Finite Group Databasebeta

← C2×#13117503 #16021645

Subgroups — C2×#13117503 #16021645

Order 3328.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88137C211yesmaximal, characteristic
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4#13117503C2116yesmaximal, direct product factor
5C2×#11718308C211yesmaximal, characteristic, complemented
6C2×#11718634C211yesmaximal, characteristic, complemented
7C2×#11718612C211yesmaximal, characteristic, complemented
8C2×#11718605C211yesmaximal, characteristic, complemented
9C2×#11718314C211yesmaximal, characteristic, complemented
10C2×#11718639C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic
12C2×#11718871C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718325C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C2×C4×C22⋊D13—28no—
30C2×C4×C22⋊D13C2218yes—
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×C4⋊C4×D13—28no—
45C2×C4⋊C4×D13C2218yescomplemented
46C2×#88137C4116yescomplemented
47C2×#88137C2218yes—
48C13×#385C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51#11718871C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718650C2218yescomplemented
61#11718639C2218yescomplemented
62#11718634C2218yescomplemented
63#11718617C2218yes—
64#11718612C2218yescomplemented
65#11718605C2218yescomplemented
66#11718327C2218yescomplemented
67#11718325C2218yescomplemented
68#11718314C2218yescomplemented
69#11718308C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—42no—
74C23×C4×C13—42no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13C2×C418yes—
85C22×C22⋊D13C2314yes—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—24no—
96C22×C4×D13—42no—
97C22×C4×D13—42no—
98C22×C4×D13—42no—
99C22×C4×D13—42no—
100C22×C4×D13C2×C418yescomplemented
101C22×C4×D13D418yes—
102C22×C4×D13C2314yes—
103C22×C4×D13C2314yes—
104C22×C4×D13C2314yes—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4—42no—
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4C2×C418yescomplemented
111C2×C13×C22⋊C4C2314yes—
112C2×C13×C22⋊C4C2314yes—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—42no—
115C2×C22⋊Dic13C2×C418yescomplemented
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C4×C22⋊D13—232no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103C2×C418yescomplemented
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×C4⋊Dic13—24no—
127C2×C4⋊Dic13C2×C418yescomplemented
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×#6101—24no—
131C2×#6101—24no—
132C2×#6101—24no—
133C2×#6101—42no—
134C2×#6101C2×C418yescomplemented
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—24no—
141C2×C4×Dic13—42no—
142C2×C4×Dic13—42no—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145C2×C4×Dic13C2314yes—
146C4⋊C4×D13—232no—
147#88137C2×C4164yescomplemented
148C13×#95C2314yes—
149C13×#95C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2322—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13C22×C414yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13C22×C414yes—
173C23×D13C2×D414yes—
174C23×D13#4114yes—
175C23×D13C2412yes—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—28no—
192C22×C4×C13—44no—
193C22×C4×C13—44no—
194C22×C4×C13—416no—
195C22×C4×C13C22×C414yes—
196C22×C4×C13C22×C414yes—
197C22×C4×C13C2×D414yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C2×C22⋊D13—232no—
205C2×C22⋊D13—28no—
206C2×C22⋊D13—28no—
207C2×C22⋊D13C22×C4116yes—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13C22×C414yes—
226C22×Dic13C22×C414yes—
227C22×Dic13C22×C414yes—
228C22×Dic13C2×D414yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C2×C4×D13—232no—
