Finite Group Databasebeta

← C2×#13118498 #16030343

Subgroups — C2×#13118498 #16030343

Order 3328.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×#88150C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D13C211yesmaximal, characteristic
4C22×C22⋊C4×D13C211yesmaximal, characteristic
5#13118498C2116yesmaximal, direct product factor
6C2×#11718610C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718608C211yesmaximal, characteristic, complemented
9C2×#11718329C211yesmaximal, characteristic, complemented
10C2×#11718650C211yesmaximal, characteristic, complemented
11C2×#11718650C211yesmaximal, characteristic, complemented
12C2×#11718650C211yesmaximal, characteristic, complemented
13C2×#11718328C211yesmaximal, characteristic, complemented
14C2×#11718648C211yesmaximal, characteristic, complemented
15C2×#11718616C211yesmaximal, characteristic
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic, complemented
23C22×C13×C4⋊C4C2211yescharacteristic, complemented
24C22×C13×C4⋊C4C2211yescharacteristic, complemented
25C22×C13×C4⋊C4C2211yescharacteristic, complemented
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic, complemented
41C22×C4⋊Dic13C2211yescharacteristic, complemented
42C22×#6101C2211yescharacteristic, complemented
43C22×#6101C2211yescharacteristic, complemented
44C22×#6101C2211yescharacteristic, complemented
45C22×#6101C2211yescharacteristic, complemented
46C2×#88151—28no—
47C2×#88151C2218yescomplemented
48C2×#88150—28no—
49C2×#88150C2218yescomplemented
50C2×C22⋊C4×D13—28no—
51C2×C22⋊C4×D13—28no—
52C2×C22⋊C4×D13C2218yes—
53C2×C22⋊C4×D13C2218yes—
54C13×#396C2218yescomplemented
55C2×C13×#95C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57C2×#88071C2211yescharacteristic, complemented
58C2×#88071C2211yescharacteristic, complemented
59C2×#88071C2211yescharacteristic, complemented
60C2×#88071C2211yescharacteristic, complemented
61#11718650C2218yescomplemented
62#11718650C2218yescomplemented
63#11718650C2218yescomplemented
64#11718648C2218yescomplemented
65#11718616C2218yes—
66#11718610C2218yescomplemented
67#11718609C2218yescomplemented
68#11718608C2218yescomplemented
69#11718329C2218yescomplemented
70#11718328C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13—24no—
73C24×D13—24no—
74C24×D13—24no—
75C24×D13—24no—
76C24×D13—42no—
77C24×D13—42no—
78C24×D13Q818yescomplemented
79C24×D13C2314yes—
80C24×D13C2311yescharacteristic
81C24×D13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C22×C4×D13—24no—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13—24no—
98C22×C4×D13—24no—
99C22×C4×D13—24no—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—42no—
103C22×C4×D13—42no—
104C22×C4×D13—42no—
105C22×C4×D13—42no—
106C22×C4×D13C2314yes—
107C22×C4×D13C2314yes—
108C22×C4×D13C2314yes—
109C22×C4×D13C2314yes—
110C22×Dic26—24no—
111C22×Dic26—24no—
112C22×Dic26—42no—
113C22×Dic26C2314yescomplemented
114C2×C13×C4⋊C4—24no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4—42no—
117C2×C13×C4⋊C4C2314yescomplemented
118C2×C13×C4⋊C4C2314yescomplemented
119C2×C13×C4⋊C4C2314yescomplemented
120C2×C13×C22⋊C4—24no—
121C2×C13×C22⋊C4—24no—
122C2×C13×C22⋊C4—42no—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C13×C22⋊C4C2314yes—
126C2×C22⋊Dic13—24no—
127C2×C22⋊Dic13—24no—
128C2×C22⋊Dic13—42no—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131C2×C22⋊Dic13C2314yes—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103—24no—
138C2×#6103D418yes—
139C2×#6103D418yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×#6103C2314yes—
146C2×#6103C2314yes—
147C2×#6103C2314yes—
148C2×C4⋊Dic13—24no—
149C2×C4⋊Dic13—24no—
150C2×C4⋊Dic13C2314yescomplemented
