Finite Group Databasebeta

← #15879201

Subgroups — #15879201

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic
3#13115804C211yesmaximal, characteristic, complemented
4#13115793C211yesmaximal, characteristic, complemented
5#13115267C211yesmaximal, characteristic, complemented
6#13115257C211yesmaximal, characteristic, complemented
7#13115143C211yesmaximal, characteristic, complemented
8#13115143C211yesmaximal, characteristic, complemented
9#13114928C211yesmaximal, characteristic, complemented
10#13114920C211yesmaximal, characteristic, complemented
11#13114838C211yesmaximal, characteristic, complemented
12#13114669C211yesmaximal, characteristic, complemented
13#13114555C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88189—21no—
21C2×#88180C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27#11719246—24no—
28#11719246C418yescomplemented
29C2×#88143—21no—
30C2×#88133—21no—
31C2×#88131—21no—
32C2×#88124C2211yescharacteristic
33C2×C4×Dic26C2211yescharacteristic
34C13×#389—21no—
35C13×#385—21no—
36C13×#385—21no—
37C13×#384C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C13×#380C2211yescharacteristic
40C4×C13×C4⋊C4C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718672—24no—
44C2×#88050C2211yescharacteristic
45C2×#88050C2211yescharacteristic
46C2×#88050C2211yescharacteristic
47C2×#88050C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13D411yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—21no—
68C22×Dic26C2311yescharacteristic
69C4×D4×C13—44no—
70C4×D4×C13C2×C414yes—
71C4×D4×C13D414yes—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4—41no—
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13—21no—
94#88189—28no—
95#88180—22no—
96#88180C2×C414yescomplemented
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13C2×C414yescomplemented
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103#88178—22no—
104#88178—22no—
105#88178C2×C414yescomplemented
106#88178C2×C414yescomplemented
107C2×#6101—21no—
108C2×#6101—21no—
109C2×#6101—21no—
110C2×#6101—21no—
111C2×#6101—21no—
112C2×C4×Dic13—21no—
113C2×C4×Dic13—21no—
114C2×#6099—22no—
115C2×#6099—22no—
116C2×#6099—41no—
117C22×#1055—22no—
118C22×#1055—22no—
119C22×#1055—41no—
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124#88143—28no—
125#88133—28no—
126#88131—28no—
127#88124—22no—
128#88124C2×C414yescomplemented
129C4×Dic26—22no—
130C4×Dic26C2×C414yescomplemented
131C13×#95—21no—
132C13×#95—21no—
133C13×#95—21no—
134C22⋊#1055—22no—
135C22⋊#1055—22no—
136#88050—22no—
137#88050—22no—
138#88050—41no—
139#88050—41no—
140C4⋊#1055—22no—
141#88043—22no—
142#22491—131nomaximal, Sylow
143C24×C13C2×D411yescharacteristic
144C24×C13C2×D411yescharacteristic
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13C22⋊C414yes—
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—42no—
161C22×C4×C13—42no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13—81no—
165C22×C4×C13—81no—
166C22×C4×C13C22×C412yes—
167C22×C4×C13C22×C412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2411yescharacteristic
175C22×Dic13—24no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—42no—
181C22×Dic13—42no—
182C2×Dic26—21no—
183C2×Dic26—21no—
184C2×Dic26—21no—
185C2×Dic26—21no—
186C2×Dic26—21no—
187C2×Dic26C22×C412yes—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—42no—
196C13×C4⋊C4—42no—
197C13×C4⋊C4—42no—
198C13×C4⋊C4—81no—
199C13×C4⋊C4C22⋊C414yes—
200C13×C4⋊C4#4112yes—
201C13×C22⋊C4—42no—
202C13×C22⋊C4—42no—
203C13×C22⋊C4C22⋊C414yes—
204C13×C22⋊C4C22⋊C414yes—
205C42×C13—42no—
206C42×C13C22×C412yes—
207C42×C13C2×D412yes—
208C22⋊Dic13—24no—
209C22⋊Dic13—24no—
210C22⋊Dic13—24no—
211C4⋊Dic13—24no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13C22×C412yes—
216C4⋊Dic13C22×C412yes—
217C4⋊Dic13C22×C412yes—
218#6101—24no—
219#6101—24no—
220#6101—24no—
221#6101—24no—
222#6101—24no—
223C4×Dic13—24no—
224C4×Dic13—24no—
225#6099—44no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—44no—
238C2×#1055#4112yes—
239C2×#552—131no—
240C2×#435—131no—
241D4×C4⋊C4D1311yescharacteristic
