Finite Group Databasebeta

← C2×#13117528 #16021672

Subgroups — C2×#13117528 #16021672

Order 3328.

3934 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88138C211yesmaximal, characteristic
2C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C22×#88146C211yesmaximal, characteristic, complemented
4#13117528C2116yesmaximal, direct product factor
5C2×#11718649C211yesmaximal, characteristic, complemented
6C2×#11718618C211yesmaximal, characteristic, complemented
7C2×#11718618C211yesmaximal, characteristic, complemented
8C2×#11718633C211yesmaximal, characteristic, complemented
9C2×#11718612C211yesmaximal, characteristic, complemented
10C2×#11718331C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic, complemented
12C2×#11718326C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718328C211yesmaximal, characteristic, complemented
15C2×#11718310C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C2×C4×C22⋊D13—28no—
30C2×C4×C22⋊D13C2218yescomplemented
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88146—28no—
49C2×#88146C2218yescomplemented
50C2×#88138C4116yescomplemented
51C2×#88138C2218yes—
52C13×#385C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55#11718874C2218yescomplemented
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718650C2218yescomplemented
61#11718649C2218yescomplemented
62#11718633C2218yescomplemented
63#11718618C2218yescomplemented
64#11718618C2218yescomplemented
65#11718612C2218yescomplemented
66#11718331C2218yescomplemented
67#11718328C2218yescomplemented
68#11718326C2218yescomplemented
69#11718310C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13—24no—
74C23×C4×C13—42no—
75C23×C4×C13—42no—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13C2×C418yes—
88C22×C22⋊D13C2×C418yescomplemented
89C22×C22⋊D13C2314yes—
90C22×C22⋊D13C2314yes—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C22×D52—42no—
98C22×D52—42no—
99C22×D52C2×C418yescomplemented
100C22×D52C2314yes—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—42no—
105C22×C4×D13—42no—
106C22×C4×D13C2×C418yescomplemented
107C22×C4×D13C2314yes—
108C22×C4×D13C2314yes—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4—42no—
111C2×C13×C4⋊C4C2314yes—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C22⋊C4—42no—
114C2×C13×C22⋊C4C2×C418yescomplemented
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C4×C22⋊D13—232no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—42no—
126C2×#6103—42no—
127C2×#6103—42no—
128C2×#6103—42no—
129C2×#6103C2×C418yescomplemented
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×C4⋊Dic13—24no—
139C2×C4⋊Dic13C2314yes—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101—42no—
143C2×#6101C2×C418yescomplemented
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×C4×Dic13—24no—
149C2×C4×Dic13—42no—
150C2×C4×Dic13—42no—
151C2×C4×Dic13D418yescomplemented
152C2×C4×Dic13C2314yes—
153C2×C4×Dic13C2314yes—
154C2×C4×Dic13C2314yes—
155C2×C4×Dic13C2314yes—
156#88146—232no—
157#88138C2×C4164yescomplemented
158C13×#95C2314yes—
159C13×#95C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2324—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C22×C414yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—22no—
185C23×D13—22no—
186C23×D13C22×C414yes—
187C23×D13C22×C414yes—
188C23×D13C2412yes—
189C23×D13C2412yes—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
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—22no—
204C22×C4×C13—22no—
205C22×C4×C13—28no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13—416no—
209C22×C4×C13C22×C414yes—
210C22×C4×C13C22×C414yes—
211C22×C4×C13C2×D414yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C2×C22⋊D13—232no—
219C2×C22⋊D13—28no—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—416no—
222C2×C22⋊D13—44no—
223C2×C22⋊D13—44no—
224C2×C22⋊D13C22×C4116yes—
225C2×C22⋊D13C22×C4116yescomplemented
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
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—22no—