151C2×C4⋊Dic13C2314yescomplemented
152C2×#6101—24no—
153C2×#6101—24no—
154C2×#6101—42no—
155C2×#6101—42no—
156C2×#6101C2314yescomplemented
157C2×#6101C2314yescomplemented
158C2×#6101C2314yescomplemented
159C2×#6101C2314yescomplemented
160#88151—232no—
161#88150—232no—
162C22⋊C4×D13—232no—
163C22⋊C4×D13—232no—
164C13×#95C2314yescomplemented
165#88071C2314yescomplemented
166#88071C2314yescomplemented
167#88071C2314yescomplemented
168#88071C2314yescomplemented
169#88071C2314yescomplemented
170C2×#2437—131nomaximal, Sylow
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13C2×Q814yes—
178C24×C13C2412yes—
179C24×C13C2411yescharacteristic
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—232no—
189C23×D13—232no—
190C23×D13—28no—
191C23×D13—28no—
192C23×D13—28no—
193C23×D13—28no—
194C23×D13—416no—
195C23×D13—44no—
196C23×D13—44no—
197C23×D13—416no—
198C23×D13—416no—
199C23×D13—416no—
200C23×D13—416no—
201C23×D13C2×D414yes—
202C23×D13C2×D414yes—
203C23×D13C2×Q814yes—
204C23×D13C2×Q814yes—
205C23×D13C2×Q8116yescomplemented
206C23×D13#4114yes—
207C23×D13#4114yes—
208C23×D13C2412yes—
209C23×D13C2412yes—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13C2×D414yes—
227C22×C4×C13C2×D414yes—
228C22×C4×C13C2412yes—
229C22×C4×C13C2412yes—
230C22×C4×C13C2412yes—
231C22×C4×C13C2412yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2412yes—
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×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13C2×D414yes—
251C22×Dic13C2×D414yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C2×C4×D13—28no—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—28no—
263C2×C4×D13—28no—
264C2×C4×D13—28no—
265C2×C4×D13—28no—
266C2×C4×D13—44no—
267C2×C4×D13—44no—
268C2×C4×D13—44no—
269C2×C4×D13—44no—
270C2×C4×D13—416no—
271C2×C4×D13—416no—
272C2×C4×D13—416no—
273C2×C4×D13—416no—
274C2×Dic26—28no—
275C2×Dic26—28no—
276C2×Dic26—44no—
277C2×Dic26—416no—
278C13×C4⋊C4—28no—
279C13×C4⋊C4—28no—
280C13×C4⋊C4—44no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—44no—
284C22⋊Dic13—28no—
285C22⋊Dic13—28no—
286C22⋊Dic13—44no—
287#6103—28no—
288#6103—28no—
289#6103—28no—
290#6103—28no—
291#6103—28no—
292#6103—28no—
293#6103C2×D4116yes—
294#6103C2×D4116yes—
295C4⋊Dic13—28no—
296C4⋊Dic13—28no—
297#6101—28no—
298#6101—28no—
299#6101—44no—
300#6101—44no—
301C22×C22⋊Q8—131no—
302C22×C22⋊Q8—131no—
303C23×C22⋊C4—131no—
304C23×C22⋊C4—131no—
305#2437—1316no—
306C2×#399—131no—
307C2×#396—131no—
308C2×#396D1311yescharacteristic, complemented
309C2×#393—131no—
310C2×#385—131no—
311C2×#385—131no—
312C2×#385—131no—
313C2×#385—131no—
314C2×#380—131no—
315C2×#380—131no—
316C2×#379—131no—
317C23×C13—28no—
318C23×C13—28no—
319C23×C13—28no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13—44no—
330C23×C13C22×D412yes—
331C23×C13C22×D412yes—
332C23×C13C22×Q814yes—
333C23×C13C22×Q812yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—28no—
343C22×D13—28no—
344C22×D13—28no—
345C22×D13—28no—
346C22×D13—28no—
347C22×D13—28no—
348C22×D13—28no—
349C22×D13—28no—
350C22×D13—28no—
351C22×D13—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—232no—
360C22×D13—232no—
361C22×D13—416no—
362C22×D13—4128no—
363C22×D13—416no—
364C22×D13—416no—
365C22×D13—416no—
366C22×D13—416no—
367C22×D13C22⋊Q8116yescomplemented
368C22×D13C22⋊Q8116yescomplemented
369C22×D13C22×D414yes—
370C22×D13C22×D414yes—
371C22×D13C22×Q814yes—
372C22×D13C22×Q814yes—
373C22×D13C2×#4114yes—
374C22×D13C2×#4114yes—
375C2×C4×C13—28no—
376C2×C4×C13—28no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—44no—
394C2×C4×C13—44no—
395C2×C4×C13—44no—
396C2×C4×C13—44no—
397C2×C4×C13C22×D414yes—
