Finite Group Databasebeta

← C2×#13117869 #16022467

Subgroups — C2×#13117869 #16022467

Order 3328.

4046 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×#88135C211yesmaximal, characteristic, complemented
3C22×#88126C211yesmaximal, characteristic, complemented
4#13117869C2116yesmaximal, direct product factor
5C2×#11718649C211yesmaximal, characteristic, complemented
6C2×#11718618C211yesmaximal, characteristic, complemented
7C2×#11718618C211yesmaximal, characteristic, complemented
8C2×#11718633C211yesmaximal, characteristic, complemented
9C2×#11718330C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic, complemented
11C2×#11718619C211yesmaximal, characteristic, complemented
12C2×#11718310C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×C4×#6103C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88138C4116yescomplemented
47C2×#88138C2218yes—
48C2×#88135—28no—
49C2×#88135C2218yescomplemented
50C2×#88126—28no—
51C2×#88126C2218yescomplemented
52C13×#388C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718649C2218yescomplemented
60#11718633C2218yescomplemented
61#11718619C2218yescomplemented
62#11718618C2218yescomplemented
63#11718618C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65C4×#6103C2218yescomplemented
66#11718330C2218yescomplemented
67#11718327C2218yescomplemented
68#11718326C2218yescomplemented
69#11718310C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—24no—
80C22×C22⋊D13—24no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13C2×C418yes—
84C22×C22⋊D13C2×C418yescomplemented
85C22×C22⋊D13C2314yes—
86C22×C22⋊D13C2314yes—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2314yes—
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—24no—
105C22×C4×D13—42no—
106C22×C4×D13C2×C418yescomplemented
107C22×C4×D13C2314yes—
108C22×C4×D13C2314yes—
109C2×C13×C4⋊C4—42no—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4—42no—
113C2×C13×C22⋊C4C2×C418yescomplemented
114C2×C13×C22⋊C4C2314yes—
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C42×C13—24no—
118C2×C42×C13C2314yes—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13C2314yes—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—42no—
128C2×#6103C2×C418yescomplemented
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6101—24no—
138C2×#6101—42no—
139C2×#6101C2×C418yescomplemented
140C2×#6101D418yescomplemented
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×C4×Dic13—24no—
146C2×C4×Dic13—24no—
147C2×C4×Dic13—24no—
148C2×C4×Dic13—42no—
149C2×C4×Dic13—42no—
150C2×C4×Dic13C2314yes—
151C2×C4×Dic13C2314yes—
152C2×C4×Dic13C2314yes—
153C2×C4×Dic13C2314yes—
154C2×C4×Dic13C2314yes—
155#88138C2×C4164yescomplemented
156#88135—232no—
157#88126—232no—
158C13×#95C2314yes—
159C13×#95C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2363—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×C13C22×C414yes—
206C22×C4×C13C22×C414yes—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C2×C22⋊D13—232no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—416no—
218C2×C22⋊D13—44no—
219C2×C22⋊D13—44no—
220C2×C22⋊D13C22×C4116yes—
221C2×C22⋊D13C22×C4116yescomplemented
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—28no—
234C22×Dic13—28no—
235C22×Dic13—44no—
236C22×Dic13—416no—
237C22×Dic13C22×C414yes—
238C22×Dic13C22×C414yes—
239C22×Dic13C2×D414yes—
240C22×Dic13C2×D414yes—
241C22×Dic13#4114yes—
242C22×Dic13#4114yes—
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—28no—
259C2×C4×D13—44no—
260C2×C4×D13—416no—
261C2×C4×D13C22×C4116yescomplemented
262C13×C4⋊C4—44no—
263C13×C22⋊C4—28no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4C22×C4116yescomplemented
266C42×C13—28no—
267C22⋊Dic13—28no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6103—28no—
272#6103—28no—
273#6103—28no—
274#6103—44no—
275#6103C22×C4116yescomplemented
276#6101—28no—
277#6101—44no—
278#6101C22×C4116yescomplemented
279#6101C2×D4116yescomplemented
280C4×Dic13—28no—
281C4×Dic13—28no—
282C4×Dic13—28no—
283C4×Dic13—44no—
284C4×Dic13—44no—
285C22×#121—131no—