237C2×C4×D13—28no—
238C2×C4×D13—28no—
239C2×C4×D13—28no—
240C2×C4×D13—416no—
241C2×C4×D13—44no—
242C2×C4×D13—44no—
243C2×C4×D13—44no—
244C2×C4×D13—44no—
245C2×C4×D13—416no—
246C2×C4×D13C22×C4116yescomplemented
247C2×C4×D13C2×D4116yes—
248C13×C4⋊C4—28no—
249C13×C4⋊C4—44no—
250C13×C22⋊C4—44no—
251C13×C22⋊C4C22×C4116yescomplemented
252C22⋊Dic13—28no—
253C22⋊Dic13—44no—
254C22⋊Dic13C22×C4116yescomplemented
255#6103—28no—
256#6103—28no—
257#6103C22×C4116yescomplemented
258C4⋊Dic13—28no—
259C4⋊Dic13C22×C4116yescomplemented
260#6101—28no—
261#6101—28no—
262#6101—28no—
263#6101—44no—
264#6101C22×C4116yescomplemented
265C4×Dic13—28no—
266C4×Dic13—44no—
267C4×Dic13—44no—
268C22×#123—131no—
269C22×C4×D4—131no—
270C23×C4⋊C4—131no—
271#2322—1316no—
272C2×#389—131no—
273C2×#389—131no—
274C2×#388—131no—
275C2×#388—131no—
276C2×#387—131no—
277C2×#387—131no—
278C2×#386—131no—
279C2×#385—131no—
280C2×#385—131no—
281C2×#385D1311yescharacteristic, complemented
282C2×#381—131no—
283C2×C4×C22⋊C4—131no—
284C23×C13—28no—
285C23×C13—28no—
286C23×C13—28no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13C23×C414yes—
298C23×C13C23×C412yes—
299C23×C13C22×D412yes—
300C23×C13C2×#4112yes—
301C23×C13H(5,𝔽2)12yes—
302C23×C13H(5,𝔽2)12yes—
303C23×C132−1+412yes—
304C23×C132−1+412yes—
305C23×C13C2511yescharacteristic
306C22×D13—28no—
307C22×D13—28no—
308C22×D13—28no—
309C22×D13—28no—
310C22×D13—28no—
311C22×D13—28no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13C4×D4116yes—
317C22×D13C23×C414yes—
318C22×D13C22×D414yes—
319C22×D13C2×#4114yes—
320C2×C4×C13—28no—
321C2×C4×C13—28no—
322C2×C4×C13—28no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
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—416no—
339C2×C4×C13—44no—
340C2×C4×C13—44no—
341C2×C4×C13—44no—
342C2×C4×C13C23×C414yes—
343C2×C4×C13C23×C414yes—
344C2×C4×C13C22×D414yes—
345C22⋊D13—232no—
346C2×Dic13—28no—
347C2×Dic13—28no—
348C2×Dic13—28no—
349C2×Dic13—28no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—44no—
368C2×Dic13—44no—
369C2×Dic13—44no—
370C2×Dic13C23×C414yes—
371C2×Dic13C23×C414yes—
372C2×Dic13C23×C414yes—
373C2×Dic13C22×D414yes—
374C4×D13—232no—
375C4×D13—416no—
376C4×D13—416no—
377C23×D4—131no—
378C24×C4—131no—
379C24×C4—131no—
380C24×C4—131no—
381C24×C4C2×D1311yescharacteristic
382C2×#123—1316no—
383C2×#123—138no—
384C2×C4×D4—138no—
385C2×C4×D4—268no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—138no—
394C22×C4⋊C4—268no—
395C22×C4⋊C4C2×D1311yescharacteristic
396C22×C4⋊C4C2×D1311yescharacteristic
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4—131no—
401C22×C22⋊C4—131no—
402C22×C22⋊C4—131no—
403C22×C22⋊C4C2×D1311yescharacteristic
404C22×C22⋊C4C2×D1311yescharacteristic
405C22×C42—131no—
406C22×C42—131no—
407C22×C42—131no—
408#389—138no—
409#389—138no—
410#388—138no—
411#388—138no—
412#387—138no—
413#387—138no—
414#386—138no—
415#385—138no—
416#385—138no—
417#385C2×D1318yescomplemented
418#381—138no—
419C4×C22⋊C4—138no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95C2×D1311yescharacteristic
429C2×#95C2×D1311yescharacteristic
430C22×C13—24no—
431C22×C13—24no—
432C22×C13—24no—
433C22×C13—416no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—42no—
437C22×C13—42no—
438C22×C13C2×C4×D414yes—
439C22×C13#52014yes—
440C22×C13#52014yes—
441C22×C13#53414yes—
442C22×C13#53614yes—
443C22×C13#53914yes—
444C22×C13#53914yes—
445C22×C13C24×C411yescharacteristic
446C22×C13C23×D411yescharacteristic
447C22×C13C22×#4111yescharacteristic
448C22×C13C2×H(5,𝔽2)11yescharacteristic
449C22×C13C2×H(5,𝔽2)11yescharacteristic
