Finite Group Databasebeta

← C2×#13117596 #16021781

Subgroups — C2×#13117596 #16021781

Order 3328.

3414 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×#88138C211yesmaximal, characteristic
2#13117596C2116yesmaximal, direct product factor
3C2×#11718600C211yesmaximal, characteristic, complemented
4C2×#11718618C211yesmaximal, characteristic, complemented
5C2×#11718612C211yesmaximal, characteristic, complemented
6C2×#11718330C211yesmaximal, characteristic, complemented
7C2×#11718316C211yesmaximal, characteristic, complemented
8C2×#11718594C211yesmaximal, characteristic, complemented
9C2×#11718874C211yesmaximal, characteristic, complemented
10C2×#11718874C211yesmaximal, characteristic, complemented
11C2×#11718326C211yesmaximal, characteristic, complemented
12C2×#11718617C211yesmaximal, characteristic, complemented
13C2×#11718325C211yesmaximal, characteristic, complemented
14C2×C4×#6103C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88138C4116yescomplemented
43C2×#88138C2218yes—
44C4×C13×C22⋊C4C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718874C2218yescomplemented
48#11718874C2218yescomplemented
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718618C2218yescomplemented
58#11718617C2218yescomplemented
59#11718612C2218yescomplemented
60#11718600C2218yescomplemented
61C4×#6103C2218yescomplemented
62C4×#6103C2218yescomplemented
63#11718594C2218yescomplemented
64#11718330C2218yescomplemented
65#11718326C2218yescomplemented
66#11718325C2218yescomplemented
67#11718316C2218yescomplemented
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—42no—
73C23×C4×C13—42no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2314yes—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13—42no—
85C22×C22⋊D13C2×C418yes—
86C22×C22⋊D13C2×C418yescomplemented
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2314yes—
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C22×D52—42no—
96C22×D52—42no—
97C22×D52C2×C418yescomplemented
98C22×D52C2314yes—
99C22×C4×D13—24no—
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13—42no—
103C22×C4×D13—42no—
104C22×C4×D13C2×C418yescomplemented
105C22×C4×D13C2314yes—
106C22×C4×D13C2314yes—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4C2×C418yescomplemented
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C42×C13—42no—
112C2×C42×C13—42no—
113C2×C42×C13C2314yes—
114C2×C42×C13C2314yes—
115C2×C22⋊Dic13—42no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—42no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103C2×C418yescomplemented
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×C4⋊Dic13—42no—
136C2×C4⋊Dic13C2314yes—
137C2×#6101—42no—
138C2×#6101C2×C418yescomplemented
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×C4×Dic13—42no—
142C2×C4×Dic13—42no—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145#88138C2×C4164yescomplemented
146C13×#95C2314yes—
147C13×#95C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2333—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C22×C414yes—
164C24×C13C2412yes—
165C24×C13C2411yescharacteristic
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13C22×C414yes—
179C23×D13C22×C414yes—
180C23×D13C2412yes—
181C23×D13C2412yes—
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—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—28no—
197C22×C4×C13—44no—
198C22×C4×C13—44no—
199C22×C4×C13—416no—
200C22×C4×C13C22×C414yes—
201C22×C4×C13C22×C414yes—
202C22×C4×C13#4114yes—
203C22×C4×C13#4114yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C2×C22⋊D13—416no—
211C2×C22⋊D13—416no—
212C2×C22⋊D13—44no—
213C2×C22⋊D13—44no—
214C2×C22⋊D13—44no—
215C2×C22⋊D13—44no—
216C2×C22⋊D13C22×C4116yes—
217C2×C22⋊D13C22×C4116yescomplemented
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—22no—
233C22×Dic13—22no—
234C22×Dic13C22×C414yes—
235C22×Dic13C22×C414yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C2×D52—416no—
243C2×D52—44no—
244C2×D52—44no—
245C2×D52C22×C4116yescomplemented
246C2×C4×D13—28no—
247C2×C4×D13—416no—
248C2×C4×D13—44no—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—416no—
253C2×C4×D13C22×C4116yescomplemented
254C13×C22⋊C4—28no—
255C13×C22⋊C4C22×C4116yescomplemented
256C42×C13—44no—
257C42×C13—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6103C22×C4116yescomplemented
268C4⋊Dic13—44no—
269#6101—44no—
270#6101C22×C4116yescomplemented
271C4×Dic13—44no—
272C4×Dic13—44no—
273C22×#121—131no—
274#2333—1316no—
275C2×#390—131no—
276C2×#390—131no—
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×#381—131no—
