Finite Group Databasebeta

← C2×#13117987 #16025510

Subgroups — C2×#13117987 #16025510

Order 3328.

3302 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×#88193C211yesmaximal, characteristic
2#13117987C2116yesmaximal, direct product factor
3C2×#11718618C211yesmaximal, characteristic, complemented
4C2×#11718606C211yesmaximal, characteristic, complemented
5C2×#11718601C211yesmaximal, characteristic, complemented
6C2×#11718594C211yesmaximal, characteristic, complemented
7C2×#11718639C211yesmaximal, characteristic, complemented
8C2×#11718881C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic, complemented
10C2×#11718617C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×#11718607C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718604C211yesmaximal, characteristic, complemented
15C2×#11718603C211yesmaximal, characteristic, complemented
16C2×C13×#390C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C2×#88193C4116yescomplemented
34C2×#88193C2218yes—
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C13×#390C2218yescomplemented
45#11718881C2218yescomplemented
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718650C2218yescomplemented
57#11718639C2218yescomplemented
58#11718619C2218yescomplemented
59#11718618C2218yescomplemented
60#11718617C2218yescomplemented
61#11718617C2218yescomplemented
62#11718607C2218yescomplemented
63#11718606C2218yescomplemented
64#11718604C2218yescomplemented
65#11718603C2218yescomplemented
66#11718601C2218yescomplemented
67#11718594C2218yescomplemented
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2×C418yescomplemented
74C22×D4×C13C2314yes—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13C2×C418yes—
85C22×C22⋊D13C2×C418yescomplemented
86C22×C22⋊D13C2314yes—
87C22×C22⋊D13C2314yes—
88C23×Dic13—42no—
89C23×Dic13—42no—
90C23×Dic13—42no—
91C23×Dic13—42no—
92C23×Dic13—42no—
93C23×Dic13C2×C418yescomplemented
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2314yes—
102C23×Dic13C2314yes—
103C22×C4×D13—42no—
104C22×C4×D13—42no—
105C22×C4×D13—42no—
106C22×C4×D13C2314yes—
107C2×C13×C4⋊C4—42no—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4—42no—
111C2×C13×C22⋊C4—42no—
112C2×C13×C22⋊C4—42no—
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C42×C13—42no—
118C2×C42×C13C2314yes—
119C2×C22⋊Dic13—42no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13—42no—
122C2×C22⋊Dic13C2×C418yescomplemented
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127#88193C2×C4164yescomplemented
128C2×#6103—42no—
129C2×#6103—42no—
130C2×#6103—42no—
131C2×#6103C2×C418yescomplemented
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6101—42no—
137C2×#6101—42no—
138C2×#6101—42no—
139C2×#6101C2×C418yescomplemented
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—42no—
145C2×C4×Dic13C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2377—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
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×C13C22×C414yes—
170C24×C13C22×C414yes—
171C24×C13C2412yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13C22×C414yes—
181C23×D13C2412yes—
182C2×D4×C13—416no—
183C2×D4×C13—44no—
184C2×D4×C13—44no—
185C2×D4×C13C22×C4116yescomplemented
186C22×C4×C13—22no—
187C22×C4×C13—22no—
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—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13C22×C414yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C2×C22⋊D13—416no—
207C2×C22⋊D13—416no—
208C2×C22⋊D13—44no—
209C2×C22⋊D13—44no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13C22×C4116yes—
213C2×C22⋊D13C22×C4116yescomplemented
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×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—416no—
233C22×Dic13—44no—
234C22×Dic13—44no—
235C22×Dic13—44no—
236C22×Dic13—44no—
237C22×Dic13—44no—
238C22×Dic13—416no—
239C22×Dic13C22×C414yes—
240C22×Dic13C22×C414yes—
241C22×Dic13C22×C414yes—
242C22×Dic13C22×C4116yescomplemented
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—44no—
253C2×C4×D13—416no—
254C13×C4⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C42×C13—44no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C22⋊Dic13C22×C4116yescomplemented
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6103C22×C4116yescomplemented
268#6101—44no—
269#6101—44no—
270#6101—44no—
271#6101C22×C4116yescomplemented
272C4×Dic13—44no—
273C22×#121—131no—
274#2377—1316no—
275C2×#390—131no—
276C2×#390D1311yescharacteristic, complemented
277C2×#388—131no—
278C2×#388—131no—
279C2×#387—131no—
280C2×#387—131no—
281C2×#386—131no—
282C2×#386—131no—
283C2×#386—131no—
284C2×#386—131no—
