Finite Group Databasebeta

← C2×#13117630 #16021817

Subgroups — C2×#13117630 #16021817

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117630C2116yesmaximal, direct product factor
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718646C211yesmaximal, characteristic, complemented
4C2×#11718612C211yesmaximal, characteristic, complemented
5C2×#11718612C211yesmaximal, characteristic, complemented
6C2×#11718612C211yesmaximal, characteristic, complemented
7C2×#11718612C211yesmaximal, characteristic, complemented
8C2×#11718642C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718881C211yesmaximal, characteristic
11C2×#11718611C211yesmaximal, characteristic, complemented
12C2×#11718873C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C13×#123C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C2×C13×#123C4116yescomplemented
21C2×C13×#123C2218yes—
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊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
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44#11718882C2218yes—
45#11718881C2218yes—
46#11718873C2218yescomplemented
47C4×C22⋊Dic13C2218yescomplemented
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718646C2218yescomplemented
59#11718642C2218yescomplemented
60#11718642C2218yescomplemented
61C4⋊C4×Dic13C2218yescomplemented
62#11718612C2218yescomplemented
63#11718612C2218yescomplemented
64#11718612C2218yescomplemented
65#11718612C2218yescomplemented
66#11718611C2218yescomplemented
67C22⋊C4×Dic13C2218yescomplemented
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C22×D4×C13—42no—
71C22×D4×C13—42no—
72C22×D4×C13C2×C418yes—
73C22×D4×C13C2314yes—
74C23×C4×C13—42no—
75C23×C4×C13—42no—
76C23×C4×C13C2×C418yescomplemented
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×Dic13—24no—
84C23×Dic13—42no—
85C23×Dic13—42no—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C13×#123C2×C4164yescomplemented
96C2×C13×C4⋊C4C2×C418yescomplemented
97C2×C13×C4⋊C4C2×C418yescomplemented
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C22⋊C4C2×C418yes—
101C2×C13×C22⋊C4C2×C418yes—
102C2×C13×C22⋊C4C2×C418yescomplemented
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C22⋊Dic13—24no—
107C2×C22⋊Dic13—24no—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13—42no—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C4⋊Dic13—24no—
121C2×C4⋊Dic13—42no—
122C2×C4⋊Dic13—42no—
123C2×C4⋊Dic13—42no—
124C2×C4⋊Dic13—42no—
125C2×C4⋊Dic13C2314yes—
126C2×C4⋊Dic13C2314yes—
127C2×C4⋊Dic13C2314yes—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×C4×Dic13—24no—
131C2×C4×Dic13—42no—
132C2×C4×Dic13—42no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13—42no—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2335—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C22×C414yes—
164C24×C13C22×C414yes—
165C24×C13C2412yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C2×D4×C13—416no—
169C2×D4×C13—44no—
170C2×D4×C13—44no—
171C2×D4×C13C22×C4116yes—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
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—416no—
183C22×C4×C13—44no—
184C22×C4×C13—44no—
185C22×C4×C13C22×C414yes—
186C22×C4×C13C22×C414yes—
187C22×C4×C13C22×C414yes—
188C22×C4×C13C22×C414yes—
189C22×C4×C13C22×C414yes—
190C22×C4×C13C22×C4116yescomplemented
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
