Finite Group Databasebeta

← C2×#13118829 #16030441

Subgroups — C2×#13118829 #16030441

Order 3328.

3958 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×#88200C211yesmaximal, characteristic, complemented
2C22×#88147C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13118829C2116yesmaximal, direct product factor
5C2×#11718652C211yesmaximal, characteristic, complemented
6C2×#11718622C211yesmaximal, characteristic, complemented
7C2×#11718892C211yesmaximal, characteristic, complemented
8C2×#11718621C211yesmaximal, characteristic
9C2×#11718651C211yesmaximal, characteristic, complemented
10C2×#11718605C211yesmaximal, characteristic, complemented
11C2×#11718642C211yesmaximal, characteristic, complemented
12C2×#11718639C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718617C211yesmaximal, characteristic, complemented
15C2×#11718650C211yesmaximal, characteristic, complemented
16C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×D52C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C2×C13×C22⋊Q8—28no—
25C2×C13×C22⋊Q8C2218yescomplemented
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C2×#88200—28no—
34C2×#88200C2218yescomplemented
35C2×C4×C22⋊D13—28no—
36C2×C4×C22⋊D13C2218yescomplemented
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6103C2211yescharacteristic
44C22×#6103C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×C4×Dic13C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C2×#88147—28no—
51C2×#88147C2218yescomplemented
52#11718892C2218yescomplemented
53#11718874C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718652C2218yescomplemented
63#11718651C2218yescomplemented
64#11718650C2218yescomplemented
65#11718642C2218yescomplemented
66#11718639C2218yescomplemented
67#11718622C2218yescomplemented
68#11718621C2218yes—
69#11718617C2218yescomplemented
70#11718605C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C22×Q8×C13—24no—
75C22×Q8×C13—24no—
76C22×Q8×C13—42no—
77C22×Q8×C13C2314yes—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—42no—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2314yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C22×C22⋊D13—24no—
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13—24no—
93C22×C22⋊D13—42no—
94C22×C22⋊D13C2314yes—
95C22×C22⋊D13C2314yes—
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C22×D52—24no—
103C22×D52—24no—
104C22×D52—24no—
105C22×D52C2314yes—
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—24no—
109C22×C4×D13—24no—
110C22×C4×D13—42no—
111C22×C4×D13—42no—
112C22×C4×D13C2314yes—
113C22×C4×D13C2314yes—
114C13×C22⋊Q8—232no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4—24no—
117C2×C13×C4⋊C4D418yescomplemented
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C4⋊C4C2314yes—
121C2×C13×C22⋊C4—24no—
122C2×C13×C22⋊C4—24no—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13—24no—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129#88200—232no—
130C4×C22⋊D13—232no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103—24no—
138C2×#6103—42no—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×#6103C2314yes—
146C2×#6103C2314yes—
147C2×C4⋊Dic13—24no—
148C2×C4⋊Dic13C2314yes—
149C2×#6101—24no—
150C2×#6101D418yescomplemented
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×C4×Dic13—24no—
154C2×C4×Dic13—24no—
155C2×C4×Dic13C2314yes—
156C2×C4×Dic13C2314yes—
157#88147—232no—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2463—131nomaximal, Sylow
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13#4114yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
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×D13—22no—
187C23×D13—22no—
188C23×D13#4114yes—
189C23×D13#4114yes—
190C23×D13C2412yes—
191C23×D13C2412yes—
192C2×Q8×C13—28no—
193C2×Q8×C13—28no—
194C2×Q8×C13—44no—
195C2×Q8×C13—416no—
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—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—28no—
211C22×C4×C13—28no—
212C22×C4×C13—44no—
213C22×C4×C13—416no—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2×D414yes—
217C22×C4×C13C2×D414yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C2×C22⋊D13—232no—
225C2×C22⋊D13—28no—
226C2×C22⋊D13—28no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13—28no—
229C2×C22⋊D13—28no—
230C2×C22⋊D13—44no—
231C2×C22⋊D13—416no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
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×Dic13C2×D414yes—
249C22×Dic13C2×D414yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C2×D52—232no—
257C2×D52—28no—
258C2×D52—28no—
259C2×D52—28no—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—28no—
263C2×C4×D13—28no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C2×C4×D13—416no—
267C2×C4×D13—416no—
268C13×C4⋊C4—28no—
269C13×C4⋊C4—28no—
