Finite Group Databasebeta

← C2×#13117626 #16021813

Subgroups — C2×#13117626 #16021813

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88183C211yesmaximal, characteristic
2#13117626C2116yesmaximal, direct product factor
3C2×#11718618C211yesmaximal, characteristic
4C2×#11718308C211yesmaximal, characteristic, complemented
5C2×#11718606C211yesmaximal, characteristic, complemented
6C2×#11718331C211yesmaximal, characteristic, complemented
7C2×#11718601C211yesmaximal, characteristic, complemented
8C2×#11718605C211yesmaximal, characteristic, complemented
9C2×#11718316C211yesmaximal, characteristic, complemented
10C2×#11718594C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic
12C2×#11718329C211yesmaximal, characteristic, complemented
13C2×#11718873C211yesmaximal, characteristic, complemented
14C2×C4×#6101C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C2×#88183C4116yescomplemented
28C2×#88183C2218yes—
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
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
44C4×C13×C22⋊C4C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718873C2218yescomplemented
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718618C2218yes—
57#11718617C2218yes—
58#11718606C2218yescomplemented
59#11718605C2218yescomplemented
60#11718601C2218yescomplemented
61C4×#6103C2218yescomplemented
62#11718594C2218yescomplemented
63C4×#6101C2218yescomplemented
64#11718331C2218yescomplemented
65#11718329C2218yescomplemented
66#11718316C2218yescomplemented
67#11718308C2218yescomplemented
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C23×C4×C13—42no—
71C23×C4×C13—42no—
72C23×C4×C13C2×C418yescomplemented
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2314yes—
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13C2×C418yes—
83C22×C22⋊D13C2314yes—
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C22×C4×D13—24no—
92C22×C4×D13—42no—
93C22×C4×D13—42no—
94C22×C4×D13C2314yes—
95C2×C13×C22⋊C4—24no—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C42×C13—42no—
100C2×C42×C13—42no—
101C2×C42×C13C2314yes—
102C2×C42×C13C2314yes—
103C2×C22⋊Dic13—42no—
104C2×C22⋊Dic13—42no—
105C2×C22⋊Dic13C2×C418yescomplemented
106C2×C22⋊Dic13C2314yes—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109#88183C2×C4164yescomplemented
110C2×#6103—24no—
111C2×#6103—42no—
112C2×#6103—42no—
113C2×#6103C2×C418yes—
114C2×#6103C2×C418yes—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×C4⋊Dic13—42no—
121C2×C4⋊Dic13—42no—
122C2×C4⋊Dic13C2314yes—
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—42no—
126C2×#6101—42no—
127C2×#6101C2×C418yescomplemented
128C2×#6101C2×C418yescomplemented
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×C4×Dic13—24no—
135C2×C4×Dic13—42no—
136C2×C4×Dic13—42no—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2335—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13C22×C414yes—
158C24×C13C2412yes—
159C24×C13C2411yescharacteristic
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13C22×C414yes—
167C23×D13C2412yes—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
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—416no—
183C22×C4×C13—44no—
184C22×C4×C13—44no—
185C22×C4×C13C22×C414yes—
186C22×C4×C13C22×C414yes—
187C22×C4×C13C22×C4116yescomplemented
188C22×C4×C13#4114yes—