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—28no—
219C22×Dic13—44no—
220C22×Dic13—44no—
221C22×Dic13—416no—
222C22×Dic13#4114yes—
223C22×Dic13#4114yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C13×C4⋊C4C22×C4116yescomplemented
233C13×C4⋊C4C22×C4116yescomplemented
234C13×C22⋊C4C22×C4116yes—
235C13×C22⋊C4C22×C4116yes—
236C13×C22⋊C4C22×C4116yescomplemented
237C22⋊Dic13—28no—
238C22⋊Dic13—28no—
239C22⋊Dic13—28no—
240C22⋊Dic13—44no—
241C22⋊Dic13—44no—
242C22⋊Dic13—44no—
243C22⋊Dic13—44no—
244C4⋊Dic13—28no—
245C4⋊Dic13—44no—
246C4⋊Dic13—44no—
247C4⋊Dic13—44no—
248C4⋊Dic13—44no—
249C4×Dic13—28no—
250C4×Dic13—44no—
251C4×Dic13—44no—
252C4×Dic13—44no—
253C4×Dic13—44no—
254C22×#123D1311yescharacteristic
255#2335—1316no—
256C2×#390—131no—
257C2×#389—131no—
258C2×#388—131no—
259C2×#388—131no—
260C2×#388—131no—
261C2×#388—131no—
262C2×#387—131no—
263C2×#387—131no—
264C2×#386—131no—
265C2×#385—131no—
266C2×#380—131no—
267C2×C4×C4⋊C4—131no—
268C2×C4×C22⋊C4—131no—
269C2×C4×C22⋊C4—131no—
270C23×C13—28no—
271C23×C13—28no—
272C23×C13—28no—
273C23×C13—28no—
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—44no—
289C23×C13—44no—
290C23×C13—44no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13C23×C414yes—
297C23×C13C23×C414yes—
298C23×C13C23×C412yes—
299C23×C13C2×#4112yes—
300C23×C13C2×#4112yes—
301C23×C13H(5,𝔽2)12yes—
302C23×C13H(5,𝔽2)12yes—
303C23×C13H(5,𝔽2)12yes—
304C23×C132−1+412yes—
305C23×C13C2511yescharacteristic
306D4×C13—416no—
307C2×C4×C13—28no—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—416no—
323C2×C4×C13C23×C414yes—
324C2×C4×C13C23×C414yes—
325C2×C4×C13C23×C414yes—
326C2×C4×C13C23×C414yes—
327C2×C4×C13C23×C414yes—
328C2×Dic13—28no—
329C2×Dic13—28no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
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—416no—
353C2×Dic13—44no—
354C2×Dic13—44no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13C2×#4114yes—
360C2×Dic13C2×#4114yes—
361C23×D4C2×D1311yescharacteristic
362C24×C4—131no—
363C24×C4C2×D1311yescharacteristic
364C2×#123Dic13116yescomplemented
365C2×#123C2×D1318yes—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4C2×D1311yescharacteristic
372C22×C4⋊C4C2×D1311yescharacteristic
373C22×C22⋊C4—131no—
374C22×C22⋊C4—131no—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4C2×D1311yescharacteristic
381C22×C22⋊C4C2×D1311yescharacteristic
382C22×C22⋊C4C2×D1311yescharacteristic
383C22×C42—131no—
384C22×C42—131no—
385C22×C42—131no—
386C22×C42—131no—
387C22×C42—131no—
388#390—138no—
389#389—138no—
390#388—138no—
391#388—138no—
392#388—138no—
393#388—138no—
394#387—138no—
395#387—138no—
396#386—138no—
397#385—138no—
398#380—138no—
399C4×C4⋊C4—138no—
400C4×C22⋊C4—138no—
401C4×C22⋊C4—138no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C22×C13—24no—
413C22×C13—24no—
414C22×C13—24no—
415C22×C13—24no—
416C22×C13—24no—
417C22×C13—24no—
418C22×C13—416no—
419C22×C13—416no—
420C22×C13—42no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—42no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13C4×#4114yes—
429C22×C13#51814yes—
430C22×C13#52014yes—
431C22×C13#53814yes—
432C22×C13#53914yes—
433C22×C13#54014yes—
434C22×C13#54214yes—
435C22×C13C24×C411yescharacteristic
436C22×C13C22×#4111yescharacteristic
437C22×C13C22×#4111yescharacteristic
438C22×C13C2×H(5,𝔽2)11yescharacteristic
