Finite Group Databasebeta

← C2×#13131568 #16808280

Subgroups — C2×#13131568 #16808280

Order 3328.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88238C211yesmaximal, characteristic, complemented
2C23×#6122C211yesmaximal, characteristic, complemented
3#13131568C2116yesmaximal, direct product factor
4C2×#11719145C211yesmaximal, characteristic, complemented
5C2×#11719066C211yesmaximal, characteristic, complemented
6C2×#11719065C211yesmaximal, characteristic, complemented
7C2×#11719144C211yesmaximal, characteristic, complemented
8C2×#11719144C211yesmaximal, characteristic, complemented
9C2×#11719064C211yesmaximal, characteristic, complemented
10C2×#11719063C211yesmaximal, characteristic, complemented
11C2×D4×#1057C211yesmaximal, characteristic, complemented
12C2×#11719067C211yesmaximal, characteristic, complemented
13C2×#11719146C211yesmaximal, characteristic, complemented
14C22×C22⋊#1057C211yesmaximal, characteristic, complemented
15C2×#11719062C211yesmaximal, characteristic, complemented
16C2×#11719291C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C22×#6129C2211yescharacteristic
19C22×#6122—28no—
20C22×#6122C2211yescharacteristic
21C22×#6122C2211yescharacteristic
22C22×#6122C2211yescharacteristic
23C22×#6122C2211yescharacteristic
24C22×#6122C2218yescomplemented
25C22×#6122C2211yescharacteristic, complemented
26C23×#1057C2211yescharacteristic
27C23×#1057C2211yescharacteristic
28C23×#1057C2211yescharacteristic
29C23×#1057C2211yescharacteristic
30C23×#1057C2211yescharacteristic, complemented
31C2×#88238—28no—
32C2×#88238C2218yescomplemented
33C22×#6118C2211yescharacteristic, complemented
34C22×D13⋊C8C2211yescharacteristic, complemented
35C2×C13×#120C411yescharacteristic
36C2×#88207C411yescharacteristic
37C2×#88193C411yescharacteristic
38C2×#88193C411yescharacteristic
39C2×#88189C411yescharacteristic
40C2×D4×Dic13C2211yescharacteristic
41C2×D4×Dic13C2211yescharacteristic
42#11719291C418yes—
43#11719291C2218yes—
44C2×#88140C411yescharacteristic
45C2×#88135C2211yescharacteristic
46C2×#88135C2211yescharacteristic
47C2×#88132C411yescharacteristic
48C2×#88132C411yescharacteristic
49C2×#88131C2211yescharacteristic
50C2×C22⋊#1057C2211yescharacteristic
51C2×C22⋊#1057C2211yescharacteristic
52C2×C22⋊#1057C2211yescharacteristic
53C2×C22⋊#1057C2211yescharacteristic
54C2×C22⋊#1057C2218yescomplemented
55C2×C22⋊#1057C2211yescharacteristic, complemented
56C2×C22⋊#1057C2211yescharacteristic, complemented
57#11719146C2218yescomplemented
58#11719145C2218yescomplemented
59#11719144C2218yescomplemented
60#11719144C2218yescomplemented
61D4×#1057C2218yescomplemented
62C2×#88112C2211yescharacteristic, complemented
63C2×#88112C2211yescharacteristic, complemented
64C2×#88111C2211yescharacteristic, complemented
65C2×#88111C2211yescharacteristic, complemented
66C2×#88110C2211yescharacteristic, complemented
67C2×#88110C2211yescharacteristic, complemented
68C2×C4⋊#1057C2211yescharacteristic, complemented
69C2×C4⋊#1057C2211yescharacteristic, complemented