242#1992—131no—
243#1989—131no—
244#1894—131no—
245#1892—131no—
246#1872—131no—
247#1872—131no—
248#1825—131no—
249#1823—131no—
250#1803—131no—
251#1763—131no—
252#1736—131no—
253C2×#340—131no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13C2×C22⋊C412yes—
265C23×C13C2×C22⋊C412yes—
266C23×C13AGL(1,ℤ/8)12yes—
267C23×C13#13712yes—
268C23×C13C22×D411yescharacteristic
269D4×C13—28no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—84no—
299C2×C4×C13—84no—
300C2×C4×C13C2×C22⋊C412yes—
301C2×C4×C13C2×C22⋊C412yes—
302C2×C4×C13C2×C22⋊C412yes—
303C2×C4×C13C2×C22⋊C412yes—
304C2×C4×C13C23×C411yescharacteristic
305C2×C4×C13C22×D411yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×C4×C132−1+411yescharacteristic
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—48no—
323Dic26—22no—
324Dic26—22no—
325Dic26—41no—
326Dic26—41no—
327#1055—22no—
328#1055—41no—
329#1055—41no—
330#1055—41no—
331C22×M16—131no—
332C23×C8—131no—
333#552—138no—
334#552—264no—
335C2×#126—261no—
336C2×#125—131no—
337C2×#125—261no—
338C2×#123—261no—
339C2×C22⋊Q8—131no—
340C2×C22⋊Q8—131no—
341C2×C4×Q8—131no—
342C2×C4×D4—21no—
343C2×C4×D4C2×D1311yescharacteristic
344C2×#117—131no—
345C2×#117—261no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C4⋊C4C2×D1311yescharacteristic
349#435—264no—
350C2×C4⋊C8—131no—
351C2×#103—131no—
352C2×#103—131no—
353C2×#103—131no—
354C2×#103—131no—
355C2×C22⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×#97—131no—
358#389—21no—
359#385—21no—
360#385—21no—
361#384C2×D1311yescharacteristic
362#380C2×D1311yescharacteristic
363#380C2×D1311yescharacteristic
364C4×C4⋊C4C2×D1311yescharacteristic
365#340—131no—
366#340—131no—
367#340—131no—
368#340—131no—
369#340—131no—
370#340—131no—
371#340—131no—
372#340—131no—
373#340—131no—
374#340—131no—
375#340—131no—
376#340—131no—
377C22×C13—22no—
378C22×C13—22no—
379C22×C13—22no—
380C22×C13—22no—
381C22×C13—22no—
382C22×C13—22no—
383C22×C13—22no—
384C22×C13—22no—
385C22×C13—22no—
386C22×C13—41no—
387C22×C13—41no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13#41714yes—
391C22×C13C22×C22⋊C411yescharacteristic
392C22×C13#54611yescharacteristic
393C22×C13#54711yescharacteristic
394C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C13C2×#13711yescharacteristic
396C22×C13#57711yescharacteristic
397C22×C13#57811yescharacteristic
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—22no—
401C4×C13—22no—
402C4×C13—42no—
403C4×C13—81no—
404C4×C13—81no—
405C4×C13—81no—
406C4×C13C4×#4111yescharacteristic
407C4×C13#52011yescharacteristic
408C4×C13#54611yescharacteristic
409C4×C13#54711yescharacteristic
410Dic13—42no—
411Dic13—42no—
412Dic13—42no—
413Dic13—42no—
414C22×Q8—131no—
415C22×D4C22⋊D1311yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—261no—
419C23×C4C22×D1311yescharacteristic
420C23×C4C22×D1311yescharacteristic
421C2×M16—262no—
422C2×M16—262no—
423C2×M16—521no—
424C22×C8—131no—
425C22×C8—131no—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8—262no—
429C22×C8—262no—
430C22×C8—521no—
431#126—268no—
432#125—134no—
433#125—268no—
434#125—262no—
435#123—268no—
436C22⋊Q8—134no—
437C22⋊Q8—134no—
438C22⋊Q8—262no—
439C22⋊Q8—262no—
440C4×Q8—134no—
441C4×Q8—262no—
442C4×D4—44no—
443C4×D4C4×D1314yes—
444C4×D4D5214yes—
445#117—134no—
446#117—262no—
447#117—268no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—134no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—261no—
462C2×C4⋊C4—261no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4C22⋊D1311yescharacteristic
468C2×C4⋊C4C22×D1311yescharacteristic
469C2×C4⋊C4C22×D1311yescharacteristic
470C2×C4⋊C4C22×D1311yescharacteristic
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—261no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4C22⋊D1311yescharacteristic
478C2×C22⋊C4C22⋊D1311yescharacteristic
479C2×C42—21no—
480C2×C42—261no—
481C2×C42—261no—
482C2×C42C22×D1311yescharacteristic
483C4⋊C8—262no—
484#103—262no—
485#103—262no—
486#103—521no—
487#103—521no—
488C22⋊C8—262no—
489C22⋊C8—262no—
490#97—262no—
491#95—21no—
