Finite Group Databasebeta

← C2×#13117884 #16022500

Subgroups — C2×#13117884 #16022500

Order 3328.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88193C211yesmaximal, characteristic
2C22×D4×Dic13C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13117884C2116yesmaximal, direct product factor
5C2×#11718331C211yesmaximal, characteristic, complemented
6C2×#11718605C211yesmaximal, characteristic, complemented
7C2×#11718316C211yesmaximal, characteristic, complemented
8C2×#11718313C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic, complemented
10C2×#11718619C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×#11718327C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88193C4116yescomplemented
32C2×#88193C2218yes—
33C2×D4×Dic13—28no—
34C2×D4×Dic13C2218yescomplemented
35C2×C4×C22⋊D13—28no—
36C2×C4×C22⋊D13C2218yescomplemented
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C13×#386C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2218yescomplemented
60#11718619C2218yescomplemented
61#11718619C2218yescomplemented
62#11718617C2218yescomplemented
63#11718605C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65C22⋊C4×Dic13C2218yescomplemented
66#11718331C2218yescomplemented
67#11718327C2218yescomplemented
68#11718316C2218yescomplemented
69#11718313C2218yescomplemented
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13C2×C418yescomplemented
76C22×D4×C13C2314yes—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—42no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2314yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C22×C22⋊D13—24no—
87C22×C22⋊D13—24no—
88C22×C22⋊D13—42no—
89C22×C22⋊D13—42no—
90C22×C22⋊D13C2×C418yescomplemented
91C22×C22⋊D13C2×C418yescomplemented
92C22×C22⋊D13C2314yes—
93C22×C22⋊D13C2314yes—
94C23×Dic13—24no—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13—42no—
99C23×Dic13—42no—
100C23×Dic13—42no—
101C23×Dic13—42no—
102C23×Dic13C2×C418yescomplemented
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2314yes—
105C23×Dic13C2314yes—
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2311yescharacteristic
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2314yes—
113C22×C4×D13—24no—
114C22×C4×D13—24no—
115C22×C4×D13—42no—
116C22×C4×D13C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—24no—
119C2×C13×C22⋊C4—42no—
120C2×C13×C22⋊C4C2314yes—
121C2×C13×C22⋊C4C2314yes—
122C2×C13×C22⋊C4C2314yes—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13C2×C418yescomplemented
125C2×C22⋊Dic13D418yescomplemented
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129#88193C2×C4164yescomplemented
130D4×Dic13—232no—
131C4×C22⋊D13—232no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—42no—
135C2×#6103C2×C418yescomplemented
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×C4⋊Dic13—24no—
141C2×C4⋊Dic13C2314yes—
142C2×#6101—24no—
143C2×#6101C2×C418yescomplemented
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×C4×Dic13—24no—
147C2×C4×Dic13—24no—
148C2×C4×Dic13—42no—
149C2×C4×Dic13—42no—
150C2×C4×Dic13C2314yes—
151C2×C4×Dic13C2314yes—
152C2×C4×Dic13C2314yes—
153C2×C4×Dic13C2314yes—
154C13×#95C2314yes—
155C13×#95C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2364—131nomaximal, Sylow
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×C13C22×C414yes—
176C24×C13C22×C414yes—
177C24×C13C2×D414yes—
178C24×C13#4114yes—
179C24×C13C2412yes—
180C24×C13C2412yes—
181C24×C13C2411yescharacteristic
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13C22×C414yes—
189C23×D13C2412yes—
190C2×D4×C13—232no—
191C2×D4×C13—28no—
192C2×D4×C13—28no—
193C2×D4×C13C22×C4116yescomplemented
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—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—22no—
208C22×C4×C13—28no—