70C2×C4×#1057C2211yescharacteristic, complemented
71C2×C4×#1057C2211yescharacteristic, complemented
72#11719067C2218yescomplemented
73#11719066C2218yescomplemented
74#11719065C2218yescomplemented
75#11719064C2218yescomplemented
76#11719063C2218yescomplemented
77#11719062C2218yescomplemented
78C25×C13C2×C411yescharacteristic
79C22×D4×C13C2×C411yescharacteristic
80C22×D4×C13C2×C411yescharacteristic
81C22×D4×C13C2×C411yescharacteristic
82C22×C22⋊D13C2×C411yescharacteristic
83C22×C22⋊D13C2×C411yescharacteristic
84C22×C22⋊D13C2×C411yescharacteristic
85C22×C22⋊D13C2×C411yescharacteristic
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13C2×C411yescharacteristic
89C23×Dic13C2×C411yescharacteristic
90C23×Dic13C2×C411yescharacteristic
91C23×Dic13C2×C414yes—
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2314yes—
96C23×Dic13C2311yescharacteristic
97C2×#6129—24no—
98C2×#6129—24no—
99C2×#6129C2×C414yes—
100C2×#6129C2314yes—
101C22×C4×D13C2311yescharacteristic
102C22×Dic26C2×C411yescharacteristic
103C2×#6122—24no—
104C2×#6122—232no—
105C2×#6122—24no—
106C2×#6122—24no—
107C2×#6122—24no—
108C2×#6122D418yescomplemented
109C2×#6122C2314yes—
110C2×#6122C2314yes—
111C2×#6122C2314yes—
112C2×#6122C2314yes—
113C2×#6122C2314yescomplemented
114C22×#1057—24no—
115C22×#1057—24no—
116C22×#1057—24no—
117C22×#1057—24no—
118C22×#1057—24no—
119C22×#1057C2311yescharacteristic
120C22×#1057C2311yescharacteristic
121C22×#1057C2311yescharacteristic
122C22×#1057C2311yescharacteristic
123C22×#1057C2314yes—
124C22×#1057C2314yes—
125C22×#1057C2311yescharacteristic
126C22×#1057C2311yescharacteristic
127C22×#1057C2314yes—
128C22×#1057C2314yes—
129C22×#1057C2311yescharacteristic
130C22×#1057C2311yescharacteristic
131C22×#1057C2314yescomplemented
132#88238—232no—
133C2×#6118—24no—
134C2×#6118C2314yescomplemented
135C2×D13⋊C8—24no—
136C2×D13⋊C8C2314yescomplemented
137C13×#120C2×C418yes—
138C2×C13×C22⋊C4C2×C411yescharacteristic
139C2×C13×C22⋊C4C2×C411yescharacteristic
140C2×C13×C22⋊C4C2×C411yescharacteristic
141#88207C2×C418yes—
142C2×C22⋊Dic13C2×C411yescharacteristic
143C2×C22⋊Dic13C2×C411yescharacteristic
144C2×C22⋊Dic13C2×C411yescharacteristic
145C2×C22⋊Dic13C2×C411yescharacteristic
146C2×C22⋊Dic13C2×C411yescharacteristic
147#88193C2×C418yes—
148#88193C2×C418yes—
149#88189C2×C418yes—
150D4×Dic13C2×C414yes—
151D4×Dic13C2×C414yes—
152D4×Dic13C2314yes—
153D4×Dic13C2314yes—
154C2×#6103C2×C411yescharacteristic
155C2×#6103C2×C411yescharacteristic
156C2×C4⋊Dic13C2×C411yescharacteristic
157C2×C4⋊Dic13C2×C411yescharacteristic
158C2×#6101C2×C411yescharacteristic
159C2×#6101C2×C411yescharacteristic
160C2×#6101C2×C411yescharacteristic
161C2×#6101C2×C411yescharacteristic
162C2×C4×Dic13C2311yescharacteristic
163C2×C4×Dic13C2311yescharacteristic
164#88140C2×C418yes—
165#88135C2×C414yes—
166#88135C2×C414yes—
167#88135C2314yes—
168#88135C2314yes—
169#88132C2×C418yes—
170#88132C2×C418yes—
171#88131C2×C414yes—
172#88131C2314yes—
173C22⋊#1057C2314yes—
