Finite Group Databasebeta

← C2×#13117782 #16022265

Subgroups — C2×#13117782 #16022265

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88135C211yesmaximal, characteristic
2C22×#88126C211yesmaximal, characteristic, complemented
3C22×#88131C211yesmaximal, characteristic, complemented
4#13117782C2116yesmaximal, direct product factor
5C2×#11718618C211yesmaximal, characteristic
6C2×#11718618C211yesmaximal, characteristic
7C2×#11718612C211yesmaximal, characteristic, complemented
8C2×#11718331C211yesmaximal, characteristic, complemented
9C2×#11718651C211yesmaximal, characteristic, complemented
10C2×#11718637C211yesmaximal, characteristic, complemented
11C2×#11718328C211yesmaximal, characteristic, complemented
12C2×#11718603C211yesmaximal, characteristic, complemented
13C2×C4×#6101C211yesmaximal, characteristic, complemented
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×#11718310C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88135C4116yescomplemented
47C2×#88135C2218yes—
48C2×#88131—28no—
49C2×#88131C2218yescomplemented
50C2×#88126—28no—
51C2×#88126C2218yescomplemented
52C13×#388C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718651C2218yescomplemented
60#11718637C2218yescomplemented
61#11718618C2218yes—
62#11718618C2218yes—
63#11718612C2218yescomplemented
64#11718603C2218yescomplemented
65C4×#6101C2218yescomplemented
66#11718331C2218yescomplemented
67#11718328C2218yescomplemented
68#11718310C2218yescomplemented
69#11718310C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C22×C22⋊D13—24no—
79C22×C22⋊D13—24no—
80C22×C22⋊D13C2×C418yes—
81C22×C22⋊D13C2314yes—
82C23×Dic13—24no—
83C23×Dic13—24no—
84C23×Dic13C2×C418yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2314yes—
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13C2×C418yes—
96C22×C4×D13C2314yes—
97C2×C13×C4⋊C4—42no—
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4C2×C418yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C42×C13—24no—
106C2×C42×C13C2314yes—
107C2×C22⋊Dic13—24no—
108C2×C22⋊Dic13—42no—
109C2×C22⋊Dic13C2314yes—
110C2×C22⋊Dic13C2314yes—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—42no—
114C2×#6103—42no—
115C2×#6103C2×C418yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×C4⋊Dic13—42no—
122C2×C4⋊Dic13C2314yes—
123C2×#6101—24no—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101C2×C418yes—
129C2×#6101D418yescomplemented
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×C4×Dic13—24no—
138C2×C4×Dic13—24no—
139C2×C4×Dic13—24no—
140C2×C4×Dic13—24no—
141C2×C4×Dic13—24no—
142C2×C4×Dic13C2×C418yes—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145C2×C4×Dic13C2314yes—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149#88135C2×C4164yescomplemented
150#88131—232no—
151#88126—232no—
152C13×#95C2314yes—
153C13×#95C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2354—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13C22×C414yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13C22×C414yes—
175C23×D13C2412yes—
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×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×C13C22×C414yes—
192C22×C4×C13C22×C414yes—
193C22×C4×C13C2×D414yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C2×C22⋊D13—232no—
201C2×C22⋊D13—28no—
202C2×C22⋊D13—28no—
203C2×C22⋊D13C22×C4116yes—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—232no—
209C22×Dic13—28no—
210C22×Dic13—28no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13C22×C4116yes—
221C22×Dic13C22×C414yes—
222C22×Dic13C22×C414yes—
223C22×Dic13C22×C414yes—