209C22×C4×C13—44no—
210C22×C4×C13—416no—
211C22×C4×C13C22×C414yes—
212C22×C4×C13#4114yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C2×C22⋊D13—232no—
219C2×C22⋊D13—28no—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—416no—
222C2×C22⋊D13—44no—
223C2×C22⋊D13—44no—
224C2×C22⋊D13C22×C4116yescomplemented
225C2×C22⋊D13C22×C4116yescomplemented
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×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—28no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—28no—
243C22×Dic13—28no—
244C22×Dic13—28no—
245C22×Dic13—416no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—416no—
251C22×Dic13—416no—
252C22×Dic13C22×C414yes—
253C22×Dic13C22×C414yes—
254C22×Dic13C22×C414yes—
255C22×Dic13C22×C4116yescomplemented
256C22×Dic13C2×D414yes—
257C22×Dic13C2×D414yes—
258C22×Dic13#4114yes—
259C22×Dic13C2412yes—
260C22×Dic13C2412yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C2×C4×D13—28no—
267C2×C4×D13—28no—
268C2×C4×D13—44no—
269C2×C4×D13—416no—
270C13×C22⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—44no—
273C22⋊Dic13—28no—
274C22⋊Dic13C22×C4116yescomplemented
275C22⋊Dic13C2×D4116yescomplemented
276#6103—28no—
277#6103—28no—
278#6103—44no—
279#6103C22×C4116yescomplemented
280C4⋊Dic13—28no—
281#6101—28no—
282#6101C22×C4116yescomplemented
283C4×Dic13—28no—
284C4×Dic13—28no—
285C4×Dic13—44no—
286C4×Dic13—44no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4—131no—
290#2364—1316no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#387—131no—
294C2×#387—131no—
295C2×#386—131no—
296C2×#386—131no—
297C2×#386—131no—
298C2×#386D1311yescharacteristic, complemented
299C2×C4×C22⋊C4—131no—
300C2×C4×C22⋊C4—131no—
301C2×C4×C22⋊C4—131no—
302C22×#95—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—28no—
314C23×C13—28no—
315C23×C13—28no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13C4×D4116yes—
327C23×C13C23×C414yes—
328C23×C13C23×C414yes—
329C23×C13C23×C412yes—
330C23×C13C22×D414yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C23×C414yes—
353D4×C13—232no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—416no—
370C2×C4×C13—44no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13C23×C414yes—
374C2×C4×C13C2×#4114yes—
375C22⋊D13—232no—
376C22⋊D13—416no—
377C2×Dic13—28no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
381C2×Dic13—28no—
382C2×Dic13—28no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—416no—
399C2×Dic13—416no—
400C2×Dic13—416no—
401C2×Dic13—44no—
402C2×Dic13C23×C414yes—
403C2×Dic13C23×C414yes—
404C2×Dic13C23×C414yes—
405C2×Dic13C22×D414yes—
406C2×Dic13C22×D414yes—
407C2×Dic13C2×#4114yes—
408C4×D13—416no—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4C2×D1311yescharacteristic
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4—131no—
416C24×C4C2×D1311yescharacteristic
417C2×#121—1316no—
418C2×#121—138no—
419C2×C4×D4—138no—
420C2×C4×D4—138no—
421C2×C4×D4—268no—
422C2×C4×D4—268no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4C2×D1311yescharacteristic
434C22×C22⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C42—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42—131no—
440#388—138no—
441#388—138no—
442#387—138no—
443#387—138no—
444#386—138no—
445#386—138no—
446#386—138no—
447#386C2×D1318yescomplemented
448C4×C22⋊C4—138no—
449C4×C22⋊C4—138no—
450C4×C22⋊C4—138no—
451C2×#95—138no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95C2×D1311yescharacteristic
461C2×#95C2×D1311yescharacteristic
462C22×C13—232no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—416no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13C2×C4×D418yes—
478C22×C13C2×C4×D414yes—
479C22×C13C4×#4114yes—
480C22×C13#51814yes—
481C22×C13#54614yes—
482C22×C13#54614yes—