286C22×C4×D4—131no—
287C22×#117—131no—
288#2363—1316no—
289C2×#390—131no—
290C2×#390—131no—
291C2×#390—131no—
292C2×#389—131no—
293C2×#388—131no—
294C2×#388D1311yescharacteristic, complemented
295C2×#386—131no—
296C2×#386—131no—
297C2×C4×C4⋊C4—131no—
298C2×C4×C22⋊C4—131no—
299C2×C4×C22⋊C4—131no—
300C2×C4×C22⋊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×C13C2×#4112yes—
319C23×C13C2×#4112yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
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—44no—
370C2×C4×C13—44no—
371C2×C4×C13—44no—
372C2×C4×C13C23×C414yes—
373C2×C4×C13C23×C414yes—
374C2×C4×C13C22×D414yes—
375C22⋊D13—232no—
376C22⋊D13—416no—
377C2×Dic13—28no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
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—416no—
393C2×Dic13—44no—
394C2×Dic13C4×D4116yes—
395C2×Dic13C23×C414yes—
396C2×Dic13C23×C414yes—
397C2×Dic13C22×D414yes—
398C2×Dic13C22×D414yes—
399C2×Dic13C2×#4114yes—
400C2×Dic13C2×#4114yes—
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×C4—131no—
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⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4C2×D1311yescharacteristic
433C22×C22⋊C4C2×D1311yescharacteristic
434C22×C42—131no—
435C22×C42—131no—
436C22×C42—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42C2×D1311yescharacteristic
440#390—138no—
441#390—138no—
442#390—138no—
443#389—138no—
444#388—138no—
445#388C2×D1318yescomplemented
446#386—138no—
447#386—138no—
448C4×C4⋊C4—138no—
449C4×C22⋊C4—138no—
450C4×C22⋊C4—138no—
451C4×C22⋊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×C13C4×#4114yes—
468C22×C13#51814yes—
469C22×C13#54614yes—
470C22×C13#55014yes—
471C22×C13#55314yes—
472C22×C13#55514yes—
473C22×C13C24×C411yescharacteristic
474C22×C13C23×D411yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C22×#4111yescharacteristic
477C22×C13C22×#4111yescharacteristic
478C22×C13C2×H(5,𝔽2)11yescharacteristic
479C22×C13C2×H(5,𝔽2)11yescharacteristic
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—24no—
505Dic13—24no—
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—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—138no—
529C23×C4—134no—
530C23×C4—131no—
531C23×C4—134no—
532C23×C4—134no—
533C23×C4—264no—
534C23×C4—264no—
535C23×C4—264no—
536C23×C4—264no—
537C23×C4—264no—
538C23×C4—264no—
539C23×C4—522no—
540C23×C4—522no—
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C23×C4C22×D1311yescharacteristic
547#121—1364no—
548C4×D4—2632no—
549#117—2632no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—138no—
552C2×C4⋊C4—138no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—134no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—264no—
558C2×C4⋊C4—522no—
559C2×C4⋊C4C22×D1314yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—138no—
563C2×C22⋊C4—134no—
564C2×C22⋊C4—134no—
565C2×C22⋊C4—134no—
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—264no—
573C2×C22⋊C4—264no—
574C2×C22⋊C4—264no—
575C2×C22⋊C4—264no—
576C2×C22⋊C4—264no—
577C2×C22⋊C4—264no—
578C2×C22⋊C4—264no—
579C2×C22⋊C4—522no—
580C2×C22⋊C4C4×D1318yescomplemented
581C2×C22⋊C4C22×D1314yes—
582C2×C22⋊C4C22×D1314yes—
583C2×C22⋊C4C22×D1314yes—
584C2×C42—24no—
585C2×C42—134no—
586C2×C42—134no—
587C2×C42—134no—
588C2×C42—134no—
589C2×C42—134no—
590C2×C42—264no—
591C2×C42—264no—
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#95C22×D1314yes—
601#95C22×D1314yes—
602C2×C13—44no—
603C2×C13#236318yescomplemented
604C2×C13C22×C4×D411yescharacteristic
605C2×C13C2×C4×#4111yescharacteristic
606C2×C13C2×#51811yescharacteristic
607C2×C13C2×#54611yescharacteristic
608C2×C13C2×#55011yescharacteristic
609C2×C13C2×#55311yescharacteristic
610C2×C13C2×#55511yescharacteristic
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—134no—
666C22×C4—134no—
667C22×C4—134no—
668C22×C4—132no—
669C22×C4—134no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—1316no—
678C22×C4—132no—
679C22×C4—268no—
680C22×C4—2632no—
681C22×C4—268no—
682C22×C4—268no—
683C22×C4—268no—