174C22⋊#1057C2314yes—
175C22⋊#1057C2314yes—
176C22⋊#1057C2314yes—
177C22⋊#1057C2314yescomplemented
178C22⋊#1057C2314yescomplemented
179#88112C2314yescomplemented
180#88112C2314yescomplemented
181#88111C2314yescomplemented
182#88111C2314yescomplemented
183#88110C2314yescomplemented
184#88110C2314yescomplemented
185C4⋊#1057C2314yescomplemented
186C4⋊#1057C2314yescomplemented
187C4×#1057C2314yescomplemented
188C4×#1057C2314yescomplemented
189C2×#2933—131nomaximal, Sylow
190C24×C13—24no—
191C24×C13—24no—
192C24×C13—42no—
193C24×C13C22×C411yescharacteristic
194C24×C13C22×C411yescharacteristic
195C24×C13C22×C414yes—
196C24×C13C22×C411yescharacteristic
197C24×C13C22×C411yescharacteristic
198C23×D13C22×C411yescharacteristic
199C2×D4×C13—24no—
200C2×D4×C13—24no—
201C2×D4×C13—42no—
202C2×D4×C13C22×C414yes—
203C2×D4×C13C22×C414yes—
204C2×D4×C13C22×C414yes—
205C22×C4×C13C22×C411yescharacteristic
206C22×C4×C13C22×C411yescharacteristic
207C22×C4×C13C22×C411yescharacteristic
208C2×C22⋊D13—24no—
209C2×C22⋊D13—24no—
210C2×C22⋊D13—24no—
211C2×C22⋊D13—42no—
212C2×C22⋊D13C22×C414yes—
213C2×C22⋊D13C22×C414yes—
214C2×C22⋊D13C22×C414yes—
215C2×C22⋊D13C22×C414yes—
216C22×Dic13—24no—
217C22×Dic13—24no—
218C22×Dic13—24no—
219C22×Dic13—216no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—28no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—28no—
228C22×Dic13C22×C414yes—
229C22×Dic13C22×C414yes—
230C22×Dic13C22×C412yes—
231C22×Dic13C22×C412yes—
232C22×Dic13C22×C414yes—
233C22×Dic13C22×C411yescharacteristic
234C22×Dic13C22×C411yescharacteristic
235C22×Dic13C22×C411yescharacteristic
236C22×Dic13C22×C411yescharacteristic
237C22×Dic13C22×C411yescharacteristic
238C22×Dic13C22×C412yes—
239C22×Dic13C22×C412yes—
240C22×Dic13C22×C411yescharacteristic
241C22×Dic13C2×D414yes—
242C22×Dic13#4114yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2411yescharacteristic
248#6129—216no—
249#6129—28no—
250#6129—28no—
251C2×C4×D13—22no—
252C2×C4×D13—22no—
253C2×C4×D13C22×C412yes—
254C2×C4×D13C2412yes—
255C2×Dic26—24no—
256C2×Dic26C22×C414yes—
257#6122—28no—
258#6122—28no—
259#6122—28no—
260#6122—28no—
261#6122C2×D4116yescomplemented
262C2×#1057—22no—
263C2×#1057—22no—
264C2×#1057—28no—
265C2×#1057—22no—
266C2×#1057—22no—
267C2×#1057—22no—
268C2×#1057—22no—
269C2×#1057—28no—
270C2×#1057—28no—
271C2×#1057—28no—
272C2×#1057—28no—
273C2×#1057C2×D414yes—
274C2×#1057C2×D414yes—
275C2×#1057C2412yes—
276C2×#1057C2412yes—
277C2×#1057C2412yes—
278C2×#1057C2412yes—
279C2×#1057C2412yes—
280C2×#1057C2412yes—
281C2×#1057C2412yes—
282C2×#1057C2412yes—
283#6118—28no—
284D13⋊C8—28no—
285C13×C22⋊C4C22×C414yes—
286C13×C22⋊C4C22×C414yes—
287C13×C22⋊C4C22×C414yes—
288C22⋊Dic13C22×C414yes—
289C22⋊Dic13C22×C414yes—
290C22⋊Dic13C22×C414yes—
291C22⋊Dic13C22×C414yes—
292C22⋊Dic13C22×C414yes—
293#6103C22×C414yes—
294#6103C22×C414yes—
295C4⋊Dic13C22×C414yes—
296C4⋊Dic13C22×C414yes—
297#6101C22×C414yes—
298#6101C22×C414yes—
299#6101C22×C414yes—
300#6101C22×C414yes—
301C4×Dic13C22×C412yes—
