Finite Group Databasebeta

← C2×#13117965 #16022632

Subgroups — C2×#13117965 #16022632

Order 3328.

3094 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×#88148C211yesmaximal, characteristic
2#13117965C2116yesmaximal, direct product factor
3C2×#11718600C211yesmaximal, characteristic
4C2×#11718601C211yesmaximal, characteristic, complemented
5C2×#11718601C211yesmaximal, characteristic, complemented
6C2×#11718651C211yesmaximal, characteristic, complemented
7C2×#11718651C211yesmaximal, characteristic, complemented
8C2×#11718316C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic
11C2×C4×#6101C211yesmaximal, characteristic, complemented
12C2×C4×#6103C211yesmaximal, characteristic, complemented
13C2×C4×#6103C211yesmaximal, characteristic, complemented
14C2×#11718327C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88148C4116yescomplemented
43C2×#88148C2218yes—
44C4×C13×C4⋊C4C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718651C2218yescomplemented
56#11718651C2218yescomplemented
57#11718642C2218yescomplemented
58#11718601C2218yescomplemented
59#11718601C2218yescomplemented
60#11718600C2218yes—
61C4×#6103C2218yescomplemented
62C4×#6103C2218yescomplemented
63C4×#6101C2218yescomplemented
64#11718327C2218yescomplemented
65#11718327C2218yescomplemented
66#11718326C2218yes—
67#11718316C2218yescomplemented
68C24×D13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C22×D52—42no—
84C22×D52—42no—
85C22×D52C2×C418yes—
86C22×D52C2314yes—
87C22×C4×D13—24no—
88C22×C4×D13—24no—
89C22×C4×D13—42no—
90C22×C4×D13—42no—
91C22×C4×D13—42no—
92C22×C4×D13C2×C418yescomplemented
93C22×C4×D13C2314yes—
94C22×C4×D13C2314yes—
95C2×C13×C4⋊C4—24no—
96C2×C13×C4⋊C4C2×C418yescomplemented
97C2×C13×C4⋊C4C2314yes—
98C2×C13×C4⋊C4C2314yes—
99C2×C42×C13—24no—
100C2×C42×C13—42no—
101C2×C42×C13—42no—
102C2×C42×C13C2314yes—
103C2×C42×C13C2314yes—
104C2×C42×C13C2314yes—
105C2×#6103—24no—
106C2×#6103—24no—
107C2×#6103—24no—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103—24no—
111C2×#6103—42no—
112C2×#6103C2×C418yes—
113C2×#6103C2×C418yes—
114C2×#6103C2×C418yescomplemented
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×C4⋊Dic13—42no—
126C2×C4⋊Dic13C2314yes—
127C2×#6101—24no—
128C2×#6101C2×C418yescomplemented
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×C4×Dic13—24no—
132C2×C4×Dic13—42no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13—42no—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139#88148C2×C4164yescomplemented
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2374—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13C22×C414yes—
165C23×D13C22×C414yes—
166C23×D13C2412yes—
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—22no—
183C22×C4×C13C22×C414yes—
184C22×C4×C13C22×C414yes—
185C22×C4×C13C22×C414yes—
186C22×C4×C13#4114yes—
187C22×C4×C13#4114yes—
188C22×C4×C13#4114yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
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×Dic13C22×C414yes—
212C22×Dic13C22×C414yes—
213C22×Dic13#4114yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C2×D52—416no—
221C2×D52—44no—
222C2×D52—44no—
223C2×D52C22×C4116yes—
224C2×C4×D13—28no—
225C2×C4×D13—28no—
226C2×C4×D13—416no—
227C2×C4×D13—44no—
228C2×C4×D13—44no—
229C2×C4×D13—44no—
