Finite Group Databasebeta

← C2×#13120672 #16029295

Subgroups — C2×#13120672 #16029295

Order 3328.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88189C211yesmaximal, characteristic, complemented
2C22×D4×Dic13C211yesmaximal, characteristic, complemented
3#13120672C2116yesmaximal, direct product factor
4C2×#11718318C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718883C211yesmaximal, characteristic, complemented
10C2×#11718883C211yesmaximal, characteristic, complemented
11C2×#11718612C211yesmaximal, characteristic, complemented
12C2×#11718313C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718607C211yesmaximal, characteristic, complemented
15C2×#11718603C211yesmaximal, characteristic, complemented
16C2×C13×#392C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88189—28no—
36C2×#88189C2218yescomplemented
37C2×D4×Dic13—28no—
38C2×D4×Dic13C2218yescomplemented
39C22×C4⋊Dic13C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C13×#392C2218yes—
49C2×C13×#95C2211yescharacteristic
50#11718883C2218yescomplemented
51#11718883C2218yescomplemented
52#11718883C2218yescomplemented
53#11718881C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718614C2218yescomplemented
62#11718612C2218yescomplemented
63#11718609C2218yescomplemented
64#11718609C2218yescomplemented
65#11718607C2218yescomplemented
66#11718603C2218yescomplemented
67#11718318C2218yescomplemented
68#11718313C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13—42no—
78C22×D4×C13—42no—
79C22×D4×C13—42no—
80C22×D4×C13—42no—
81C22×D4×C13C2314yes—
82C22×D4×C13C2314yes—
83C22×D4×C13C2314yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×Dic13—24no—
89C23×Dic13—42no—
90C23×Dic13—42no—
91C23×Dic13—42no—
92C23×Dic13—42no—
93C23×Dic13D418yescomplemented
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2314yes—
103C23×Dic13C2314yes—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4—42no—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—24no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13—42no—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130#88189—232no—
131D4×Dic13—232no—
132C2×C4⋊Dic13—24no—
133C2×C4⋊Dic13—42no—
134C2×C4⋊Dic13C2314yes—
135C2×C4⋊Dic13C2314yes—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—42no—
140C2×#6101—42no—
141C2×#6101—42no—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×C4×Dic13—24no—
149C2×C4×Dic13C2314yes—
150C13×#95C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2630—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13C2×D414yes—
179C24×C13#4114yes—
180C24×C13C2412yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C2×D4×C13—232no—
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13—28no—
188C2×D4×C13—28no—
189C2×D4×C13—28no—
190C2×D4×C13—44no—
191C2×D4×C13—44no—
192C2×D4×C13—44no—
193C2×D4×C13—44no—
194C2×D4×C13—416no—
195C2×D4×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#4114yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
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×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—28no—
235C22×Dic13—416no—
236C22×Dic13—44no—
237C22×Dic13—44no—
238C22×Dic13—44no—
239C22×Dic13—44no—
240C22×Dic13—416no—
241C22×Dic13C2×D414yes—
242C22×Dic13C2×D414yes—
243C22×Dic13C2×D4116yescomplemented
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—44no—
254C13×C22⋊C4—44no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—28no—
259C22⋊Dic13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C22⋊Dic13—44no—
264C22⋊Dic13—44no—
265C4⋊Dic13—28no—
266C4⋊Dic13—44no—
267#6101—28no—
268#6101—28no—
269#6101—28no—
270#6101—44no—
271#6101—44no—
272#6101—44no—
273C4×Dic13—28no—
274C22×#123—131no—
275C22×C4×D4—131no—
276#2630—1316no—
277C2×#398—131no—
278C2×#397—131no—
279C2×#396—131no—
280C2×#396—131no—
281C2×#394—131no—
282C2×#394—131no—
283C2×#394—131no—
284C2×#392D1311yescharacteristic
285C2×#388—131no—
286C2×#387—131no—
287C2×#386—131no—
288C2×#385—131no—
289C2×#380—131no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13—44no—
318C23×C13—44no—
319C23×C13—44no—
320C23×C13—44no—
321C23×C13—44no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13—44no—
330C23×C13C22×D414yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13H(5,𝔽2)12yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C132−1+412yes—
339C23×C13C2511yescharacteristic
340D4×C13—232no—
341D4×C13—416no—
342D4×C13—416no—
343C2×C4×C13—28no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—44no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13C2×#4114yes—
359C2×Dic13—28no—
360C2×Dic13—28no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—416no—
384C2×Dic13—416no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13—44no—
391C2×Dic13C22×D414yes—
392C2×Dic13C22×D414yes—
393C23×D4C2×D1311yescharacteristic
394C23×D4C2×D1311yescharacteristic
395C23×D4C2×D1311yescharacteristic
396C24×C4—131no—
397C24×C4—131no—
398C2×#123—138no—
399C2×#123—268no—
400C2×C4×D4—138no—
401C2×C4×D4—268no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42—131no—
424#398—138no—
425#397—138no—
426#396—138no—
427#396—138no—
428#394—138no—
429#394—138no—
430#394—138no—
431#392C2×D1318yes—
432#388—138no—
433#387—138no—
434#386—138no—
435#385—138no—
436#380—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95C2×D1311yescharacteristic
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13—24no—
451C22×C13—416no—
452C22×C13—416no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—88no—