239C22×Dic13C22×C414yes—
240C22×Dic13C22×C414yes—
241C22×Dic13C2×D414yes—
242C22×Dic13C2×D414yes—
243C22×Dic13#4114yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×D52—416no—
251C2×D52—44no—
252C2×D52—44no—
253C2×D52C22×C4116yescomplemented
254C2×C4×D13—232no—
255C2×C4×D13—28no—
256C2×C4×D13—28no—
257C2×C4×D13—28no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—416no—
261C2×C4×D13C22×C4116yescomplemented
262C13×C4⋊C4—28no—
263C13×C4⋊C4—44no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4C22×C4116yescomplemented
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274#6103—44no—
275#6103C22×C4116yescomplemented
276C4⋊Dic13—28no—
277#6101—28no—
278#6101—28no—
279#6101—44no—
280#6101C22×C4116yescomplemented
281C4×Dic13—28no—
282C4×Dic13—44no—
283C4×Dic13—44no—
284C4×Dic13C2×D4116yescomplemented
285C22×#121—131no—
286C22×C4×D4—131no—
287C22×#117—131no—
288#2324—1316no—
289C2×#390—131no—
290C2×#390—131no—
291C2×#390—131no—
292C2×#389—131no—
293C2×#388—131no—
294C2×#388—131no—
295C2×#386—131no—
296C2×#386—131no—
297C2×#385—131no—
298C2×#385D1311yescharacteristic, complemented
299C2×#380—131no—
300C2×C4×C4⋊C4—131no—
301C23×C13—28no—
302C23×C13—28no—
303C23×C13—28no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13C23×C414yes—
315C23×C13C23×C412yes—
316C23×C13C22×D412yes—
317C23×C13C2×#4112yes—
318C23×C13H(5,𝔽2)12yes—
319C23×C13H(5,𝔽2)12yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C132−1+412yes—
322C23×C13C2511yescharacteristic
323C22×D13—28no—
324C22×D13—28no—
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—44no—
342C22×D13—44no—
343C22×D13—44no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13C23×C414yes—
350C22×D13C23×C414yes—
351C2×C4×C13—28no—
352C2×C4×C13—28no—
353C2×C4×C13—28no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
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—44no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13C23×C414yes—
374C2×C4×C13C23×C414yes—
375C2×C4×C13C22×D414yes—
376C22⋊D13—232no—
377C22⋊D13—416no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—22no—
381C2×Dic13—22no—
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—44no—
394C2×Dic13—44no—
395C2×Dic13—44no—
396C2×Dic13C4×D4116yes—
397C2×Dic13C23×C414yes—
398C2×Dic13C23×C414yes—
399C2×Dic13C22×D414yes—
400C2×Dic13C22×D414yes—
401C2×Dic13C2×#4114yes—
402D52—416no—
403C4×D13—232no—
404C4×D13—416no—
405C23×D4—131no—
406C23×D4—131no—
407C23×D4—131no—
408C24×C4—131no—
409C24×C4—131no—
410C24×C4C2×D1311yescharacteristic
411C2×#121—1316no—
412C2×#121—138no—
413C2×C4×D4—138no—
414C2×C4×D4—268no—
415C2×#117—138no—
416C2×#117—268no—
417C22×C4⋊C4—131no—
418C22×C4⋊C4—131no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4C2×D1311yescharacteristic
423C22×C4⋊C4C2×D1311yescharacteristic
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
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×C42—131no—
440#390—138no—
441#390—138no—
442#390—138no—
443#389—138no—
444#388—138no—
445#388—138no—
446#386—138no—
447#386—138no—
448#385—138no—
449#385C2×D1318yescomplemented
450#380—138no—
451C4×C4⋊C4—138no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95C2×D1311yescharacteristic
457C2×#95C2×D1311yescharacteristic
458C22×C13—24no—
459C22×C13—24no—
460C22×C13—24no—
461C22×C13—416no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13C2×C4×D414yes—
467C22×C13#51814yes—
468C22×C13#52014yes—
469C22×C13#53514yes—
470C22×C13#53714yes—
471C22×C13#54014yes—
472C22×C13#54214yes—
473C22×C13C24×C411yescharacteristic
474C22×C13C23×D411yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C2×H(5,𝔽2)11yescharacteristic
477C22×C13C2×H(5,𝔽2)11yescharacteristic
478C22×C13C2×H(5,𝔽2)11yescharacteristic
479C22×C13C2×2−1+411yescharacteristic
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—24no—
483C2×D13—24no—
484C2×D13—24no—
485C2×D13—24no—
486C2×D13—416no—
487C2×D13—416no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C4×C13—24no—
497C4×C13—24no—
