Finite Group Databasebeta

← C2×#13117943 #16022593

Subgroups — C2×#13117943 #16022593

Order 3328.

3158 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88139C211yesmaximal, characteristic
2#13117943C2116yesmaximal, direct product factor
3C2×#11718635C211yesmaximal, characteristic, complemented
4C2×#11718307C211yesmaximal, characteristic, complemented
5C2×#11718606C211yesmaximal, characteristic, complemented
6C2×#11718651C211yesmaximal, characteristic, complemented
7C2×#11718330C211yesmaximal, characteristic, complemented
8C2×#11718619C211yesmaximal, characteristic
9C2×#11718617C211yesmaximal, characteristic
10C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
12C2×C4×#6103C211yesmaximal, characteristic, complemented
13C2×#11718327C211yesmaximal, characteristic, complemented
14C2×#11718593C211yesmaximal, characteristic, complemented
15C2×#11718309C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88139C4116yescomplemented
41C2×#88139C2218yes—
42C13×#388C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718651C2218yescomplemented
56#11718635C2218yescomplemented
57#11718619C2218yes—
58#11718617C2218yes—
59#11718606C2218yescomplemented
60C22⋊C4×Dic13C2218yescomplemented
61C22⋊C4×Dic13C2218yescomplemented
62C4×#6103C2218yescomplemented
63#11718593C2218yescomplemented
64#11718330C2218yescomplemented
65#11718327C2218yescomplemented
66#11718309C2218yescomplemented
67#11718307C2218yescomplemented
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C22×C22⋊D13—42no—
77C22×C22⋊D13—42no—
78C22×C22⋊D13C2×C418yes—
79C22×C22⋊D13C2314yes—
80C23×Dic13—24no—
81C23×Dic13—24no—
82C23×Dic13—42no—
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2314yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C22×C4×D13—24no—
92C22×C4×D13—24no—
93C22×C4×D13—42no—
94C22×C4×D13C2314yes—
95C22×Dic26—42no—
96C22×Dic26—42no—
97C22×Dic26C2×C418yescomplemented
98C22×Dic26C2314yes—
99C2×C13×C4⋊C4—42no—
100C2×C13×C4⋊C4C2314yes—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—42no—
103C2×C13×C22⋊C4C2×C418yescomplemented
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C42×C13—24no—
108C2×C42×C13C2314yes—
109C2×C22⋊Dic13—24no—
110C2×C22⋊Dic13C2×C418yescomplemented
111C2×C22⋊Dic13C2314yes—
112C2×C22⋊Dic13C2314yes—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—42no—
116C2×#6103C2×C418yescomplemented
117C2×#6103C2×C418yescomplemented
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6101—42no—
124C2×#6101C2314yes—
125C2×C4×Dic13—24no—
126C2×C4×Dic13—24no—
127C2×C4×Dic13—24no—
128C2×C4×Dic13—42no—
129C2×C4×Dic13—42no—
130C2×C4×Dic13C2×C418yescomplemented
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133C2×C4×Dic13C2314yes—
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137#88139C2×C4164yescomplemented
138C13×#95C2314yes—
139C13×#95C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2372—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—22no—
183C22×C4×C13C22×C414yes—
184C22×C4×C13C22×C414yes—
185C22×C4×C13#4114yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C2×C22⋊D13—416no—
193C2×C22⋊D13—44no—
194C2×C22⋊D13—44no—
195C2×C22⋊D13C22×C4116yes—
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×Dic13—28no—
212C22×Dic13—28no—
213C22×Dic13—44no—
214C22×Dic13—416no—
215C22×Dic13C22×C414yes—
216C22×Dic13C22×C414yes—
217C22×Dic13C22×C414yes—
218C22×Dic13#4114yes—
219C22×Dic13#4114yes—
220C22×Dic13#4114yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C2×C4×D13—28no—
