Finite Group Databasebeta

← C2×#13118810 #16030780

Subgroups — C2×#13118810 #16030780

Order 3328.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88201C211yesmaximal, characteristic, complemented
2C22×#88148C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13118810C2116yesmaximal, direct product factor
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718890C211yesmaximal, characteristic, complemented
7C2×#11718622C211yesmaximal, characteristic, complemented
8C2×#11718621C211yesmaximal, characteristic
9C2×#11718618C211yesmaximal, characteristic, complemented
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718651C211yesmaximal, characteristic, complemented
12C2×#11718651C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718650C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic13C211yesmaximal, 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
23C2×C13×C22⋊Q8—28no—
24C2×C13×C22⋊Q8C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C2×#88201—28no—
33C2×#88201C2218yescomplemented
34C2×C4×C22⋊D13—28no—
35C2×C4×C22⋊D13C2218yescomplemented
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×#6103C2211yescharacteristic
44C22×#6103C2211yescharacteristic
45C22×C4⋊Dic13C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C22×C4×Dic13C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C2×#88148—28no—
53C2×#88148C2218yescomplemented
54#11718890C2218yescomplemented
55#11718874C2218yescomplemented
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718655C2218yescomplemented
63#11718651C2218yescomplemented
64#11718651C2218yescomplemented
65#11718650C2218yescomplemented
66C4⋊C4×Dic13C2218yescomplemented
67#11718622C2218yescomplemented
68#11718621C2218yes—
69#11718618C2218yescomplemented
70#11718606C2218yescomplemented
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—42no—
105C22×D52C2314yes—
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—42no—
109C22×C4×D13C2314yes—
110C13×C22⋊Q8—232no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4—24no—
113C2×C13×C4⋊C4D418yescomplemented
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C4⋊C4C2314yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—24no—
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125#88201—232no—
126C4×C22⋊D13—232no—
127C2×#6103—24no—
128C2×#6103—24no—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103D418yescomplemented
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×C4⋊Dic13—24no—
146C2×C4⋊Dic13C2314yes—
147C2×#6101—24no—
148C2×#6101—24no—
149C2×#6101—42no—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×C4×Dic13—24no—
154C2×C4×Dic13—24no—
155C2×C4×Dic13—24no—
156C2×C4×Dic13C2314yes—
157C2×C4×Dic13C2314yes—
158C2×C4×Dic13C2314yes—
159#88148—232no—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2461—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—22no—
189C23×D13C2×D414yes—
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×Dic13C2×D414yes—
248C22×Dic13#4114yes—
249C22×Dic13#4114yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C2×D52—28no—
257C2×D52—28no—
258C2×D52—44no—
259C2×D52—416no—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—44no—
263C2×C4×D13—416no—
264C13×C4⋊C4—28no—
265C13×C4⋊C4—28no—
266C13×C4⋊C4C2×D4116yescomplemented
267C13×C22⋊C4—28no—
268C13×C22⋊C4—28no—
269C22⋊Dic13—28no—
270C22⋊Dic13—28no—
271#6103—28no—
272#6103—28no—
273#6103—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103C2×D4116yescomplemented
280C4⋊Dic13—28no—
281#6101—28no—
282#6101—28no—
283#6101—44no—
284C4×Dic13—28no—
285C4×Dic13—28no—
286C4×Dic13—28no—
287C22×#124—131no—
288C22×#123—131no—
289C22×C22⋊Q8D1311yescharacteristic, complemented
290C22×C4×D4—131no—
291#2461—1316no—
292C2×#396—131no—
293C2×#395—131no—
294C2×#394—131no—
295C2×#392—131no—
296C2×#390—131no—
297C2×#388—131no—
298C2×#388—131no—
299C2×#388—131no—
300C2×#386—131no—
301C2×#385—131no—
302C2×C4×C4⋊C4—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C22×D412yes—
317C23×C13C22×D412yes—
318C23×C13C2×#4114yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C132−1+412yes—
324C23×C13C2511yescharacteristic
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—22no—
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×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C22×D414yes—
