Finite Group Databasebeta

← C2×#13117881 #16022497

Subgroups — C2×#13117881 #16022497

Order 3328.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88193C211yesmaximal, characteristic
2C22×#88135C211yesmaximal, characteristic, complemented
3#13117881C2116yesmaximal, direct product factor
4C2×#11718606C211yesmaximal, characteristic, complemented
5C2×#11718651C211yesmaximal, characteristic, complemented
6C2×#11718594C211yesmaximal, characteristic, complemented
7C2×#11718639C211yesmaximal, characteristic, complemented
8C2×#11718881C211yesmaximal, characteristic, complemented
9C2×#11718874C211yesmaximal, characteristic, complemented
10C2×#11718874C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
13C2×C4×#6103C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C2×C4×D4×C13—28no—
26C2×C4×D4×C13C2218yescomplemented
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88193C4116yescomplemented
36C2×#88193C2218yes—
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88135—28no—
47C2×#88135C2218yescomplemented
48#11718881C2218yescomplemented
49#11718874C2218yescomplemented
50#11718874C2218yescomplemented
51C4×C22⋊Dic13C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2218yescomplemented
63#11718651C2218yescomplemented
64#11718639C2218yescomplemented
65#11718617C2218yescomplemented
66#11718606C2218yescomplemented
67C22⋊C4×Dic13C2218yescomplemented
68C4×#6103C2218yescomplemented
69#11718594C2218yescomplemented
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13C2×C418yescomplemented
76C22×D4×C13C2314yes—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—42no—
82C23×C4×C13—42no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2314yes—
85C23×C4×C13C2314yes—
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13—42no—
93C22×C22⋊D13—42no—
94C22×C22⋊D13C2×C418yescomplemented
95C22×C22⋊D13C2×C418yescomplemented
96C22×C22⋊D13C2314yes—
97C22×C22⋊D13C2314yes—
98C23×Dic13—24no—
99C23×Dic13—24no—
100C23×Dic13—42no—
101C23×Dic13—42no—
102C23×Dic13—42no—
103C23×Dic13C2×C418yescomplemented
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2314yes—
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2311yescharacteristic
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2314yes—
113C22×C4×D13—24no—
114C22×C4×D13—24no—
115C22×C4×D13—42no—
116C22×C4×D13C2314yes—
117C4×D4×C13—232no—
118C2×C13×C4⋊C4—24no—
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C22⋊C4—24no—
121C2×C13×C22⋊C4D418yescomplemented
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2314yes—
124C2×C42×C13—24no—
125C2×C42×C13C2314yes—
126C2×C22⋊Dic13—24no—
127C2×C22⋊Dic13—24no—
128C2×C22⋊Dic13—42no—
129C2×C22⋊Dic13C2×C418yescomplemented
130C2×C22⋊Dic13C2314yes—
131C2×C22⋊Dic13C2314yes—
132C2×C22⋊Dic13C2314yes—
133C2×C22⋊Dic13C2314yes—
134#88193C2×C4164yescomplemented
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103—42no—
138C2×#6103C2×C418yescomplemented
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6101—24no—
144C2×#6101C2×C418yescomplemented
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×C4×Dic13—24no—
148C2×C4×Dic13—42no—
149C2×C4×Dic13—42no—
150C2×C4×Dic13C2314yes—
151C2×C4×Dic13C2314yes—
152C2×C4×Dic13C2314yes—
153#88135—232no—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2364—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13C22×C414yes—
176C24×C13C22×C414yes—
177C24×C13C2×D414yes—
178C24×C13#4114yes—
179C24×C13C2412yes—
180C24×C13C2412yes—
181C24×C13C2411yescharacteristic
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13C22×C414yes—
189C23×D13C2412yes—
190C2×D4×C13—232no—
191C2×D4×C13—28no—
192C2×D4×C13—28no—
193C2×D4×C13C22×C4116yescomplemented
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—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—28no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—28no—