302C4×Dic13C22×C412yes—
303C4×Dic13C2412yes—
304C4×Dic13C2412yes—
305C22×#131—131no—
306C23×M16—131no—
307C2×#525—131no—
308#2933—1316no—
309C2×#436—131no—
310C2×#436—131no—
311C2×#435—131no—
312C2×#435—131no—
313C2×#435—131no—
314C2×#435—131no—
315C2×C8×D4—131no—
316C2×C8×D4—131no—
317C2×#424—131no—
318C2×#408—131no—
319C22×C22⋊C8—131no—
320C2×#405—131no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—28no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—28no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—44no—
334C23×C13—416no—
335C23×C13C4×D414yes—
336C23×C13#13114yescomplemented
337C23×C13C23×C412yes—
338C23×C13C23×C412yes—
339C23×C13C23×C412yes—
340C23×C13C23×C412yes—
341C23×C13C23×C411yescharacteristic
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13C23×C412yes—
346D4×C13—28no—
347D4×C13—28no—
348D4×C13—44no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13C23×C412yes—
353C2×C4×C13C23×C412yes—
354C2×C4×C13C23×C412yes—
355C22⋊D13—28no—
356C22⋊D13—28no—
357C22⋊D13—28no—
358C22⋊D13—44no—
359C2×Dic13—22no—
360C2×Dic13—28no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—24no—
366C2×Dic13—28no—
367C2×Dic13—28no—
368C2×Dic13—24no—
369C2×Dic13—24no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13C4×D414yes—
377C2×Dic13C4×D418yes—
378C2×Dic13C23×C412yes—
379C2×Dic13C23×C412yes—
380C2×Dic13C23×C412yes—
381C2×Dic13C23×C412yes—
382C2×Dic13C23×C412yes—
383C2×Dic13C23×C411yescharacteristic
384C2×Dic13C23×C412yes—
385C2×Dic13C22×D412yes—
386C2×Dic13C22×D414yes—
387C2×Dic13C2×#4112yes—
388C2×Dic13C2×#4114yes—
389C2×Dic13C2511yescharacteristic
390C4×D13—24no—
391C4×D13—22no—
392C4×D13—22no—
393Dic26—28no—
394#1057—22no—
395#1057—22no—
396#1057—22no—
397#1057—22no—
398#1057—22no—
399#1057—22no—
400#1057C22×D414yes—
401#1057C22×D414yes—
402C22×#41—131no—
403C24×C4—131no—
404C2×#131—138no—
405C2×#131—268no—
406C22×M16—131no—
407C22×M16—131no—
408C22×M16—131no—
409C22×M16—131no—
410C22×M16—131no—
411C22×M16—131no—
412C22×M16—138no—
413C22×M16—268no—
414C23×C8—131no—
415C23×C8—131no—
416C23×C8—131no—
417C23×C8—131no—
418C23×C8—131no—
419C23×C8—131no—
420#525—138no—
421#525—138no—
422C2×#123—131no—
423C2×#123—131no—
424C2×C22⋊Q8—131no—
425C2×C22⋊Q8—131no—
426C2×#121—131no—
427C2×#121—131no—
428C2×#120—131no—
429C2×#120#26111yescharacteristic
430C2×C4×D4—131no—
431C2×C4×D4—131no—
432C2×C4×D4—131no—
433C2×C4×D4—131no—
434C2×#117—131no—
435#436—138no—
436#436—138no—
437#435—138no—
438#435—138no—
439#435—138no—
440#435—138no—
441C8×D4—138no—
442C8×D4—138no—
443#424—138no—
444C2×C4⋊C8—131no—
445C2×C4⋊C8—131no—
446C2×C4⋊C8—131no—
447C2×C4⋊C8—131no—
448#408—138no—
449C2×C22⋊C8—131no—
450C2×C22⋊C8—131no—
451C2×C22⋊C8—131no—
452C2×C22⋊C8—131no—
453C2×C22⋊C8—138no—
454C2×C22⋊C8—131no—
455C2×C22⋊C8—131no—
456C2×C22⋊C8—131no—
457C2×C22⋊C8—131no—
458#405—138no—
459C2×#97—131no—
460C2×#97—131no—
461C2×C4×C8—131no—
462C2×C4×C8—131no—
463C22×C13—22no—
464C22×C13—28no—
465C22×C13—28no—
466C22×C13—22no—