224C22×Dic13C2×D414yes—
225C22×Dic13C2×D414yes—
226C22×Dic13#4114yes—
227C22×Dic13#4114yes—
228C22×Dic13#4114yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C2×C4×D13—232no—
237C2×C4×D13—28no—
238C2×C4×D13—28no—
239C2×C4×D13C22×C4116yes—
240C13×C4⋊C4—44no—
241C13×C22⋊C4—28no—
242C13×C22⋊C4—44no—
243C13×C22⋊C4C22×C4116yes—
244C42×C13—28no—
245C22⋊Dic13—28no—
246C22⋊Dic13—44no—
247#6103—28no—
248#6103—28no—
249#6103—44no—
250#6103—44no—
251#6103C22×C4116yes—
252C4⋊Dic13—44no—
253#6101—28no—
254#6101—28no—
255#6101—28no—
256#6101—28no—
257#6101—28no—
258#6101C22×C4116yes—
259#6101C2×D4116yescomplemented
260C4×Dic13—28no—
261C4×Dic13—28no—
262C4×Dic13—28no—
263C4×Dic13—28no—
264C4×Dic13—28no—
265C4×Dic13C22×C4116yes—
266C22×C4×D4—131no—
267C22×#117—131no—
268C22×#117—131no—
269#2354—1316no—
270C2×#390—131no—
271C2×#390—131no—
272C2×#388—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×#388D1311yescharacteristic, complemented
276C2×#384—131no—
277C2×#380—131no—
278C2×#380—131no—
279C2×C4×C4⋊C4—131no—
280C2×C4×C4⋊C4—131no—
281C2×C4×C4⋊C4—131no—
282C23×C13—28no—
283C23×C13—28no—
284C23×C13—28no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13C23×C414yes—
296C23×C13C23×C412yes—
297C23×C13C22×D412yes—
298C23×C13C2×#4112yes—
299C23×C13C2×#4112yes—
300C23×C13C2×#4112yes—
301C23×C13H(5,𝔽2)12yes—
302C23×C132−1+412yes—
303C23×C13C2511yescharacteristic
304C22×D13—28no—
305C22×D13—28no—
306C22×D13—28no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—44no—
314C22×D13—44no—
315C22×D13—44no—
316C22×D13—44no—
317C22×D13C23×C414yes—
318C2×C4×C13—28no—
319C2×C4×C13—28no—
320C2×C4×C13—28no—
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—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—44no—
337C2×C4×C13—44no—
338C2×C4×C13—44no—
339C2×C4×C13C23×C414yes—
340C2×C4×C13C23×C414yes—
341C2×C4×C13C22×D414yes—
342C22⋊D13—232no—
343C2×Dic13—28no—
344C2×Dic13—28no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—232no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13#117116yescomplemented
363C2×Dic13C4×D4116yes—
364C2×Dic13C23×C414yes—
365C2×Dic13C23×C414yes—
366C2×Dic13C23×C414yes—
367C2×Dic13C22×D414yes—
368C2×Dic13C22×D414yes—
369C2×Dic13C2×#4114yes—
370C2×Dic13C2×#4114yes—
371C2×Dic13C2×#4114yes—
372C4×D13—232no—
373C23×D4—131no—
374C24×C4—131no—
375C24×C4—131no—
376C2×C4×D4—1316no—
377C2×C4×D4—138no—
378C2×#117—138no—
379C2×#117—138no—
380C2×#117—268no—
381C2×#117—268no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4C2×D1311yescharacteristic
391C22×C22⋊C4—131no—
392C22×C22⋊C4—131no—
393C22×C22⋊C4—131no—
394C22×C22⋊C4—131no—
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4C2×D1311yescharacteristic
399C22×C22⋊C4C2×D1311yescharacteristic
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C42—131no—
402C22×C42—131no—
403C22×C42—131no—
404C22×C42—131no—
405C22×C42—131no—
406C22×C42—131no—
407C22×C42C2×D1311yescharacteristic
408#390—138no—
409#390—138no—
410#388—138no—
411#388—138no—
412#388—138no—
413#388C2×D1318yescomplemented
414#384—138no—
415#380—138no—
416#380—138no—
417C4×C4⋊C4—138no—
418C4×C4⋊C4—138no—
419C4×C4⋊C4—138no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95C2×D1311yescharacteristic
425C2×#95C2×D1311yescharacteristic
426C22×C13—24no—
427C22×C13—24no—
428C22×C13—24no—
429C22×C13—416no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13C2×#11714yes—
435C22×C13C2×C4×D414yes—
436C22×C13#52014yes—
437C22×C13#54714yes—
438C22×C13#55014yes—
439C22×C13#55514yes—
440C22×C13#55614yes—
441C22×C13C24×C411yescharacteristic
442C22×C13C23×D411yescharacteristic