398C2×C4×C13C22×D414yes—
399C2×Dic13—28no—
400C2×Dic13—28no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—44no—
418C2×Dic13—44no—
419C2×Dic13—44no—
420C2×Dic13—44no—
421C2×Dic13C22×D414yes—
422C2×Dic13C22×D414yes—
423C4×D13—416no—
424C4×D13—416no—
425C4×D13—416no—
426C4×D13—416no—
427Dic26—416no—
428C26—131no—
429C23×Q8—131no—
430C24×C4—131no—
431C24×C4—131no—
432C24×C4—131no—
433C24×C4—131no—
434C2×C22⋊Q8—138no—
435C2×C22⋊Q8—138no—
436C2×C22⋊Q8—268no—
437C2×C22⋊Q8—268no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4C2×D1311yescharacteristic, complemented
445C22×C4⋊C4C2×D1311yescharacteristic, complemented
446C22×C4⋊C4C2×D1311yescharacteristic, complemented
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—138no—
459C22×C22⋊C4—138no—
460C22×C22⋊C4—268no—
461C22×C22⋊C4—268no—
462C22×C22⋊C4C2×D1311yescharacteristic
463C22×C22⋊C4C2×D1311yescharacteristic
464C22×C22⋊C4C2×D1311yescharacteristic
465#399—138no—
466#396—138no—
467#396C2×D1318yescomplemented
468#393—138no—
469#385—138no—
470#385—138no—
471#385—138no—
472#385—138no—
473#380—138no—
474#380—138no—
475#379—138no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95C2×D1311yescharacteristic, complemented
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—24no—
485C22×C13—416no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13C2×C22⋊Q814yes—
491C22×C13C2×C22⋊Q814yes—
492C22×C13#54314yes—
493C22×C13D4214yes—
494C22×C13#54614yes—
495C22×C13#54614yes—
496C22×C13#55114yes—
497C22×C13C23×D411yescharacteristic
498C22×C13C23×D411yescharacteristic
499C22×C13C23×Q811yescharacteristic
500C22×C13C22×#4111yescharacteristic
501C22×C13C22×#4111yescharacteristic
502C22×C13C2×H(5,𝔽2)11yescharacteristic
503C22×C13C2×H(5,𝔽2)11yescharacteristic
504C2×D13—24no—
505C2×D13—24no—
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—232no—
509C2×D13—232no—
510C2×D13—24no—
511C2×D13—24no—
512C2×D13—24no—
513C2×D13—24no—
514C2×D13—24no—
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—464no—
519C2×D13C2×C22⋊Q818yescomplemented
520C2×D13C2×C22⋊Q818yescomplemented
521C4×C13—24no—
522C4×C13—24no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—42no—
527Dic13—24no—
528Dic13—24no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—42no—
533C25—131no—
534C25—131no—
535C25—138no—
536C25—134no—
537C25—264no—
538C25—264no—
539C25—264no—
540C25—264no—
541C25—522no—
542C25—522no—
543C25C22×D1311yescharacteristic
544C22×Q8—134no—
545C22×Q8—264no—
546C22×Q8—264no—
547C22×Q8—522no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—134no—
555C23×C4—134no—
556C23×C4—134no—
557C23×C4—134no—
558C23×C4—264no—
559C23×C4—264no—
560C23×C4—264no—
561C23×C4—264no—
562C23×C4—264no—
563C23×C4—264no—
564C23×C4—264no—
565C23×C4—264no—
566C23×C4—522no—
567C23×C4—522no—
568C23×C4—522no—
569C23×C4—522no—
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573C23×C4C22×D1311yescharacteristic
574C23×C4C22×D1311yescharacteristic
575C23×C4C22×D1311yescharacteristic
576C22⋊Q8—2632no—
577C22⋊Q8—2632no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—42no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—264no—
588C2×C4⋊C4—264no—
589C2×C4⋊C4—264no—
590C2×C4⋊C4—264no—
591C2×C4⋊C4—522no—
592C2×C4⋊C4—522no—
593C2×C4⋊C4C22×D1314yescomplemented
594C2×C4⋊C4C22×D1314yescomplemented
595C2×C4⋊C4C22×D1314yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—138no—
600C2×C22⋊C4—138no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—134no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—134no—
610C2×C22⋊C4—134no—
611C2×C22⋊C4—134no—
612C2×C22⋊C4—2632no—
613C2×C22⋊C4—2632no—
614C2×C22⋊C4—264no—
615C2×C22⋊C4—264no—