450C22×C13C2×2−1+411yescharacteristic
451C22×C13C2×2−1+411yescharacteristic
452C2×D13—232no—
453C2×D13—24no—
454C2×D13—24no—
455C2×D13—24no—
456C2×D13—24no—
457C2×D13—24no—
458C2×D13—24no—
459C2×D13C2×C4×D418yes—
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—24no—
463C4×C13—42no—
464C4×C13—42no—
465C4×C13—42no—
466Dic13—24no—
467Dic13—24no—
468Dic13—24no—
469Dic13—24no—
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473C25—131no—
474C25C22×D1311yescharacteristic
475C22×D4—138no—
476C22×D4—134no—
477C22×D4—264no—
478C22×D4—264no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—42no—
482C23×C4—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—138no—
487C23×C4—134no—
488C23×C4—138no—
489C23×C4—134no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—131no—
493C23×C4—134no—
494C23×C4—264no—
495C23×C4—264no—
496C23×C4—264no—
497C23×C4—522no—
498C23×C4—522no—
499C23×C4—522no—
500C23×C4—522no—
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1314yes—
508#123—1364no—
509C4×D4—2632no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—138no—
513C2×C4⋊C4—138no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—134no—
521C2×C4⋊C4—2632no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—264no—
525C2×C4⋊C4—264no—
526C2×C4⋊C4—522no—
527C2×C4⋊C4C22×D1314yes—
528C2×C4⋊C4C22×D1314yes—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—138no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—138no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—264no—
539C2×C22⋊C4—264no—
540C2×C22⋊C4—264no—
541C2×C22⋊C4—522no—
542C2×C22⋊C4C4×D1318yescomplemented
543C2×C22⋊C4C22×D1314yes—
544C2×C22⋊C4C22×D1314yes—
545C2×C42—134no—
546C2×C42—134no—
547C2×C42—134no—
548C2×C42—264no—
549C2×C42—522no—
550C2×C42—522no—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95C22×D1314yes—
560#95C22×D1314yes—
561C2×C13—44no—
562C2×C13#232218yescomplemented
563C2×C13C22×C4×D411yescharacteristic
564C2×C13C2×#52011yescharacteristic
565C2×C13C2×#52011yescharacteristic
566C2×C13C2×#53411yescharacteristic
567C2×C13C2×#53611yescharacteristic
568C2×C13C2×#53911yescharacteristic
569C2×C13C2×#53911yescharacteristic
570D13—28no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—134no—
578C24—134no—
579C24—134no—
580C24—132no—
581C24—262no—
582C24—262no—
583C24—262no—
584C24—262no—
585C24C2×C4×D1314yes—
586C24C23×D1312yes—
587C24C23×D1311yescharacteristic
588C2×D4—1316no—
589C2×D4—268no—
590C2×D4—2632no—
591C2×D4—268no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—416no—
611C22×C4—134no—
612C22×C4—134no—
613C22×C4—134no—
614C22×C4—134no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—1316no—
620C22×C4—1316no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—268no—
625C22×C4—2632no—
626C22×C4—268no—
627C22×C4—268no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—5216no—
646C22×C4—524no—
647C22×C4—524no—
648C22×C4—524no—
649C22×C4—524no—
650C22×C4—5216no—
651C22×C4C2×C4×D1314yes—
652C22×C4C2×C4×D1314yes—
653C22×C4D4×D1314yes—
654C22×C4C23×D1312yes—
655C22×C4C23×D1312yes—
656C22×C4C23×D1312yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C4⋊C4—28no—
661C4⋊C4—44no—
662C4⋊C4—1316no—
663C4⋊C4—1316no—
664C4⋊C4—268no—
665C4⋊C4—268no—
666C4⋊C4—268no—
667C4⋊C4—268no—
668C4⋊C4—524no—
669C22⋊C4—44no—
670C22⋊C4—1316no—
671C22⋊C4—1316no—
672C22⋊C4—268no—
673C22⋊C4—268no—
674C22⋊C4—268no—
675C22⋊C4—524no—
676C22⋊C4C2×C4×D13116yescomplemented
677C42—268no—
678C42—524no—
679C42—524no—
680C13C2×#232211yescharacteristic, complemented, Sylow
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—1316no—
695C23—134no—
