Finite Group Databasebeta

← C2×#13118943 #16031488

Subgroups — C2×#13118943 #16031488

Order 3328.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88146C211yesmaximal, characteristic, complemented
2#13118943C2116yesmaximal, direct product factor
3C2×#11718610C211yesmaximal, characteristic, complemented
4C2×#11718614C211yesmaximal, characteristic, complemented
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718884C211yesmaximal, characteristic
7C2×#11718882C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic, complemented
9C2×#11718605C211yesmaximal, characteristic, complemented
10C2×#11718642C211yesmaximal, characteristic, complemented
11C2×#11718639C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718617C211yesmaximal, characteristic, complemented
14C2×#11718617C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C13×#123C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C2×C13×#123—28no—
23C2×C13×#123C2218yescomplemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88146—28no—
47C2×#88146C2218yescomplemented
48#11718884C2218yes—
49#11718882C2218yescomplemented
50#11718874C2218yescomplemented
51C4×C22⋊Dic13C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718655C2218yescomplemented
61#11718642C2218yescomplemented
62#11718639C2218yescomplemented
63#11718618C2218yescomplemented
64#11718617C2218yescomplemented
65#11718617C2218yescomplemented
66#11718614C2218yescomplemented
67#11718610C2218yescomplemented
68#11718605C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—42no—
75C22×D4×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—42no—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×C22⋊D13—24no—
86C22×C22⋊D13—24no—
87C22×C22⋊D13—24no—
88C22×C22⋊D13—24no—
89C22×C22⋊D13—42no—
90C22×C22⋊D13—42no—
91C22×C22⋊D13C2314yes—
92C22×C22⋊D13C2314yes—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13C2314yes—
104C13×#123—232no—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4D418yescomplemented
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4C2314yes—
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C22⋊Dic13—24no—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13—42no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×#6103—24no—
128C2×#6103—24no—
129C2×#6103—42no—
130C2×#6103—42no—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×C4⋊Dic13—24no—
136C2×C4⋊Dic13—42no—
137C2×C4⋊Dic13C2314yes—
138C2×C4⋊Dic13C2314yes—
139C2×#6101—24no—
140C2×#6101—42no—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149#88146—232no—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2471—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13#4114yes—
183C23×D13C2412yes—
184C2×D4×C13—28no—
185C2×D4×C13—28no—
186C2×D4×C13—44no—
187C2×D4×C13—416no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—28no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—28no—
202C22×C4×C13—44no—
203C22×C4×C13—416no—
204C22×C4×C13C2×D414yes—
205C22×C4×C13C2×D414yes—
206C22×C4×C13C2×D414yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—416no—
219C2×C22⋊D13—416no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13#4114yes—
240C22×Dic13#4114yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C2×C4×D13—232no—
249C2×C4×D13—28no—
250C2×C4×D13—28no—
251C2×C4×D13—28no—
252C13×C4⋊C4—28no—
253C13×C4⋊C4C2×D4116yescomplemented
254C13×C22⋊C4—28no—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—28no—
259C22⋊Dic13—28no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263#6103—28no—
264#6103—28no—
265#6103—44no—
266#6103—44no—
267C4⋊Dic13—28no—
268C4⋊Dic13—44no—
269#6101—28no—
270#6101—44no—
271C4×Dic13—28no—
272C4×Dic13—28no—
273C4×Dic13—44no—
274C22×#123D1311yescharacteristic, complemented
275C22×#117—131no—
276#2471—1316no—
277C2×#399—131no—
278C2×#397—131no—
279C2×#396—131no—
280C2×#392—131no—
281C2×#390—131no—
282C2×#390—131no—
283C2×#388—131no—
284C2×#387—131no—
285C2×#387—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×C4×C22⋊C4—131no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13C22×D412yes—
318C23×C13C2×#4114yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13H(5,𝔽2)12yes—
325C23×C13C2511yescharacteristic
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13C2×#4114yes—
340D4×C13—416no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—416no—
357C2×C4×C13—44no—
358C2×C4×C13—44no—
359C2×C4×C13C22×D414yes—
360C2×C4×C13C22×D414yes—
361C2×C4×C13C22×D414yes—
362C22⋊D13—416no—
363C22⋊D13—416no—
364C2×Dic13—28no—
365C2×Dic13—28no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13C2×#4114yes—
391C2×Dic13C2×#4114yes—
392C4×D13—232no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4C2×D1311yescharacteristic
396C24×C4—131no—
397C24×C4C2×D1311yescharacteristic
398C2×#123—28no—
399C2×#123C2×D1318yescomplemented
400C2×#117—138no—
401C2×#117—268no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4C2×D1311yescharacteristic
407C22×C4⋊C4C2×D1311yescharacteristic
408C22×C22⋊C4—131no—
409C22×C22⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424#399—138no—
425#397—138no—
426#396—138no—
427#392—138no—
428#390—138no—
429#390—138no—
430#388—138no—
431#387—138no—
432#387—138no—
433#386—138no—
434#386—138no—
435#386—138no—
436C4×C22⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—416no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—88no—
461C22×C13#52514yes—
462C22×C13#52914yes—
463C22×C13#54014yes—
464C22×C13#54614yes—
465C22×C13#55014yes—
466C22×C13#55114yes—
467C22×C13#55114yes—
468C22×C13C23×D411yescharacteristic
469C22×C13C22×#4111yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C2×H(5,𝔽2)11yescharacteristic