189C22×C4×C13#4114yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C2×C22⋊D13—416no—
197C2×C22⋊D13—44no—
198C2×C22⋊D13—44no—
199C2×C22⋊D13C22×C4116yes—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
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×Dic13C22×C414yes—
219C22×Dic13C22×C414yes—
220C22×Dic13C22×C414yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C2×C4×D13—28no—
229C2×C4×D13—44no—
230C2×C4×D13—44no—
231C2×C4×D13—416no—
232C13×C22⋊C4—28no—
233C13×C22⋊C4—28no—
234C42×C13—44no—
235C42×C13—44no—
236C22⋊Dic13—44no—
237C22⋊Dic13—44no—
238C22⋊Dic13C22×C4116yescomplemented
239#6103—28no—
240#6103—44no—
241#6103—44no—
242#6103C22×C4116yes—
243#6103C22×C4116yes—
244C4⋊Dic13—44no—
245C4⋊Dic13—44no—
246#6101—28no—
247#6101—44no—
248#6101—44no—
249#6101C22×C4116yescomplemented
250#6101C22×C4116yescomplemented
251C4×Dic13—28no—
252C4×Dic13—44no—
253C4×Dic13—44no—
254C22×#123—131no—
255#2335—1316no—
256C2×#390—131no—
257C2×#389—131no—
258C2×#388—131no—
259C2×#388—131no—
260C2×#388—131no—
261C2×#388—131no—
262C2×#387—131no—
263C2×#387—131no—
264C2×#386—131no—
265C2×#385—131no—
266C2×#380—131no—
267C2×C4×C4⋊C4—131no—
268C2×C4×C22⋊C4—131no—
269C2×C4×C22⋊C4D1311yescharacteristic, complemented
270C23×C13—28no—
271C23×C13—28no—
272C23×C13—28no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—44no—
280C23×C13—44no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13C23×C414yes—
284C23×C13C23×C412yes—
285C23×C13C2×#4112yes—
286C23×C13C2×#4112yes—
287C23×C13H(5,𝔽2)12yes—
288C23×C13H(5,𝔽2)12yes—
289C23×C13H(5,𝔽2)12yes—
290C23×C132−1+412yes—
291C23×C13C2511yescharacteristic
292C22×D13—28no—
293C22×D13—28no—
294C22×D13—28no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13C23×C414yes—
306C2×C4×C13—28no—
307C2×C4×C13—28no—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—416no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13C23×C414yes—
328C2×C4×C13C23×C414yes—
329C2×C4×C13C2×#4114yes—
330C2×C4×C13C2×#4114yes—
331C22⋊D13—416no—
332C2×Dic13—28no—
333C2×Dic13—28no—
334C2×Dic13—28no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—44no—
354C2×Dic13—44no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13C23×C414yes—
358C2×Dic13C23×C414yes—
359C2×Dic13C23×C414yes—
360C4×D13—416no—
361C23×D4—131no—
362C24×C4—131no—
363C24×C4C2×D1311yescharacteristic
364C2×#123—1316no—
365C2×#123—138no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C22⋊C4—131no—
374C22×C22⋊C4—131no—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4—131no—
381C22×C22⋊C4C2×D1311yescharacteristic
382C22×C22⋊C4C2×D1311yescharacteristic
383C22×C42—131no—
384C22×C42—131no—
385C22×C42—131no—
386C22×C42C2×D1311yescharacteristic
387C22×C42C2×D1311yescharacteristic
388#390—138no—
389#389—138no—
390#388—138no—
391#388—138no—
392#388—138no—
393#388—138no—
394#387—138no—
395#387—138no—
396#386—138no—
397#385—138no—
398#380—138no—
399C4×C4⋊C4—138no—
400C4×C22⋊C4—138no—
401C4×C22⋊C4C2×D1318yescomplemented
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95C2×D1311yescharacteristic
411C2×#95C2×D1311yescharacteristic
412C22×C13—24no—
413C22×C13—24no—
414C22×C13—24no—
415C22×C13—416no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13C4×#4114yes—
421C22×C13#51814yes—
422C22×C13#52014yes—
423C22×C13#53814yes—
424C22×C13#53914yes—
