Finite Group Databasebeta

← C2×#13118887 #16030609

Subgroups — C2×#13118887 #16030609

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×#88130C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3#13118887C2116yesmaximal, direct product factor
4C2×#11718610C211yesmaximal, characteristic, complemented
5C2×#11718620C211yesmaximal, characteristic, complemented
6C2×#11718620C211yesmaximal, characteristic, complemented
7C2×#11718621C211yesmaximal, characteristic
8C2×#11718600C211yesmaximal, characteristic, complemented
9C2×#11718601C211yesmaximal, characteristic, complemented
10C2×#11718330C211yesmaximal, characteristic, complemented
11C2×#11718594C211yesmaximal, characteristic, complemented
12C2×#11718315C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718326C211yesmaximal, characteristic, complemented
15C2×#11718328C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C2×C4×C22⋊D13—28no—
29C2×C4×C22⋊D13C2218yescomplemented
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88130—28no—
47C2×#88130C2218yescomplemented
48C4×C13×C22⋊C4C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51#11718874C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718621C2218yes—
59#11718620C2218yescomplemented
60#11718620C2218yescomplemented
61#11718610C2218yescomplemented
62#11718601C2218yescomplemented
63#11718600C2218yescomplemented
64#11718594C2218yescomplemented
65#11718330C2218yescomplemented
66#11718328C2218yescomplemented
67#11718326C2218yescomplemented
68#11718315C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—24no—
74C23×C4×C13—42no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2314yes—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—24no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13C2314yes—
89C22×C22⋊D13C2314yes—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C22×D52—24no—
97C22×D52—24no—
98C22×D52—42no—
99C22×D52C2314yes—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—42no—
103C22×C4×D13C2314yes—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C42×C13—24no—
109C2×C42×C13—42no—
110C2×C42×C13C2314yes—
111C2×C42×C13C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—42no—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C4×C22⋊D13—232no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×C4⋊Dic13—24no—
136C2×C4⋊Dic13C2314yes—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—42no—
140C2×#6101—42no—
141C2×#6101D418yescomplemented
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×C4×Dic13—24no—
148C2×C4×Dic13C2314yes—
149#88130—232no—
150C13×#95C2314yes—
151C13×#95C2314yes—
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#4114yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13#4114yes—
182C23×D13C2412yes—
183C23×D13C2412yes—
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—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—28no—
200C22×C4×C13—28no—
201C22×C4×C13—44no—
202C22×C4×C13—416no—
203C22×C4×C13C2×D414yes—
204C22×C4×C13#4114yes—
205C22×C4×C13#4114yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—232no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—44no—
219C2×C22⋊D13—416no—
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—22no—
235C22×Dic13—22no—
236C22×Dic13C2×D414yes—
237C22×Dic13C2×D414yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×D52—28no—
245C2×D52—28no—
246C2×D52—44no—
247C2×D52—416no—
248C2×C4×D13—28no—
249C2×C4×D13—28no—
250C2×C4×D13—44no—
251C2×C4×D13—416no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—28no—
254C42×C13—28no—
255C42×C13—44no—
256C22⋊Dic13—28no—
257C22⋊Dic13—44no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—28no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267C4⋊Dic13—28no—
268#6101—28no—
269#6101—28no—
270#6101—44no—
271#6101—44no—
272#6101C2×D4116yescomplemented
273C4×Dic13—28no—
274C22×#126—131no—
275C22×C4×D4—131no—
276#2467—1316no—
277C2×#399—131no—
278C2×#394—131no—
279C2×#394—131no—
280C2×#392—131no—
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⋊C4D1311yescharacteristic, complemented
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13C22×D412yes—
304C23×C13C2×#4114yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13C2×#4112yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C13C2511yescharacteristic
312C22×D13—28no—
313C22×D13—28no—
314C22×D13—28no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—44no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13C2×#4114yes—
340C2×C4×C13—28no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—22no—
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—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—416no—
359C2×C4×C13—44no—
360C2×C4×C13—44no—
361C2×C4×C13—44no—
362C2×C4×C13C22×D414yes—
363C2×C4×C13C2×#4114yes—
364C2×C4×C13C2×#4114yes—
365C22⋊D13—232no—
366C22⋊D13—416no—
367C2×Dic13—28no—
368C2×Dic13—28no—
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—22no—
384C2×Dic13—22no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13C22×D414yes—
390C2×Dic13C22×D414yes—
391D52—416no—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4—131no—
396C24×C4—131no—
397C24×C4C2×D1311yescharacteristic
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⋊C4—131no—
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#399—138no—
425#394—138no—
426#394—138no—
427#392—138no—
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⋊C4C2×D1318yescomplemented
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95C2×D1311yescharacteristic
444C2×#95C2×D1311yescharacteristic
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—416no—
453C22×C13#52514yes—
454C22×C13#52914yes—
455C22×C13#53814yes—
456C22×C13#54614yes—
457C22×C13#55014yes—
458C22×C13#55114yes—
459C22×C13#55314yes—
