Finite Group Databasebeta

← #15878489

Subgroups — #15878489

Order 3328.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic
2C2×#11718886C211yesmaximal, characteristic, complemented
3C22×#88075C211yesmaximal, characteristic, complemented
4#13117765C211yesmaximal, characteristic
5#13115760C211yesmaximal, characteristic, complemented
6#13115657C211yesmaximal, characteristic, complemented
7#13115270C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115149C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13114851C211yesmaximal, characteristic, complemented
12#13114771C211yesmaximal, characteristic, complemented
13#13114771C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C13C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C23×Q8×C13C2211yescharacteristic
18D4×Q8×C13—24no—
19D4×Q8×C13C418yescomplemented
20C2×C13×C4⋊Q8—21no—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33#11718886—24no—
34C2×#88075—24no—
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40C2×#88075C2211yescharacteristic
41C2×#88075C2211yescharacteristic
42C2×#88075C2211yescharacteristic
43C2×#88075C2211yescharacteristic
44C2×#88075C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47#11718881—21no—
48#11718873C2211yescharacteristic
49#11718873C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718672—24no—
53#11718642—21no—
54#11718612—21no—
55C22⋊C4×Dic13—21no—
56#11718597C2211yescharacteristic
57C4×C4⋊Dic13C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×#88043C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C22×Q8×C13—21no—
65C22×Q8×C13—21no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—22no—
69C22×Q8×C13—22no—
70C22×Q8×C13—22no—
71C22×Q8×C13—22no—
72C22×Q8×C13—41no—
73C22×Q8×C13—41no—
74C22×Q8×C13—41no—
75C22×Q8×C13—41no—
76C22×Q8×C13C2×C414yes—
77C22×Q8×C13C2×C414yescomplemented
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C22×Q8×C13C2311yescharacteristic
81C22×D4×C13D411yescharacteristic
82C23×C4×C13—21no—
83C23×C4×C13—21no—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13—21no—
87C13×C4⋊Q8—28no—
88C13×C4⋊Q8—22no—
89C13×C4⋊Q8C2×C414yescomplemented
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—28no—
93C13×C22⋊Q8—28no—
94C13×C22⋊Q8C2×C414yes—
95C13×C22⋊Q8C2×C414yescomplemented
96C4×Q8×C13—22no—
97C4×Q8×C13C2×C414yescomplemented
98C4×D4×C13—28no—
99C4×D4×C13C2×C414yes—
100C4×D4×C13D414yes—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4D411yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4D411yescharacteristic
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C42×C13—21no—
113C2×C42×C13C2311yescharacteristic
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117#88180—22no—
118#88180—41no—
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—41no—
122C2×C4⋊Dic13C2311yescharacteristic
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×#6099—22no—
129C2×#6099—22no—
130C2×#6099—41no—
131C22×#1055—22no—
132C22×#1055—22no—
133C22×#1055—41no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138#88075—22no—
139#88075—22no—
140#88075—22no—
141#88075—22no—
142#88075—22no—
143#88075—22no—
144#88075—22no—
145#88075—41no—
146#88075—41no—
147#88075—41no—
148#88075—41no—
149#88075D414yescomplemented
150#88071—21no—
151#88071—21no—
152#88071—21no—
153#88071—21no—
154#88071—21no—
155C22⋊#1055—22no—
156C22⋊#1055—22no—
157C4⋊#1055—22no—
158#88043—22no—
159#22425—131nomaximal, Sylow
160C24×C13C2×D411yescharacteristic
161C24×C13C2×D411yescharacteristic
162C2×Q8×C13—24no—
163C2×Q8×C13—24no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13—21no—
169C2×Q8×C13—28no—
170C2×Q8×C13—28no—
171C2×Q8×C13—21no—
172C2×Q8×C13—21no—
173C2×Q8×C13—21no—