230C2×C4×D13—416no—
231C2×C4×D13C22×C4116yescomplemented
232C13×C4⋊C4—28no—
233C13×C4⋊C4C22×C4116yescomplemented
234C42×C13—28no—
235C42×C13—44no—
236C42×C13—44no—
237#6103—28no—
238#6103—28no—
239#6103—28no—
240#6103—28no—
241#6103—28no—
242#6103—28no—
243#6103—44no—
244#6103C22×C4116yes—
245#6103C22×C4116yes—
246#6103C22×C4116yescomplemented
247C4⋊Dic13—44no—
248#6101—28no—
249#6101C22×C4116yescomplemented
250C4×Dic13—28no—
251C4×Dic13—44no—
252C4×Dic13—44no—
253C4×Dic13—44no—
254C22×#123—131no—
255#2374—1316no—
256C2×#390—131no—
257C2×#388—131no—
258C2×#388—131no—
259C2×#388—131no—
260C2×#388—131no—
261C2×#387—131no—
262C2×#387—131no—
263C2×#386—131no—
264C2×C4×C4⋊C4—131no—
265C2×C4×C4⋊C4D1311yescharacteristic, complemented
266C2×C4×C22⋊C4—131no—
267C2×C4×C22⋊C4—131no—
268C2×C4×C22⋊C4—131no—
269C2×C4×C22⋊C4—131no—
270C23×C13C23×C412yes—
271C23×C13C2×#4112yes—
272C23×C13C2×#4112yes—
273C23×C13C2×#4112yes—
274C23×C13C2×#4112yes—
275C23×C13H(5,𝔽2)12yes—
276C23×C13H(5,𝔽2)12yes—
277C23×C13C2511yescharacteristic
278C22×D13—28no—
279C22×D13—28no—
280C22×D13—28no—
281C22×D13—28no—
282C22×D13—28no—
283C22×D13—28no—
284C22×D13—22no—
285C22×D13—22no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—44no—
297C22×D13—44no—
298C22×D13—44no—
299C22×D13—44no—
300C22×D13—44no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13C23×C414yes—
305C22×D13C23×C414yes—
306C2×C4×C13—28no—
307C2×C4×C13—28no—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
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—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—44no—
328C2×C4×C13C23×C414yes—
329C2×C4×C13C23×C414yes—
330C2×C4×C13C23×C414yes—
331C2×C4×C13C2×#4114yes—
332C2×C4×C13C2×#4114yes—
333C2×C4×C13C2×#4114yes—
334C2×Dic13—28no—
335C2×Dic13—28no—
336C2×Dic13—28no—
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—44no—
353C2×Dic13—44no—
354C2×Dic13—44no—
355C2×Dic13C23×C414yes—
356C2×Dic13C23×C414yes—
357C2×Dic13C2×#4114yes—
358D52—416no—
359C4×D13—416no—
360C4×D13—416no—
361C23×D4—131no—
362C24×C4—131no—
363C24×C4—131no—
364C2×#123—1316no—
365C2×#123—138no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4C2×D1311yescharacteristic
370C22×C4⋊C4C2×D1311yescharacteristic
371C22×C22⋊C4—131no—
372C22×C22⋊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×C42—131no—
382C22×C42—131no—
383C22×C42—131no—
384C22×C42—131no—
385C22×C42C2×D1311yescharacteristic
386C22×C42C2×D1311yescharacteristic
387C22×C42C2×D1311yescharacteristic
388#390—138no—
389#388—138no—
390#388—138no—
391#388—138no—
392#388—138no—
393#387—138no—
394#387—138no—
395#386—138no—
396C4×C4⋊C4—138no—
397C4×C4⋊C4C2×D1318yescomplemented
398C4×C22⋊C4—138no—
399C4×C22⋊C4—138no—
400C4×C22⋊C4—138no—
401C4×C22⋊C4—138no—
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×C13C4×#4114yes—
413C22×C13C4×#4114yes—
414C22×C13#51814yes—
415C22×C13#55114yes—
416C22×C13#55314yes—
417C22×C13#55314yes—
418C22×C13#55914yes—
419C22×C13C24×C411yescharacteristic
420C22×C13C22×#4111yescharacteristic
421C22×C13C22×#4111yescharacteristic
422C22×C13C22×#4111yescharacteristic
423C22×C13C22×#4111yescharacteristic
424C22×C13C2×H(5,𝔽2)11yescharacteristic
425C22×C13C2×H(5,𝔽2)11yescharacteristic
426C2×D13—24no—
427C2×D13—24no—
428C2×D13—24no—