207C22×C4×C13—28no—
208C22×C4×C13—28no—
209C22×C4×C13—44no—
210C22×C4×C13—44no—
211C22×C4×C13—416no—
212C22×C4×C13—416no—
213C22×C4×C13C22×C414yes—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2×D414yes—
216C22×C4×C13#4114yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C2×C22⋊D13—232no—
223C2×C22⋊D13—28no—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—416no—
226C2×C22⋊D13—44no—
227C2×C22⋊D13—44no—
228C2×C22⋊D13C22×C4116yescomplemented
229C2×C22⋊D13C22×C4116yescomplemented
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—28no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—28no—
249C22×Dic13—416no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13—44no—
253C22×Dic13—416no—
254C22×Dic13C22×C414yes—
255C22×Dic13C22×C414yes—
256C22×Dic13C22×C414yes—
257C22×Dic13C22×C4116yescomplemented
258C22×Dic13#4114yes—
259C22×Dic13C2412yes—
260C22×Dic13C2412yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C2×C4×D13—28no—
267C2×C4×D13—28no—
268C2×C4×D13—44no—
269C2×C4×D13—416no—
270C13×C4⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4C2×D4116yescomplemented
273C42×C13—28no—
274C22⋊Dic13—28no—
275C22⋊Dic13—28no—
276C22⋊Dic13—44no—
277C22⋊Dic13C22×C4116yescomplemented
278#6103—28no—
279#6103—28no—
280#6103—44no—
281#6103C22×C4116yescomplemented
282#6101—28no—
283#6101C22×C4116yescomplemented
284C4×Dic13—28no—
285C4×Dic13—44no—
286C4×Dic13—44no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4D1311yescharacteristic, complemented
290#2364—1316no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#387—131no—
294C2×#387—131no—
295C2×#386—131no—
296C2×#386—131no—
297C2×#386—131no—
298C2×#386—131no—
299C2×C4×C22⋊C4—131no—
300C2×C4×C22⋊C4—131no—
301C2×C4×C22⋊C4—131no—
302C22×#95—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—28no—
314C23×C13—28no—
315C23×C13—28no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13C4×D4116yes—
327C23×C13C23×C414yes—
328C23×C13C23×C414yes—
329C23×C13C23×C412yes—
330C23×C13C22×D414yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C23×C414yes—
353D4×C13—232no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—28no—
357C2×C4×C13—28no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—416no—
370C2×C4×C13—416no—
371C2×C4×C13—44no—
372C2×C4×C13C23×C414yes—
373C2×C4×C13C22×D414yes—
374C2×C4×C13C22×D414yes—
375C2×C4×C13C2×#4114yes—
376C22⋊D13—232no—
377C22⋊D13—416no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
381C2×Dic13—28no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—416no—
400C2×Dic13—416no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13C23×C414yes—
405C2×Dic13C23×C414yes—
406C2×Dic13C23×C414yes—
407C2×Dic13C2×#4114yes—
408C4×D13—416no—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4C2×D1311yescharacteristic
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4C2×D1311yescharacteristic
416C24×C4C2×D1311yescharacteristic
417C2×#121—1316no—
418C2×#121—138no—
419C2×C4×D4—28no—
420C2×C4×D4—138no—
421C2×C4×D4—268no—
422C2×C4×D4C2×D1318yescomplemented
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4C2×D1311yescharacteristic
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C42—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42C2×D1311yescharacteristic
440#388—138no—
441#388—138no—
442#387—138no—
443#387—138no—
444#386—138no—
445#386—138no—
446#386—138no—
447#386—138no—
448C4×C22⋊C4—138no—
449C4×C22⋊C4—138no—
450C4×C22⋊C4—138no—
451C2×#95—138no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C22×C13—232no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—416no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13C2×C4×D418yes—
478C22×C13C2×C4×D414yes—
479C22×C13C4×#4114yes—
480C22×C13#51814yes—
481C22×C13#54614yes—
482C22×C13#54614yes—
483C22×C13#55314yes—
484C22×C13#55314yes—