285C2×#385—131no—
286C2×#385—131no—
287C2×#381—131no—
288C2×#380—131no—
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
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—22no—
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×C13C23×C414yes—
316C23×C13C23×C414yes—
317C23×C13C23×C412yes—
318C23×C13H(5,𝔽2)12yes—
319C23×C13H(5,𝔽2)12yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C132−1+412yes—
324C23×C13C2511yescharacteristic
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13C23×C414yes—
339D4×C13—416no—
340C2×C4×C13—28no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
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—44no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13—44no—
359C2×C4×C13C23×C414yes—
360C22⋊D13—416no—
361C22⋊D13—416no—
362C2×Dic13—28no—
363C2×Dic13—28no—
364C2×Dic13—28no—
365C2×Dic13—22no—
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—416no—
384C2×Dic13—416no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13C23×C414yes—
390C2×Dic13C23×C414yes—
391C2×Dic13C23×C414yes—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4C2×D1311yescharacteristic
396C24×C4—131no—
397C24×C4—131no—
398C24×C4—131no—
399C2×#121—1316no—
400C2×#121—138no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4C2×D1311yescharacteristic
406C22×C22⋊C4—131no—
407C22×C22⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
415C22×C22⋊C4C2×D1311yescharacteristic
416C22×C22⋊C4C2×D1311yescharacteristic
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C42—131no—
419C22×C42C2×D1311yescharacteristic
420#390—138no—
421#390C2×D1318yescomplemented
422#388—138no—
423#388—138no—
424#387—138no—
425#387—138no—
426#386—138no—
427#386—138no—
428#386—138no—
429#386—138no—
430#385—138no—
431#385—138no—
432#381—138no—
433#380—138no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13—416no—
451C22×C13—416no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13#51814yes—
461C22×C13#51814yes—
462C22×C13#52014yes—
463C22×C13#56014yes—
464C22×C13#56014yes—
465C22×C13#56214yes—
466C22×C13#56214yes—
467C22×C13C24×C411yescharacteristic
468C22×C13C2×H(5,𝔽2)11yescharacteristic
469C22×C13C2×H(5,𝔽2)11yescharacteristic
470C22×C13C2×H(5,𝔽2)11yescharacteristic
471C22×C13C2×H(5,𝔽2)11yescharacteristic
472C22×C13C2×H(5,𝔽2)11yescharacteristic
473C22×C13C2×2−1+411yescharacteristic
474C2×D13—24no—
475C2×D13—24no—
476C2×D13—24no—
477C2×D13—416no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C4×C13—24no—
483C4×C13—42no—
484C4×C13—42no—
485C4×C13—42no—
486C4×C13—42no—
487Dic13—24no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494C25—131no—
495C25C22×D1311yescharacteristic
496C25C22×D1311yescharacteristic
497C22×D4—42no—
498C22×D4—42no—
499C22×D4—138no—
500C22×D4—138no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—522no—
504C22×D4—522no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4C4×D1318yescomplemented
508C22×D4C22×D1314yes—
509C23×C4—131no—
510C23×C4—131no—
511C23×C4—131no—
512C23×C4—138no—
513C23×C4—134no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—134no—
519C23×C4—134no—
520C23×C4—522no—
521C23×C4—522no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4—522no—
527C23×C4—522no—
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533#121—1364no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—138no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—522no—
541C2×C4⋊C4—522no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—138no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—138no—
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—134no—
558C2×C22⋊C4—522no—
559C2×C22⋊C4—522no—
560C2×C22⋊C4—522no—
561C2×C22⋊C4—522no—
562C2×C22⋊C4—522no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4C22×D1314yes—
565C2×C22⋊C4C22×D1314yes—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—42no—
569C2×C42—134no—
570C2×C42—522no—
571C2×C42C22×D1314yes—
572#95—134no—
573#95—134no—
574#95—134no—
575#95—134no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582C2×C13—44no—
583C2×C13—44no—
584C2×C13#237718yescomplemented
585C2×C13C2×#51811yescharacteristic
586C2×C13C2×#51811yescharacteristic
587C2×C13C2×#52011yescharacteristic
588C2×C13C2×#56011yescharacteristic
589C2×C13C2×#56011yescharacteristic
590C2×C13C2×#56211yescharacteristic
591C2×C13C2×#56211yescharacteristic
592D13—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—134no—
606C24—132no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24C2×C4×D1314yes—
614C24C2×C4×D1314yes—
615C24C23×D1312yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—416no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—1316no—
