Finite Group Databasebeta

← C2×#13120034 #16034141

Subgroups — C2×#13120034 #16034141

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3#13120034C2116yesmaximal, direct product factor
4C2×#11718337C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic
9C2×#11718618C211yesmaximal, characteristic
10C2×#11718329C211yesmaximal, characteristic, complemented
11C2×#11718871C211yesmaximal, characteristic, complemented
12C2×#11718650C211yesmaximal, characteristic, complemented
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×#11718311C211yesmaximal, characteristic, complemented
15C2×#11718310C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C2×C4×C22⋊D13—28no—
28C2×C4×C22⋊D13C2218yes—
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88143—28no—
49C2×#88143C2218yescomplemented
50C13×#385C2218yescomplemented
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53#11718871C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718655C2218yescomplemented
59#11718650C2218yescomplemented
60#11718637C2218yescomplemented
61#11718618C2218yes—
62#11718618C2218yes—
63#11718609C2218yescomplemented
64#11718609C2218yescomplemented
65#11718337C2218yescomplemented
66#11718329C2218yescomplemented
67#11718311C2218yescomplemented
68#11718310C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—42no—
73C23×C4×C13—42no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2314yes—
81C22×C22⋊D13—24no—
82C22×C22⋊D13—24no—
83C22×C22⋊D13Q818yes—
84C22×C22⋊D13C2314yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×C4×D13—24no—
93C22×C4×D13—42no—
94C22×C4×D13—42no—
95C22×C4×D13C2314yes—
96C2×C13×C4⋊C4—24no—
97C2×C13×C4⋊C4—42no—
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—42no—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C4×C22⋊D13—232no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—42no—
115C2×#6103—42no—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×C4⋊Dic13—24no—
122C2×C4⋊Dic13—42no—
123C2×C4⋊Dic13C2314yes—
124C2×C4⋊Dic13C2314yes—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—24no—
130C2×#6101—24no—
131C2×#6101—24no—
132C2×#6101—42no—
133C2×#6101—42no—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—24no—
145C2×C4×Dic13D418yes—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149#88143—232no—
150C13×#95C2314yes—
151C13×#95C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2566—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C2×Q814yes—
164C24×C13C2412yes—
165C24×C13C2411yescharacteristic
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13C2×Q814yes—
173C23×D13C2412yes—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—28no—
191C22×C4×C13—44no—
192C22×C4×C13—44no—
193C22×C4×C13—416no—
194C22×C4×C13C2×D414yes—
195C22×C4×C13#4114yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C2×C22⋊D13—232no—
203C2×C22⋊D13—28no—
204C2×C22⋊D13—28no—
205C2×C22⋊D13C2×Q8116yes—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13C2×D414yes—
223C22×Dic13C2×D414yes—
224C22×Dic13C2×Q814yes—
225C22×Dic13#4114yes—
226C22×Dic13#4114yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C2×C4×D13—28no—
235C2×C4×D13—44no—
236C2×C4×D13—44no—
237C2×C4×D13—416no—
238C13×C4⋊C4—28no—
239C13×C4⋊C4—44no—
240C13×C22⋊C4—28no—
241C13×C22⋊C4—44no—
242C22⋊Dic13—28no—
243C22⋊Dic13—28no—
244C22⋊Dic13—44no—
245#6103—28no—
246#6103—28no—
247#6103—28no—
248#6103—44no—
249#6103—44no—
250C4⋊Dic13—28no—
251C4⋊Dic13—44no—
252#6101—28no—
253#6101—28no—
254#6101—28no—
255#6101—28no—
256#6101—28no—
257#6101—28no—
258#6101—28no—
259#6101—44no—
260#6101—44no—
261C4×Dic13—28no—
262C4×Dic13—28no—
263C4×Dic13C2×D4116yes—
264C22×#125—131no—
265C22×C4×D4—131no—
266#2566—1316no—
267C2×#396—131no—
268C2×#396—131no—
269C2×#396—131no—
270C2×#396—131no—
271C2×#390—131no—
272C2×#390—131no—
273C2×#385—131no—
274C2×#385—131no—
275C2×#385—131no—
276C2×#385D1311yescharacteristic, complemented
277C2×#384—131no—
278C2×#382—131no—
279C2×C4×C4⋊C4—131no—
280C23×C13—28no—
281C23×C13—28no—
282C23×C13—28no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—44no—
290C23×C13—44no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13C22×D412yes—
294C23×C13C22×Q814yes—
295C23×C13C22×Q812yes—
296C23×C13C2×#4112yes—
297C23×C13C2×#4112yes—
298C23×C13C2×#4112yes—