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
432C2×D13—416no—
433C2×D13—416no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
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—24no—
447C4×C13—24no—
448C4×C13—42no—
449Dic13—24no—
450Dic13—24no—
451Dic13—24no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455C25—131no—
456C25—131no—
457C22×D4—138no—
458C22×D4—134no—
459C22×D4—522no—
460C22×D4—522no—
461C23×C4—131no—
462C23×C4—131no—
463C23×C4—131no—
464C23×C4—138no—
465C23×C4—134no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—134no—
470C23×C4—264no—
471C23×C4—264no—
472C23×C4—522no—
473C23×C4—522no—
474C23×C4—522no—
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482#123—1364no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—138no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—522no—
490C2×C4⋊C4C4×D1318yescomplemented
491C2×C4⋊C4C22×D1314yes—
492C2×C4⋊C4C22×D1314yes—
493C2×C22⋊C4—138no—
494C2×C22⋊C4—138no—
495C2×C22⋊C4—138no—
496C2×C22⋊C4—134no—
497C2×C22⋊C4—134no—
498C2×C22⋊C4—134no—
499C2×C22⋊C4—134no—
500C2×C22⋊C4—134no—
501C2×C22⋊C4—134no—
502C2×C22⋊C4—134no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—264no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—522no—
513C2×C42—24no—
514C2×C42—42no—
515C2×C42—42no—
516C2×C42—134no—
517C2×C42—134no—
518C2×C42—134no—
519C2×C42—134no—
520C2×C42—264no—
521C2×C42—522no—
522C2×C42—522no—
523C2×C42—522no—
524C2×C42C22×D1314yes—
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#237418yescomplemented
538C2×C13C2×C4×#4111yescharacteristic
539C2×C13C2×C4×#4111yescharacteristic
540C2×C13C2×#51811yescharacteristic
541C2×C13C2×#55111yescharacteristic
542C2×C13C2×#55311yescharacteristic
543C2×C13C2×#55311yescharacteristic
544C2×C13C2×#55911yescharacteristic
545D13—44no—
546D13—44no—
547C24—134no—
548C24—134no—
549C24—132no—
550C24—132no—
551C24—262no—
552C24—262no—
553C24—262no—
554C24—262no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
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—22no—
583C22×C4—134no—
584C22×C4—134no—
585C22×C4—134no—
586C22×C4—132no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—1316no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—268no—
594C22×C4—262no—
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—268no—
610C22×C4—5216no—
611C22×C4—524no—
612C22×C4—524no—
613C22×C4—524no—
614C22×C4—5216no—
615C22×C4C2×C4×D1314yes—
616C22×C4C2×C4×D1314yes—
617C22×C4C2×C4×D1314yes—
618C22×C4#612714yes—
619C22×C4#612714yes—
620C22×C4#613114yes—
621C22×C4C23×D1312yes—
622C22×C4C23×D1312yes—
623C22×C4C23×D1312yes—
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C4⋊C4—28no—
629C4⋊C4—1316no—
630C4⋊C4—268no—
631C4⋊C4—524no—
632C4⋊C4C2×C4×D13116yescomplemented
633C22⋊C4—1316no—
634C22⋊C4—1316no—
635C22⋊C4—1316no—
636C22⋊C4—268no—
637C22⋊C4—268no—
638C22⋊C4—268no—
639C22⋊C4—268no—
640C22⋊C4—268no—
641C22⋊C4—268no—
642C22⋊C4—524no—
643C42—28no—
644C42—44no—
645C42—44no—
646C42—268no—
647C42—524no—
648C42—524no—
649C42—524no—
650C13C2×#237411yescharacteristic, complemented, Sylow
651C23—134no—
652C23—134no—
653C23—268no—
654C23—268no—
655C23—268no—
656C23—268no—
657C23—268no—
658C23—268no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—524no—
672C23—524no—
