Finite Group Databasebeta

← C2×#13117988 #16025511

Subgroups — C2×#13117988 #16025511

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×#88192C211yesmaximal, characteristic
2#13117988C2116yesmaximal, direct product factor
3C2×#11718618C211yesmaximal, characteristic, complemented
4C2×#11718618C211yesmaximal, characteristic, complemented
5C2×#11718606C211yesmaximal, characteristic, complemented
6C2×#11718605C211yesmaximal, characteristic, complemented
7C2×#11718314C211yesmaximal, characteristic, complemented
8C2×#11718315C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic, complemented
10C2×#11718874C211yesmaximal, characteristic, complemented
11C2×#11718619C211yesmaximal, characteristic, complemented
12C2×#11718871C211yesmaximal, characteristic, complemented
13C2×#11718607C211yesmaximal, characteristic, complemented
14C2×#11718325C211yesmaximal, characteristic, complemented
15C2×#11718328C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88192C4116yescomplemented
32C2×#88192C2218yes—
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C13×#386C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718881C2218yescomplemented
48#11718874C2218yescomplemented
49#11718871C2218yescomplemented
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718619C2218yescomplemented
59#11718618C2218yescomplemented
60#11718618C2218yescomplemented
61#11718607C2218yescomplemented
62#11718606C2218yescomplemented
63#11718605C2218yescomplemented
64#11718328C2218yescomplemented
65#11718325C2218yescomplemented
66#11718315C2218yescomplemented
67#11718314C2218yescomplemented
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2×C418yes—
74C22×D4×C13C2314yes—
75C23×C4×C13—42no—
76C23×C4×C13—42no—
77C23×C4×C13—42no—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2314yes—
84C22×C22⋊D13—42no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13C2×C418yescomplemented
89C22×C22⋊D13C2×C418yescomplemented
90C22×C22⋊D13C2314yes—
91C22×C22⋊D13C2314yes—
92C23×Dic13—42no—
93C23×Dic13—42no—
94C23×Dic13—42no—
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2314yes—
103C22×C4×D13—42no—
104C22×C4×D13—42no—
105C22×C4×D13C2×C418yescomplemented
106C22×C4×D13C2314yes—
107C2×C13×C22⋊C4—42no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C13×C22⋊C4C2314yes—
113C2×C22⋊Dic13—42no—
114C2×C22⋊Dic13—42no—
115C2×C22⋊Dic13—42no—
116C2×C22⋊Dic13C2×C418yescomplemented
117C2×C22⋊Dic13C2×C418yescomplemented
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123#88192C2×C4164yescomplemented
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103—42no—
127C2×#6103—42no—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×C4⋊Dic13C2×C418yescomplemented
133C2×C4⋊Dic13C2314yes—
134C2×#6101—42no—
135C2×#6101—42no—
136C2×#6101—42no—
137C2×#6101—42no—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×C4×Dic13—42no—
143C2×C4×Dic13—42no—
144C2×C4×Dic13C2314yes—
145C2×C4×Dic13C2314yes—
146C13×#95C2314yes—
147C13×#95C2314yes—
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×C4116yes—
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×C13—44no—
201C22×C4×C13—44no—
202C22×C4×C13—44no—
203C22×C4×C13—416no—
204C22×C4×C13C22×C414yes—
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×C4116yescomplemented
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×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—44no—
237C22×Dic13—44no—
238C22×Dic13—44no—
239C22×Dic13—416no—
240C22×Dic13C22×C414yes—
241C22×Dic13C22×C414yes—
242C22×Dic13C22×C414yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×C4×D13—416no—
251C2×C4×D13—44no—
252C2×C4×D13—44no—
253C2×C4×D13C22×C4116yescomplemented
254C13×C22⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C22⋊Dic13—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260C22⋊Dic13C22×C4116yescomplemented
261C22⋊Dic13C22×C4116yescomplemented
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266C4⋊Dic13C22×C4116yescomplemented
267#6101—44no—
268#6101—44no—
269#6101—44no—
270#6101—44no—
271C4×Dic13—44no—
272C4×Dic13—44no—
273C22×#121—131no—
274#2377—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×#386D1311yescharacteristic, complemented
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—416no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13C23×C414yes—
361C22⋊D13—416no—
362C22⋊D13—416no—
363C2×Dic13—28no—
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—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×C4C2×D1311yescharacteristic
399C2×#121—1316no—
400C2×#121—138no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊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⋊C4—131no—