229C2×C4×D13—28no—
230C2×C4×D13—44no—
231C2×C4×D13—416no—
232C2×Dic26—416no—
233C2×Dic26—44no—
234C2×Dic26—44no—
235C2×Dic26C22×C4116yescomplemented
236C13×C4⋊C4—44no—
237C13×C22⋊C4—28no—
238C13×C22⋊C4—44no—
239C13×C22⋊C4C22×C4116yescomplemented
240C42×C13—28no—
241C22⋊Dic13—28no—
242C22⋊Dic13C22×C4116yescomplemented
243#6103—28no—
244#6103—28no—
245#6103—44no—
246#6103C22×C4116yescomplemented
247#6103C22×C4116yescomplemented
248#6101—44no—
249C4×Dic13—28no—
250C4×Dic13—28no—
251C4×Dic13—28no—
252C4×Dic13—44no—
253C4×Dic13—44no—
254C4×Dic13C22×C4116yescomplemented
255C22×#124—131no—
256#2372—1316no—
257C2×#391—131no—
258C2×#391—131no—
259C2×#388—131no—
260C2×#388—131no—
261C2×#388—131no—
262C2×#388D1311yescharacteristic, complemented
263C2×#386—131no—
264C2×#386—131no—
265C2×C4×C22⋊C4—131no—
266C2×C4×C22⋊C4—131no—
267C2×C4×C22⋊C4—131no—
268C2×C4×C22⋊C4—131no—
269C2×#376—131no—
270C2×#376—131no—
271C23×C13—28no—
272C23×C13—28no—
273C23×C13—28no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—44no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13—44no—
284C23×C13C23×C414yes—
285C23×C13C23×C412yes—
286C23×C13C2×#4112yes—
287C23×C13C2×#4112yes—
288C23×C13C2×#4112yes—
289C23×C13C2×#4112yes—
290C23×C13H(5,𝔽2)12yes—
291C23×C13H(5,𝔽2)12yes—
292C23×C13C2511yescharacteristic
293C22×D13—28no—
294C22×D13—28no—
295C22×D13—28no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13C23×C414yes—
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—22no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13—44no—
328C2×C4×C13C23×C414yes—
329C2×C4×C13C23×C414yes—
330C2×C4×C13C2×#4114yes—
331C22⋊D13—416no—
332C2×Dic13—28no—
333C2×Dic13—28no—
334C2×Dic13—28no—
335C2×Dic13—28no—
336C2×Dic13—28no—
337C2×Dic13—28no—
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—416no—
354C2×Dic13—44no—
355C2×Dic13C23×C414yes—
356C2×Dic13C23×C414yes—
357C2×Dic13C23×C414yes—
358C2×Dic13C2×#4114yes—
359C2×Dic13C2×#4114yes—
360C2×Dic13C2×#4114yes—
361C4×D13—416no—
362Dic26—416no—
363C23×Q8—131no—
364C23×D4—131no—
365C24×C4—131no—
366C24×C4—131no—
367C2×#124—1316no—
368C2×#124—138no—
369C22×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
379C22×C22⋊C4C2×D1311yescharacteristic
380C22×C22⋊C4C2×D1311yescharacteristic
381C22×C42—131no—
382C22×C42—131no—
383C22×C42—131no—
384C22×C42—131no—
385C22×C42—131no—
386C22×C42—131no—
387C22×C42C2×D1311yescharacteristic
388#391—138no—
389#391—138no—
390#388—138no—
391#388—138no—
392#388—138no—
393#388C2×D1318yescomplemented
394#386—138no—
395#386—138no—
396C4×C22⋊C4—138no—
397C4×C22⋊C4—138no—
398C4×C22⋊C4—138no—
399C4×C22⋊C4—138no—
400#376—138no—
401#376—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×#95—131no—
411C2×#95—131no—
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C22×C13—24no—
415C22×C13—24no—
416C22×C13—24no—
417C22×C13—416no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—42no—
421C22×C13—42no—
422C22×C13C4×#4114yes—
423C22×C13C4×#4114yes—
424C22×C13#51814yes—
425C22×C13#55114yes—
426C22×C13#55114yes—
427C22×C13#55514yes—
428C22×C13#55514yes—
429C22×C13C24×C411yescharacteristic
430C22×C13C22×#4111yescharacteristic
431C22×C13C22×#4111yescharacteristic
432C22×C13C22×#4111yescharacteristic
433C22×C13C22×#4111yescharacteristic
434C22×C13C2×H(5,𝔽2)11yescharacteristic
435C22×C13C2×H(5,𝔽2)11yescharacteristic
436C2×D13—24no—
437C2×D13—24no—
438C2×D13—24no—