439C22×C13C2×H(5,𝔽2)11yescharacteristic
440C22×C13C2×H(5,𝔽2)11yescharacteristic
441C22×C13C2×2−1+411yescharacteristic
442C4×C13—24no—
443C4×C13—24no—
444C4×C13—24no—
445C4×C13—24no—
446C4×C13—24no—
447Dic13—24no—
448Dic13—24no—
449Dic13—42no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455C25C22×D1311yescharacteristic
456C25C22×D1311yescharacteristic
457C22×D4—42no—
458C22×D4—42no—
459C22×D4C2×Dic1318yes—
460C22×D4C22×D1314yes—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—134no—
472C23×C4—264no—
473C23×C4—522no—
474C23×C4—522no—
475C23×C4C2×Dic1318yescomplemented
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1314yes—
482#123C2×Dic13164yescomplemented
483C2×C4⋊C4—134no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—522no—
490C2×C4⋊C4—522no—
491C2×C4⋊C4—522no—
492C2×C4⋊C4—522no—
493C2×C4⋊C4C2×Dic1318yescomplemented
494C2×C4⋊C4C2×Dic1318yescomplemented
495C2×C4⋊C4C22×D1314yes—
496C2×C4⋊C4C22×D1314yes—
497C2×C22⋊C4—134no—
498C2×C22⋊C4—134no—
499C2×C22⋊C4—134no—
500C2×C22⋊C4—134no—
501C2×C22⋊C4—134no—
502C2×C22⋊C4—134no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—522no—
508C2×C22⋊C4—522no—
509C2×C22⋊C4—522no—
510C2×C22⋊C4—522no—
511C2×C22⋊C4C2×Dic1318yes—
512C2×C22⋊C4C2×Dic1318yes—
513C2×C22⋊C4C2×Dic1318yescomplemented
514C2×C22⋊C4C22×D1314yes—
515C2×C22⋊C4C22×D1314yes—
516C2×C22⋊C4C22×D1314yes—
517C2×C42—134no—
518C2×C42—134no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—134no—
522C2×C42—264no—
523C2×C42—522no—
524C2×C42—522no—
525C2×C42—522no—
526C2×C42—522no—
527#95—134no—
528#95—134no—
529#95—134no—
530#95—134no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537C2×C13—44no—
538C2×C13—44no—
539C2×C13#233518yescomplemented
540C2×C13C2×C4×#4111yescharacteristic
541C2×C13C2×#51811yescharacteristic
542C2×C13C2×#52011yescharacteristic
543C2×C13C2×#53811yescharacteristic
544C2×C13C2×#53911yescharacteristic
545C2×C13C2×#54011yescharacteristic
546C2×C13C2×#54211yescharacteristic
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24C22×Dic1314yes—
560C24C22×Dic1314yes—
561C24C23×D1312yes—
562C24C23×D1312yes—
563C24C23×D1311yescharacteristic
564C2×D4—416no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4C22×Dic13116yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—416no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—134no—
582C22×C4—134no—
583C22×C4—132no—
584C22×C4—132no—
585C22×C4—132no—
586C22×C4—132no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—268no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—524no—
615C22×C4—524no—
616C22×C4—5216no—
617C22×C4C22×Dic1314yes—
618C22×C4C22×Dic1314yes—
619C22×C4C22×Dic1314yes—
620C22×C4C22×Dic1314yes—
621C22×C4C22×Dic1314yes—
622C22×C4C22×Dic13116yescomplemented
623C22×C4C23×D1312yes—
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C4⋊C4—268no—
629C4⋊C4—524no—
630C4⋊C4—524no—
631C4⋊C4—524no—
632C4⋊C4—524no—
633C4⋊C4C22×Dic13116yescomplemented
634C4⋊C4C22×Dic13116yescomplemented
635C22⋊C4—268no—
636C22⋊C4—268no—
637C22⋊C4—268no—
638C22⋊C4—524no—
639C22⋊C4—524no—
640C22⋊C4—524no—
641C22⋊C4—524no—
642C22⋊C4C22×Dic13116yes—
643C22⋊C4C22×Dic13116yes—
644C22⋊C4C22×Dic13116yescomplemented
645C42—268no—
646C42—524no—
647C42—524no—
648C42—524no—
649C42—524no—
650C13C2×#233511yescharacteristic, complemented, Sylow
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23#8825112yes—