425C22×C13#54014yes—
426C22×C13#54214yes—
427C22×C13C24×C411yescharacteristic
428C22×C13C22×#4111yescharacteristic
429C22×C13C22×#4111yescharacteristic
430C22×C13C2×H(5,𝔽2)11yescharacteristic
431C22×C13C2×H(5,𝔽2)11yescharacteristic
432C22×C13C2×H(5,𝔽2)11yescharacteristic
433C22×C13C2×2−1+411yescharacteristic
434C2×D13—24no—
435C2×D13—24no—
436C2×D13—24no—
437C2×D13—416no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C4×C13—24no—
443C4×C13—24no—
444C4×C13—24no—
445C4×C13—24no—
446C4×C13—42no—
447C4×C13—42no—
448Dic13—24no—
449Dic13—24no—
450Dic13—24no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455C25—131no—
456C25C22×D1311yescharacteristic
457C22×D4—138no—
458C22×D4—134no—
459C22×D4—522no—
460C22×D4—522no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—134no—
471C23×C4—264no—
472C23×C4—522no—
473C23×C4—522no—
474C23×C4C4×D1318yescomplemented
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1314yes—
482#123—1364no—
483C2×C4⋊C4—138no—
484C2×C4⋊C4—138no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—264no—
493C2×C4⋊C4—522no—
494C2×C4⋊C4—522no—
495C2×C4⋊C4—522no—
496C2×C4⋊C4—522no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—138no—
500C2×C22⋊C4—134no—
501C2×C22⋊C4—138no—
502C2×C22⋊C4—138no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—522no—
512C2×C22⋊C4—522no—
513C2×C22⋊C4—522no—
514C2×C22⋊C4—522no—
515C2×C22⋊C4C22×D1314yes—
516C2×C22⋊C4C22×D1314yes—
517C2×C42—42no—
518C2×C42—42no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—134no—
522C2×C42—264no—
523C2×C42—522no—
524C2×C42—522no—
525C2×C42C22×D1314yes—
526C2×C42C22×D1314yes—
527#95—134no—
528#95—134no—
529#95—134no—
530#95—134no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95C22×D1314yes—
536#95C22×D1314yes—
537C2×C13—44no—
538C2×C13#233518yescomplemented
539C2×C13C2×C4×#4111yescharacteristic
540C2×C13C2×#51811yescharacteristic
541C2×C13C2×#52011yescharacteristic
542C2×C13C2×#53811yescharacteristic
543C2×C13C2×#53911yescharacteristic
544C2×C13C2×#54011yescharacteristic
545C2×C13C2×#54211yescharacteristic
546D13—44no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—134no—
554C24—132no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24C2×C4×D1314yes—
562C24C23×D1312yes—
563C24C23×D1311yescharacteristic
564C2×D4—1316no—
565C2×D4—5216no—
566C2×D4—524no—
567C2×D4—524no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—416no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—134no—
586C22×C4—134no—
587C22×C4—134no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—268no—
614C22×C4—524no—
615C22×C4—524no—
616C22×C4—5216no—
617C22×C4C2×C4×D1314yes—
618C22×C4C2×C4×D1314yes—
619C22×C4C2×C4×D13116yescomplemented
620C22×C4#612714yes—
621C22×C4#612714yes—
622C22×C4C23×D1312yes—
623C22×C4C23×D1312yes—
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C4⋊C4—1316no—
629C4⋊C4—1316no—
630C4⋊C4—268no—
631C4⋊C4—524no—
632C4⋊C4—524no—
633C4⋊C4—524no—
634C4⋊C4—524no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—1316no—
638C22⋊C4—1316no—
639C22⋊C4—1316no—
640C22⋊C4—268no—
641C22⋊C4—524no—
642C22⋊C4—524no—
643C22⋊C4—524no—
644C22⋊C4—524no—
645C42—44no—
646C42—44no—
647C42—268no—
648C42—524no—
649C42—524no—
650C13C2×#233511yescharacteristic, complemented, Sylow
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—134no—