299C23×C13H(5,𝔽2)12yes—
300C23×C13H(5,𝔽2)12yes—
301C23×C13C2511yescharacteristic
302C22×D13—28no—
303C22×D13—28no—
304C22×D13—28no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—44no—
312C22×D13—44no—
313C22×D13—44no—
314C22×D13—44no—
315C22×D13C22×Q814yes—
316C2×C4×C13—28no—
317C2×C4×C13—28no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—416no—
335C2×C4×C13—44no—
336C2×C4×C13—44no—
337C2×C4×C13—44no—
338C2×C4×C13—44no—
339C2×C4×C13C22×D414yes—
340C2×C4×C13C2×#4114yes—
341C22⋊D13—232no—
342C2×Dic13—28no—
343C2×Dic13—28no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13—44no—
363C2×Dic13—44no—
364C2×Dic13C22⋊Q8116yes—
365C2×Dic13C22×D414yes—
366C2×Dic13C22×D414yes—
367C2×Dic13C22×Q814yes—
368C2×Dic13C2×#4114yes—
369C2×Dic13C2×#4114yes—
370C4×D13—416no—
371C23×D4—131no—
372C24×C4—131no—
373C24×C4C2×D1311yescharacteristic
374C2×#125—138no—
375C2×#125—268no—
376C2×C4×D4—138no—
377C2×C4×D4—268no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4C2×D1311yescharacteristic
390C22×C4⋊C4C2×D1311yescharacteristic
391C22×C22⋊C4—131no—
392C22×C22⋊C4—131no—
393C22×C22⋊C4—131no—
394C22×C22⋊C4—131no—
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4C2×D1311yescharacteristic
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C42—131no—
402C22×C42—131no—
403C22×C42—131no—
404#396—138no—
405#396—138no—
406#396—138no—
407#396—138no—
408#390—138no—
409#390—138no—
410#385—138no—
411#385—138no—
412#385—138no—
413#385C2×D1318yescomplemented
414#384—138no—
415#382—138no—
416C4×C4⋊C4—138no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95C2×D1311yescharacteristic
422C2×#95C2×D1311yescharacteristic
423C22×C13—24no—
424C22×C13—24no—
425C22×C13—24no—
426C22×C13—416no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13C2×C22⋊Q814yes—
432C22×C13#53214yes—
433C22×C13#53514yes—
434C22×C13#55314yes—
435C22×C13#55314yes—
436C22×C13#55414yes—
437C22×C13#55414yes—
438C22×C13C23×D411yescharacteristic
439C22×C13C23×Q811yescharacteristic
440C22×C13C22×#4111yescharacteristic
441C22×C13C22×#4111yescharacteristic
442C22×C13C22×#4111yescharacteristic
443C22×C13C2×H(5,𝔽2)11yescharacteristic
444C22×C13C2×H(5,𝔽2)11yescharacteristic
445C2×D13—24no—
446C2×D13—24no—
447C2×D13—24no—
448C2×D13—416no—
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—42no—
453C4×C13—24no—
454C4×C13—24no—
455C4×C13—42no—
456C4×C13—42no—
457C4×C13—42no—
458C4×C13—42no—
459Dic13—24no—
460Dic13—24no—
461Dic13—42no—
462Dic13—42no—
463Dic13—42no—
464Dic13—42no—
465Dic13C2×C22⋊Q818yes—
466C25—131no—
467C25C22×D1311yescharacteristic
468C22×D4—138no—
469C22×D4—134no—
470C22×D4—264no—
471C22×D4—264no—
472C23×C4—24no—
473C23×C4—42no—
474C23×C4—42no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—131no—
482C23×C4—134no—
483C23×C4—264no—
484C23×C4—522no—
485C23×C4—522no—
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1314yes—
493#125—2632no—
494C4×D4—2632no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—264no—
509C2×C4⋊C4—264no—
510C2×C4⋊C4—264no—
511C2×C4⋊C4—264no—
512C2×C4⋊C4—264no—
513C2×C4⋊C4—264no—
514C2×C4⋊C4—264no—
515C2×C4⋊C4—264no—
516C2×C4⋊C4—522no—
517C2×C4⋊C4—522no—
518C2×C4⋊C4—522no—
519C2×C4⋊C4C22×D1314yes—
520C2×C4⋊C4C22×D1314yes—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—134no—
524C2×C22⋊C4—134no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—134no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—264no—
532C2×C22⋊C4—264no—
533C2×C22⋊C4—264no—
534C2×C22⋊C4—264no—
535C2×C22⋊C4—264no—
536C2×C22⋊C4—522no—
537C2×C22⋊C4—522no—
538C2×C22⋊C4—522no—
539C2×C22⋊C4C22×D1314yes—
540C2×C22⋊C4C22×D1314yes—
541C2×C42—138no—
542C2×C42—134no—
543C2×C42—134no—
544C2×C42—134no—
545C2×C42—264no—
546C2×C42—264no—
547#95—134no—
548#95—134no—
549#95—134no—
550#95—134no—
551#95C22×D1314yes—
552#95C22×D1314yes—
553C2×C13—44no—
554C2×C13#256618yescomplemented
555C2×C13C22×C22⋊Q811yescharacteristic
556C2×C13C2×#53211yescharacteristic
557C2×C13C2×#53511yescharacteristic
558C2×C13C2×#55311yescharacteristic
559C2×C13C2×#55311yescharacteristic
560C2×C13C2×#55411yescharacteristic
561C2×C13C2×#55411yescharacteristic
562D13—44no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—134no—
570C24—132no—
571C24—262no—
572C24—262no—
573C24—262no—
574C24—262no—