286C2×C4×C22⋊C4—131no—
287C2×C4×C22⋊C4—131no—
288C2×C4×C22⋊C4D1311yescharacteristic, complemented
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13C23×C414yes—
303C23×C13C23×C412yes—
304C23×C13C2×#4112yes—
305C23×C13C2×#4112yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13C2511yescharacteristic
311C22×D13—28no—
312C22×D13—28no—
313C22×D13—28no—
314C22×D13—28no—
315C22×D13—28no—
316C22×D13—28no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13C23×C414yes—
338C22×D13C23×C414yes—
339C2×C4×C13—28no—
340C2×C4×C13—28no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
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—22no—
356C2×C4×C13—22no—
357C2×C4×C13—416no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13C23×C414yes—
361C2×C4×C13C23×C414yes—
362C2×C4×C13C2×#4114yes—
363C2×C4×C13C2×#4114yes—
364C22⋊D13—416no—
365C22⋊D13—416no—
366C2×Dic13—28no—
367C2×Dic13—28no—
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—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13C23×C414yes—
389C2×Dic13C23×C414yes—
390D52—416no—
391C4×D13—416no—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4—131no—
396C24×C4—131no—
397C24×C4—131no—
398C24×C4C2×D1311yescharacteristic
399C2×#121—1316no—
400C2×#121—138no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C22⋊C4—131no—
405C22×C22⋊C4—131no—
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×C42—131no—
417C22×C42—131no—
418C22×C42C2×D1311yescharacteristic
419C22×C42C2×D1311yescharacteristic
420#390—138no—
421#390—138no—
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#381—138no—
431C4×C22⋊C4—138no—
432C4×C22⋊C4—138no—
433C4×C22⋊C4C2×D1318yescomplemented
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×#95C2×D1311yescharacteristic
443C2×#95C2×D1311yescharacteristic
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—416no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13C4×#4114yes—
453C22×C13#51814yes—
454C22×C13#51814yes—
455C22×C13#53814yes—
456C22×C13#53814yes—
457C22×C13#54014yes—
458C22×C13#54014yes—
459C22×C13C24×C411yescharacteristic
460C22×C13C22×#4111yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C2×H(5,𝔽2)11yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×H(5,𝔽2)11yescharacteristic
465C22×C13C2×H(5,𝔽2)11yescharacteristic
466C2×D13—24no—
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—24no—
471C2×D13—24no—
472C2×D13—416no—
473C2×D13—416no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C4×C13—24no—
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—
494C25—131no—
495C25—131no—
496C25C22×D1311yescharacteristic
497C22×D4—138no—
498C22×D4—138no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—138no—
502C22×D4—134no—
503C22×D4—522no—
504C22×D4—522no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4—522no—
508C22×D4—522no—
509C23×C4—24no—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—138no—
515C23×C4—134no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—134no—
521C23×C4—264no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1314yes—
533#121—1364no—
534C2×C4⋊C4—138no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—522no—
539C2×C4⋊C4—522no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—138no—
542C2×C22⋊C4—134no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—134no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—264no—
553C2×C22⋊C4—264no—
554C2×C22⋊C4—264no—
555C2×C22⋊C4—522no—
556C2×C22⋊C4—522no—
557C2×C22⋊C4—522no—
558C2×C22⋊C4—522no—
559C2×C22⋊C4—522no—
560C2×C22⋊C4—522no—
561C2×C22⋊C4C4×D1318yescomplemented
562C2×C22⋊C4C22×D1314yes—
563C2×C22⋊C4C22×D1314yes—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—134no—
567C2×C42—134no—
568C2×C42—522no—
569C2×C42—522no—
570C2×C42C22×D1314yes—
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#95C22×D1314yes—
581#95C22×D1314yes—
582C2×C13—44no—
583C2×C13#233318yescomplemented
584C2×C13C2×C4×#4111yescharacteristic
585C2×C13C2×#51811yescharacteristic
586C2×C13C2×#51811yescharacteristic
587C2×C13C2×#53811yescharacteristic
588C2×C13C2×#53811yescharacteristic
589C2×C13C2×#54011yescharacteristic
590C2×C13C2×#54011yescharacteristic
591D13—44no—
592D13—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—134no—
600C24—134no—
601C24—132no—
602C24—132no—
603C24—262no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24C2×C4×D1314yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—1316no—
619C2×D4—1316no—
620C2×D4—1316no—
621C2×D4—5216no—
622C2×D4—524no—
623C2×D4—524no—
624C2×D4—5216no—