483C22×C13#55314yes—
484C22×C13#55314yes—
485C22×C13C24×C411yescharacteristic
486C22×C13C23×D411yescharacteristic
487C22×C13C22×#4111yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C22×#4111yescharacteristic
490C22×C13C2×H(5,𝔽2)11yescharacteristic
491C22×C13C2×H(5,𝔽2)11yescharacteristic
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—24no—
495C2×D13—416no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13—42no—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—42no—
503C4×C13—42no—
504C4×C13—42no—
505Dic13—24no—
506Dic13—24no—
507Dic13—24no—
508Dic13—24no—
509Dic13—24no—
510Dic13—24no—
511Dic13—42no—
512C25—131no—
513C25C22×D1311yescharacteristic
514C25C22×D1311yescharacteristic
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—138no—
520C22×D4—134no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—522no—
524C22×D4—522no—
525C22×D4C4×D1318yescomplemented
526C22×D4C22×D1314yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—42no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—138no—
537C23×C4—134no—
538C23×C4—131no—
539C23×C4—134no—
540C23×C4—134no—
541C23×C4—134no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—264no—
548C23×C4—522no—
549C23×C4—522no—
550C23×C4—522no—
551C23×C4—522no—
552C23×C4—522no—
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C23×C4C22×D1314yes—
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559#121—1364no—
560C4×D4—2632no—
561C4×D4—2632no—
562C2×C4⋊C4—138no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—138no—
572C2×C22⋊C4—138no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—138no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—522no—
585C2×C22⋊C4C22×D1314yes—
586C2×C22⋊C4C22×D1314yes—
587C2×C22⋊C4C22×D1314yes—
588C2×C42—134no—
589C2×C42—134no—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—264no—
593C2×C42—264no—
594C2×C42—522no—
595C2×C42—522no—
596#95—134no—
597#95—134no—
598#95—134no—
599#95—134no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95C22×D1314yes—
605#95C22×D1314yes—
606C2×C13—28no—
607C2×C13—44no—
608C2×C13#236418yescomplemented
609C2×C13C22×C4×D411yescharacteristic
610C2×C13C2×C4×#4111yescharacteristic
611C2×C13C2×#51811yescharacteristic
612C2×C13C2×#54611yescharacteristic
613C2×C13C2×#54611yescharacteristic
614C2×C13C2×#55311yescharacteristic
615C2×C13C2×#55311yescharacteristic
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—134no—
628C24—132no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24C2×C4×D1314yes—
636C24C2×C4×D1314yes—
637C24D4×D1314yes—
638C24#612914yes—
639C24C23×D1312yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—232no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—1316no—
646C2×D4—1316no—
647C2×D4—2632no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—5216no—
651C2×D4—524no—
652C2×D4—524no—
653C2×D4C2×C4×D13116yescomplemented
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—134no—
674C22×C4—134no—
675C22×C4—134no—
676C22×C4—134no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—1316no—
684C22×C4—132no—
685C22×C4—268no—
686C22×C4—268no—
687C22×C4—268no—
688C22×C4—268no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—262no—
702C22×C4—268no—
703C22×C4—262no—
704C22×C4—262no—
705C22×C4—268no—
706C22×C4—524no—
707C22×C4—5216no—
708C22×C4—5216no—
709C22×C4—524no—
710C22×C4—524no—
711C22×C4—524no—
712C22×C4—524no—
713C22×C4—5216no—
714C22×C4—5216no—
715C22×C4C2×C4×D1314yes—
716C22×C4#612914yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1312yes—
722C4⋊C4—1316no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—44no—
728C22⋊C4—1316no—
729C22⋊C4—1316no—
730C22⋊C4—1316no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—524no—
735C42—268no—
736C42—268no—
737C42—524no—
738C42—524no—