474C22×C13C2×H(5,𝔽2)11yescharacteristic
475C2×D13—24no—
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—416no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—42no—
487C4×C13—42no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25—131no—
496C25C22×D1311yescharacteristic
497C25C22×D1311yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—42no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—264no—
506C22×D4—264no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4C22×D1314yes—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—42no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—134no—
521C23×C4—264no—
522C23×C4—264no—
523C23×C4—264no—
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1314yes—
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530#123—232no—
531#117—2632no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—264no—
538C2×C4⋊C4—264no—
539C2×C4⋊C4—522no—
540C2×C4⋊C4—522no—
541C2×C4⋊C4C22⋊D1318yescomplemented
542C2×C4⋊C4C22×D1314yes—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—522no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42—264no—
575C2×C42—522no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584C2×C13—44no—
585C2×C13—82no—
586C2×C13#247118yescomplemented
587C2×C13C2×#52511yescharacteristic
588C2×C13C2×#52911yescharacteristic
589C2×C13C2×#54011yescharacteristic
590C2×C13C2×#54611yescharacteristic
591C2×C13C2×#55011yescharacteristic
592C2×C13C2×#55111yescharacteristic
593C2×C13C2×#55111yescharacteristic
594D13—44no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—134no—
609C24—132no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24#612914yes—
617C24C23×D1312yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—268no—
627C2×D4—268no—
628C2×D4—524no—
629C2×D4—524no—
630C2×D4—5216no—
631C2×D4—5216no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—28no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—268no—
658C22×C4—268no—
659C22×C4—2632no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—268no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4C2×C22⋊D1314yes—
681C22×C4C2×C22⋊D1314yes—
682C22×C4C2×C22⋊D1314yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—28no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C4⋊C4C2×C22⋊D13116yescomplemented
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—268no—
708C42—268no—
709C42—524no—
710C13C2×#247111yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—134no—
739C23—268no—
740C23—268no—
741C23—268no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—262no—
747C23—262no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23C2×#612914yes—
753C23C2×#612912yes—
754C23#8825112yes—
755C23#41×D1312yes—
756C23#41×D1312yes—
757C23#41×D1312yes—
758C23#8825612yes—
759C23C22×C22⋊D1312yes—
760C23C24×D1311yescharacteristic
761D4—416no—
762D4—5216no—
763D4—5216no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—134no—
783C2×C4—134no—
784C2×C4—2632no—
785C2×C4—268no—
786C2×C4—268no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4C22×C22⋊D1314yes—
812C2×C4C22×C22⋊D1314yes—
813C2×C4C22×C22⋊D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—264no—
831C22—264no—
832C22—264no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—5216no—
838C22#1171935414yes—
839C22#1171936314yes—
840C22#1171936414yes—
841C22#1171936814yes—
842C22#1171951114yes—
843C22#1171953314yes—
844C22#1171953914yes—
845C22C22×#612911yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C2×#41×D1311yescharacteristic
848C22C2×#41×D1311yescharacteristic
849C22C2×#41×D1311yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C23×C22⋊D1311yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—264no—
858C4—264no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—82no—
866C2—524no—
867C2#1311894318yesdirect product factor
868C2C2×#1171953311yescharacteristic
869C2C2×#1171935411yescharacteristic
870C2C2×#1171936811yescharacteristic
871C2C2×#1171951111yescharacteristic
872C2C2×#1171953911yescharacteristic
873C2C2×#1171936311yescharacteristic
874C2C2×#1171936411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×#123D13
hypocenterC13C2×#2471
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88146C2semidirect
2. #13118943C2direct (N × H)
3. C2×#11718610C2semidirect
4. C2×#11718614C2semidirect
5. C2×#11718655C2semidirect
7. C2×#11718882C2semidirect
8. C2×#11718618C2semidirect
9. C2×#11718605C2semidirect
10. C2×#11718642C2semidirect
11. C2×#11718639C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718617C2semidirect
14. C2×#11718617C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C22×C13×#123C2semidirect
23. C2×C13×#123C22semidirect
47. C2×#88146C22semidirect
49. #11718882C22semidirect
50. #11718874C22semidirect
51. C4×C22⋊Dic13C22semidirect
60. #11718655C22semidirect
61. #11718642C22semidirect
62. #11718639C22semidirect
63. #11718618C22semidirect
64. #11718617C22semidirect
65. #11718617C22semidirect
66. #11718614C22semidirect
67. #11718610C22semidirect
68. #11718605C22semidirect
106. C2×C13×C4⋊C4D4semidirect
253. C13×C4⋊C4C2×D4semidirect
274. C22×#123D13semidirect
399. C2×#123C2×D13semidirect
541. C2×C4⋊C4C22⋊D13semidirect
586. C2×C13#2471semidirect
693. C4⋊C4C2×C22⋊D13semidirect
710. C13C2×#2471semidirect
867. C2#13118943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881462
#131189432
C2×#117186102
C2×#117186142
C2×#117186552
C2×#117188842
C2×#117188822
C2×#117186182
C2×#117186052
C2×#117186422
C2×#117186392
C2×#117188742
C2×#117186172
C2×C4×C22⋊Dic132
C22×C13×#1232
C2×#247113