469C22×C13#52514yes—
470C22×C13#53414yes—
471C22×C13#53714yes—
472C22×C13#53814yes—
473C22×C13#53914yes—
474C22×C13#54014yes—
475C22×C13#54214yes—
476C22×C13C23×D411yescharacteristic
477C22×C13C22×#4111yescharacteristic
478C22×C13C22×#4111yescharacteristic
479C22×C13C2×H(5,𝔽2)11yescharacteristic
480C22×C13C2×H(5,𝔽2)11yescharacteristic
481C22×C13C2×H(5,𝔽2)11yescharacteristic
482C22×C13C2×2−1+411yescharacteristic
483C4×C13—24no—
484C4×C13—42no—
485C4×C13—42no—
486C4×C13—42no—
487Dic13—24no—
488Dic13—24no—
489Dic13—42no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25C22×D1311yescharacteristic
496C25C22×D1311yescharacteristic
497C25C22×D1311yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—42no—
504C22×D4—42no—
505C22×D4—42no—
506C22×D4—42no—
507C22×D4C22×D1314yes—
508C22×D4C22×D1314yes—
509C22×D4C22×D1314yes—
510C23×C4—131no—
511C23×C4—131no—
512C23×C4—138no—
513C23×C4—134no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—134no—
521C23×C4—264no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530#123—2632no—
531C4×D4—2632no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—522no—
545C2×C4⋊C4—522no—
546C2×C4⋊C4—522no—
547C2×C4⋊C4—522no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—264no—
567C2×C22⋊C4—522no—
568C2×C22⋊C4—522no—
569C2×C22⋊C4—522no—
570C2×C22⋊C4—522no—
571C2×C22⋊C4C22×D1314yes—
572C2×C22⋊C4C22×D1314yes—
573C2×C22⋊C4C22×D1314yes—
574C2×C42—134no—
575C2×C42—264no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95C22×D1314yes—
584C2×C13—44no—
585C2×C13—44no—
586C2×C13—82no—
587C2×C13#263018yescomplemented
588C2×C13C2×#52511yescharacteristic
589C2×C13C2×#53411yescharacteristic
590C2×C13C2×#53711yescharacteristic
591C2×C13C2×#53811yescharacteristic
592C2×C13C2×#53911yescharacteristic
593C2×C13C2×#54011yescharacteristic
594C2×C13C2×#54211yescharacteristic
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24D4×D1314yes—
615C24#612914yes—
616C24C23×D1312yes—
617C24C23×D1312yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—232no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—416no—
631C2×D4—416no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—134no—
644C22×C4—134no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—1316no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—268no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—5216no—
678C22×C4—524no—
679C22×C4—524no—
680C22×C4—524no—
681C22×C4—524no—
682C22×C4—5216no—
683C22×C4#612914yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—268no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C4⋊C4—524no—
696C22⋊C4—28no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—268no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C42—268no—
710C13C2×#263011yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23C2×D4×D1314yes—
752C23C2×D4×D1312yes—
753C23C2×#612914yes—
754C23C2×#612912yes—
755C23C2×#612912yes—
756C23#8825112yes—
757C23#8825112yes—
758C23#8825112yes—
759C23#8825712yes—
760C23C24×D1311yescharacteristic
761D4—232no—
762D4—416no—
763D4—416no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—134no—
780C2×C4—134no—
781C2×C4—268no—
782C2×C4—268no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—5216no—
806C2×C4—5216no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4—524no—
813C2×C4C2×#612914yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#1171929114yes—
839C22#1171929414yes—
840C22#1171929814yes—
841C22#1171930214yes—
842C22#1171930714yes—
843C22#1171930814yes—
844C22#1171942414yes—
845C22C22×D4×D1311yescharacteristic
846C22C22×#612911yescharacteristic
847C22C22×#612911yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#8825111yescharacteristic
851C22C2×#8825711yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—264no—
857C4—264no—
858C4—522no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1312067218yesdirect product factor
868C2C2×#1171929111yescharacteristic
869C2C2×#1171929411yescharacteristic
870C2C2×#1171930211yescharacteristic
871C2C2×#1171929811yescharacteristic
872C2C2×#1171930711yescharacteristic
873C2C2×#1171942411yescharacteristic
874C2C2×#1171930811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC2×C13×#392C2
socleC24×C13C24
hypercenterC2×#392D13
hypocenterC13C2×#2630
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#88189C2semidirect
2. C22×D4×Dic13C2semidirect
3. #13120672C2direct (N × H)
4. C2×#11718318C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718883C2semidirect
9. C2×#11718883C2semidirect
10. C2×#11718883C2semidirect
11. C2×#11718612C2semidirect
12. C2×#11718313C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718607C2semidirect
15. C2×#11718603C2semidirect
36. C2×#88189C22semidirect
38. C2×D4×Dic13C22semidirect
50. #11718883C22semidirect
51. #11718883C22semidirect
52. #11718883C22semidirect
53. #11718881C22semidirect
61. #11718614C22semidirect
62. #11718612C22semidirect
63. #11718609C22semidirect
64. #11718609C22semidirect
65. #11718607C22semidirect
66. #11718603C22semidirect
67. #11718318C22semidirect
68. #11718313C22semidirect
93. C23×Dic13D4semidirect
243. C22×Dic13C2×D4semidirect
587. C2×C13#2630semidirect
710. C13C2×#2630semidirect
867. C2#13120672direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881892
C22×D4×Dic132
#131206722
C2×#117183182
C2×#117186142
C2×#117186092
C2×#117188832
C2×#117186122
C2×#117183132
C2×#117188812
C2×#117186072
C2×#117186032
C2×C13×#3922
C2×#263013