270C13×C4⋊C4C2×D4116yescomplemented
271C13×C22⋊C4—28no—
272C13×C22⋊C4—28no—
273C22⋊Dic13—28no—
274C22⋊Dic13—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—28no—
280#6103—28no—
281#6103—28no—
282#6103—44no—
283C4⋊Dic13—28no—
284#6101—28no—
285#6101C2×D4116yescomplemented
286C4×Dic13—28no—
287C4×Dic13—28no—
288C22×C22⋊Q8—131no—
289C22×C22⋊Q8D1311yescharacteristic, complemented
290C22×C4×D4—131no—
291C22×C4×D4—131no—
292#2463—1316no—
293C2×#394—131no—
294C2×#394—131no—
295C2×#393—131no—
296C2×#392—131no—
297C2×#388—131no—
298C2×#388—131no—
299C2×#387—131no—
300C2×#387—131no—
301C2×#386—131no—
302C2×#386—131no—
303C2×#385—131no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13C22×D412yes—
318C23×C13C22×D412yes—
319C23×C13C2×#4114yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C132−1+412yes—
325C23×C13C2511yescharacteristic
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—28no—
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—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C2×#4114yes—
353C22×D13C2×#4114yes—
354Q8×C13—416no—
355C2×C4×C13—28no—
356C2×C4×C13—28no—
357C2×C4×C13—28no—
358C2×C4×C13—28no—
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—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—416no—
374C2×C4×C13—44no—
375C2×C4×C13—44no—
376C2×C4×C13C22×D414yes—
377C2×C4×C13C22×D414yes—
378C2×C4×C13C22×D414yes—
379C2×C4×C13C22×D414yes—
380C22⋊D13—232no—
381C22⋊D13—416no—
382C2×Dic13—28no—
383C2×Dic13—28no—
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—22no—
400C2×Dic13—44no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13C22×D414yes—
405C2×Dic13C22×D414yes—
406D52—232no—
407C4×D13—416no—
408C4×D13—416no—
409C23×Q8C2×D1311yescharacteristic
410C23×D4—131no—
411C23×D4—131no—
412C23×D4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4C2×D1311yescharacteristic
416C2×C22⋊Q8—28no—
417C2×C22⋊Q8—138no—
418C2×C22⋊Q8—268no—
419C2×C22⋊Q8C2×D1318yescomplemented
420C2×C4×D4—138no—
421C2×C4×D4—138no—
422C2×C4×D4—268no—
423C2×C4×D4—268no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4C2×D1311yescharacteristic
428C22×C4⋊C4C2×D1311yescharacteristic
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C42—131no—
443C22×C42—131no—
444#394—138no—
445#394—138no—
446#393—138no—
447#392—138no—
448#388—138no—
449#388—138no—
450#387—138no—
451#387—138no—
452#386—138no—
453#386—138no—
454#385—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—416no—
471C22×C13#52514yes—
472C22×C13#52514yes—
473C22×C13#53914yes—
474C22×C13D4214yes—
475C22×C13#54814yes—
476C22×C13#54814yes—
477C22×C13#55114yes—
478C22×C13C23×D411yescharacteristic
479C22×C13C23×D411yescharacteristic
480C22×C13C22×#4111yescharacteristic
481C22×C13C22×#4111yescharacteristic
482C22×C13C22×#4111yescharacteristic
483C22×C13C2×H(5,𝔽2)11yescharacteristic
484C22×C13C2×2−1+411yescharacteristic
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—24no—
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13—416no—
500C2×D13—416no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—42no—
506C4×C13—42no—
507Dic13—24no—
508Dic13—24no—
509Dic13—42no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513C25—131no—
514C25—131no—
515C25C22×D1311yescharacteristic
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8—42no—
519C22×Q8C22×D1314yes—
520C22×D4—134no—
521C22×D4—134no—
522C22×D4—134no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—264no—
526C22×D4—264no—
527C22×D4—264no—
528C22×D4—264no—
529C22×D4—264no—
530C22×D4—264no—
531C22×D4—522no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—42no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—134no—
542C23×C4—134no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—522no—
548C23×C4—522no—
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1314yes—
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C22⋊Q8—232no—
557C22⋊Q8—2632no—
558C4×D4—2632no—
559C4×D4—2632no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—138no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4C22⋊D1318yescomplemented
569C2×C4⋊C4C22×D1314yes—
570C2×C4⋊C4C22×D1314yes—
571C2×C4⋊C4C22×D1314yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—264no—
586C2×C22⋊C4—264no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—264no—
592C2×C22⋊C4—264no—
593C2×C22⋊C4—522no—
594C2×C22⋊C4C22×D1314yes—
595C2×C22⋊C4C22×D1314yes—
596C2×C42—134no—
597C2×C42—134no—
598C2×C42—264no—
599C2×C42—264no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606#95—134no—
607#95—134no—
608C2×C13—44no—
609C2×C13#246318yescomplemented
610C2×C13C2×#52511yescharacteristic
611C2×C13C2×#52511yescharacteristic
612C2×C13C2×#53911yescharacteristic
613C2×C13C2×D4211yescharacteristic
614C2×C13C2×#54811yescharacteristic
615C2×C13C2×#54811yescharacteristic
616C2×C13C2×#55111yescharacteristic