492#95—21no—
493#95—21no—
494C2×C13—24no—
495C2×C13—42no—
496C2×C13#233911yescharacteristic
497C2×C13C2×#41711yescharacteristic
498C2×C13#289811yescharacteristic
499C2×C13#331011yescharacteristic
500C2×C13#331211yescharacteristic
501C2×C13#334311yescharacteristic
502C2×C13#334411yescharacteristic
503C24C2×C22⋊D1311yescharacteristic
504C24C2×C22⋊D1311yescharacteristic
505C2×Q8—132no—
506C2×Q8—261no—
507C2×Q8—261no—
508C2×Q8—261no—
509C2×Q8—261no—
510C2×Q8—261no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4#610314yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—264no—
533C22×C4—261no—
534C22×C4—261no—
535C22×C4—261no—
536C22×C4—261no—
537C22×C4—522no—
538C22×C4—522no—
539C22×C4C2×C4×D1312yes—
540C22×C4C2×C4×D1312yes—
541C22×C4C2×D5212yes—
542C22×C4C2×D5212yes—
543C22×C4C2×C22⋊D1311yescharacteristic
544C22×C4C2×C22⋊D1311yescharacteristic
545C22×C4C2×C22⋊D1311yescharacteristic
546C22×C4C2×C22⋊D1311yescharacteristic
547C22×C4C23×D1311yescharacteristic
548M16—524no—
549C2×C8—132no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—261no—
561C2×C8—524no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—132no—
574C4⋊C4—132no—
575C4⋊C4—132no—
576C4⋊C4—264no—
577C4⋊C4—264no—
578C4⋊C4—264no—
579C4⋊C4—264no—
580C4⋊C4—264no—
581C4⋊C4—264no—
582C4⋊C4—261no—
583C4⋊C4—261no—
584C4⋊C4—261no—
585C4⋊C4#610314yes—
586C4⋊C4#612912yes—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—264no—
590C22⋊C4—264no—
591C22⋊C4—264no—
592C22⋊C4#610314yes—
593C22⋊C4#610314yes—
594C42—42no—
595C42—264no—
596C42—264no—
597C42C2×C4×D1312yes—
598C42C2×D5212yes—
599C13#2249111yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×#610312yes—
611C23C2×#610312yes—
612C23#8818612yes—
613C23#8819612yes—
614C23C22×C22⋊D1311yescharacteristic
615Q8—262no—
616Q8—262no—
617Q8—521no—
618Q8—521no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—262no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4—521no—
657C2×C4—521no—
658C2×C4—521no—
659C2×C4—521no—
660C2×C4—521no—
661C2×C4—521no—
662C2×C4—528no—
663C2×C4C2×#610312yes—
664C2×C4C2×#610312yes—
665C2×C4C2×#610312yes—
666C2×C4C2×#610312yes—
667C2×C4C22×C4×D1311yescharacteristic
668C2×C4C22×D5211yescharacteristic
669C2×C4C2×#612911yescharacteristic
670C2×C4#8825111yescharacteristic
671C2×C4#41×D1311yescharacteristic
672C2×C4#8825711yescharacteristic
673C8—262no—
674C8—521no—
675C8—521no—
676C8—521no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1171862714yes—
691C22C22×#610311yescharacteristic
692C22C2×#8818611yescharacteristic
693C22#1171951111yescharacteristic
694C22C2×#8819611yescharacteristic
695C22#1171952911yescharacteristic
696C22#1171954111yescharacteristic
697C22#1171954311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—522no—
707C4—522no—
708C4—522no—
709C4—522no—
710C4C4×#612911yescharacteristic
711C4#1171925111yescharacteristic
712C4#1171925911yescharacteristic
713C4#1171926011yescharacteristic
714C2—24no—
715C2—42no—
716C2#1311766111yescharacteristic
717C2C2×#1171862711yescharacteristic
718C2#1312336611yescharacteristic
719C2#1312685711yescharacteristic
720C2#1312688711yescharacteristic
721C2#1312727011yescharacteristic
722C2#1312728511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenterD4×C4⋊C4D13
hypocenterC13#22491
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13115804C2semidirect
4. #13115793C2semidirect
5. #13115267C2semidirect
6. #13115257C2semidirect
7. #13115143C2semidirect
8. #13115143C2semidirect
9. #13114928C2semidirect
10. #13114920C2semidirect
11. #13114838C2semidirect
12. #13114669C2semidirect
13. #13114555C2semidirect
14. C2×#11718121C2semidirect
28. #11719246C4semidirect
96. #88180C2×C4semidirect
99. C2×C4⋊Dic13C2×C4semidirect
105. #88178C2×C4semidirect
106. #88178C2×C4semidirect
128. #88124C2×C4semidirect
130. C4×Dic26C2×C4semidirect
599. C13#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#117192462
C2×#117186722
#131158042
#131157932
#131152672
#131152572
#131151432
#131149282
#131149202
#131148382
#131146692
#131145552
C2×#117181212
D4×C13×C4⋊C42
#2249113