443C22×C13C22×#4111yescharacteristic
444C22×C13C22×#4111yescharacteristic
445C22×C13C22×#4111yescharacteristic
446C22×C13C2×H(5,𝔽2)11yescharacteristic
447C22×C13C2×2−1+411yescharacteristic
448C2×D13—24no—
449C2×D13—24no—
450C2×D13—24no—
451C2×D13—416no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—42no—
456C4×C13—24no—
457C4×C13—24no—
458C4×C13—24no—
459C4×C13—42no—
460C4×C13—42no—
461C4×C13—42no—
462Dic13—24no—
463Dic13—24no—
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467Dic13C2×#11718yescomplemented
468Dic13C2×C4×D418yes—
469C25—131no—
470C25C22×D1311yescharacteristic
471C22×D4—138no—
472C22×D4—134no—
473C22×D4—264no—
474C22×D4—264no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—138no—
478C23×C4—134no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—138no—
482C23×C4—134no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—264no—
487C23×C4—264no—
488C23×C4—264no—
489C23×C4—264no—
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C4×D4—1364no—
497#117—2632no—
498#117—2632no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—138no—
501C2×C4⋊C4—138no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—134no—
509C2×C4⋊C4—134no—
510C2×C4⋊C4—264no—
511C2×C4⋊C4—264no—
512C2×C4⋊C4—264no—
513C2×C4⋊C4—264no—
514C2×C4⋊C4—264no—
515C2×C4⋊C4—522no—
516C2×C4⋊C4C22×D1314yes—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—138no—
520C2×C22⋊C4—134no—
521C2×C22⋊C4—134no—
522C2×C22⋊C4—134no—
523C2×C22⋊C4—134no—
524C2×C22⋊C4—134no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—264no—
528C2×C22⋊C4—264no—
529C2×C22⋊C4—264no—
530C2×C22⋊C4—522no—
531C2×C22⋊C4—522no—
532C2×C22⋊C4—522no—
533C2×C22⋊C4C4×D1318yes—
534C2×C22⋊C4C22×D1314yes—
535C2×C22⋊C4C22×D1314yes—
536C2×C22⋊C4C22×D1314yes—
537C2×C42—24no—
538C2×C42—138no—
539C2×C42—134no—
540C2×C42—134no—
541C2×C42—134no—
542C2×C42—134no—
543C2×C42—134no—
544C2×C42—134no—
545C2×C42—264no—
546C2×C42—264no—
547C2×C42—264no—
548C2×C42—264no—
549C2×C42—264no—
550C2×C42C22×D1314yes—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95C22×D1314yes—
556#95C22×D1314yes—
557C2×C13—44no—
558C2×C13#235418yescomplemented
559C2×C13C22×#11711yescharacteristic
560C2×C13C22×C4×D411yescharacteristic
561C2×C13C2×#52011yescharacteristic
562C2×C13C2×#54711yescharacteristic
563C2×C13C2×#55011yescharacteristic
564C2×C13C2×#55511yescharacteristic
565C2×C13C2×#55611yescharacteristic
566D13—44no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—134no—
574C24—132no—
575C24—262no—
576C24—262no—
577C24—262no—
578C24—262no—
579C24—262no—
580C24—262no—
581C24C2×C4×D1314yes—
582C24C23×D1312yes—
583C24C23×D1311yescharacteristic
584C2×D4—1316no—
585C2×D4—2632no—
586C2×D4—268no—
587C2×D4—268no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—134no—
604C22×C4—134no—
605C22×C4—134no—
606C22×C4—134no—
607C22×C4—134no—
608C22×C4—134no—
609C22×C4—132no—
610C22×C4—132no—
611C22×C4—134no—
612C22×C4—1316no—
613C22×C4—134no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—1316no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—268no—
621C22×C4—2632no—
622C22×C4—268no—
623C22×C4—268no—
624C22×C4—2632no—
625C22×C4—268no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4C2×C4×D1314yes—
640C22×C4C2×C4×D1314yes—
641C22×C4D4×D1314yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C22×C4C23×D1312yes—
645C22×C4C23×D1312yes—
646C22×C4C23×D1312yes—
647C22×C4C23×D1312yes—
648C4⋊C4—44no—
649C4⋊C4—1316no—
650C4⋊C4—1316no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—268no—
654C4⋊C4—268no—
655C4⋊C4—268no—
656C4⋊C4—524no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—1316no—
