
257#1984—131no—
258#1984—131no—
259#1984—131no—
260#1984D1311yescharacteristic, complemented
261#1729—131no—
262#1729—131no—
263#1728—131no—
264C2×#336—131no—
265C23×C13C23×C411yescharacteristic
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13—21no—
270C22×D13C2×C22⋊C412yes—
271C22×D13C4×Q812yes—
272C22×D13C4×Q812yes—
273Q8×C13—44no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13C2×C22⋊C412yes—
290C2×C4×C13C2×C22⋊C412yes—
291C2×C4×C13#13112yes—
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C22×D411yescharacteristic
294C2×C4×C13C22×Q811yescharacteristic
295C2×C4×C13C22×Q811yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C2×C4×C13C2×#4111yescharacteristic
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13—21no—
301C2×Dic13—21no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13C2×C22⋊C412yes—
314C2×Dic13C2×C22⋊C412yes—
315C2×Dic13C2×C22⋊C412yes—
316C2×Dic13C4×Q812yes—
317C2×Dic13C4×Q812yes—
318C2×Dic13#13112yes—
319C4×D13—44no—
320C4×D13—44no—
321C4×D13C22⋊Q814yes—
322C4×D13C22⋊Q814yes—
323C4×D13#12414yes—
324C4×D13C4⋊Q814yes—
325Dic26—44no—
326Dic26—44no—
327Dic26—44no—
328C8×C13—22no—
329C8×C13—22no—
330C8×C13—41no—
331C8×C13—41no—
332#1055—22no—
333#1055—22no—
334#1055—41no—
335#1055—41no—
336C22×M16—131no—
337C22×M16—131no—
338C23×C8—131no—
339C23×C8—131no—
340#533—264no—
341#533—264no—
342C2×C4⋊Q8—131no—
343C2×C4⋊Q8—131no—
344C2×#125—131no—
345C2×#125—131no—
346C2×C22⋊Q8—131no—
347C2×C22⋊Q8—131no—
348C2×C22⋊Q8—131no—
349C2×C22⋊Q8—131no—
350C2×C4×Q8—131no—
351C2×C4×Q8—131no—
352C2×C4×Q8—131no—
353C2×C4×Q8C2×D1311yescharacteristic
354C2×#117—131no—
355C2×#117—131no—
356C22×C42—131no—
357#424—264no—
358C2×C4⋊C8—131no—
359C2×C4⋊C8—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8C2×D1311yescharacteristic
362#405—264no—
363C2×#97—131no—
364C2×#97—131no—
365C2×C4×C8—131no—
366C2×C4×C8C2×D1311yescharacteristic
367#336—131no—
368#336—131no—
369#336—131no—
370#336—131no—
371#336—131no—
372#336—131no—
373#336—131no—
374#336—131no—
375#336—131no—
376#336—131no—
377#336—131no—
378#336—131no—
379#336C2×D1311yescharacteristic
380#336C2×D1311yescharacteristic
381#336C2×D1311yescharacteristic
382#336C2×D1311yescharacteristic
383C22×C13C22×C22⋊C411yescharacteristic
384C22×C13C2×C4×Q811yescharacteristic
385C22×C13C2×C4×Q811yescharacteristic
386C22×C13C2×#13111yescharacteristic
387C22×C13C2×#13111yescharacteristic
388C22×C13#56811yescharacteristic
389C22×C13#56811yescharacteristic
390C2×D13—22no—
391C2×D13—22no—
392C2×D13—22no—
393C2×D13—22no—
394C2×D13—22no—
395C2×D13—22no—
396C2×D13#39114yes—
397C4×C13—22no—
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—41no—
401C4×C13—41no—
402C4×C13—41no—
403C4×C13C2×C22⋊Q811yescharacteristic
404C4×C13C2×C22⋊Q811yescharacteristic
405C4×C13C2×#12411yescharacteristic
406C4×C13C2×C4⋊Q811yescharacteristic
407Dic13—22no—
408Dic13—22no—
409Dic13—22no—
410Dic13—41no—
411Dic13—41no—
412Dic13—41no—
413Dic13#39114yes—