617D13—44no—
618D13—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—134no—
626C24—134no—
627C24—132no—
628C24—132no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24—262no—
640C24—262no—
641C24#613114yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8—416no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—2632no—
651C2×D4—268no—
652C2×D4—268no—
653C2×D4—2632no—
654C2×D4—268no—
655C2×D4—268no—
656C2×D4—268no—
657C2×D4—268no—
658C2×D4—524no—
659C2×D4—5216no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—44no—
677C22×C4—416no—
678C22×C4—134no—
679C22×C4—134no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—268no—
687C22×C4—268no—
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—524no—
708C22×C4—5216no—
709C22×C4—5216no—
710C22×C4D4×D1314yes—
711C22×C4C2×C22⋊D1314yes—
712C22×C4C2×C22⋊D1314yes—
713C22×C4C2×C22⋊D1314yes—
714C22×C4C23×D1312yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—1316no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C4⋊C4C2×C22⋊D13116yescomplemented
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—268no—
735C22⋊C4—268no—
736C22⋊C4—268no—
737C22⋊C4—524no—
738C42—268no—
739C42—268no—
740C13C2×#246311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—134no—
755C23—134no—
756C23—268no—
757C23—268no—
758C23—268no—
759C23—268no—
760C23—268no—
761C23—268no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23—524no—
779C23—524no—
780C23—524no—
781C23—524no—
782C23C2×D4×D1312yes—
783C23#8825112yes—
784C23C2×#613114yes—
785C23C2×#613112yes—
786C23#8825412yes—
787C23#41×D1312yes—
788C23#41×D1312yes—
789C23C22×C22⋊D1312yes—
790C23C24×D1311yescharacteristic
791Q8—416no—
792D4—2632no—
793D4—2632no—
794D4—5216no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
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—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—416no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—134no—
817C2×C4—134no—
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—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—524no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4C2×D4×D1314yes—
843C2×C4C22×C22⋊D1314yes—
844C2×C4C22×C22⋊D1314yes—
845C2×C4C22×C22⋊D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—264no—
855C22—264no—
856C22—264no—
857C22—264no—
858C22—264no—
859C22—264no—
860C22—522no—
861C22—522no—
862C22—5216no—
863C22—5216no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—522no—
869C22—522no—
870C22#1171933214yes—
871C22#1171933814yes—
872C22#1171934214yes—
873C22#1171934314yes—
874C22D4×C22⋊D1314yes—
875C22#1171952214yes—
876C22#1171953314yes—
877C22C22×D4×D1311yescharacteristic
878C22C2×#8825111yescharacteristic
879C22C22×#613111yescharacteristic
880C22C2×#8825411yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#41×D1311yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—264no—
891C4—264no—
892C4—522no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—44no—
897C2—524no—
898C2—524no—
899C2#1311882918yesdirect product factor
900C2C2×#1171953311yescharacteristic
901C2C2×#1171933211yescharacteristic
902C2C2×#1171934311yescharacteristic
903C2C2×D4×C22⋊D1311yescharacteristic
904C2C2×#1171933811yescharacteristic
905C2C2×#1171952211yescharacteristic
906C2C2×#1171934211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2463
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88200C2semidirect
2. C22×#88147C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13118829C2direct (N × H)
5. C2×#11718652C2semidirect
6. C2×#11718622C2semidirect
7. C2×#11718892C2semidirect
9. C2×#11718651C2semidirect
10. C2×#11718605C2semidirect
11. C2×#11718642C2semidirect
12. C2×#11718639C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718617C2semidirect
15. C2×#11718650C2semidirect
16. C22×C13×C22⋊Q8C2semidirect
25. C2×C13×C22⋊Q8C22semidirect
34. C2×#88200C22semidirect
36. C2×C4×C22⋊D13C22semidirect
51. C2×#88147C22semidirect
52. #11718892C22semidirect
53. #11718874C22semidirect
62. #11718652C22semidirect
63. #11718651C22semidirect
64. #11718650C22semidirect
65. #11718642C22semidirect
66. #11718639C22semidirect
67. #11718622C22semidirect
69. #11718617C22semidirect
70. #11718605C22semidirect
117. C2×C13×C4⋊C4D4semidirect
150. C2×#6101D4semidirect
270. C13×C4⋊C4C2×D4semidirect
285. #6101C2×D4semidirect
289. C22×C22⋊Q8D13semidirect
419. C2×C22⋊Q8C2×D13semidirect
568. C2×C4⋊C4C22⋊D13semidirect
609. C2×C13#2463semidirect
725. C4⋊C4C2×C22⋊D13semidirect
740. C13C2×#2463semidirect
899. C2#13118829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×#881472
C22×C4×C22⋊D132
#131188292
C2×#117186522
C2×#117186222
C2×#117188922
C2×#117186212
C2×#117186512
C2×#117186052
C2×#117186422
C2×#117186392
C2×#117188742
C2×#117186172
C2×#117186502
C22×C13×C22⋊Q82
C2×#246313