696C23—134no—
697C23—134no—
698C23—268no—
699C23—268no—
700C23—268no—
701C23—268no—
702C23—268no—
703C23—268no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23—262no—
708C23C22×C4×D1314yes—
709C23C22×C4×D1312yes—
710C23C2×D4×D1312yes—
711C23#8825112yes—
712C23#8825112yes—
713C23#8825412yes—
714C23#41×D1312yes—
715C23#8825712yes—
716C23C24×D1311yescharacteristic
717D4—2632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
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—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—134no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—134no—
744C2×C4—2632no—
745C2×C4—268no—
746C2×C4—268no—
747C2×C4—268no—
748C2×C4—268no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—5216no—
767C2×C4—5216no—
768C2×C4—524no—
769C2×C4—524no—
770C2×C4—524no—
771C2×C4C22×C4×D1314yes—
772C2×C4C22×C4×D1314yes—
773C2×C4C2×D4×D1314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—138no—
783C22—2632no—
784C22—264no—
785C22—264no—
786C22—264no—
787C22—264no—
788C22—264no—
789C22—264no—
790C22#1171920914yes—
791C22C4×D4×D1314yes—
792C22#1171925114yes—
793C22#1171929414yes—
794C22#1171933314yes—
795C22#1171934314yes—
796C22#1171936514yes—
797C22C23×C4×D1311yescharacteristic
798C22C22×D4×D1311yescharacteristic
799C22C2×#8825111yescharacteristic
800C22C2×#8825111yescharacteristic
801C22C2×#8825411yescharacteristic
802C22C2×#41×D1311yescharacteristic
803C22C2×#8825711yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—264no—
811C4—264no—
812C4—264no—
813C4—264no—
814C4—522no—
815C4—522no—
816C4—522no—
817C2—44no—
818C2—268no—
819C2#1311750318yesdirect product factor
820C2C2×C4×D4×D1311yescharacteristic
821C2C2×#1171925111yescharacteristic
822C2C2×#1171920911yescharacteristic
823C2C2×#1171929411yescharacteristic
824C2C2×#1171933311yescharacteristic
825C2C2×#1171936511yescharacteristic
826C2C2×#1171934311yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×#2322
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D13C2semidirect
4. #13117503C2direct (N × H)
5. C2×#11718308C2semidirect
6. C2×#11718634C2semidirect
7. C2×#11718612C2semidirect
8. C2×#11718605C2semidirect
9. C2×#11718314C2semidirect
10. C2×#11718639C2semidirect
12. C2×#11718871C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718325C2semidirect
15. C2×#11718327C2semidirect
16. C2×C13×#385C2semidirect
45. C2×C4⋊C4×D13C22semidirect
46. C2×#88137C4semidirect
48. C13×#385C22semidirect
51. #11718871C22semidirect
60. #11718650C22semidirect
61. #11718639C22semidirect
62. #11718634C22semidirect
64. #11718612C22semidirect
65. #11718605C22semidirect
66. #11718327C22semidirect
67. #11718325C22semidirect
68. #11718314C22semidirect
69. #11718308C22semidirect
100. C22×C4×D13C2×C4semidirect
110. C2×C13×C22⋊C4C2×C4semidirect
115. C2×C22⋊Dic13C2×C4semidirect
122. C2×#6103C2×C4semidirect
127. C2×C4⋊Dic13C2×C4semidirect
134. C2×#6101C2×C4semidirect
147. #88137C2×C4semidirect
246. C2×C4×D13C22×C4semidirect
251. C13×C22⋊C4C22×C4semidirect
254. C22⋊Dic13C22×C4semidirect
257. #6103C22×C4semidirect
259. C4⋊Dic13C22×C4semidirect
264. #6101C22×C4semidirect
281. C2×#385D13semidirect
417. #385C2×D13semidirect
542. C2×C22⋊C4C4×D13semidirect
562. C2×C13#2322semidirect
676. C22⋊C4C2×C4×D13semidirect
680. C13C2×#2322semidirect
819. C2#13117503direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881372
C22×C4×C22⋊D132
C22×C4⋊C4×D132
#131175032
C2×#117183082
C2×#117186342
C2×#117186122
C2×#117186052
C2×#117183142
C2×#117186392
C2×#117186172
C2×#117188712
C2×#117186502
C2×#117183252
C2×#117183272
C2×C13×#3852
C2×#232213