684C22×C4—268no—
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—268no—
697C22×C4—524no—
698C22×C4—5216no—
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—44no—
711C4⋊C4—1316no—
712C4⋊C4—1316no—
713C4⋊C4—268no—
714C4⋊C4—524no—
715C22⋊C4—28no—
716C22⋊C4—44no—
717C22⋊C4—1316no—
718C22⋊C4—268no—
719C22⋊C4—268no—
720C22⋊C4—268no—
721C22⋊C4—268no—
722C22⋊C4—268no—
723C22⋊C4—268no—
724C22⋊C4—268no—
725C22⋊C4—524no—
726C22⋊C4C2×C4×D13116yescomplemented
727C42—28no—
728C42—268no—
729C42—268no—
730C42—268no—
731C42—524no—
732C42—524no—
733C13C2×#236311yescharacteristic, 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#41×D1312yes—
780C23#41×D1312yes—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—1316no—
809C2×C4—134no—
810C2×C4—134no—
811C2×C4—134no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—2632no—
817C2×C4—268no—
818C2×C4—268no—
819C2×C4—268no—
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—268no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—5216no—
833C2×C4—5216no—
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—42no—
844C22—416no—
845C22—42no—
846C22—264no—
847C22—264no—
848C22—264no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—522no—
853C22—522no—
854C22—522no—
855C22—522no—
856C22—522no—
857C22—522no—
858C22—5216no—
859C22—5216no—
860C22—522no—
861C22—522no—
862C22#1171922714yes—
863C22C4×D4×D1314yes—
864C22#1171925014yes—
865C22#1171930414yes—
866C22#1171935914yes—
867C22#1171937514yes—
868C22#1171941414yes—
869C22C23×C4×D1311yescharacteristic
870C22C22×D4×D1311yescharacteristic
871C22C2×#8825111yescharacteristic
872C22C2×#41×D1311yescharacteristic
873C22C2×#41×D1311yescharacteristic
874C22C2×#41×D1311yescharacteristic
875C22C2×#8825611yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—138no—
883C4—264no—
884C4—264no—
885C4—264no—
886C4—264no—
887C4—522no—
888C2—44no—
889C2—524no—
890C2—524no—
891C2#1311786918yesdirect product factor
892C2C2×C4×D4×D1311yescharacteristic
893C2C2×#1171922711yescharacteristic
894C2C2×#1171925011yescharacteristic
895C2C2×#1171935911yescharacteristic
896C2C2×#1171930411yescharacteristic
897C2C2×#1171941411yescharacteristic
898C2C2×#1171937511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2363
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#88135C2semidirect
3. C22×#88126C2semidirect
4. #13117869C2direct (N × H)
5. C2×#11718649C2semidirect
6. C2×#11718618C2semidirect
7. C2×#11718618C2semidirect
8. C2×#11718633C2semidirect
9. C2×#11718330C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718619C2semidirect
12. C2×#11718310C2semidirect
13. C2×C22⋊C4×Dic13C2semidirect
14. C2×C4×#6103C2semidirect
15. C2×#11718327C2semidirect
16. C2×C13×#388C2semidirect
46. C2×#88138C4semidirect
49. C2×#88135C22semidirect
51. C2×#88126C22semidirect
52. C13×#388C22semidirect
59. #11718649C22semidirect
60. #11718633C22semidirect
61. #11718619C22semidirect
62. #11718618C22semidirect
63. #11718618C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. C4×#6103C22semidirect
66. #11718330C22semidirect
67. #11718327C22semidirect
68. #11718326C22semidirect
69. #11718310C22semidirect
84. C22×C22⋊D13C2×C4semidirect
99. C22×D52C2×C4semidirect
106. C22×C4×D13C2×C4semidirect
113. C2×C13×C22⋊C4C2×C4semidirect
128. C2×#6103C2×C4semidirect
139. C2×#6101C2×C4semidirect
140. C2×#6101D4semidirect
155. #88138C2×C4semidirect
221. C2×C22⋊D13C22×C4semidirect
253. C2×D52C22×C4semidirect
261. C2×C4×D13C22×C4semidirect
265. C13×C22⋊C4C22×C4semidirect
275. #6103C22×C4semidirect
278. #6101C22×C4semidirect
279. #6101C2×D4semidirect
294. C2×#388D13semidirect
445. #388C2×D13semidirect
580. C2×C22⋊C4C4×D13semidirect
603. C2×C13#2363semidirect
726. C22⋊C4C2×C4×D13semidirect
733. C13C2×#2363semidirect
891. C2#13117869direct (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×#881352
C22×#881262
#131178692
C2×#117186492
C2×#117186182
C2×#117186332
C2×#117183302
C2×#117183262
C2×#117186192
C2×#117183102
C2×C22⋊C4×Dic132
C2×C4×#61032
C2×#117183272
C2×C13×#3882
C2×#236313