467C22×C13—22no—
468C22×C13—22no—
469C22×C13—22no—
470C22×C13—22no—
471C22×C13—22no—
472C22×C13—22no—
473C22×C13—22no—
474C22×C13—22no—
475C22×C13—416no—
476C22×C13—44no—
477C22×C13—44no—
478C22×C13C2×C4×D414yes—
479C22×C13C2×C4×D412yes—
480C22×C13C2×#13112yes—
481C22×C13C2×#13114yescomplemented
482C22×C13#56812yes—
483C22×C13C24×C411yescharacteristic
484C2×D13—22no—
485C2×D13—22no—
486C2×D13—22no—
487C2×D13—44no—
488C4×C13—22no—
489C4×C13—22no—
490C4×C13—22no—
491Dic13—22no—
492Dic13—22no—
493Dic13—22no—
494Dic13—22no—
495Dic13—22no—
496Dic13C2×C4×D414yes—
497Dic13C2×C4×D412yes—
498Dic13C23×D411yescharacteristic
499Dic13C22×#4111yescharacteristic
500C25C2×#26111yescharacteristic
501C2×#41—134no—
502C2×#41—134no—
503C2×#41—264no—
504C2×#41—264no—
505C22×Q8—131no—
506C22×D4—131no—
507C22×D4—131no—
508C22×D4—131no—
509C22×D4—131no—
510C22×D4C2×#26111yescharacteristic
511C22×D4C2×#26111yescharacteristic
512C22×D4C2×#26111yescharacteristic
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—134no—
521C23×C4—134no—
522C23×C4—131no—
523C23×C4—264no—
524C23×C4—264no—
525#131—2632no—
526C2×M16—134no—
527C2×M16—138no—
528C2×M16—134no—
529C2×M16—134no—
530C2×M16—134no—
531C2×M16—134no—
532C2×M16—134no—
533C2×M16—264no—
534C2×M16—264no—
535C2×M16—264no—
536C2×M16—264no—
537C2×M16—2632no—
538C2×M16—264no—
539C22×C8—131no—
540C22×C8—131no—
541C22×C8—131no—
542C22×C8—131no—
543C22×C8—131no—
544C22×C8—131no—
545C22×C8—134no—
546C22×C8—134no—
547C22×C8—134no—
548C22×C8—134no—
549C22×C8—134no—
550C22×C8—131no—
551C22×C8—131no—
552C22×C8—134no—
553C22×C8—264no—
554C22×C8—264no—
555C22×C8—264no—
556C22×C8—264no—
557C22×C8—264no—
558C22×C8—264no—
559#123—138no—
560#123—138no—
561C22⋊Q8—138no—
562C22⋊Q8—138no—
563#121—138no—
564#121—138no—
565#120—138no—
566#120C2×#26118yes—
567C4×D4—134no—
568C4×D4—134no—
569C4×D4—134no—
570C4×D4—134no—
571C4×D4—134no—
572C4×D4—134no—
573C4×D4—134no—
574C4×D4—134no—
575#117—134no—
576#117—134no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—131no—
581C2×C4⋊C4—131no—
582C2×C4⋊C4—131no—
583C2×C22⋊C4—131no—
584C2×C22⋊C4—131no—
585C2×C22⋊C4—131no—
586C2×C22⋊C4—131no—
587C2×C22⋊C4—131no—
588C2×C22⋊C4—131no—
589C2×C22⋊C4—131no—
590C2×C22⋊C4C2×#26111yescharacteristic
591C2×C22⋊C4C2×#26111yescharacteristic
592C2×C22⋊C4C2×#26111yescharacteristic
593C2×C42—131no—
594C2×C42—131no—
595C4⋊C8—134no—
596C4⋊C8—134no—
597C4⋊C8—134no—
598C4⋊C8—134no—
599C22⋊C8—134no—
600C22⋊C8—134no—
601C22⋊C8—134no—
602C22⋊C8—134no—
603C22⋊C8—134no—
604C22⋊C8—134no—
605C22⋊C8—134no—
606C22⋊C8—134no—
607#97—134no—
608#97—134no—
609C4×C8—134no—
610C4×C8—134no—
611C2×C13—24no—
612C2×C13—24no—
613C2×C13—42no—
614C2×C13—42no—
615C2×C13#293314yescomplemented
616C2×C13C22×C4×D411yescharacteristic
617C2×C13C22×#13111yescharacteristic
618C2×C13C2×#56811yescharacteristic
619D13—42no—
620C24—24no—
621C24—24no—
622C24—42no—
623C24—131no—
624C24C22×#26111yescharacteristic
625C24C22×#26111yescharacteristic
626C24C22×#26114yes—
627C24C22×#26111yescharacteristic