439C2×D13—416no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C4×C13—24no—
445C4×C13—24no—
446C4×C13—24no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13—42no—
450Dic13—24no—
451Dic13—24no—
452Dic13—24no—
453Dic13—24no—
454Dic13—24no—
455Dic13—24no—
456Dic13—42no—
457C25—131no—
458C25C22×D1311yescharacteristic
459C22×Q8—138no—
460C22×Q8—134no—
461C22×Q8—522no—
462C22×Q8—522no—
463C22×D4—138no—
464C22×D4—134no—
465C22×D4—522no—
466C22×D4—522no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—134no—
475C23×C4—134no—
476C23×C4—264no—
477C23×C4—264no—
478C23×C4—264no—
479C23×C4—264no—
480C23×C4—522no—
481C23×C4—522no—
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488#124—1364no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—522no—
492C2×C4⋊C4C22×D1314yes—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—138no—
496C2×C22⋊C4—134no—
497C2×C22⋊C4—138no—
498C2×C22⋊C4—138no—
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—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—522no—
509C2×C22⋊C4C4×D1318yescomplemented
510C2×C22⋊C4C22×D1314yes—
511C2×C22⋊C4C22×D1314yes—
512C2×C22⋊C4C22×D1314yes—
513C2×C42—24no—
514C2×C42—138no—
515C2×C42—134no—
516C2×C42—134no—
517C2×C42—134no—
518C2×C42—134no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—264no—
522C2×C42—264no—
523C2×C42—264no—
524C2×C42—522no—
525C2×C42—522no—
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#95—134no—
536#95—134no—
537#95C22×D1314yes—
538#95C22×D1314yes—
539C2×C13—44no—
540C2×C13#237218yescomplemented
541C2×C13C2×C4×#4111yescharacteristic
542C2×C13C2×C4×#4111yescharacteristic
543C2×C13C2×#51811yescharacteristic
544C2×C13C2×#55111yescharacteristic
545C2×C13C2×#55111yescharacteristic
546C2×C13C2×#55511yescharacteristic
547C2×C13C2×#55511yescharacteristic
548D13—44no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—134no—
556C24—132no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24C2×C4×D1314yes—
564C24C23×D1312yes—
565C24C23×D1311yescharacteristic
566C2×Q8—1316no—
567C2×Q8—5216no—
568C2×Q8—524no—
569C2×Q8—524no—
570C2×D4—1316no—
571C2×D4—5216no—
572C2×D4—524no—
573C2×D4—524no—
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—134no—
590C22×C4—134no—
591C22×C4—134no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—134no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—268no—
603C22×C4—268no—
604C22×C4—268no—
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—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—268no—
621C22×C4—524no—
622C22×C4—5216no—
623C22×C4—524no—
624C22×C4—5216no—
625C22×C4C2×C4×D1314yes—
626C22×C4C2×C4×D1314yes—
627C22×C4#612914yes—
628C22×C4C23×D1312yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1312yes—
631C22×C4C23×D1312yes—
632C22×C4C23×D1312yes—
633C22×C4C23×D1312yes—
634C4⋊C4—44no—
635C4⋊C4—524no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—1316no—
639C22⋊C4—1316no—
640C22⋊C4—1316no—
641C22⋊C4—268no—
642C22⋊C4—268no—
643C22⋊C4—268no—
644C22⋊C4—524no—
645C22⋊C4C2×C4×D13116yescomplemented
646C42—28no—
647C42—1316no—
648C42—268no—
649C42—268no—
650C42—268no—
651C42—524no—
652C42—524no—
653C13C2×#237211yescharacteristic, complemented, Sylow
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—134no—
668C23—268no—
669C23—268no—
670C23—268no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—524no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23C22×C4×D1314yes—
682C23C22×C4×D1312yes—
