Finite Group Databasebeta

← C2×#13117615 #16021801

Subgroups — C2×#13117615 #16021801

Order 3328.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117615C2116yesmaximal, direct product factor
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718646C211yesmaximal, characteristic, complemented
4C2×#11718612C211yesmaximal, characteristic
5C2×#11718612C211yesmaximal, characteristic
6C2×#11718612C211yesmaximal, characteristic
7C2×#11718642C211yesmaximal, characteristic, complemented
8C2×#11718642C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718611C211yesmaximal, characteristic
11C2×#11718611C211yesmaximal, characteristic
12C2×#11718597C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic
16C22×C13×#126C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C2×C13×#126C4116yescomplemented
19C2×C13×#126C2218yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718646C2218yescomplemented
55#11718646C2218yescomplemented
56#11718642C2218yescomplemented
57#11718642C2218yescomplemented
58#11718642C2218yescomplemented
59C4⋊C4×Dic13C2218yescomplemented
60#11718612C2218yes—
61#11718612C2218yes—
62#11718612C2218yes—
63#11718611C2218yes—
64#11718611C2218yes—
65C22⋊C4×Dic13C2218yes—
66#11718597C2218yescomplemented
67C4×C4⋊Dic13C2218yescomplemented
68C25×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×Dic13—24no—
76C23×Dic13—42no—
77C23×Dic13—42no—
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2314yes—
87C13×#126C2×C4164yescomplemented
88C2×C13×C4⋊C4C2×C418yescomplemented
89C2×C13×C4⋊C4C2×C418yescomplemented
90C2×C13×C4⋊C4C2×C418yescomplemented
91C2×C13×C4⋊C4C2314yes—
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C22⋊C4C2×C418yes—
95C2×C13×C22⋊C4C2×C418yes—
96C2×C13×C22⋊C4C2×C418yes—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2314yes—
100C2×C42×C13C2×C418yescomplemented
101C2×C42×C13C2314yes—
102C2×C22⋊Dic13—24no—
103C2×C22⋊Dic13—42no—
104C2×C22⋊Dic13—42no—
105C2×C22⋊Dic13C2314yes—
106C2×C22⋊Dic13C2314yes—
107C2×C22⋊Dic13C2314yes—
108C2×C4⋊Dic13—24no—
109C2×C4⋊Dic13—24no—
110C2×C4⋊Dic13—24no—
111C2×C4⋊Dic13—42no—
112C2×C4⋊Dic13—42no—
113C2×C4⋊Dic13—42no—
114C2×C4⋊Dic13—42no—
115C2×C4⋊Dic13C2314yes—
116C2×C4⋊Dic13C2314yes—
117C2×C4⋊Dic13C2314yes—
118C2×C4⋊Dic13C2314yes—
119C2×C4⋊Dic13C2314yes—
120C2×C4⋊Dic13C2314yes—
121C2×C4⋊Dic13C2314yes—
122C2×C4×Dic13—24no—
123C2×C4×Dic13—42no—
124C2×C4×Dic13—42no—
125C2×C4×Dic13—42no—
126C2×C4×Dic13—42no—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130C2×C4×Dic13C2314yes—
131C2×C4×Dic13C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2334—131nomaximal, Sylow
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13C22×C414yes—
152C24×C13C2412yes—
153C24×C13C2411yescharacteristic
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13C22×C414yes—
167C22×C4×C13C22×C414yes—
168C22×C4×C13C22×C414yes—
169C22×C4×C13C22×C414yes—
170C22×C4×C13C22×C414yes—
171C22×C4×C13C22×C414yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2412yes—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—28no—
201C22×Dic13—44no—
202C22×Dic13—44no—
203C22×Dic13—416no—
204C22×Dic13#4114yes—
205C22×Dic13#4114yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C13×C4⋊C4C22×C4116yescomplemented
215C13×C4⋊C4C22×C4116yescomplemented
