Finite Group Databasebeta

← C2×#13118882 #16030610

Subgroups — C2×#13118882 #16030610

Order 3328.

3330 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×#88133C211yesmaximal, characteristic, complemented
2C22×D4×Dic13C211yesmaximal, characteristic, complemented
3#13118882C2116yesmaximal, direct product factor
4C2×#11718610C211yesmaximal, characteristic, complemented
5C2×#11718883C211yesmaximal, characteristic, complemented
6C2×#11718883C211yesmaximal, characteristic, complemented
7C2×#11718882C211yesmaximal, characteristic, complemented
8C2×#11718606C211yesmaximal, characteristic, complemented
9C2×#11718605C211yesmaximal, characteristic, complemented
10C2×#11718314C211yesmaximal, characteristic, complemented
11C2×#11718315C211yesmaximal, characteristic, complemented
12C2×#11718881C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, 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×D4×Dic13—28no—
36C2×D4×Dic13C2218yescomplemented
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88133—28no—
47C2×#88133C2218yescomplemented
48C13×#392C2218yes—
49C2×C13×#95C2211yescharacteristic
50#11718883C2218yescomplemented
51#11718883C2218yescomplemented
52#11718882C2218yescomplemented
53#11718881C2218yescomplemented
54#11718881C2218yescomplemented
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718610C2218yescomplemented
63#11718606C2218yescomplemented
64#11718605C2218yescomplemented
65#11718603C2218yescomplemented
66C22⋊C4×Dic13C2218yescomplemented
67#11718315C2218yescomplemented
68#11718314C2218yescomplemented
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—24no—
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—24no—
90C23×Dic13—24no—
91C23×Dic13—24no—
92C23×Dic13—42no—
93C23×Dic13—42no—
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2314yes—
100C23×Dic13C2314yes—
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
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—24no—
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—
130D4×Dic13—232no—
131C2×C4⋊Dic13—24no—
132C2×C4⋊Dic13D418yescomplemented
133C2×C4⋊Dic13C2314yes—
134C2×C4⋊Dic13C2314yes—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101—42no—
138C2×#6101—42no—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149#88133—232no—
150C13×#95C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2467—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×C13#4114yes—
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—28no—
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×C13C2×D414yes—
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—28no—
234C22×Dic13—28no—
235C22×Dic13—28no—
236C22×Dic13—28no—
237C22×Dic13—44no—
238C22×Dic13—44no—
239C22×Dic13—416no—
240C22×Dic13—416no—
241C22×Dic13C2×D414yes—
242C22×Dic13C2×D414yes—
243C22×Dic13#4114yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—28no—
254C13×C22⋊C4—44no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—28no—
259C22⋊Dic13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262C22⋊Dic13—44no—
263C22⋊Dic13—44no—
264C22⋊Dic13—44no—
265C4⋊Dic13—28no—
266C4⋊Dic13C2×D4116yescomplemented
267#6101—28no—
268#6101—28no—
269#6101—44no—
270#6101—44no—
271C4×Dic13—28no—
272C4×Dic13—28no—
273C4×Dic13—44no—
274C22×#126—131no—
275C22×C4×D4—131no—
276#2467—1316no—
277C2×#399—131no—
278C2×#394—131no—
279C2×#394—131no—
280C2×#392D1311yescharacteristic
281C2×#390—131no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#387—131no—
285C2×#387—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#380—131no—
289C2×C4×C22⋊C4—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×D412yes—
331C23×C13C2×#4114yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13C2×#4112yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13H(5,𝔽2)12yes—
339C23×C13C2511yescharacteristic
340D4×C13—232no—
341D4×C13—416no—
342D4×C13—416no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
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×C13C22×D414yes—
358C2×C4×C13C2×#4114yes—
359C2×Dic13—28no—
360C2×Dic13—28no—
361C2×Dic13—28no—
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×Dic13C22×D414yes—
391C2×Dic13C22×D414yes—
392C2×Dic13C2×#4114yes—
393C23×D4C2×D1311yescharacteristic
394C23×D4C2×D1311yescharacteristic
395C23×D4C2×D1311yescharacteristic
396C24×C4—131no—
397C24×C4—131no—
398C2×#126—138no—
399C2×#126—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×C22⋊C4—131no—
409C22×C22⋊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⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424#399—138no—
425#394—138no—
426#394—138no—
427#392C2×D1318yes—
428#390—138no—
429#388—138no—
430#388—138no—
431#387—138no—
432#387—138no—
433#386—138no—
434#386—138no—
435#380—138no—
436C4×C22⋊C4—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—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—416no—
460C22×C13—416no—
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#52914yes—
471C22×C13#53814yes—
472C22×C13#54614yes—
473C22×C13#55014yes—
474C22×C13#55114yes—