683C23C2×#612912yes—
684C23#8825112yes—
685C23#41×D1312yes—
686C23#41×D1312yes—
687C23#41×D1312yes—
688C23#8825612yes—
689C23C24×D1311yescharacteristic
690Q8—5216no—
691D4—5216no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
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—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—134no—
714C2×C4—134no—
715C2×C4—134no—
716C2×C4—134no—
717C2×C4—134no—
718C2×C4—134no—
719C2×C4—268no—
720C2×C4—268no—
721C2×C4—268no—
722C2×C4—268no—
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—262no—
734C2×C4—262no—
735C2×C4—268no—
736C2×C4—268no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—5216no—
741C2×C4—5216no—
742C2×C4—524no—
743C2×C4C22×C4×D1314yes—
744C2×C4C22×C4×D1314yes—
745C2×C4C2×#612914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—264no—
755C22—264no—
756C22—264no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—5216no—
762C22#1171922714yes—
763C22C4×#612914yes—
764C22#1171925014yes—
765C22#1171932114yes—
766C22#1171936314yes—
767C22#1171937514yes—
768C22#1171941014yes—
769C22C23×C4×D1311yescharacteristic
770C22C22×#612911yescharacteristic
771C22C2×#8825111yescharacteristic
772C22C2×#41×D1311yescharacteristic
773C22C2×#41×D1311yescharacteristic
774C22C2×#41×D1311yescharacteristic
775C22C2×#8825611yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—264no—
783C4—264no—
784C4—264no—
785C4—264no—
786C4—264no—
787C4—264no—
788C4—522no—
789C2—44no—
790C2—524no—
791C2#1311794318yesdirect product factor
792C2C2×C4×#612911yescharacteristic
793C2C2×#1171922711yescharacteristic
794C2C2×#1171925011yescharacteristic
795C2C2×#1171936311yescharacteristic
796C2C2×#1171941011yescharacteristic
797C2C2×#1171937511yescharacteristic
798C2C2×#1171932111yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2372
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #13117943C2direct (N × H)
3. C2×#11718635C2semidirect
4. C2×#11718307C2semidirect
5. C2×#11718606C2semidirect
6. C2×#11718651C2semidirect
7. C2×#11718330C2semidirect
10. C2×C22⋊C4×Dic13C2semidirect
11. C2×C22⋊C4×Dic13C2semidirect
12. C2×C4×#6103C2semidirect
13. C2×#11718327C2semidirect
14. C2×#11718593C2semidirect
15. C2×#11718309C2semidirect
16. C2×C13×#388C2semidirect
40. C2×#88139C4semidirect
42. C13×#388C22semidirect
55. #11718651C22semidirect
56. #11718635C22semidirect
59. #11718606C22semidirect
60. C22⋊C4×Dic13C22semidirect
61. C22⋊C4×Dic13C22semidirect
62. C4×#6103C22semidirect
63. #11718593C22semidirect
64. #11718330C22semidirect
65. #11718327C22semidirect
66. #11718309C22semidirect
67. #11718307C22semidirect
97. C22×Dic26C2×C4semidirect
103. C2×C13×C22⋊C4C2×C4semidirect
110. C2×C22⋊Dic13C2×C4semidirect
116. C2×#6103C2×C4semidirect
117. C2×#6103C2×C4semidirect
130. C2×C4×Dic13C2×C4semidirect
137. #88139C2×C4semidirect
235. C2×Dic26C22×C4semidirect
239. C13×C22⋊C4C22×C4semidirect
242. C22⋊Dic13C22×C4semidirect
246. #6103C22×C4semidirect
247. #6103C22×C4semidirect
254. C4×Dic13C22×C4semidirect
262. C2×#388D13semidirect
393. #388C2×D13semidirect
509. C2×C22⋊C4C4×D13semidirect
540. C2×C13#2372semidirect
645. C22⋊C4C2×C4×D13semidirect
653. C13C2×#2372semidirect
791. C2#13117943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881392
#131179432
C2×#117186352
C2×#117183072
C2×#117186062
C2×#117186512
C2×#117183302
C2×#117186192
C2×#117186172
C2×C22⋊C4×Dic132
C2×C4×#61032
C2×#117183272
C2×#117185932
C2×#117183092
C2×C13×#3882
C2×#237213