622C2×D4—1316no—
623C2×D4—5216no—
624C2×D4—5216no—
625C2×D4—524no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—524no—
629C2×D4C2×C4×D13116yescomplemented
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—134no—
645C22×C4—134no—
646C22×C4—134no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—1316no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
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—524no—
674C22×C4—524no—
675C22×C4—524no—
676C22×C4—5216no—
677C22×C4—5216no—
678C22×C4—524no—
679C22×C4—524no—
680C22×C4—524no—
681C22×C4—524no—
682C22×C4—524no—
683C22×C4—5216no—
684C22×C4C2×C4×D1314yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C22×C4C23×D1312yes—
689C22×C4C23×D1312yes—
690C4⋊C4—44no—
691C4⋊C4—1316no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—1316no—
700C22⋊C4—1316no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—44no—
708C42—524no—
709C13C2×#237711yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—134no—
737C23—268no—
738C23—268no—
739C23—268no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23C22×C4×D1314yes—
751C23C22×C4×D1314yes—
752C23C22×C4×D1312yes—
753C23#8825112yes—
754C23#8825112yes—
755C23#8825112yes—
756C23#8825112yes—
757C23#8825612yes—
758C23#8825712yes—
759C23C24×D1311yescharacteristic
760D4—416no—
761D4—5216no—
762D4—5216no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
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—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—134no—
783C2×C4—134no—
784C2×C4—134no—
785C2×C4—268no—
786C2×C4—268no—
787C2×C4—268no—
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—5216no—
807C2×C4—5216no—
808C2×C4—5216no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4—524no—
813C2×C4C22×C4×D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—416no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—264no—
831C22—264no—
832C22—264no—
833C22—522no—
834C22—5216no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22#1171919114yes—
839C22#1171925014yes—
840C22#1171925114yes—
841C22#1171932514yes—
842C22#1171932614yes—
843C22#1171938914yes—
844C22#1171942514yes—
845C22C23×C4×D1311yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C2×#8825111yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C2×#8825711yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—264no—
858C4—264no—
859C4—264no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—44no—
866C2—524no—
867C2#1311798718yesdirect product factor
868C2C2×#1171925011yescharacteristic
869C2C2×#1171919111yescharacteristic
870C2C2×#1171925111yescharacteristic
871C2C2×#1171942511yescharacteristic
872C2C2×#1171932511yescharacteristic
873C2C2×#1171938911yescharacteristic
874C2C2×#1171932611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC22×#88193C2
cosocleC23×C13C25
hypercenterC2×#390D13
hypocenterC13C2×#2377
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. #13117987C2direct (N × H)
3. C2×#11718618C2semidirect
4. C2×#11718606C2semidirect
5. C2×#11718601C2semidirect
6. C2×#11718594C2semidirect
7. C2×#11718639C2semidirect
8. C2×#11718881C2semidirect
9. C2×#11718619C2semidirect
10. C2×#11718617C2semidirect
11. C2×#11718617C2semidirect
12. C2×#11718607C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718604C2semidirect
15. C2×#11718603C2semidirect
16. C2×C13×#390C2semidirect
33. C2×#88193C4semidirect
44. C13×#390C22semidirect
45. #11718881C22semidirect
56. #11718650C22semidirect
57. #11718639C22semidirect
58. #11718619C22semidirect
59. #11718618C22semidirect
60. #11718617C22semidirect
61. #11718617C22semidirect
62. #11718607C22semidirect
63. #11718606C22semidirect
64. #11718604C22semidirect
65. #11718603C22semidirect
66. #11718601C22semidirect
67. #11718594C22semidirect
73. C22×D4×C13C2×C4semidirect
85. C22×C22⋊D13C2×C4semidirect
93. C23×Dic13C2×C4semidirect
122. C2×C22⋊Dic13C2×C4semidirect
127. #88193C2×C4semidirect
131. C2×#6103C2×C4semidirect
139. C2×#6101C2×C4semidirect
185. C2×D4×C13C22×C4semidirect
213. C2×C22⋊D13C22×C4semidirect
242. C22×Dic13C22×C4semidirect
263. C22⋊Dic13C22×C4semidirect
267. #6103C22×C4semidirect
271. #6101C22×C4semidirect
276. C2×#390D13semidirect
421. #390C2×D13semidirect
507. C22×D4C4×D13semidirect
584. C2×C13#2377semidirect
629. C2×D4C2×C4×D13semidirect
709. C13C2×#2377semidirect
867. C2#13117987direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881932
#131179872
C2×#117186182
C2×#117186062
C2×#117186012
C2×#117185942
C2×#117186392
C2×#117188812
C2×#117186192
C2×#117186172
C2×#117186072
C2×#117186502
C2×#117186042
C2×#117186032
C2×C13×#3902
C2×#237713