628C24C22×#26111yescharacteristic
629#41—268no—
630#41—268no—
631#41—2616no—
632C2×Q8—134no—
633C2×Q8—264no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—42no—
637C2×D4—134no—
638C2×D4—134no—
639C2×D4—134no—
640C2×D4—134no—
641C2×D4—264no—
642C2×D4—264no—
643C2×D4—264no—
644C2×D4—522no—
645C2×D4C22×#26114yes—
646C2×D4C22×#26114yes—
647C2×D4C22×#26114yes—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—131no—
653C22×C4—131no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—134no—
661C22×C4—134no—
662C22×C4—134no—
663C22×C4—131no—
664C22×C4—131no—
665C22×C4—131no—
666C22×C4—131no—
667C22×C4—131no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—268no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—268no—
679C22×C4—264no—
680C22×C4—264no—
681C22×C4—2616no—
682C22×C4—262no—
683C22×C4—264no—
684C22×C4C22×#26111yescharacteristic
685C22×C4C22×#26111yescharacteristic
686C22×C4C22×#26111yescharacteristic
687M16—1316no—
688M16—268no—
689M16—268no—
690M16—268no—
691M16—268no—
692M16—268no—
693C2×C8—132no—
694C2×C8—132no—
695C2×C8—134no—
696C2×C8—134no—
697C2×C8—132no—
698C2×C8—132no—
699C2×C8—132no—
700C2×C8—132no—
701C2×C8—132no—
702C2×C8—132no—
703C2×C8—268no—
704C2×C8—268no—
705C2×C8—268no—
706C2×C8—268no—
707C2×C8—262no—
708C2×C8—262no—
709C2×C8—262no—
710C2×C8—262no—
711C2×C8—268no—
712C2×C8—262no—
713C2×C8—262no—
714C2×C8—268no—
715C4⋊C4—134no—
716C4⋊C4—134no—
717C4⋊C4—134no—
718C4⋊C4—134no—
719C4⋊C4—134no—
720C4⋊C4—134no—
721C22⋊C4—134no—
722C22⋊C4—134no—
723C22⋊C4—134no—
724C22⋊C4—134no—
725C22⋊C4—134no—
726C22⋊C4—134no—
727C22⋊C4—134no—
728C22⋊C4C22×#26114yes—
729C22⋊C4C22×#26114yes—
730C22⋊C4C22×#26114yes—
731C42—132no—
732C42—132no—
733C42—132no—
734C42—132no—
735C13C2×#293311yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—416no—
750C23—132no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23#8823814yescomplemented
755C23D4×#26114yes—
756C23C23×#26112yes—
757C23C23×#26112yes—
758C23C23×#26112yes—
759C23C23×#26112yes—
760C23C23×#26111yescharacteristic
761Q8—268no—
762D4—28no—
763D4—28no—
764D4—44no—
765D4—268no—
766D4—268no—
767D4—268no—
768D4—524no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—132no—
773C2×C4—134no—
774C2×C4—132no—
775C2×C4—134no—
776C2×C4—134no—
777C2×C4—138no—
778C2×C4—131no—
779C2×C4—131no—
780C2×C4—132no—
781C2×C4—132no—
782C2×C4—132no—
783C2×C4—132no—
784C2×C4—132no—
785C2×C4—132no—
786C2×C4—262no—
787C2×C4—264no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—264no—
793C2×C4—264no—
794C2×C4—268no—
795C2×C4—268no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—264no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—268no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4C23×#26112yes—
807C2×C4C23×#26112yes—
808C2×C4C23×#26112yes—
809C8—134no—
810C8—134no—
811C8—262no—
812C8—262no—
813C8—262no—
814C8—262no—
815C8—262no—
816C8—262no—
817C22—22no—
818C22—28no—
819C22—28no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—416no—