665C23—268no—
666C23—268no—
667C23—268no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23C22×C4×D1314yes—
679C23C22×C4×D1312yes—
680C23C2×#612712yes—
681C23C2×#612712yes—
682C23#8825112yes—
683C23#8825112yes—
684C23#8825612yes—
685C23#8825712yes—
686C23C24×D1311yescharacteristic
687D4—5216no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—416no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—134no—
710C2×C4—134no—
711C2×C4—134no—
712C2×C4—268no—
713C2×C4—268no—
714C2×C4—268no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—5216no—
734C2×C4—524no—
735C2×C4—524no—
736C2×C4—524no—
737C2×C4—524no—
738C2×C4C22×C4×D1314yes—
739C2×C4C22×C4×D1314yes—
740C2×C4C2×#612714yes—
741C2×C4C2×#612714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—416no—
748C22—42no—
749C22—42no—
750C22—264no—
751C22—264no—
752C22—264no—
753C22—522no—
754C22—522no—
755C22—5216no—
756C22—522no—
757C22—522no—
758C22C4×#612714yes—
759C22#1171919114yes—
760C22#1171922814yes—
761C22#1171926514yes—
762C22#1171926614yes—
763C22#1171926714yes—
764C22#1171926914yes—
765C22C23×C4×D1311yescharacteristic
766C22C22×#612711yescharacteristic
767C22C22×#612711yescharacteristic
768C22C2×#8825111yescharacteristic
769C22C2×#8825111yescharacteristic
770C22C2×#8825611yescharacteristic
771C22C2×#8825711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—264no—
779C4—264no—
780C4—264no—
781C4—522no—
782C4—522no—
783C4—522no—
784C4—522no—
785C2—44no—
786C2—524no—
787C2#1311762618yesdirect product factor
788C2C2×C4×#612711yescharacteristic
789C2C2×#1171919111yescharacteristic
790C2C2×#1171922811yescharacteristic
791C2C2×#1171926511yescharacteristic
792C2C2×#1171926911yescharacteristic
793C2C2×#1171926711yescharacteristic
794C2C2×#1171926611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2335
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. #13117626C2direct (N × H)
4. C2×#11718308C2semidirect
5. C2×#11718606C2semidirect
6. C2×#11718331C2semidirect
7. C2×#11718601C2semidirect
8. C2×#11718605C2semidirect
9. C2×#11718316C2semidirect
10. C2×#11718594C2semidirect
12. C2×#11718329C2semidirect
13. C2×#11718873C2semidirect
14. C2×C4×#6101C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
27. C2×#88183C4semidirect
44. C4×C13×C22⋊C4C22semidirect
47. #11718873C22semidirect
58. #11718606C22semidirect
59. #11718605C22semidirect
60. #11718601C22semidirect
61. C4×#6103C22semidirect
62. #11718594C22semidirect
63. C4×#6101C22semidirect
64. #11718331C22semidirect
65. #11718329C22semidirect
66. #11718316C22semidirect
67. #11718308C22semidirect
72. C23×C4×C13C2×C4semidirect
105. C2×C22⋊Dic13C2×C4semidirect
109. #88183C2×C4semidirect
127. C2×#6101C2×C4semidirect
128. C2×#6101C2×C4semidirect
187. C22×C4×C13C22×C4semidirect
238. C22⋊Dic13C22×C4semidirect
249. #6101C22×C4semidirect
250. #6101C22×C4semidirect
269. C2×C4×C22⋊C4D13semidirect
401. C4×C22⋊C4C2×D13semidirect
474. C23×C4C4×D13semidirect
538. C2×C13#2335semidirect
619. C22×C4C2×C4×D13semidirect
650. C13C2×#2335semidirect
787. C2#13117626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
#131176262
C2×#117186182
C2×#117183082
C2×#117186062
C2×#117183312
C2×#117186012
C2×#117186052
C2×#117183162
C2×#117185942
C2×#117186172
C2×#117183292
C2×#117188732
C2×C4×#61012
C2×C4×#61032
C2×C4×C13×C22⋊C42
C2×#233513