498C4×C13—24no—
499C4×C13—42no—
500C4×C13—42no—
501C4×C13—42no—
502Dic13—24no—
503Dic13—24no—
504Dic13—42no—
505Dic13—42no—
506Dic13—42no—
507Dic13C2×C4×D418yes—
508C25—131no—
509C25—131no—
510C25C22×D1311yescharacteristic
511C22×D4—138no—
512C22×D4—134no—
513C22×D4—138no—
514C22×D4—134no—
515C22×D4—138no—
516C22×D4—134no—
517C22×D4—264no—
518C22×D4—264no—
519C22×D4—522no—
520C22×D4—522no—
521C22×D4—522no—
522C22×D4—522no—
523C23×C4—24no—
524C23×C4—42no—
525C23×C4—42no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—138no—
530C23×C4—134no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—134no—
535C23×C4—264no—
536C23×C4—264no—
537C23×C4—264no—
538C23×C4—522no—
539C23×C4—522no—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C23×C4C22×D1314yes—
547#121—1364no—
548C4×D4—2632no—
549#117—2632no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4—138no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—134no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—264no—
559C2×C4⋊C4—264no—
560C2×C4⋊C4—264no—
561C2×C4⋊C4—522no—
562C2×C4⋊C4C22×D1314yes—
563C2×C4⋊C4C22×D1314yes—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—138no—
566C2×C22⋊C4—134no—
567C2×C22⋊C4—134no—
568C2×C22⋊C4—134no—
569C2×C22⋊C4—134no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—264no—
577C2×C22⋊C4—264no—
578C2×C22⋊C4—264no—
579C2×C22⋊C4—264no—
580C2×C22⋊C4—522no—
581C2×C22⋊C4—522no—
582C2×C22⋊C4—522no—
583C2×C22⋊C4—522no—
584C2×C22⋊C4—522no—
585C2×C22⋊C4C4×D1318yescomplemented
586C2×C22⋊C4C22×D1314yes—
587C2×C22⋊C4C22×D1314yes—
588C2×C42—138no—
589C2×C42—134no—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—134no—
593C2×C42—264no—
594C2×C42—522no—
595C2×C42—522no—
596#95—134no—
597#95—134no—
598#95—134no—
599#95—134no—
600#95C22×D1314yes—
601#95C22×D1314yes—
602C2×C13—44no—
603C2×C13#232418yescomplemented
604C2×C13C22×C4×D411yescharacteristic
605C2×C13C2×#51811yescharacteristic
606C2×C13C2×#52011yescharacteristic
607C2×C13C2×#53511yescharacteristic
608C2×C13C2×#53711yescharacteristic
609C2×C13C2×#54011yescharacteristic
610C2×C13C2×#54211yescharacteristic
611D13—44no—
612D13—44no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—134no—
620C24—134no—
621C24—132no—
622C24—132no—
623C24—262no—
624C24—262no—
625C24—262no—
626C24—262no—
627C24—262no—
628C24—262no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24C2×C4×D1314yes—
636C24C23×D1312yes—
637C24C23×D1311yescharacteristic
638C2×D4—1316no—
639C2×D4—1316no—
640C2×D4—1316no—
641C2×D4—268no—
642C2×D4—2632no—
643C2×D4—268no—
644C2×D4—5216no—
645C2×D4—524no—
646C2×D4—524no—
647C2×D4—5216no—
648C2×D4—524no—
649C2×D4—524no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
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—44no—
667C22×C4—44no—
668C22×C4—416no—
669C22×C4—134no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—132no—
673C22×C4—134no—
674C22×C4—134no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—1316no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—268no—
682C22×C4—2632no—
683C22×C4—268no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
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—268no—
698C22×C4—524no—
699C22×C4—524no—
700C22×C4—5216no—
701C22×C4C2×C4×D1314yes—
702C22×C4C2×C4×D1314yes—
703C22×C4D4×D1314yes—
704C22×C4C23×D1312yes—
705C22×C4C23×D1312yes—
706C22×C4C23×D1312yes—
707C22×C4C23×D1312yes—
708C22×C4C23×D1312yes—
709C22×C4C23×D1312yes—
710C4⋊C4—28no—
711C4⋊C4—44no—
712C4⋊C4—1316no—
713C4⋊C4—268no—
714C4⋊C4—268no—
715C4⋊C4—268no—
716C4⋊C4—524no—
717C22⋊C4—44no—
718C22⋊C4—1316no—
719C22⋊C4—268no—
720C22⋊C4—268no—
721C22⋊C4—268no—
722C22⋊C4—268no—
723C22⋊C4—524no—
724C22⋊C4—524no—
725C22⋊C4—524no—
726C22⋊C4—524no—
727C22⋊C4—524no—
728C22⋊C4C2×C4×D13116yescomplemented
729C42—1316no—
730C42—268no—
731C42—524no—
732C42—524no—
733C13C2×#232411yescharacteristic, complemented, Sylow
734C23—28no—
735C23—28no—
736C23—28no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—134no—