830C22—44no—
831C22—44no—
832C22—262no—
833C22—262no—
834C22—262no—
835C22—524no—
836C22C2×#8823812yes—
837C22C2×#8823814yescomplemented
838C22#1171962112yes—
839C22C2×D4×#26114yes—
840C22C2×D4×#26112yes—
841C22C24×#26111yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—132no—
846C4—134no—
847C4—131no—
848C4—131no—
849C4—262no—
850C4—262no—
851C4—262no—
852C4—262no—
853C4—262no—
854C2—24no—
855C2—24no—
856C2—42no—
857C2—42no—
858C2—522no—
859C2#1313156814yesdirect product factor
860C2C22×D4×#26111yescharacteristic
861C2C22×#8823811yescharacteristic
862C2C2×#1171962111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#120C4
socleC23×C13C23×C4
prime radicalC2×#11719291C2
cosocleC2×Dic13C25
hypercenterC2×#120#261
hypocenterC13C2×#2933
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C22×#88238C2semidirect
2. C23×#6122C2semidirect
3. #13131568C2direct (N × H)
4. C2×#11719145C2semidirect
5. C2×#11719066C2semidirect
6. C2×#11719065C2semidirect
7. C2×#11719144C2semidirect
8. C2×#11719144C2semidirect
9. C2×#11719064C2semidirect
10. C2×#11719063C2semidirect
11. C2×D4×#1057C2semidirect
12. C2×#11719067C2semidirect
13. C2×#11719146C2semidirect
14. C22×C22⋊#1057C2semidirect
15. C2×#11719062C2semidirect
24. C22×#6122C22semidirect
25. C22×#6122C22semidirect
30. C23×#1057C22semidirect
32. C2×#88238C22semidirect
33. C22×#6118C22semidirect
34. C22×D13⋊C8C22semidirect
54. C2×C22⋊#1057C22semidirect
55. C2×C22⋊#1057C22semidirect
56. C2×C22⋊#1057C22semidirect
57. #11719146C22semidirect
58. #11719145C22semidirect
59. #11719144C22semidirect
60. #11719144C22semidirect
61. D4×#1057C22semidirect
62. C2×#88112C22semidirect
63. C2×#88112C22semidirect
64. C2×#88111C22semidirect
65. C2×#88111C22semidirect
66. C2×#88110C22semidirect
67. C2×#88110C22semidirect
68. C2×C4⋊#1057C22semidirect
69. C2×C4⋊#1057C22semidirect
70. C2×C4×#1057C22semidirect
71. C2×C4×#1057C22semidirect
72. #11719067C22semidirect
73. #11719066C22semidirect
74. #11719065C22semidirect
75. #11719064C22semidirect
76. #11719063C22semidirect
77. #11719062C22semidirect
108. C2×#6122D4semidirect
113. C2×#6122C23semidirect
131. C22×#1057C23semidirect
134. C2×#6118C23semidirect
136. C2×D13⋊C8C23semidirect
177. C22⋊#1057C23semidirect
178. C22⋊#1057C23semidirect
179. #88112C23semidirect
180. #88112C23semidirect
181. #88111C23semidirect
182. #88111C23semidirect
183. #88110C23semidirect
184. #88110C23semidirect
185. C4⋊#1057C23semidirect
186. C4⋊#1057C23semidirect
187. C4×#1057C23semidirect
188. C4×#1057C23semidirect
261. #6122C2×D4semidirect
336. C23×C13#131semidirect
481. C22×C13C2×#131semidirect
615. C2×C13#2933semidirect
735. C13C2×#2933semidirect
754. C23#88238semidirect
837. C22C2×#88238semidirect
859. C2#13131568direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882382
C23×#61222
#131315682
C2×#117191452
C2×#117190662
C2×#117190652
C2×#117191442
C2×#117190642
C2×#117190632
C2×D4×#10572
C2×#117190672
C2×#117191462
C22×C22⋊#10572
C2×#117190622
C2×#117192912
C2×#293313