414C22×Q8—131no—
415C22×Q8—131no—
416C22×Q8—131no—
417C22×Q8C4×D1311yescharacteristic
418C23×C4—131no—
419C23×C4—131no—
420C23×C4—131no—
421C2×M16—134no—
422C2×M16—262no—
423C2×M16—262no—
424C2×M16—262no—
425C2×M16—262no—
426C2×M16—262no—
427C22×C8—131no—
428C22×C8—131no—
429C22×C8—134no—
430C22×C8—131no—
431C22×C8—131no—
432C22×C8—262no—
433C22×C8—262no—
434C22×C8—262no—
435C22×C8—262no—
436C22×C8—262no—
437C22×C8C22×D1311yescharacteristic
438C22×C8C22×D1311yescharacteristic
439C22×C8C22×D1311yescharacteristic
440C22×C8C22×D1311yescharacteristic
441C4⋊Q8—264no—
442C4⋊Q8—264no—
443#125—264no—
444#125—264no—
445C22⋊Q8—264no—
446C22⋊Q8—264no—
447C22⋊Q8—264no—
448C22⋊Q8—264no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—262no—
452C4×Q8—262no—
453C4×Q8—262no—
454C4×Q8—262no—
455C4×Q8—262no—
456C4×Q8—262no—
457#117—134no—
458#117—134no—
459#117—262no—
460#117—262no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—131no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4C4×D1311yescharacteristic
475C2×C4⋊C4C4×D1311yescharacteristic
476C2×C4⋊C4C4×D1311yescharacteristic
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42—131no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42C22×D1311yescharacteristic
489C2×C42C22×D1311yescharacteristic
490C2×C42C22×D1311yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—262no—
493C4⋊C8—262no—
494C4⋊C8—262no—
495#97—262no—
496#97—262no—
497C4×C8—22no—
498C4×C8—262no—
499C2×C13C2×#39111yescharacteristic
500C2×C13#288011yescharacteristic
501C2×C13#288011yescharacteristic
502C2×C13#296011yescharacteristic
503C2×C13#296111yescharacteristic
504C2×C13#296211yescharacteristic
505C2×C13#296211yescharacteristic
506D13—24no—
507C24—131no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—41no—
511C2×Q8—262no—
512C2×Q8—262no—
513C2×Q8—262no—
514C2×Q8—262no—
515C2×Q8—262no—
516C2×Q8—262no—
517C2×Q8—521no—
518C2×Q8—521no—
519C2×Q8—521no—
520C22×C4—131no—
521C22×C4—132no—
522C22×C4—132no—
523C22×C4—132no—
524C22×C4—132no—
525C22×C4—132no—
526C22×C4—132no—
527C22×C4—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—521no—
538C22×C4—521no—
539C22×C4C2×C4×D1311yescharacteristic
540C22×C4C2×C4×D1311yescharacteristic
541C22×C4C2×C4×D1311yescharacteristic
542C22×C4C2×C4×D1311yescharacteristic
543C22×C4C2×C4×D1311yescharacteristic
544C22×C4C2×C4×D1311yescharacteristic
545C22×C4C23×D1311yescharacteristic
546M16—268no—
547M16—524no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—132no—
559C2×C8—132no—
560C2×C8—268no—
561C2×C8—261no—
562C2×C8—261no—
563C2×C8—261no—
564C2×C8—261no—
565C2×C8—261no—
566C2×C8—261no—
567C2×C8—261no—
568C2×C8—261no—
569C2×C8—261no—
570C2×C8—261no—
571C2×C8—524no—
572C2×C8Q8×D1312yes—
573C2×C8Q8×D1312yes—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—134no—
578C4⋊C4—134no—
579C4⋊C4—262no—
580C4⋊C4—262no—
581C4⋊C4—262no—
582C4⋊C4—262no—
583C4⋊C4—262no—
584C4⋊C4—262no—
585C4⋊C4—262no—
586C4⋊C4—262no—
587C4⋊C4—262no—