216C13×C4⋊C4C22×C4116yescomplemented
217C13×C22⋊C4C22×C4116yes—
218C13×C22⋊C4C22×C4116yes—
219C13×C22⋊C4C22×C4116yes—
220C42×C13C22×C4116yescomplemented
221C22⋊Dic13—28no—
222C22⋊Dic13—44no—
223C22⋊Dic13—44no—
224C4⋊Dic13—28no—
225C4⋊Dic13—28no—
226C4⋊Dic13—28no—
227C4⋊Dic13—44no—
228C4⋊Dic13—44no—
229C4⋊Dic13—44no—
230C4⋊Dic13—44no—
231C4×Dic13—28no—
232C4×Dic13—44no—
233C4×Dic13—44no—
234C4×Dic13—44no—
235C4×Dic13—44no—
236C22×#126D1311yescharacteristic
237#2334—1316no—
238C2×#389—131no—
239C2×#389—131no—
240C2×#388—131no—
241C2×#388—131no—
242C2×#388—131no—
243C2×#387—131no—
244C2×#387—131no—
245C2×#387—131no—
246C2×#385—131no—
247C2×#385—131no—
248C2×#382—131no—
249C2×C4×C4⋊C4—131no—
250C2×C4×C4⋊C4—131no—
251C2×C4×C22⋊C4—131no—
252C23×C13—28no—
253C23×C13—28no—
254C23×C13—28no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—44no—
262C23×C13—44no—
263C23×C13—44no—
264C23×C13—44no—
265C23×C13C23×C414yes—
266C23×C13C23×C412yes—
267C23×C13C2×#4112yes—
268C23×C13C2×#4112yes—
269C23×C13H(5,𝔽2)12yes—
270C23×C13H(5,𝔽2)12yes—
271C23×C132−1+412yes—
272C23×C132−1+412yes—
273C23×C13C2511yescharacteristic
274C2×C4×C13—28no—
275C2×C4×C13—28no—
276C2×C4×C13—28no—
277C2×C4×C13—28no—
278C2×C4×C13—28no—
279C2×C4×C13—28no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13C23×C414yes—
293C2×C4×C13C23×C414yes—
294C2×C4×C13C23×C414yes—
295C2×C4×C13C23×C414yes—
296C2×C4×C13C23×C414yes—
297C2×C4×C13C23×C414yes—
298C2×Dic13—28no—
299C2×Dic13—28no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—416no—
323C2×Dic13—44no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13—44no—
328C2×Dic13—44no—
329C2×Dic13C2×#4114yes—
330C2×Dic13C2×#4114yes—
331C24×C4—131no—
332C2×#126Dic13116yescomplemented
333C2×#126C2×D1318yes—
334C22×C4⋊C4—131no—
335C22×C4⋊C4—131no—
336C22×C4⋊C4—131no—
337C22×C4⋊C4—131no—
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4C2×D1311yescharacteristic
342C22×C4⋊C4C2×D1311yescharacteristic
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4—131no—
347C22×C22⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4C2×D1311yescharacteristic
349C22×C22⋊C4C2×D1311yescharacteristic
350C22×C42—131no—
351C22×C42—131no—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—131no—
355C22×C42C2×D1311yescharacteristic
356#389—138no—
357#389—138no—
358#388—138no—
359#388—138no—
360#388—138no—
361#387—138no—
362#387—138no—
363#387—138no—
364#385—138no—
365#385—138no—
366#382—138no—
367C4×C4⋊C4—138no—
368C4×C4⋊C4—138no—
369C4×C22⋊C4—138no—
370C2×#95—131no—
371C2×#95—131no—
372C2×#95—131no—
373C2×#95—131no—
374C2×#95—131no—
375C2×#95—131no—
376C2×#95—131no—
377C2×#95—131no—
378C2×#95—131no—
379C2×#95—131no—
380C2×#95—131no—
381C2×#95—131no—
382C22×C13—24no—
383C22×C13—24no—
384C22×C13—24no—
385C22×C13—416no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13C4×#4114yes—
391C22×C13#52014yes—
392C22×C13#52014yes—
393C22×C13#53814yes—
394C22×C13#53914yes—
395C22×C13#54114yes—
396C22×C13#54214yes—
397C22×C13C24×C411yescharacteristic
398C22×C13C22×#4111yescharacteristic
399C22×C13C22×#4111yescharacteristic
400C22×C13C2×H(5,𝔽2)11yescharacteristic
401C22×C13C2×H(5,𝔽2)11yescharacteristic
402C22×C13C2×2−1+411yescharacteristic
403C22×C13C2×2−1+411yescharacteristic
404C4×C13—24no—