748C23—134no—
749C23—268no—
750C23—268no—
751C23—268no—
752C23—268no—
753C23—268no—
754C23—268no—
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—524no—
768C23—524no—
769C23—524no—
770C23—524no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23—524no—
775C23C22×C4×D1314yes—
776C23C22×C4×D1312yes—
777C23C2×D4×D1312yes—
778C23#8825112yes—
779C23#8825112yes—
780C23#8825412yes—
781C23#41×D1312yes—
782C23#8825612yes—
783C23C24×D1311yescharacteristic
784D4—2632no—
785D4—5216no—
786D4—5216no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
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—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—1316no—
810C2×C4—134no—
811C2×C4—134no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—2632no—
816C2×C4—268no—
817C2×C4—268no—
818C2×C4—262no—
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—5216no—
832C2×C4—524no—
833C2×C4—524no—
834C2×C4—524no—
835C2×C4C22×C4×D1314yes—
836C2×C4C22×C4×D1314yes—
837C2×C4C2×D4×D1314yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—416no—
844C22—42no—
845C22—42no—
846C22—264no—
847C22—264no—
848C22—264no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—522no—
853C22—522no—
854C22—522no—
855C22—522no—
856C22—5216no—
857C22—5216no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—522no—
862C22#1171920914yes—
863C22C4×D4×D1314yes—
864C22#1171925014yes—
865C22#1171929714yes—
866C22#1171933414yes—
867C22#1171934514yes—
868C22#1171936814yes—
869C22C23×C4×D1311yescharacteristic
870C22C22×D4×D1311yescharacteristic
871C22C2×#8825111yescharacteristic
872C22C2×#8825111yescharacteristic
873C22C2×#8825411yescharacteristic
874C22C2×#41×D1311yescharacteristic
875C22C2×#8825611yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—138no—
883C4—264no—
884C4—264no—
885C4—522no—
886C4—522no—
887C4—522no—
888C2—44no—
889C2—524no—
890C2—524no—
891C2#1311752818yesdirect product factor
892C2C2×C4×D4×D1311yescharacteristic
893C2C2×#1171925011yescharacteristic
894C2C2×#1171920911yescharacteristic
895C2C2×#1171929711yescharacteristic
896C2C2×#1171933411yescharacteristic
897C2C2×#1171936811yescharacteristic
898C2C2×#1171934511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×#2324
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D13C2semidirect
3. C22×#88146C2semidirect
4. #13117528C2direct (N × H)
5. C2×#11718649C2semidirect
6. C2×#11718618C2semidirect
7. C2×#11718618C2semidirect
8. C2×#11718633C2semidirect
9. C2×#11718612C2semidirect
10. C2×#11718331C2semidirect
11. C2×#11718874C2semidirect
12. C2×#11718326C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718328C2semidirect
15. C2×#11718310C2semidirect
16. C2×C13×#385C2semidirect
30. C2×C4×C22⋊D13C22semidirect
49. C2×#88146C22semidirect
50. C2×#88138C4semidirect
52. C13×#385C22semidirect
55. #11718874C22semidirect
60. #11718650C22semidirect
61. #11718649C22semidirect
62. #11718633C22semidirect
63. #11718618C22semidirect
64. #11718618C22semidirect
65. #11718612C22semidirect
66. #11718331C22semidirect
67. #11718328C22semidirect
68. #11718326C22semidirect
69. #11718310C22semidirect
88. C22×C22⋊D13C2×C4semidirect
99. C22×D52C2×C4semidirect
106. C22×C4×D13C2×C4semidirect
114. C2×C13×C22⋊C4C2×C4semidirect
129. C2×#6103C2×C4semidirect
143. C2×#6101C2×C4semidirect
151. C2×C4×Dic13D4semidirect
157. #88138C2×C4semidirect
225. C2×C22⋊D13C22×C4semidirect
253. C2×D52C22×C4semidirect
261. C2×C4×D13C22×C4semidirect
265. C13×C22⋊C4C22×C4semidirect
275. #6103C22×C4semidirect
280. #6101C22×C4semidirect
284. C4×Dic13C2×D4semidirect
298. C2×#385D13semidirect
449. #385C2×D13semidirect
585. C2×C22⋊C4C4×D13semidirect
603. C2×C13#2324semidirect
728. C22⋊C4C2×C4×D13semidirect
733. C13C2×#2324semidirect
891. C2#13117528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
C22×C4×C22⋊D132
C22×#881462
#131175282
C2×#117186492
C2×#117186182
C2×#117186332
C2×#117186122
C2×#117183312
C2×#117188742
C2×#117183262
C2×#117186502
C2×#117183282
C2×#117183102
C2×C13×#3852
C2×#232413