616C2×C22⋊C4—264no—
617C2×C22⋊C4—264no—
618C2×C22⋊C4—264no—
619C2×C22⋊C4—264no—
620C2×C22⋊C4—264no—
621C2×C22⋊C4—264no—
622C2×C22⋊C4—522no—
623C2×C22⋊C4C22×D1314yes—
624C2×C22⋊C4C22×D1314yes—
625C2×C22⋊C4C22×D1314yes—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95—134no—
631#95C22×D1314yescomplemented
632C2×C13—44no—
633C2×C13#243718yescomplemented
634C2×C13C22×C22⋊Q811yescharacteristic
635C2×C13C22×C22⋊Q811yescharacteristic
636C2×C13C2×#54311yescharacteristic
637C2×C13C2×D4211yescharacteristic
638C2×C13C2×#54611yescharacteristic
639C2×C13C2×#54611yescharacteristic
640C2×C13C2×#55111yescharacteristic
641D13—28no—
642D13—28no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—134no—
650C24—134no—
651C24—134no—
652C24—134no—
653C24—134no—
654C24—134no—
655C24—132no—
656C24—132no—
657C24—1316no—
658C24—268no—
659C24—268no—
660C24—2632no—
661C24—2632no—
662C24—268no—
663C24—268no—
664C24—262no—
665C24—262no—
666C24—262no—
667C24—262no—
668C24—262no—
669C24—262no—
670C24—262no—
671C24—262no—
672C24—5216no—
673C24—524no—
674C24—524no—
675C24—5216no—
676C24—5216no—
677C24—5216no—
678C24—5216no—
679C24Q8×D1314yes—
680C24C23×D1312yes—
681C24C23×D1311yescharacteristic
682C2×Q8—268no—
683C2×Q8—268no—
684C2×Q8—524no—
685C2×Q8—5216no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—134no—
703C22×C4—134no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—268no—
711C22×C4—268no—
712C22×C4—268no—
713C22×C4—268no—
714C22×C4—268no—
715C22×C4—268no—
716C22×C4—262no—
717C22×C4—262no—
718C22×C4—262no—
719C22×C4—262no—
720C22×C4—262no—
721C22×C4—262no—
722C22×C4—262no—
723C22×C4—262no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—262no—
728C22×C4—262no—
729C22×C4—262no—
730C22×C4—262no—
731C22×C4—262no—
732C22×C4—268no—
733C22×C4—268no—
734C22×C4—524no—
735C22×C4—524no—
736C22×C4—524no—
737C22×C4—524no—
738C22×C4—5216no—
739C22×C4—5216no—
740C22×C4—5216no—
741C22×C4—5216no—
742C22×C4D4×D1314yes—
743C22×C4D4×D1314yes—
744C22×C4C23×D1312yes—
745C22×C4C23×D1312yes—
746C22×C4C23×D1312yes—
747C22×C4C23×D1312yes—
748C22×C4C23×D1312yes—
749C22×C4C23×D1312yes—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C4⋊C4—268no—
754C4⋊C4—268no—
755C4⋊C4—268no—
756C4⋊C4—268no—
757C4⋊C4—524no—
758C4⋊C4—524no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—44no—
762C22⋊C4—1316no—
763C22⋊C4—1316no—
764C22⋊C4—268no—
765C22⋊C4—268no—
766C22⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—268no—
769C22⋊C4—268no—
770C22⋊C4—268no—
771C22⋊C4—268no—
772C22⋊C4—524no—
773C13C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—1316no—
788C23—1316no—
789C23—134no—
790C23—134no—
791C23—134no—
792C23—134no—
793C23—134no—
794C23—134no—
795C23—2632no—
796C23—2632no—
797C23—268no—
798C23—268no—
799C23—268no—
800C23—268no—
801C23—268no—
802C23—268no—
803C23—268no—
804C23—268no—
805C23—268no—
806C23—268no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—262no—
812C23—262no—
813C23—262no—
814C23—262no—
815C23—268no—
816C23—268no—
817C23—5216no—
818C23—52128no—
819C23—5216no—
820C23—5216no—
821C23—5216no—
822C23—5216no—
823C23C2×D4×D1312yes—
824C23C2×D4×D1312yes—
825C23#8825112yes—
826C23C2×Q8×D1314yes—
827C23C2×Q8×D1312yes—
828C23#41×D1312yes—
829C23#41×D1312yes—
830C23#8825612yes—
831C23C24×D1311yescharacteristic
832Q8—5216no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—134no—
856C2×C4—134no—
857C2×C4—268no—
858C2×C4—268no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—5216no—
876C2×C4—5216no—
877C2×C4—5216no—
878C2×C4—5216no—
879C2×C4—524no—
880C2×C4—524no—
881C2×C4—524no—
882C2×C4—524no—
883C2×C4C2×D4×D1314yes—