475C22×C13#55314yes—
476C22×C13C23×D411yescharacteristic
477C22×C13C22×#4111yescharacteristic
478C22×C13C22×#4111yescharacteristic
479C22×C13C22×#4111yescharacteristic
480C22×C13C22×#4111yescharacteristic
481C22×C13C2×H(5,𝔽2)11yescharacteristic
482C22×C13C2×H(5,𝔽2)11yescharacteristic
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—42no—
486C4×C13—42no—
487Dic13—24no—
488Dic13—24no—
489Dic13—24no—
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—24no—
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—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—134no—
519C23×C4—134no—
520C23×C4—264no—
521C23×C4—264no—
522C23×C4—264no—
523C23×C4—264no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530#126—2632no—
531C4×D4—2632no—
532C2×C4⋊C4—138no—
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—264no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4—522no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
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—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42—264no—
575C2×C42—522no—
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#246718yescomplemented
588C2×C13C2×#52511yescharacteristic
589C2×C13C2×#52911yescharacteristic
590C2×C13C2×#53811yescharacteristic
591C2×C13C2×#54611yescharacteristic
592C2×C13C2×#55011yescharacteristic
593C2×C13C2×#55111yescharacteristic
594C2×C13C2×#55311yescharacteristic
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—
614C24#612914yes—
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—28no—
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—134no—
643C22×C4—134no—
644C22×C4—134no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—268no—
654C22×C4—268no—
655C22×C4—268no—
656C22×C4—268no—
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—262no—
678C22×C4—524no—
679C22×C4—524no—
680C22×C4—5216no—
681C22×C4—5216no—
682C22×C4D4×D1314yes—
683C22×C4#612914yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—1316no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—44no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—268no—
708C42—268no—
709C42—524no—
710C13C2×#246711yescharacteristic, 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×D1312yes—
752C23C2×#612914yes—
753C23C2×#612914yes—
754C23C2×#612912yes—
755C23C2×#612912yes—
756C23C2×#612912yes—
757C23#8825112yes—
758C23#8825112yes—
759C23#41×D1312yes—
760C23C24×D1311yescharacteristic
761D4—232no—
762D4—416no—
763D4—416no—
764C2×C4—28no—
765C2×C4—28no—
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—134no—
779C2×C4—134no—
780C2×C4—134no—
781C2×C4—268no—
782C2×C4—268no—
783C2×C4—268no—
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×C4C2×D4×D1314yes—
813C2×C4C2×#612914yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—416no—
827C22—416no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#1171929114yes—
839C22#1171929214yes—
840C22#1171929814yes—
841C22#1171930514yes—
842C22#1171930614yes—
843C22#1171931714yes—
844C22#1171942314yes—
845C22C22×D4×D1311yescharacteristic
846C22C22×#612911yescharacteristic
847C22C22×#612911yescharacteristic
848C22C22×#612911yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#8825111yescharacteristic
851C22C2×#41×D1311yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—264no—
857C4—264no—
858C4—264no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1311888218yesdirect product factor
868C2C2×#1171929111yescharacteristic
869C2C2×#1171930511yescharacteristic
870C2C2×#1171929811yescharacteristic
871C2C2×#1171931711yescharacteristic
872C2C2×#1171942311yescharacteristic
873C2C2×#1171929211yescharacteristic
874C2C2×#1171930611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC2×C13×#392C2
socleC24×C13C24
hypercenterC2×#392D13
hypocenterC13C2×#2467
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
2. C22×D4×Dic13C2semidirect
3. #13118882C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718883C2semidirect
6. C2×#11718883C2semidirect
7. C2×#11718882C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718605C2semidirect
10. C2×#11718314C2semidirect
11. C2×#11718315C2semidirect
12. C2×#11718881C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718603C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
36. C2×D4×Dic13C22semidirect
47. C2×#88133C22semidirect
50. #11718883C22semidirect
51. #11718883C22semidirect
52. #11718882C22semidirect
53. #11718881C22semidirect
54. #11718881C22semidirect
62. #11718610C22semidirect
63. #11718606C22semidirect
64. #11718605C22semidirect
65. #11718603C22semidirect
66. C22⋊C4×Dic13C22semidirect
67. #11718315C22semidirect
68. #11718314C22semidirect
132. C2×C4⋊Dic13D4semidirect
266. C4⋊Dic13C2×D4semidirect
587. C2×C13#2467semidirect
710. C13C2×#2467semidirect
867. C2#13118882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881332
C22×D4×Dic132
#131188822
C2×#117186102
C2×#117188832
C2×#117188822
C2×#117186062
C2×#117186052
C2×#117183142
C2×#117183152
C2×#117188812
C2×#117186032
C2×C22⋊C4×Dic132
C2×C13×#3922
C2×#246713