673C23—524no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23—524no—
679C23C22×C4×D1312yes—
680C23C2×#612712yes—
681C23C2×#612712yes—
682C23#8825112yes—
683C23C2×#613112yes—
684C23#41×D1312yes—
685C23#8825612yes—
686C23C24×D1311yescharacteristic
687D4—5216no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—134no—
711C2×C4—134no—
712C2×C4—134no—
713C2×C4—268no—
714C2×C4—268no—
715C2×C4—268no—
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—5216no—
732C2×C4—5216no—
733C2×C4—524no—
734C2×C4—524no—
735C2×C4—524no—
736C2×C4C22×C4×D1314yes—
737C2×C4C22×C4×D1314yes—
738C2×C4C22×C4×D1314yes—
739C2×C4C2×#612714yes—
740C2×C4C2×#612714yes—
741C2×C4C2×#613114yes—
742C22—264no—
743C22—264no—
744C22—264no—
745C22—264no—
746C22—264no—
747C22—264no—
748C22—5216no—
749C22—5216no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22C4×#612714yes—
759C22#1171921914yes—
760C22#1171923214yes—
761C22#1171924514yes—
762C22#1171925014yes—
763C22C4×#613114yes—
764C22#1171929014yes—
765C22C23×C4×D1311yescharacteristic
766C22C22×#612711yescharacteristic
767C22C22×#612711yescharacteristic
768C22C2×#8825111yescharacteristic
769C22C22×#613111yescharacteristic
770C22C2×#41×D1311yescharacteristic
771C22C2×#8825611yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—24no—
778C4—42no—
779C4—264no—
780C4—264no—
781C4—264no—
782C4—522no—
783C4—522no—
784C4—522no—
785C2—524no—
786C2—524no—
787C2#1311796518yesdirect product factor
788C2C2×C4×#612711yescharacteristic
789C2C2×C4×#613111yescharacteristic
790C2C2×#1171925011yescharacteristic
791C2C2×#1171923211yescharacteristic
792C2C2×#1171921911yescharacteristic
793C2C2×#1171924511yescharacteristic
794C2C2×#1171929011yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC23×D52C22
cosocleC23×C13C25
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#2374
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13117965C2direct (N × H)
4. C2×#11718601C2semidirect
5. C2×#11718601C2semidirect
6. C2×#11718651C2semidirect
7. C2×#11718651C2semidirect
8. C2×#11718316C2semidirect
9. C2×#11718642C2semidirect
11. C2×C4×#6101C2semidirect
12. C2×C4×#6103C2semidirect
13. C2×C4×#6103C2semidirect
14. C2×#11718327C2semidirect
15. C2×#11718327C2semidirect
16. C2×C4×C13×C4⋊C4C2semidirect
42. C2×#88148C4semidirect
44. C4×C13×C4⋊C4C22semidirect
55. #11718651C22semidirect
56. #11718651C22semidirect
57. #11718642C22semidirect
58. #11718601C22semidirect
59. #11718601C22semidirect
61. C4×#6103C22semidirect
62. C4×#6103C22semidirect
63. C4×#6101C22semidirect
64. #11718327C22semidirect
65. #11718327C22semidirect
67. #11718316C22semidirect
92. C22×C4×D13C2×C4semidirect
96. C2×C13×C4⋊C4C2×C4semidirect
114. C2×#6103C2×C4semidirect
128. C2×#6101C2×C4semidirect
139. #88148C2×C4semidirect
231. C2×C4×D13C22×C4semidirect
233. C13×C4⋊C4C22×C4semidirect
246. #6103C22×C4semidirect
249. #6101C22×C4semidirect
265. C2×C4×C4⋊C4D13semidirect
397. C4×C4⋊C4C2×D13semidirect
490. C2×C4⋊C4C4×D13semidirect
537. C2×C13#2374semidirect
632. C4⋊C4C2×C4×D13semidirect
650. C13C2×#2374semidirect
787. C2#13117965direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881482
#131179652
C2×#117186002
C2×#117186012
C2×#117186512
C2×#117183162
C2×#117186422
C2×#117183262
C2×C4×#61012
C2×C4×#61032
C2×#117183272
C2×C4×C13×C4⋊C42
C2×#237413