174C2×Q8×C13—21no—
175C2×Q8×C13—21no—
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—42no—
180C2×Q8×C13—42no—
181C2×Q8×C13—42no—
182C2×Q8×C13—42no—
183C2×Q8×C13—44no—
184C2×Q8×C13—44no—
185C2×Q8×C13—44no—
186C2×Q8×C13—44no—
187C2×Q8×C13—44no—
188C2×Q8×C13—44no—
189C2×Q8×C13C22×C412yes—
190C2×Q8×C13C22×C412yes—
191C2×Q8×C13C22×C412yes—
192C2×Q8×C13C2×D412yes—
193C2×Q8×C13#4112yes—
194C2×D4×C13—22no—
195C2×D4×C13—22no—
196C2×D4×C13C22⋊C414yes—
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—21no—
205C22×C4×C13—21no—
206C22×C4×C13—24no—
207C22×C4×C13—24no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—42no—
212C22×C4×C13—42no—
213C22×C4×C13—42no—
214C22×C4×C13—42no—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C22×C412yes—
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D412yes—
222C22×C4×C13C2×D412yes—
223C22×C4×C13C2411yescharacteristic
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—42no—
229C22×Dic13—42no—
230C22×Dic13—81no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4C22⋊C414yes—
238C13×C4⋊C4C22×C412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4C22⋊C414yes—
242C13×C22⋊C4C22⋊C414yes—
243C42×C13—24no—
244C42×C13C22×C412yes—
245C42×C13C2×D412yes—
246C22⋊Dic13—42no—
247C22⋊Dic13—42no—
248C22⋊Dic13—81no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—42no—
257C4⋊Dic13C2×D412yes—
258C4×Dic13—42no—
259C4×Dic13—81no—
260#6099—44no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—21no—
268C2×#1055—21no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—21no—
272C2×#1055—44no—
273C2×#1055C2×D412yes—
274C2×D4×Q8D1311yescharacteristic
275C2×#435—131no—
276C2×#419—131no—
277C22×#103—131no—
278#2352—131no—
279#1981—131no—
280#1960—131no—
281#1894—131no—
282#1892—131no—
283#1873—131no—
284#1872—131no—
285#1805—131no—
286#1787—131no—
287#1787—131no—
288#1763—131no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13C2×C22⋊C412yes—
300C23×C13C2×C22⋊C412yes—
301C23×C13#13712yes—
302C23×C13#13712yes—
303C23×C13C22×D411yescharacteristic
304Q8×C13—22no—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13—22no—
308Q8×C13—22no—
309Q8×C13—22no—
310Q8×C13—22no—
311Q8×C13—48no—
312Q8×C13—48no—
313Q8×C13—41no—
314Q8×C13—41no—
315Q8×C13—41no—
316Q8×C13—41no—
317Q8×C13C4×D414yes—
318D4×C13—28no—
319C2×C4×C13—22no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—22no—
323C2×C4×C13—21no—
324C2×C4×C13—21no—
325C2×C4×C13—22no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—48no—
342C2×C4×C13—48no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13C2×C22⋊C412yes—
350C2×C4×C13C2×C22⋊C412yes—
351C2×C4×C13C2×C22⋊C412yes—
352C2×C4×C13C2×C22⋊C412yes—
353C2×C4×C13C23×C411yescharacteristic
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C2×#4111yescharacteristic
357C2×C4×C13H(5,𝔽2)11yescharacteristic
358C2×C4×C13H(5,𝔽2)11yescharacteristic
359C2×Dic13—22no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362C2×Dic13—41no—
363C2×Dic13—41no—
364C2×Dic13—41no—
365C2×Dic13—41no—
366C2×Dic13—41no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—84no—
372#1055—22no—
373#1055—41no—
374#1055—41no—
375#1055—41no—
376C23×Q8C2×D1311yescharacteristic
377C23×Q8C2×D1311yescharacteristic
378C22×M16—131no—
379C23×C8—131no—
380D4×Q8—24no—
381D4×Q8Dic1318yescomplemented
382C2×C4⋊Q8—21no—
383C2×C4⋊Q8C2×D1311yescharacteristic
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—21no—
386C2×C22⋊Q8C2×D1311yescharacteristic
387C2×C22⋊Q8C2×D1311yescharacteristic
388C2×C4×Q8C2×D1311yescharacteristic
389C2×C4×D4—21no—
390C2×C4×D4C2×D1311yescharacteristic
391C2×#117—131no—
392C22×C4⋊C4—131no—
393#435—264no—
394C2×C4⋊C8—131no—