485C22×C13C24×C411yescharacteristic
486C22×C13C23×D411yescharacteristic
487C22×C13C22×#4111yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C22×#4111yescharacteristic
490C22×C13C2×H(5,𝔽2)11yescharacteristic
491C22×C13C2×H(5,𝔽2)11yescharacteristic
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—24no—
495C2×D13—416no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13—42no—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—42no—
505Dic13—24no—
506Dic13—24no—
507Dic13—24no—
508Dic13—24no—
509Dic13—42no—
510Dic13—42no—
511Dic13—42no—
512C25—131no—
513C25C22×D1311yescharacteristic
514C25C22×D1311yescharacteristic
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—138no—
520C22×D4—134no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—522no—
524C22×D4—522no—
525C22×D4C4×D1318yescomplemented
526C22×D4C22×D1314yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—138no—
538C23×C4—134no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—134no—
543C23×C4—134no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—264no—
548C23×C4—522no—
549C23×C4—522no—
550C23×C4—522no—
551C23×C4—522no—
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1314yes—
554C23×C4C22×D1314yes—
555C23×C4C22×D1311yescharacteristic
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559#121—1364no—
560C4×D4—232no—
561C4×D4—2632no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—138no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—138no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—138no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—264no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—522no—
584C2×C22⋊C4—522no—
585C2×C22⋊C4C22⋊D1318yescomplemented
586C2×C22⋊C4C22×D1314yes—
587C2×C22⋊C4C22×D1314yes—
588C2×C42—24no—
589C2×C42—134no—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—264no—
593C2×C42—522no—
594C2×C42—522no—
595C2×C42C22×D1314yes—
596#95—134no—
597#95—134no—
598#95—134no—
599#95—134no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606C2×C13—28no—
607C2×C13—44no—
608C2×C13#236418yescomplemented
609C2×C13C22×C4×D411yescharacteristic
610C2×C13C2×C4×#4111yescharacteristic
611C2×C13C2×#51811yescharacteristic
612C2×C13C2×#54611yescharacteristic
613C2×C13C2×#54611yescharacteristic
614C2×C13C2×#55311yescharacteristic
615C2×C13C2×#55311yescharacteristic
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—134no—
628C24—132no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24C2×C4×D1314yes—
636C24C2×C4×D1314yes—
637C24#612714yes—
638C24C2×C22⋊D1314yes—
639C24C23×D1312yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—232no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—1316no—
646C2×D4—1316no—
647C2×D4—2632no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—5216no—
651C2×D4—524no—
652C2×D4—524no—
653C2×D4C2×C4×D13116yescomplemented
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—416no—
673C22×C4—134no—
674C22×C4—134no—
675C22×C4—134no—
676C22×C4—134no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—1316no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—268no—
686C22×C4—268no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—262no—
702C22×C4—262no—
703C22×C4—262no—
704C22×C4—268no—
705C22×C4—268no—
706C22×C4—524no—
707C22×C4—5216no—
708C22×C4—5216no—
709C22×C4—524no—
710C22×C4—524no—
711C22×C4—524no—
712C22×C4—5216no—
713C22×C4C2×C4×D1314yes—
714C22×C4#612914yes—
715C22×C4C2×C22⋊D1314yes—
716C22×C4C2×C22⋊D1314yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1312yes—
722C4⋊C4—28no—
723C4⋊C4—1316no—
724C4⋊C4—268no—
725C22⋊C4—28no—
726C22⋊C4—1316no—
727C22⋊C4—1316no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—524no—
733C22⋊C4—524no—
734C22⋊C4C2×C22⋊D13116yescomplemented
735C42—28no—
736C42—268no—
737C42—524no—
738C42—524no—