625C2×D4—5216no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—524no—
629C2×D4—524no—
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—28no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—1316no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
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—268no—
674C22×C4—5216no—
675C22×C4—524no—
676C22×C4—524no—
677C22×C4—524no—
678C22×C4—524no—
679C22×C4—5216no—
680C22×C4C2×C4×D1314yes—
681C22×C4C2×C4×D1314yes—
682C22×C4#612714yes—
683C22×C4#612714yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C22×C4C23×D1312yes—
689C22×C4C23×D1312yes—
690C4⋊C4—1316no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C22⋊C4—28no—
694C22⋊C4—1316no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—524no—
699C22⋊C4—524no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4C2×C4×D13116yescomplemented
705C42—44no—
706C42—44no—
707C42—524no—
708C42—524no—
709C13C2×#233311yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—134no—
724C23—134no—
725C23—268no—
726C23—268no—
727C23—268no—
728C23—268no—
729C23—268no—
730C23—268no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23C22×C4×D1314yes—
752C23C22×C4×D1312yes—
753C23C2×#612712yes—
754C23C2×#612712yes—
755C23#8825112yes—
756C23#8825112yes—
757C23#8825612yes—
758C23#8825612yes—
759C23C24×D1311yescharacteristic
760D4—5216no—
761D4—5216no—
762D4—5216no—
763C2×C4—28no—
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—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—134no—
785C2×C4—134no—
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—5216no—
805C2×C4—5216no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4C22×C4×D1314yes—
811C2×C4C22×C4×D1314yes—
812C2×C4C2×#612714yes—
813C2×C4C2×#612714yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—416no—
820C22—42no—
821C22—42no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—264no—
826C22—264no—
827C22—264no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—5216no—
833C22—5216no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22C4×#612714yes—
839C22#1171919914yes—
840C22#1171924014yes—
841C22#1171925014yes—
842C22#1171925014yes—
843C22#1171926514yes—
844C22#1171926714yes—
845C22C23×C4×D1311yescharacteristic
846C22C22×#612711yescharacteristic
847C22C22×#612711yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C2×#8825611yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—264no—
859C4—264no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—524no—
866C2—524no—
867C2#1311759618yesdirect product factor
868C2C2×C4×#612711yescharacteristic
869C2C2×#1171925011yescharacteristic
870C2C2×#1171925011yescharacteristic
871C2C2×#1171926511yescharacteristic
872C2C2×#1171919911yescharacteristic
873C2C2×#1171926711yescharacteristic
874C2C2×#1171924011yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2333
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13117596C2direct (N × H)
3. C2×#11718600C2semidirect
4. C2×#11718618C2semidirect
5. C2×#11718612C2semidirect
6. C2×#11718330C2semidirect
7. C2×#11718316C2semidirect
8. C2×#11718594C2semidirect
9. C2×#11718874C2semidirect
10. C2×#11718874C2semidirect
11. C2×#11718326C2semidirect
12. C2×#11718617C2semidirect
13. C2×#11718325C2semidirect
14. C2×C4×#6103C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
42. C2×#88138C4semidirect
44. C4×C13×C22⋊C4C22semidirect
47. #11718874C22semidirect
48. #11718874C22semidirect
57. #11718618C22semidirect
58. #11718617C22semidirect
59. #11718612C22semidirect
60. #11718600C22semidirect
61. C4×#6103C22semidirect
62. C4×#6103C22semidirect
63. #11718594C22semidirect
64. #11718330C22semidirect
65. #11718326C22semidirect
66. #11718325C22semidirect
67. #11718316C22semidirect
86. C22×C22⋊D13C2×C4semidirect
97. C22×D52C2×C4semidirect
104. C22×C4×D13C2×C4semidirect
108. C2×C13×C22⋊C4C2×C4semidirect
126. C2×#6103C2×C4semidirect
138. C2×#6101C2×C4semidirect
145. #88138C2×C4semidirect
217. C2×C22⋊D13C22×C4semidirect
245. C2×D52C22×C4semidirect
253. C2×C4×D13C22×C4semidirect
255. C13×C22⋊C4C22×C4semidirect
267. #6103C22×C4semidirect
270. #6101C22×C4semidirect
288. C2×C4×C22⋊C4D13semidirect
433. C4×C22⋊C4C2×D13semidirect
561. C2×C22⋊C4C4×D13semidirect
583. C2×C13#2333semidirect
704. C22⋊C4C2×C4×D13semidirect
709. C13C2×#2333semidirect
867. C2#13117596direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
#131175962
C2×#117186002
C2×#117186182
C2×#117186122
C2×#117183302
C2×#117183162
C2×#117185942
C2×#117188742
C2×#117183262
C2×#117186172
C2×#117183252
C2×C4×#61032
C2×C4×C13×C22⋊C42
C2×#233313