395#419—264no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—264no—
409C2×C22⋊C8—131no—
410C2×C22⋊C8—131no—
411C2×#97—131no—
412#388—261no—
413#387—261no—
414#386—261no—
415#382—131no—
416#380—131no—
417#380—131no—
418C4×C4⋊C4—131no—
419C4×C22⋊C4—261no—
420#340—131no—
421#340—131no—
422#340—131no—
423#340—131no—
424C22×C13—22no—
425C22×C13—22no—
426C22×C13—22no—
427C22×C13—22no—
428C22×C13—22no—
429C22×C13—22no—
430C22×C13—22no—
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—41no—
434C22×C13—41no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13#41914yescomplemented
438C22×C13C22×C22⋊C411yescharacteristic
439C22×C13D4211yescharacteristic
440C22×C13#54611yescharacteristic
441C22×C13C2×#13711yescharacteristic
442C22×C13C2×#13711yescharacteristic
443C22×C13#57711yescharacteristic
444C22×C13#57811yescharacteristic
445C4×C13—22no—
446C4×C13—22no—
447C4×C13—24no—
448C4×C13—22no—
449C4×C13—22no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13C2×C4×D411yescharacteristic
454C4×C13#51811yescharacteristic
455C4×C13D4211yescharacteristic
456C4×C13#54611yescharacteristic
457Dic13—42no—
458Dic13—81no—
459Dic13—81no—
460Dic13—81no—
461C22×Q8—21no—
462C22×Q8—21no—
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—41no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8—41no—
473C22×Q8C2×Dic1314yes—
474C22×Q8C2×Dic1314yescomplemented
475C22×Q8C22×D1311yescharacteristic
476C22×Q8C22×D1311yescharacteristic
477C22×Q8C22×D1311yescharacteristic
478C22×D4C22⋊D1311yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—261no—
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C2×M16—262no—
485C2×M16—262no—
486C2×M16—521no—
487C22×C8—131no—
488C22×C8—131no—
489C22×C8—131no—
490C22×C8—131no—
491C22×C8—262no—
492C22×C8—262no—
493C22×C8—521no—
494C4⋊Q8—28no—
495C4⋊Q8—22no—
496C4⋊Q8C2×Dic1314yescomplemented
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—28no—
500C22⋊Q8—28no—
501C22⋊Q8C2×Dic1314yes—
502C22⋊Q8C2×Dic1314yescomplemented
503C4×Q8—22no—
504C4×Q8C2×Dic1314yescomplemented
505C4×D4—28no—
506C4×D4C2×Dic1314yes—
507C4×D4C22⋊D1314yes—
508#117—262no—
509#117—521no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—131no—
516C2×C4⋊C4—131no—
517C2×C4⋊C4—131no—
518C2×C4⋊C4—131no—
519C2×C4⋊C4—262no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4—521no—
522C2×C4⋊C4C22⋊D1311yescharacteristic
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C22⋊C4C22⋊D1311yescharacteristic
530C2×C22⋊C4C22⋊D1311yescharacteristic
531C2×C42—21no—
532C2×C42—261no—
533C2×C42—261no—
534C2×C42C22×D1311yescharacteristic
535C4⋊C8—262no—
536#103—134no—
537#103—262no—
538#103—262no—
539#103—262no—
540#103—262no—
541#103—262no—
542#103—262no—
543#103—262no—
544#103—521no—
545#103—521no—
546#103—521no—
547#103—521no—
548C22⋊C8—262no—
549C22⋊C8—262no—
550#97—262no—
551#95—261no—
552#95—261no—
553#95—261no—
554#95—261no—
555#95—261no—
556C2×C13—24no—
557C2×C13—42no—
558C2×C13D4×C22⋊C411yescharacteristic
559C2×C13C2×#41911yescharacteristic
560C2×C13#289811yescharacteristic
561C2×C13#326611yescharacteristic
562C2×C13#327011yescharacteristic
563C2×C13#331211yescharacteristic
564C2×C13#332011yescharacteristic
565C24C2×C22⋊D1311yescharacteristic
566C24C2×C22⋊D1311yescharacteristic
567C2×Q8—24no—
568C2×Q8—24no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—28no—
575C2×Q8—28no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—42no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—42no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8D4×D1312yes—
595C2×Q8#612912yes—
596C2×Q8C22×Dic1312yes—
597C2×Q8C22×Dic1312yes—
598C2×Q8C22×Dic1312yes—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4C22⋊Dic1314yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—522no—