353Q8×C13—416no—
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—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—416no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13C22×D414yes—
376C2×C4×C13C22×D414yes—
377C2×C4×C13C22×D414yes—
378C2×C4×C13C22×D414yes—
379C22⋊D13—232no—
380C22⋊D13—416no—
381C2×Dic13—28no—
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—44no—
400C2×Dic13—44no—
401C2×Dic13—44no—
402C2×Dic13C22×D414yes—
403C2×Dic13C2×#4114yes—
404C2×Dic13C2×#4114yes—
405D52—416no—
406C4×D13—416no—
407C23×Q8C2×D1311yescharacteristic
408C23×D4—131no—
409C23×D4—131no—
410C23×D4—131no—
411C24×C4—131no—
412C24×C4C2×D1311yescharacteristic
413C2×#124—138no—
414C2×#124—268no—
415C2×#123—138no—
416C2×#123—268no—
417C2×C22⋊Q8—28no—
418C2×C22⋊Q8C2×D1318yescomplemented
419C2×C4×D4—138no—
420C2×C4×D4—268no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4C2×D1311yescharacteristic
426C22×C4⋊C4C2×D1311yescharacteristic
427C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C42—131no—
442C22×C42—131no—
443C22×C42—131no—
444#396—138no—
445#395—138no—
446#394—138no—
447#392—138no—
448#390—138no—
449#388—138no—
450#388—138no—
451#388—138no—
452#386—138no—
453#385—138no—
454C4×C4⋊C4—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—416no—
469C22×C13#52514yes—
470C22×C13#53214yes—
471C22×C13#54214yes—
472C22×C13D4214yes—
473C22×C13#54714yes—
474C22×C13#54814yes—
475C22×C13#55114yes—
476C22×C13C23×D411yescharacteristic
477C22×C13C23×D411yescharacteristic
478C22×C13C22×#4111yescharacteristic
479C22×C13C22×#4111yescharacteristic
480C22×C13C22×#4111yescharacteristic
481C22×C13C2×H(5,𝔽2)11yescharacteristic
482C22×C13C2×2−1+411yescharacteristic
483C2×D13—24no—
484C2×D13—24no—
485C2×D13—24no—
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—416no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—88no—
499C4×C13—24no—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—42no—
504C4×C13—42no—
505Dic13—24no—
506Dic13—24no—
507Dic13—24no—
508Dic13—42no—
509Dic13—42no—
510Dic13—42no—
511C25—131no—
512C25—131no—
513C25C22×D1311yescharacteristic
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—42no—
517C22×Q8C22×D1314yes—
518C22×D4—134no—
519C22×D4—134no—
520C22×D4—134no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—264no—
526C22×D4—264no—
527C22×D4—264no—
528C22×D4—522no—
529C22×D4—522no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—134no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4—522no—
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1314yes—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550#124—2632no—
551#123—2632no—
552C22⋊Q8—232no—
553C4×D4—2632no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—264no—
561C2×C4⋊C4—264no—
562C2×C4⋊C4—264no—
563C2×C4⋊C4—522no—
564C2×C4⋊C4C22⋊D1318yescomplemented
565C2×C4⋊C4C22×D1314yes—
566C2×C4⋊C4C22×D1314yes—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—138no—
571C2×C22⋊C4—134no—
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—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
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⋊C4C22×D1314yes—
593C2×C22⋊C4C22×D1314yes—
594C2×C42—134no—
595C2×C42—134no—
596C2×C42—134no—
597C2×C42—264no—
598C2×C42—264no—
599C2×C42—264no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606C2×C13—44no—
607C2×C13#246118yescomplemented
608C2×C13C2×#52511yescharacteristic
609C2×C13C2×#53211yescharacteristic
610C2×C13C2×#54211yescharacteristic
611C2×C13C2×D4211yescharacteristic
612C2×C13C2×#54711yescharacteristic
613C2×C13C2×#54811yescharacteristic
614C2×C13C2×#55111yescharacteristic
615D13—44no—
616D13—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—134no—
624C24—132no—
625C24—132no—
626C24—262no—
627C24—262no—
628C24—262no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24#613114yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×Q8—28no—
643C2×Q8—28no—
644C2×Q8—44no—
645C2×Q8—416no—
646C2×D4—268no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—2632no—
651C2×D4—268no—
652C2×D4—268no—
653C2×D4—268no—
654C2×D4—524no—
655C2×D4—5216no—
656C2×D4—524no—
657C2×D4—5216no—
658C22×C4—22no—
659C22×C4—22no—
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—28no—