739C13C2×#236411yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—134no—
764C23—268no—
765C23—268no—
766C23—268no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23#88135116yes—
778C23C22×C4×D1314yes—
779C23C22×C4×D1314yes—
780C23C22×C4×D1312yes—
781C23C2×D4×D1314yes—
782C23C2×D4×D1312yes—
783C23C2×#612914yes—
784C23C2×#612912yes—
785C23C2×#612912yes—
786C23#8825112yes—
787C23#41×D1312yes—
788C23#8825612yes—
789C23C24×D1311yescharacteristic
790D4—232no—
791D4—2632no—
792D4—5216no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—268no—
819C2×C4—268no—
820C2×C4—268no—
821C2×C4—268no—
822C2×C4—268no—
823C2×C4—268no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—5216no—
840C2×C4—5216no—
841C2×C4—5216no—
842C2×C4—5216no—
843C2×C4—524no—
844C2×C4C22×C4×D1314yes—
845C2×C4C2×#612914yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—264no—
862C22—264no—
863C22—264no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—5216no—
869C22C2×#8813518yes—
870C22C2×#8813514yes—
871C22C4×#612914yes—
872C22#1171925014yes—
873C22#1171929614yes—
874C22#1171930614yes—
875C22#1171932314yes—
876C22#1171935914yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×D4×D1311yescharacteristic
879C22C22×#612911yescharacteristic
880C22C22×#612911yescharacteristic
881C22C2×#8825111yescharacteristic
882C22C2×#41×D1311yescharacteristic
883C22C2×#8825611yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—264no—
894C4—264no—
895C4—522no—
896C2—28no—
897C2—44no—
898C2—524no—
899C2#1311788418yesdirect product factor
900C2C22×#8813511yescharacteristic
901C2C2×C4×#612911yescharacteristic
902C2C2×#1171925011yescharacteristic
903C2C2×#1171929611yescharacteristic
904C2C2×#1171935911yescharacteristic
905C2C2×#1171930611yescharacteristic
906C2C2×#1171932311yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC22×#88193C2
cosocleC23×C13C25
hypercenterC2×#386D13
hypocenterC13C2×#2364
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic13C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13117884C2direct (N × H)
5. C2×#11718331C2semidirect
6. C2×#11718605C2semidirect
7. C2×#11718316C2semidirect
8. C2×#11718313C2semidirect
9. C2×#11718619C2semidirect
10. C2×#11718619C2semidirect
11. C2×#11718617C2semidirect
12. C2×C22⋊C4×Dic13C2semidirect
13. C2×C22⋊C4×Dic13C2semidirect
14. C2×#11718327C2semidirect
15. C22×#88071C2semidirect
16. C2×C13×#386C2semidirect
31. C2×#88193C4semidirect
34. C2×D4×Dic13C22semidirect
36. C2×C4×C22⋊D13C22semidirect
48. C13×#386C22semidirect
59. C2×#88071C22semidirect
60. #11718619C22semidirect
61. #11718619C22semidirect
62. #11718617C22semidirect
63. #11718605C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. C22⋊C4×Dic13C22semidirect
66. #11718331C22semidirect
67. #11718327C22semidirect
68. #11718316C22semidirect
69. #11718313C22semidirect
75. C22×D4×C13C2×C4semidirect
90. C22×C22⋊D13C2×C4semidirect
91. C22×C22⋊D13C2×C4semidirect
102. C23×Dic13C2×C4semidirect
124. C2×C22⋊Dic13C2×C4semidirect
125. C2×C22⋊Dic13D4semidirect
129. #88193C2×C4semidirect
135. C2×#6103C2×C4semidirect
143. C2×#6101C2×C4semidirect
193. C2×D4×C13C22×C4semidirect
224. C2×C22⋊D13C22×C4semidirect
225. C2×C22⋊D13C22×C4semidirect
255. C22×Dic13C22×C4semidirect
274. C22⋊Dic13C22×C4semidirect
275. C22⋊Dic13C2×D4semidirect
279. #6103C22×C4semidirect
282. #6101C22×C4semidirect
298. C2×#386D13semidirect
447. #386C2×D13semidirect
525. C22×D4C4×D13semidirect
608. C2×C13#2364semidirect
653. C2×D4C2×C4×D13semidirect
739. C13C2×#2364semidirect
899. C2#13117884direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881932
C22×D4×Dic132
C22×C4×C22⋊D132
#131178842
C2×#117183312
C2×#117186052
C2×#117183162
C2×#117183132
C2×#117186192
C2×#117186172
C2×C22⋊C4×Dic132
C2×#117183272
C22×#880712
C2×C13×#3862
C2×#236413