460C22×C13C23×D411yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C22×#4111yescharacteristic
464C22×C13C22×#4111yescharacteristic
465C22×C13C2×H(5,𝔽2)11yescharacteristic
466C22×C13C2×H(5,𝔽2)11yescharacteristic
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—416no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—88no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—42no—
487C4×C13—42no—
488C4×C13—42no—
489Dic13—24no—
490Dic13—24no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25—131no—
496C25—131no—
497C25C22×D1311yescharacteristic
498C22×D4—134no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—264no—
502C22×D4—264no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—264no—
506C22×D4—264no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4—522no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—42no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—134no—
520C23×C4—264no—
521C23×C4—264no—
522C23×C4—522no—
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1314yes—
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—134no—
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⋊C4—522no—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—24no—
571C2×C42—42no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42C22×D1314yes—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95C22×D1314yes—
583#95C22×D1314yes—
584C2×C13—44no—
585C2×C13#246718yescomplemented
586C2×C13C2×#52511yescharacteristic
587C2×C13C2×#52911yescharacteristic
588C2×C13C2×#53811yescharacteristic
589C2×C13C2×#54611yescharacteristic
590C2×C13C2×#55011yescharacteristic
591C2×C13C2×#55111yescharacteristic
592C2×C13C2×#55311yescharacteristic
593D13—44no—
594D13—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—134no—
602C24—132no—
603C24—132no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24—262no—
617C24#612714yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—268no—
621C2×D4—268no—
622C2×D4—268no—
623C2×D4—2632no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—268no—
627C2×D4—524no—
628C2×D4—5216no—
629C2×D4—524no—
630C2×D4—524no—
631C2×D4—5216no—
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—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—134no—
652C22×C4—134no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—268no—
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—268no—
677C22×C4—524no—
678C22×C4—5216no—
679C22×C4#612714yes—
680C22×C4#612714yes—
681C22×C4D4×D1314yes—
682C22×C4C23×D1312yes—
683C22×C4C23×D1312yes—
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—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—28no—
708C42—44no—
709C42—268no—
710C13C2×#246711yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—134no—
725C23—268no—
726C23—268no—
727C23—268no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—524no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23C2×#612714yes—
753C23C2×#612712yes—
754C23C2×#612712yes—
755C23C2×#612712yes—
756C23C2×D4×D1312yes—
757C23#8825112yes—
758C23#41×D1312yes—
759C23#8825612yes—
760C23C24×D1311yescharacteristic
761D4—2632no—
762D4—5216no—
763D4—5216no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—134no—
787C2×C4—134no—
788C2×C4—268no—
789C2×C4—268no—
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—262no—
806C2×C4—5216no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4C2×#612714yes—
812C2×C4C2×#612714yes—
813C2×C4C2×D4×D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—522no—
826C22—522no—
827C22—522no—
828C22—5216no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—1048no—
838C22#1171918414yes—
839C22#1171919514yes—
840C22#1171923514yes—
841C22#1171925214yes—
842C22#1171925814yes—
843C22#1171926114yes—
844C22#1171926514yes—
845C22C22×#612711yescharacteristic
846C22C22×#612711yescharacteristic
847C22C22×#612711yescharacteristic
848C22C22×D4×D1311yescharacteristic
849C22C2×#8825111yescharacteristic
850C22C2×#41×D1311yescharacteristic
851C22C2×#8825611yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—264no—
859C4—264no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—524no—
866C2—1042no—
867C2#1311888718yesdirect product factor
868C2C2×#1171925211yescharacteristic
869C2C2×#1171918411yescharacteristic
870C2C2×#1171926511yescharacteristic
871C2C2×#1171919511yescharacteristic
872C2C2×#1171925811yescharacteristic
873C2C2×#1171926111yescharacteristic
874C2C2×#1171923511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2467
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88130C2semidirect
2. C22×C4×C22⋊D13C2semidirect
3. #13118887C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718620C2semidirect
6. C2×#11718620C2semidirect
8. C2×#11718600C2semidirect
9. C2×#11718601C2semidirect
10. C2×#11718330C2semidirect
11. C2×#11718594C2semidirect
12. C2×#11718315C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718326C2semidirect
15. C2×#11718328C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
29. C2×C4×C22⋊D13C22semidirect
47. C2×#88130C22semidirect
48. C4×C13×C22⋊C4C22semidirect
51. #11718874C22semidirect
59. #11718620C22semidirect
60. #11718620C22semidirect
61. #11718610C22semidirect
62. #11718601C22semidirect
63. #11718600C22semidirect
64. #11718594C22semidirect
65. #11718330C22semidirect
66. #11718328C22semidirect
67. #11718326C22semidirect
68. #11718315C22semidirect
141. C2×#6101D4semidirect
272. #6101C2×D4semidirect
289. C2×C4×C22⋊C4D13semidirect
436. C4×C22⋊C4C2×D13semidirect
585. C2×C13#2467semidirect
710. C13C2×#2467semidirect
867. C2#13118887direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881302
C22×C4×C22⋊D132
#131188872
C2×#117186102
C2×#117186202
C2×#117186212
C2×#117186002
C2×#117186012
C2×#117183302
C2×#117185942
C2×#117183152
C2×#117188742
C2×#117183262
C2×#117183282
C2×C4×C13×C22⋊C42
C2×#246713