673C22×C4—28no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—134no—
677C22×C4—134no—
678C22×C4—134no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—268no—
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—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—268no—
702C22×C4—524no—
703C22×C4—5216no—
704C22×C4D4×D1314yes—
705C22×C4C2×C22⋊D1314yes—
706C22×C4C2×C22⋊D1314yes—
707C22×C4C2×C22⋊D1314yes—
708C22×C4C23×D1312yes—
709C22×C4C23×D1312yes—
710C22×C4C23×D1312yes—
711C22×C4C23×D1312yes—
712C22×C4C23×D1312yes—
713C22×C4C23×D1312yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—268no—
717C4⋊C4—268no—
718C4⋊C4—268no—
719C4⋊C4—524no—
720C4⋊C4C2×C22⋊D13116yescomplemented
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—1316no—
724C22⋊C4—268no—
725C22⋊C4—268no—
726C22⋊C4—268no—
727C22⋊C4—268no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C42—268no—
735C42—268no—
736C42—268no—
737C13C2×#246111yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—134no—
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—262no—
768C23—524no—
769C23—524no—
770C23—524no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23—524no—
779C23C2×D4×D1312yes—
780C23#8825112yes—
781C23C2×#613114yes—
782C23C2×#613112yes—
783C23#8825412yes—
784C23#41×D1312yes—
785C23#41×D1312yes—
786C23C22×C22⋊D1312yes—
787C23C24×D1311yescharacteristic
788Q8—416no—
789D4—2632no—
790D4—5216no—
791D4—5216no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—134no—
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—5216no—
835C2×C4—524no—
836C2×C4—524no—
837C2×C4—524no—
838C2×C4C2×D4×D1314yes—
839C2×C4C22×C22⋊D1314yes—
840C2×C4C22×C22⋊D1314yes—
841C2×C4C22×C22⋊D1314yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—416no—
848C22—42no—
849C22—42no—
850C22—264no—
851C22—264no—
852C22—264no—
853C22—522no—
854C22—5216no—
855C22—522no—
856C22—522no—
857C22—522no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—1048no—
866C22#1171933214yes—
867C22#1171933614yes—
868C22#1171934214yes—
869C22#1171934514yes—
870C22D4×C22⋊D1314yes—
871C22#1171952214yes—
872C22#1171953714yes—
873C22C22×D4×D1311yescharacteristic
874C22C2×#8825111yescharacteristic
875C22C22×#613111yescharacteristic
876C22C2×#8825411yescharacteristic
877C22C2×#41×D1311yescharacteristic
878C22C2×#41×D1311yescharacteristic
879C22C23×C22⋊D1311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—264no—
887C4—264no—
888C4—264no—
889C4—522no—
890C4—522no—
891C4—522no—
892C2—44no—
893C2—524no—
894C2—1042no—
895C2#1311881018yesdirect product factor
896C2C2×#1171933211yescharacteristic
897C2C2×#1171953711yescharacteristic
898C2C2×#1171934511yescharacteristic
899C2C2×D4×C22⋊D1311yescharacteristic
900C2C2×#1171933611yescharacteristic
901C2C2×#1171952211yescharacteristic
902C2C2×#1171934211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2461
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×#88201C2semidirect
2. C22×#88148C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13118810C2direct (N × H)
5. C2×#11718655C2semidirect
6. C2×#11718890C2semidirect
7. C2×#11718622C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718651C2semidirect
12. C2×#11718651C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718650C2semidirect
15. C2×C4⋊C4×Dic13C2semidirect
16. C22×C13×C22⋊Q8C2semidirect
24. C2×C13×C22⋊Q8C22semidirect
33. C2×#88201C22semidirect
35. C2×C4×C22⋊D13C22semidirect
53. C2×#88148C22semidirect
54. #11718890C22semidirect
55. #11718874C22semidirect
62. #11718655C22semidirect
63. #11718651C22semidirect
64. #11718651C22semidirect
65. #11718650C22semidirect
66. C4⋊C4×Dic13C22semidirect
67. #11718622C22semidirect
69. #11718618C22semidirect
70. #11718606C22semidirect
113. C2×C13×C4⋊C4D4semidirect
135. C2×#6103D4semidirect
266. C13×C4⋊C4C2×D4semidirect
279. #6103C2×D4semidirect
289. C22×C22⋊Q8D13semidirect
418. C2×C22⋊Q8C2×D13semidirect
564. C2×C4⋊C4C22⋊D13semidirect
607. C2×C13#2461semidirect
720. C4⋊C4C2×C22⋊D13semidirect
737. C13C2×#2461semidirect
895. C2#13118810direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882012
C22×#881482
C22×C4×C22⋊D132
#131188102
C2×#117186552
C2×#117188902
C2×#117186222
C2×#117186212
C2×#117186182
C2×#117186062
C2×#117186512
C2×#117188742
C2×#117186502
C2×C4⋊C4×Dic132
C22×C13×C22⋊Q82
C2×#246113