678C23#8825112yes—
679C23#41×D1312yes—
680C23#41×D1312yes—
681C23#8825612yes—
682C23#8825712yes—
683C23C23×Dic1314yes—
684C23C23×Dic1314yes—
685C23C23×Dic1312yes—
686C23C24×D1311yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—134no—
705C2×C4—134no—
706C2×C4—268no—
707C2×C4—268no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—5216no—
731C2×C4—524no—
732C2×C4—524no—
733C2×C4—524no—
734C2×C4—524no—
735C2×C4—524no—
736C2×C4—524no—
737C2×C4C23×Dic1314yes—
738C2×C4C23×Dic1314yes—
739C2×C4C23×Dic1314yes—
740C2×C4C23×Dic1314yes—
741C2×C4C23×Dic1314yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22#1171936214yes—
759C22#1171936514yes—
760C22#1171936714yes—
761C22#1171936814yes—
762C22#1171950314yes—
763C22#41×Dic1314yes—
764C22#1171953214yes—
765C22C2×#8825111yescharacteristic
766C22C2×#8825111yescharacteristic
767C22C2×#41×D1311yescharacteristic
768C22C2×#41×D1311yescharacteristic
769C22C2×#8825611yescharacteristic
770C22C2×#8825711yescharacteristic
771C22C24×Dic1311yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—264no—
778C4—264no—
779C4—522no—
780C4—522no—
781C4—522no—
782C4—522no—
783C4—522no—
784C4—522no—
785C2—44no—
786C2—44no—
787C2#1311763018yesdirect product factor
788C2C2×#41×Dic1311yescharacteristic
789C2C2×#1171950311yescharacteristic
790C2C2×#1171953211yescharacteristic
791C2C2×#1171936211yescharacteristic
792C2C2×#1171936511yescharacteristic
793C2C2×#1171936811yescharacteristic
794C2C2×#1171936711yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC23×D4×C13C22
cosocleC23×C13C25
hypercenterC22×#123D13
hypocenterC13C2×#2335
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #13117630C2direct (N × H)
3. C2×#11718646C2semidirect
4. C2×#11718612C2semidirect
5. C2×#11718612C2semidirect
6. C2×#11718612C2semidirect
7. C2×#11718612C2semidirect
8. C2×#11718642C2semidirect
9. C2×#11718642C2semidirect
11. C2×#11718611C2semidirect
12. C2×#11718873C2semidirect
13. C2×C4⋊C4×Dic13C2semidirect
14. C2×C22⋊C4×Dic13C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
20. C2×C13×#123C4semidirect
46. #11718873C22semidirect
47. C4×C22⋊Dic13C22semidirect
58. #11718646C22semidirect
59. #11718642C22semidirect
60. #11718642C22semidirect
61. C4⋊C4×Dic13C22semidirect
62. #11718612C22semidirect
63. #11718612C22semidirect
64. #11718612C22semidirect
65. #11718612C22semidirect
66. #11718611C22semidirect
67. C22⋊C4×Dic13C22semidirect
76. C23×C4×C13C2×C4semidirect
95. C13×#123C2×C4semidirect
96. C2×C13×C4⋊C4C2×C4semidirect
97. C2×C13×C4⋊C4C2×C4semidirect
102. C2×C13×C22⋊C4C2×C4semidirect
190. C22×C4×C13C22×C4semidirect
232. C13×C4⋊C4C22×C4semidirect
233. C13×C4⋊C4C22×C4semidirect
236. C13×C22⋊C4C22×C4semidirect
364. C2×#123Dic13semidirect
475. C23×C4C2×Dic13semidirect
482. #123C2×Dic13semidirect
493. C2×C4⋊C4C2×Dic13semidirect
494. C2×C4⋊C4C2×Dic13semidirect
513. C2×C22⋊C4C2×Dic13semidirect
539. C2×C13#2335semidirect
622. C22×C4C22×Dic13semidirect
633. C4⋊C4C22×Dic13semidirect
634. C4⋊C4C22×Dic13semidirect
644. C22⋊C4C22×Dic13semidirect
650. C13C2×#2335semidirect
787. C2#13117630direct (N × H)

Maximal subgroups

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

subgroupindex
#131176302
C2×#117188822
C2×#117186462
C2×#117186122
C2×#117186422
C2×#117188812
C2×#117186112
C2×#117188732
C2×C4⋊C4×Dic132
C2×C22⋊C4×Dic132
C2×C4×C22⋊Dic132
C22×C13×#1232
C2×#233513