405C4×C13—24no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—24no—
409C4×C13—24no—
410Dic13—24no—
411Dic13—24no—
412Dic13—42no—
413Dic13—42no—
414Dic13—42no—
415Dic13—42no—
416Dic13—42no—
417Dic13—42no—
418C25C22×D1311yescharacteristic
419C23×C4—131no—
420C23×C4—131no—
421C23×C4—131no—
422C23×C4—131no—
423C23×C4—131no—
424C23×C4—131no—
425C23×C4—131no—
426C23×C4—131no—
427C23×C4—134no—
428C23×C4—264no—
429C23×C4—522no—
430C23×C4—522no—
431C23×C4C22×D1311yescharacteristic
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437#126C2×Dic13164yescomplemented
438C2×C4⋊C4—134no—
439C2×C4⋊C4—134no—
440C2×C4⋊C4—134no—
441C2×C4⋊C4—134no—
442C2×C4⋊C4—134no—
443C2×C4⋊C4—134no—
444C2×C4⋊C4—134no—
445C2×C4⋊C4—264no—
446C2×C4⋊C4—264no—
447C2×C4⋊C4—264no—
448C2×C4⋊C4—522no—
449C2×C4⋊C4—522no—
450C2×C4⋊C4—522no—
451C2×C4⋊C4—522no—
452C2×C4⋊C4C2×Dic1318yescomplemented
453C2×C4⋊C4C2×Dic1318yescomplemented
454C2×C4⋊C4C2×Dic1318yescomplemented
455C2×C4⋊C4C22×D1314yes—
456C2×C4⋊C4C22×D1314yes—
457C2×C4⋊C4C22×D1314yes—
458C2×C22⋊C4—134no—
459C2×C22⋊C4—134no—
460C2×C22⋊C4—134no—
461C2×C22⋊C4—264no—
462C2×C22⋊C4—522no—
463C2×C22⋊C4—522no—
464C2×C22⋊C4C2×Dic1318yes—
465C2×C22⋊C4C2×Dic1318yes—
466C2×C22⋊C4C2×Dic1318yes—
467C2×C22⋊C4C22×D1314yes—
468C2×C22⋊C4C22×D1314yes—
469C2×C22⋊C4C22×D1314yes—
470C2×C42—134no—
471C2×C42—134no—
472C2×C42—134no—
473C2×C42—134no—
474C2×C42—134no—
475C2×C42—264no—
476C2×C42—522no—
477C2×C42—522no—
478C2×C42—522no—
479C2×C42—522no—
480C2×C42C2×Dic1318yescomplemented
481C2×C42C22×D1314yes—
482#95—134no—
483#95—134no—
484#95—134no—
485#95—134no—
486#95—134no—
487#95—134no—
488#95—134no—
489#95—134no—
490#95—134no—
491#95—134no—
492#95—134no—
493#95—134no—
494C2×C13—44no—
495C2×C13#233418yescomplemented
496C2×C13C2×C4×#4111yescharacteristic
497C2×C13C2×#52011yescharacteristic
498C2×C13C2×#52011yescharacteristic
499C2×C13C2×#53811yescharacteristic
500C2×C13C2×#53911yescharacteristic
501C2×C13C2×#54111yescharacteristic
502C2×C13C2×#54211yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24C22×Dic1314yes—
510C24C23×D1312yes—
511C24C23×D1311yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—134no—
525C22×C4—134no—
526C22×C4—132no—
527C22×C4—132no—
528C22×C4—132no—
529C22×C4—132no—
530C22×C4—132no—
531C22×C4—132no—
532C22×C4—132no—
533C22×C4—132no—
534C22×C4—268no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—524no—
558C22×C4—524no—
559C22×C4—5216no—
560C22×C4C22×Dic1314yes—
561C22×C4C22×Dic1314yes—
562C22×C4C22×Dic1314yes—
563C22×C4C22×Dic1314yes—
564C22×C4C22×Dic1314yes—
565C22×C4C22×Dic1314yes—
566C22×C4C23×D1312yes—
567C22×C4C23×D1312yes—
568C22×C4C23×D1312yes—
569C22×C4C23×D1312yes—
570C22×C4C23×D1312yes—
571C22×C4C23×D1312yes—
572C4⋊C4—268no—
573C4⋊C4—268no—
574C4⋊C4—268no—
575C4⋊C4—524no—
576C4⋊C4—524no—
577C4⋊C4—524no—
578C4⋊C4—524no—
579C4⋊C4C22×Dic13116yescomplemented
580C4⋊C4C22×Dic13116yescomplemented
581C4⋊C4C22×Dic13116yescomplemented
582C22⋊C4—268no—
583C22⋊C4—524no—
584C22⋊C4—524no—
585C22⋊C4C22×Dic13116yes—
586C22⋊C4C22×Dic13116yes—
587C22⋊C4C22×Dic13116yes—
588C42—268no—
589C42—524no—
590C42—524no—
591C42—524no—
592C42—524no—
593C42C22×Dic13116yescomplemented
594C13C2×#233411yescharacteristic, complemented, Sylow
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23#41×D1312yes—