588C4⋊C4—262no—
589C4⋊C4—262no—
590C22⋊C4—134no—
591C22⋊C4—134no—
592C22⋊C4—262no—
593C22⋊C4—262no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—132no—
599C42—132no—
600C42—262no—
601C42—262no—
602C42—261no—
603C42—261no—
604C42—261no—
605C42—261no—
606C42D4×D1312yes—
607C42D4×D1312yes—
608C13#2130411yescharacteristic, complemented, Sylow
609C23—132no—
610C23—132no—
611C23—132no—
612C23—261no—
613C23—261no—
614C23—261no—
615C23—261no—
616C23C22×C4×D1311yescharacteristic
617Q8—44no—
618Q8—524no—
619Q8—524no—
620Q8—524no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—132no—
637C2×C4—132no—
638C2×C4—132no—
639C2×C4—134no—
640C2×C4—134no—
641C2×C4—134no—
642C2×C4—134no—
643C2×C4—132no—
644C2×C4—132no—
645C2×C4—132no—
646C2×C4—261no—
647C2×C4—261no—
648C2×C4—261no—
649C2×C4—261no—
650C2×C4—261no—
651C2×C4—261no—
652C2×C4—261no—
653C2×C4—261no—
654C2×C4—261no—
655C2×C4—261no—
656C2×C4—261no—
657C2×C4—261no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—524no—
662C2×C4—524no—
663C2×C4C22⋊C4×D1312yes—
664C2×C4C22⋊C4×D1312yes—
665C2×C4#8815512yes—
666C2×C4C2×D4×D1311yescharacteristic
667C2×C4C2×D4×D1311yescharacteristic
668C2×C4C2×Q8×D1311yescharacteristic
669C2×C4C2×Q8×D1311yescharacteristic
670C2×C4#41×D1311yescharacteristic
671C2×C4#41×D1311yescharacteristic
672C8—22no—
673C8—22no—
674C8—41no—
675C8—41no—
676C8—262no—
677C8—262no—
678C8—521no—
679C8—521no—
680C22—134no—
681C22—262no—
682C22—262no—
683C22—262no—
684C22—262no—
685C22—262no—
686C22—262no—
687C22C2×C22⋊C4×D1311yescharacteristic
688C22C4×Q8×D1311yescharacteristic
689C22C4×Q8×D1311yescharacteristic
690C22C2×#8815511yescharacteristic
691C22#1171945011yescharacteristic
692C22D13×#13111yescharacteristic
693C22#1171945511yescharacteristic
694C4—22no—
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—134no—
701C4—262no—
702C4—262no—
703C4—262no—
704C4—521no—
705C4—521no—
706C4—521no—
707C4D13×C22⋊Q811yescharacteristic
708C4D13×C22⋊Q811yescharacteristic
709C4D13×#12411yescharacteristic
710C4D13×C4⋊Q811yescharacteristic
711C2—264no—
712C2D13×#39111yescharacteristic
713C2#1312328211yescharacteristic
714C2#1312328411yescharacteristic
715C2#1312376511yescharacteristic
716C2#1312377211yescharacteristic
717C2#1312377811yescharacteristic
718C2#1312378111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1984C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1984D13
hypocenterC13#21304
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
4. #13115777C2semidirect
5. #13115775C2semidirect
6. #13115774C2semidirect
7. #13115774C2semidirect
8. #13115772C2semidirect
9. #13115770C2semidirect
10. #13115770C2semidirect
15. C13×#1984C2semidirect
115. C2×#6094Q8semidirect
121. C2×C8×D13Q8semidirect
260. #1984D13semidirect
608. C13#21304semidirect

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×#117185002
C2×#117183502
#131157772
#131157752
#131157742
#131157722
#131157702
#131145312
#131145282
D13×#3362
C13×#19842
#2130413