739C13C2×#236411yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—134no—
764C23—268no—
765C23—268no—
766C23—268no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23C4×C22⋊D13116yes—
778C23C22×C4×D1314yes—
779C23C22×C4×D1314yes—
780C23C22×C4×D1312yes—
781C23C2×#612714yes—
782C23C2×#612712yes—
783C23C2×#612912yes—
784C23#8825112yes—
785C23#41×D1312yes—
786C23#8825612yes—
787C23C22×C22⋊D1314yes—
788C23C22×C22⋊D1312yes—
789C23C24×D1311yescharacteristic
790D4—232no—
791D4—2632no—
792D4—5216no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—134no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—268no—
816C2×C4—268no—
817C2×C4—268no—
818C2×C4—268no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—5216no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4C22×C4×D1314yes—
843C2×C4C2×#612914yes—
844C2×C4C22×C22⋊D1314yes—
845C2×C4C22×C22⋊D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—264no—
862C22—264no—
863C22—264no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—5216no—
869C22C4×#612914yes—
870C22#1171924514yes—
871C22#1171925014yes—
872C22#1171927014yes—
873C22C2×C4×C22⋊D1318yes—
874C22C2×C4×C22⋊D1314yes—
875C22#1171951114yes—
876C22#1171953414yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×#612711yescharacteristic
879C22C22×#612911yescharacteristic
880C22C2×#8825111yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#8825611yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—28no—
897C2—44no—
898C2—524no—
899C2#1311788118yesdirect product factor
900C2C22×C4×C22⋊D1311yescharacteristic
901C2C2×C4×#612911yescharacteristic
902C2C2×#1171925011yescharacteristic
903C2C2×#1171953411yescharacteristic
904C2C2×#1171951111yescharacteristic
905C2C2×#1171927011yescharacteristic
906C2C2×#1171924511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC22×#88193C2
cosocleC23×C13C25
hypercenterC22×C4×D4D13
hypocenterC13C2×#2364
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#88135C2semidirect
3. #13117881C2direct (N × H)
4. C2×#11718606C2semidirect
5. C2×#11718651C2semidirect
6. C2×#11718594C2semidirect
7. C2×#11718639C2semidirect
8. C2×#11718881C2semidirect
9. C2×#11718874C2semidirect
10. C2×#11718874C2semidirect
11. C2×#11718617C2semidirect
12. C2×C22⋊C4×Dic13C2semidirect
13. C2×C4×#6103C2semidirect
14. C2×C4×C22⋊Dic13C2semidirect
15. C22×#88071C2semidirect
16. C22×C4×D4×C13C2semidirect
26. C2×C4×D4×C13C22semidirect
35. C2×#88193C4semidirect
47. C2×#88135C22semidirect
48. #11718881C22semidirect
49. #11718874C22semidirect
50. #11718874C22semidirect
51. C4×C22⋊Dic13C22semidirect
62. C2×#88071C22semidirect
63. #11718651C22semidirect
64. #11718639C22semidirect
65. #11718617C22semidirect
66. #11718606C22semidirect
67. C22⋊C4×Dic13C22semidirect
68. C4×#6103C22semidirect
69. #11718594C22semidirect
75. C22×D4×C13C2×C4semidirect
94. C22×C22⋊D13C2×C4semidirect
95. C22×C22⋊D13C2×C4semidirect
103. C23×Dic13C2×C4semidirect
121. C2×C13×C22⋊C4D4semidirect
129. C2×C22⋊Dic13C2×C4semidirect
134. #88193C2×C4semidirect
138. C2×#6103C2×C4semidirect
144. C2×#6101C2×C4semidirect
193. C2×D4×C13C22×C4semidirect
228. C2×C22⋊D13C22×C4semidirect
229. C2×C22⋊D13C22×C4semidirect
257. C22×Dic13C22×C4semidirect
272. C13×C22⋊C4C2×D4semidirect
277. C22⋊Dic13C22×C4semidirect
281. #6103C22×C4semidirect
283. #6101C22×C4semidirect
289. C22×C4×D4D13semidirect
422. C2×C4×D4C2×D13semidirect
525. C22×D4C4×D13semidirect
585. C2×C22⋊C4C22⋊D13semidirect
608. C2×C13#2364semidirect
653. C2×D4C2×C4×D13semidirect
734. C22⋊C4C2×C22⋊D13semidirect
739. C13C2×#2364semidirect
899. C2#13117881direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881932
C22×#881352
#131178812
C2×#117186062
C2×#117186512
C2×#117185942
C2×#117186392
C2×#117188812
C2×#117188742
C2×#117186172
C2×C22⋊C4×Dic132
C2×C4×#61032
C2×C4×C22⋊Dic132
C22×#880712
C22×C4×D4×C132
C2×#236413