625C22×C4—522no—
626C22×C4—1041no—
627C22×C4C22×Dic1312yes—
628C22×C4C22×Dic1312yes—
629C22×C4C2×C22⋊D1311yescharacteristic
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1312yes—
634C22×C4C2×C22⋊D1312yes—
635C22×C4C23×D1311yescharacteristic
636M16—524no—
637C2×C8—132no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8—261no—
644C2×C8—261no—
645C2×C8—261no—
646C2×C8—261no—
647C2×C8—261no—
648C2×C8—261no—
649C2×C8—524no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—132no—
657C4⋊C4—261no—
658C4⋊C4—261no—
659C4⋊C4—261no—
660C4⋊C4—261no—
661C4⋊C4—261no—
662C4⋊C4—261no—
663C4⋊C4—261no—
664C4⋊C4—522no—
665C4⋊C4C22⋊Dic1314yes—
666C4⋊C4C22×Dic1312yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—522no—
670C22⋊C4—522no—
671C22⋊C4—1041no—
672C22⋊C4C22⋊Dic1314yes—
673C22⋊C4C22⋊Dic1314yes—
674C42—24no—
675C42—522no—
676C42—1041no—
677C42C22×Dic1312yes—
678C42C2×C22⋊D1312yes—
679C13#2242511yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23#8819612yes—
691C23#8819612yes—
692C23C2×C22⋊Dic1312yes—
693C23C2×C22⋊Dic1312yes—
694C23C22×C22⋊D1311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—48no—
703Q8—48no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8D4×Dic1314yes—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—262no—
741C2×C4—521no—
742C2×C4—521no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—1044no—
753C2×C4C2×C22⋊Dic1312yes—
754C2×C4C2×C22⋊Dic1312yes—
755C2×C4C2×C22⋊Dic1312yes—
756C2×C4C2×C22⋊Dic1312yes—
757C2×C4C2×D4×D1311yescharacteristic
758C2×C4C2×#612911yescharacteristic
759C2×C4#8825111yescharacteristic
760C2×C4#8825111yescharacteristic
761C2×C4C23×Dic1311yescharacteristic
762C2×C4C22×C22⋊D1311yescharacteristic
763C8—262no—
764C8—521no—
765C8—521no—
766C8—521no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1171888614yescomplemented
781C22D4×C22⋊D1311yescharacteristic
782C22#1171951111yescharacteristic
783C22C2×#8819611yescharacteristic
784C22C2×#8819611yescharacteristic
785C22#1171954211yescharacteristic
786C22#1171954311yescharacteristic
787C22C22×C22⋊Dic1311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—522no—
797C4—1041no—
798C4—1041no—
799C4—1041no—
800C4C2×D4×Dic1311yescharacteristic
801C4#1171950311yescharacteristic
802C4D4×C22⋊D1311yescharacteristic
803C4#1171951111yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×C22⋊Dic1311yescharacteristic
807C2C2×#1171888611yescharacteristic
808C2#1312336911yescharacteristic
809C2#1312634711yescharacteristic
810C2#1312640711yescharacteristic
811C2#1312688711yescharacteristic
812C2#1312700711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenterC2×D4×Q8D13
hypocenterC13#22425
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11718886C2semidirect
3. C22×#88075C2semidirect
5. #13115760C2semidirect
6. #13115657C2semidirect
7. #13115270C2semidirect
8. #13115260C2semidirect
9. #13115149C2semidirect
10. #13115144C2semidirect
11. #13114851C2semidirect
12. #13114771C2semidirect
13. #13114771C2semidirect
14. #13114666C2semidirect
19. D4×Q8×C13C4semidirect
77. C22×Q8×C13C2×C4semidirect
89. C13×C4⋊Q8C2×C4semidirect
95. C13×C22⋊Q8C2×C4semidirect
97. C4×Q8×C13C2×C4semidirect
149. #88075D4semidirect
381. D4×Q8Dic13semidirect
437. C22×C13#419semidirect
474. C22×Q8C2×Dic13semidirect
496. C4⋊Q8C2×Dic13semidirect
502. C22⋊Q8C2×Dic13semidirect
504. C4×Q8C2×Dic13semidirect
679. C13#22425semidirect
780. C22#11718886semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
C2×#117188862
C22×#880752
#131177652
#131157602
#131156572
#131152702
#131152602
#131151492
#131151442
#131148512
#131147712
#131146662
C2×D4×Q8×C132
#2242513