609C23#41×D1312yes—
610C23#8825612yes—
611C23#8825612yes—
612C23#8825712yes—
613C23#8825712yes—
614C23C23×Dic1314yes—
615C23C23×Dic1312yes—
616C23C24×D1311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—134no—
636C2×C4—134no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—268no—
642C2×C4—268no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—262no—
654C2×C4—262no—
655C2×C4—262no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—5216no—
662C2×C4—524no—
663C2×C4—524no—
664C2×C4—524no—
665C2×C4—524no—
666C2×C4—524no—
667C2×C4—524no—
668C2×C4C23×Dic1314yes—
669C2×C4C23×Dic1314yes—
670C2×C4C23×Dic1314yes—
671C2×C4C23×Dic1314yes—
672C2×C4C23×Dic1314yes—
673C2×C4C23×Dic1314yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—416no—
680C22—42no—
681C22—42no—
682C22#1171940614yes—
683C22#1171940914yes—
684C22#1171941214yes—
685C22#1171941514yes—
686C22#41×Dic1314yes—
687C22#1171953214yes—
688C22#1171953214yes—
689C22C2×#41×D1311yescharacteristic
690C22C2×#41×D1311yescharacteristic
691C22C2×#8825611yescharacteristic
692C22C2×#8825611yescharacteristic
693C22C2×#8825711yescharacteristic
694C22C2×#8825711yescharacteristic
695C22C24×Dic1311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—264no—
703C4—264no—
704C4—522no—
705C4—522no—
706C4—522no—
707C4—522no—
708C4—522no—
709C4—522no—
710C2—44no—
711C2#1311761518yesdirect product factor
712C2C2×#41×Dic1311yescharacteristic
713C2C2×#1171953211yescharacteristic
714C2C2×#1171953211yescharacteristic
715C2C2×#1171940911yescharacteristic
716C2C2×#1171941211yescharacteristic
717C2C2×#1171940611yescharacteristic
718C2C2×#1171941511yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C13×#126C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC22×#126D13
hypocenterC13C2×#2334
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #13117615C2direct (N × H)
2. C2×#11718646C2semidirect
3. C2×#11718646C2semidirect
7. C2×#11718642C2semidirect
8. C2×#11718642C2semidirect
9. C2×#11718642C2semidirect
12. C2×#11718597C2semidirect
13. C2×C4⋊C4×Dic13C2semidirect
14. C2×C4×C4⋊Dic13C2semidirect
18. C2×C13×#126C4semidirect
54. #11718646C22semidirect
55. #11718646C22semidirect
56. #11718642C22semidirect
57. #11718642C22semidirect
58. #11718642C22semidirect
59. C4⋊C4×Dic13C22semidirect
66. #11718597C22semidirect
67. C4×C4⋊Dic13C22semidirect
87. C13×#126C2×C4semidirect
88. C2×C13×C4⋊C4C2×C4semidirect
89. C2×C13×C4⋊C4C2×C4semidirect
90. C2×C13×C4⋊C4C2×C4semidirect
100. C2×C42×C13C2×C4semidirect
214. C13×C4⋊C4C22×C4semidirect
215. C13×C4⋊C4C22×C4semidirect
216. C13×C4⋊C4C22×C4semidirect
220. C42×C13C22×C4semidirect
332. C2×#126Dic13semidirect
437. #126C2×Dic13semidirect
452. C2×C4⋊C4C2×Dic13semidirect
453. C2×C4⋊C4C2×Dic13semidirect
454. C2×C4⋊C4C2×Dic13semidirect
480. C2×C42C2×Dic13semidirect
495. C2×C13#2334semidirect
579. C4⋊C4C22×Dic13semidirect
580. C4⋊C4C22×Dic13semidirect
581. C4⋊C4C22×Dic13semidirect
593. C42C22×Dic13semidirect
594. C13C2×#2334semidirect
711. C2#13117615direct (N × H)

Maximal subgroups

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

subgroupindex
#131176152
C2×#117186462
C2×#117186122
C2×#117186422
C2×#117186112
C2×#117185972
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
C2×C22⋊C4×Dic132
C22×C13×#1262
C2×#233413