884C2×C4C2×D4×D1314yes—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—416no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—138no—
894C22—138no—
895C22—2632no—
896C22—2632no—
897C22—264no—
898C22—264no—
899C22—264no—
900C22—264no—
901C22—264no—
902C22—264no—
903C22—264no—
904C22—264no—
905C22—264no—
906C22—264no—
907C22—264no—
908C22—264no—
909C22—5264no—
910C22#1171931414yes—
911C22#1171931514yes—
912C22#1171931714yes—
913C22D13×C22⋊Q814yes—
914C22D13×C22⋊Q814yes—
915C22#1171933914yes—
916C22#1171941014yes—
917C22C22×D4×D1311yescharacteristic
918C22C22×D4×D1311yescharacteristic
919C22C2×#8825111yescharacteristic
920C22C22×Q8×D1311yescharacteristic
921C22C2×#41×D1311yescharacteristic
922C22C2×#41×D1311yescharacteristic
923C22C2×#8825611yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—264no—
931C4—264no—
932C4—522no—
933C4—522no—
934C4—522no—
935C4—522no—
936C2—44no—
937C2—268no—
938C2—268no—
939C2#1311849818yesdirect product factor
940C2C2×D13×C22⋊Q811yescharacteristic
941C2C2×D13×C22⋊Q811yescharacteristic
942C2C2×#1171933911yescharacteristic
943C2C2×#1171931411yescharacteristic
944C2C2×#1171931511yescharacteristic
945C2C2×#1171931711yescharacteristic
946C2C2×#1171941011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#396D13
hypocenterC13C2×#2437
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
2. C22×#88150C2semidirect
5. #13118498C2direct (N × H)
6. C2×#11718610C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718608C2semidirect
9. C2×#11718329C2semidirect
10. C2×#11718650C2semidirect
11. C2×#11718650C2semidirect
12. C2×#11718650C2semidirect
13. C2×#11718328C2semidirect
14. C2×#11718648C2semidirect
16. C2×C13×#396C2semidirect
22. C23×Dic26C22semidirect
23. C22×C13×C4⋊C4C22semidirect
24. C22×C13×C4⋊C4C22semidirect
25. C22×C13×C4⋊C4C22semidirect
40. C22×C4⋊Dic13C22semidirect
41. C22×C4⋊Dic13C22semidirect
42. C22×#6101C22semidirect
43. C22×#6101C22semidirect
44. C22×#6101C22semidirect
45. C22×#6101C22semidirect
47. C2×#88151C22semidirect
49. C2×#88150C22semidirect
54. C13×#396C22semidirect
55. C2×C13×#95C22semidirect
56. C2×#88071C22semidirect
57. C2×#88071C22semidirect
58. C2×#88071C22semidirect
59. C2×#88071C22semidirect
60. C2×#88071C22semidirect
61. #11718650C22semidirect
62. #11718650C22semidirect
63. #11718650C22semidirect
64. #11718648C22semidirect
66. #11718610C22semidirect
67. #11718609C22semidirect
68. #11718608C22semidirect
69. #11718329C22semidirect
70. #11718328C22semidirect
78. C24×D13Q8semidirect
113. C22×Dic26C23semidirect
117. C2×C13×C4⋊C4C23semidirect
118. C2×C13×C4⋊C4C23semidirect
119. C2×C13×C4⋊C4C23semidirect
150. C2×C4⋊Dic13C23semidirect
151. C2×C4⋊Dic13C23semidirect
156. C2×#6101C23semidirect
157. C2×#6101C23semidirect
158. C2×#6101C23semidirect
159. C2×#6101C23semidirect
164. C13×#95C23semidirect
165. #88071C23semidirect
166. #88071C23semidirect
167. #88071C23semidirect
168. #88071C23semidirect
169. #88071C23semidirect
205. C23×D13C2×Q8semidirect
308. C2×#396D13semidirect
367. C22×D13C22⋊Q8semidirect
368. C22×D13C22⋊Q8semidirect
444. C22×C4⋊C4C2×D13semidirect
445. C22×C4⋊C4C2×D13semidirect
446. C22×C4⋊C4C2×D13semidirect
467. #396C2×D13semidirect
481. C2×#95C2×D13semidirect
519. C2×D13C2×C22⋊Q8semidirect
520. C2×D13C2×C22⋊Q8semidirect
593. C2×C4⋊C4C22×D13semidirect
594. C2×C4⋊C4C22×D13semidirect
595. C2×C4⋊C4C22×D13semidirect
631. #95C22×D13semidirect
633. C2×C13#2437semidirect
773. C13C2×#2437semidirect
939. C2#13118498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×#881502
C22×C22⋊C4×D132
#131184982
C2×#117186102
C2×#117186092
C2×#117186082
C2×#117183292
C2×#117186502
C2×#117183282
C2×#117186482
C2×#117186162
C2×C13×#3962
C2×#243713