660C22⋊C4—268no—
661C22⋊C4—268no—
662C22⋊C4—268no—
663C22⋊C4—524no—
664C22⋊C4—524no—
665C22⋊C4—524no—
666C22⋊C4C2×C4×D13116yes—
667C42—28no—
668C42—1316no—
669C42—268no—
670C42—268no—
671C42—268no—
672C42—268no—
673C42—268no—
674C13C2×#235411yescharacteristic, complemented, Sylow
675C23—28no—
676C23—28no—
677C23—28no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—134no—
689C23—268no—
690C23—268no—
691C23—268no—
692C23—262no—
693C23—262no—
694C23—262no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—524no—
699C23—524no—
700C23—524no—
701C23—524no—
702C23C22×C4×D1314yes—
703C23C22×C4×D1312yes—
704C23C2×D4×D1312yes—
705C23#8825112yes—
706C23#41×D1312yes—
707C23#41×D1312yes—
708C23#41×D1312yes—
709C23#8825712yes—
710C23C24×D1311yescharacteristic
711D4—2632no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—1316no—
734C2×C4—1316no—
735C2×C4—134no—
736C2×C4—134no—
737C2×C4—134no—
738C2×C4—134no—
739C2×C4—134no—
740C2×C4—134no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—2632no—
744C2×C4—2632no—
745C2×C4—268no—
746C2×C4—268no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—524no—
761C2×C4—524no—
762C2×C4—524no—
763C2×C4C22×C4×D1314yes—
764C2×C4C22×C4×D1314yes—
765C2×C4C2×D4×D1314yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—264no—
775C22—264no—
776C22—264no—
777C22—5216no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—522no—
782C22D13×#11714yes—
783C22C4×D4×D1314yes—
784C22#1171925114yes—
785C22#1171930414yes—
786C22#1171936014yes—
787C22#1171937514yes—
788C22#1171940714yes—
789C22C23×C4×D1311yescharacteristic
790C22C22×D4×D1311yescharacteristic
791C22C2×#8825111yescharacteristic
792C22C2×#41×D1311yescharacteristic
793C22C2×#41×D1311yescharacteristic
794C22C2×#41×D1311yescharacteristic
795C22C2×#8825711yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—138no—
803C4—138no—
804C4—264no—
805C4—264no—
806C4—522no—
807C4—522no—
808C4—522no—
809C2—44no—
810C2—524no—
811C2#1311778218yesdirect product factor
812C2C2×D13×#11711yescharacteristic
813C2C2×C4×D4×D1311yescharacteristic
814C2C2×#1171925111yescharacteristic
815C2C2×#1171936011yescharacteristic
816C2C2×#1171930411yescharacteristic
817C2C2×#1171937511yescharacteristic
818C2C2×#1171940711yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2354
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#88126C2semidirect
3. C22×#88131C2semidirect
4. #13117782C2direct (N × H)
7. C2×#11718612C2semidirect
8. C2×#11718331C2semidirect
9. C2×#11718651C2semidirect
10. C2×#11718637C2semidirect
11. C2×#11718328C2semidirect
12. C2×#11718603C2semidirect
13. C2×C4×#6101C2semidirect
14. C2×#11718310C2semidirect
15. C2×#11718310C2semidirect
16. C2×C13×#388C2semidirect
46. C2×#88135C4semidirect
49. C2×#88131C22semidirect
51. C2×#88126C22semidirect
52. C13×#388C22semidirect
59. #11718651C22semidirect
60. #11718637C22semidirect
63. #11718612C22semidirect
64. #11718603C22semidirect
65. C4×#6101C22semidirect
66. #11718331C22semidirect
67. #11718328C22semidirect
68. #11718310C22semidirect
69. #11718310C22semidirect
129. C2×#6101D4semidirect
149. #88135C2×C4semidirect
259. #6101C2×D4semidirect
275. C2×#388D13semidirect
362. C2×Dic13#117semidirect
413. #388C2×D13semidirect
467. Dic13C2×#117semidirect
558. C2×C13#2354semidirect
674. C13C2×#2354semidirect
811. C2#13117782direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881352
C22×#881262
C22×#881312
#131177822
C2×#117186182
C2×#117186122
C2×#117183312
C2×#117186512
C2×#117186372
C2×#117183282
C2×#117186032
C2×C4×#61012
C2×#117183102
C2×C13×#3882
C2×#235413