415C22×C22⋊C4C2×D1311yescharacteristic
416C22×C22⋊C4C2×D1311yescharacteristic
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C42—131no—
419C22×C42—131no—
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#386C2×D1318yescomplemented
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×#95C2×D1311yescharacteristic
443C2×#95C2×D1311yescharacteristic
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×D1318yes—
508C22×D4C22×D1314yes—
509C23×C4—42no—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—138no—
516C23×C4—134no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—134no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4—522no—
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—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—522no—
541C2×C4⋊C4—522no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4—522no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—138no—
548C2×C22⋊C4—138no—
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—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⋊C4—522no—
565C2×C22⋊C4C22×D1314yes—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—134no—
569C2×C42—134no—
570C2×C42—522no—
571C2×C42—522no—
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—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×D13116yes—
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—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—134no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—1316no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
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—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
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—1316no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—1316no—
699C22⋊C4—1316no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—524no—
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—416no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—134no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—268no—
787C2×C4—268no—
788C2×C4—268no—
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—262no—
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—42no—
823C22—42no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—264no—
831C22—264no—
832C22—264no—
833C22—522no—
834C22—522no—
835C22—5216no—
836C22—522no—
837C22—522no—
838C22#1171919114yes—
839C22#1171925014yes—
840C22#1171925114yes—
841C22#1171930014yes—
842C22#1171932514yes—
843C22#1171932614yes—
844C22#1171937214yes—
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#1311798818yesdirect product factor
868C2C2×#1171925011yescharacteristic
869C2C2×#1171919111yescharacteristic
870C2C2×#1171925111yescharacteristic
871C2C2×#1171932511yescharacteristic
872C2C2×#1171930011yescharacteristic
873C2C2×#1171932611yescharacteristic
874C2C2×#1171937211yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC22×#88192C2
cosocleC23×C13C25
hypercenterC2×#386D13
hypocenterC13C2×#2377
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #13117988C2direct (N × H)
3. C2×#11718618C2semidirect
4. C2×#11718618C2semidirect
5. C2×#11718606C2semidirect
6. C2×#11718605C2semidirect
7. C2×#11718314C2semidirect
8. C2×#11718315C2semidirect
9. C2×#11718881C2semidirect
10. C2×#11718874C2semidirect
11. C2×#11718619C2semidirect
12. C2×#11718871C2semidirect
13. C2×#11718607C2semidirect
14. C2×#11718325C2semidirect
15. C2×#11718328C2semidirect
16. C2×C13×#386C2semidirect
31. C2×#88192C4semidirect
44. C13×#386C22semidirect
47. #11718881C22semidirect
48. #11718874C22semidirect
49. #11718871C22semidirect
58. #11718619C22semidirect
59. #11718618C22semidirect
60. #11718618C22semidirect
61. #11718607C22semidirect
62. #11718606C22semidirect
63. #11718605C22semidirect
64. #11718328C22semidirect
65. #11718325C22semidirect
66. #11718315C22semidirect
67. #11718314C22semidirect
88. C22×C22⋊D13C2×C4semidirect
89. C22×C22⋊D13C2×C4semidirect
105. C22×C4×D13C2×C4semidirect
116. C2×C22⋊Dic13C2×C4semidirect
117. C2×C22⋊Dic13C2×C4semidirect
123. #88192C2×C4semidirect
132. C2×C4⋊Dic13C2×C4semidirect
216. C2×C22⋊D13C22×C4semidirect
217. C2×C22⋊D13C22×C4semidirect
253. C2×C4×D13C22×C4semidirect
260. C22⋊Dic13C22×C4semidirect
261. C22⋊Dic13C22×C4semidirect
266. C4⋊Dic13C22×C4semidirect
284. C2×#386D13semidirect
429. #386C2×D13semidirect
584. C2×C13#2377semidirect
709. C13C2×#2377semidirect
867. C2#13117988direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881922
#131179882
C2×#117186182
C2×#117186062
C2×#117186052
C2×#117183142
C2×#117183152
C2×#117188812
C2×#117188742
C2×#117186192
C2×#117188712
C2×#117186072
C2×#117183252
C2×#117183282
C2×C13×#3862
C2×#237713