575C24—262no—
576C24—262no—
577C24Q8×D1314yes—
578C24C23×D1312yes—
579C24C23×D1311yescharacteristic
580C2×D4—1316no—
581C2×D4—268no—
582C2×D4—2632no—
583C2×D4—268no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—416no—
604C22×C4—134no—
605C22×C4—134no—
606C22×C4—134no—
607C22×C4—132no—
608C22×C4—134no—
609C22×C4—134no—
610C22×C4—132no—
611C22×C4—132no—
612C22×C4—132no—
613C22×C4—132no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—268no—
633C22×C4—524no—
634C22×C4—524no—
635C22×C4—5216no—
636C22×C4#612714yes—
637C22×C4D4×D1314yes—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—28no—
645C4⋊C4—44no—
646C4⋊C4—268no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C4⋊C4—268no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—268no—
654C4⋊C4—524no—
655C4⋊C4—524no—
656C4⋊C4—524no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—268no—
660C22⋊C4—268no—
661C22⋊C4—268no—
662C22⋊C4—268no—
663C22⋊C4—268no—
664C22⋊C4—524no—
665C22⋊C4—524no—
666C22⋊C4—524no—
667C42—1316no—
668C42—268no—
669C42—268no—
670C13C2×#256611yescharacteristic, complemented, Sylow
671C23—28no—
672C23—28no—
673C23—28no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—134no—
685C23—268no—
686C23—268no—
687C23—268no—
688C23—262no—
689C23—262no—
690C23—262no—
691C23—262no—
692C23—262no—
693C23—262no—
694C23—524no—
695C23—524no—
696C23—524no—
697C23—524no—
698C23C2×#612712yes—
699C23C2×D4×D1312yes—
700C23#8825112yes—
701C23#8825112yes—
702C23C2×Q8×D1314yes—
703C23C2×Q8×D1312yes—
704C23#41×D1312yes—
705C23#41×D1312yes—
706C23C24×D1311yescharacteristic
707D4—2632no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—416no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—1316no—
732C2×C4—134no—
733C2×C4—134no—
734C2×C4—134no—
735C2×C4—134no—
736C2×C4—134no—
737C2×C4—268no—
738C2×C4—268no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—5216no—
756C2×C4—524no—
757C2×C4—524no—
758C2×C4—524no—
759C2×C4—524no—
760C2×C4C2×#612714yes—
761C2×C4C2×D4×D1314yes—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—416no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—264no—
771C22—264no—
772C22—264no—
773C22—5216no—
774C22—522no—
775C22—522no—
776C22—522no—
777C22—522no—
778C22#1171921614yes—
779C22#1171924514yes—
780C22#1171925314yes—
781C22#1171929714yes—
782C22D13×C22⋊Q814yes—
783C22#1171934114yes—
784C22#1171936614yes—
785C22C22×#612711yescharacteristic
786C22C22×D4×D1311yescharacteristic
787C22C2×#8825111yescharacteristic
788C22C2×#8825111yescharacteristic
789C22C22×Q8×D1311yescharacteristic
790C22C2×#41×D1311yescharacteristic
791C22C2×#41×D1311yescharacteristic
792C4—24no—
793C4—24no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—138no—
799C4—264no—
800C4—264no—
801C4—522no—
802C4—522no—
803C4—522no—
804C4—522no—
805C2—44no—
806C2—524no—
807C2#1312003418yesdirect product factor
808C2C2×D13×C22⋊Q811yescharacteristic
809C2C2×#1171925311yescharacteristic
810C2C2×#1171929711yescharacteristic
811C2C2×#1171936611yescharacteristic
812C2C2×#1171924511yescharacteristic
813C2C2×#1171934111yescharacteristic
814C2C2×#1171921611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#385D13
hypocenterC13C2×#2566
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
3. #13120034C2direct (N × H)
4. C2×#11718337C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718655C2semidirect
10. C2×#11718329C2semidirect
11. C2×#11718871C2semidirect
12. C2×#11718650C2semidirect
13. C2×#11718637C2semidirect
14. C2×#11718311C2semidirect
15. C2×#11718310C2semidirect
16. C2×C13×#385C2semidirect
49. C2×#88143C22semidirect
50. C13×#385C22semidirect
53. #11718871C22semidirect
58. #11718655C22semidirect
59. #11718650C22semidirect
60. #11718637C22semidirect
63. #11718609C22semidirect
64. #11718609C22semidirect
65. #11718337C22semidirect
66. #11718329C22semidirect
67. #11718311C22semidirect
68. #11718310C22semidirect
276. C2×#385D13semidirect
413. #385C2×D13semidirect
554. C2×C13#2566semidirect
670. C13C2×#2566semidirect
807. C2#13120034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×C4×C22⋊D132
#131200342
C2×#117183372
C2×#117186092
C2×#117186552
C2×#117186182
C2×#117183292
C2×#117188712
C2×#117186502
C2×#117186372
C2×#117183112
C2×#117183102
C2×C13×#3852
C2×#256613