Finite Group Databasebeta

← C2×#13117540 #16021698

Subgroups — C2×#13117540 #16021698

Order 3328.

4150 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×#88138C211yesmaximal, characteristic
2C22×C4×D52C211yesmaximal, characteristic, complemented
3C22×#88135C211yesmaximal, characteristic, complemented
4#13117540C2116yesmaximal, direct product factor
5C2×#11718651C211yesmaximal, characteristic, complemented
6C2×#11718316C211yesmaximal, characteristic, complemented
7C2×#11718594C211yesmaximal, characteristic, complemented
8C2×#11718326C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic, complemented
10C2×#11718617C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×#11718611C211yesmaximal, characteristic, complemented
13C2×#11718329C211yesmaximal, characteristic, complemented
14C2×#11718648C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88138C4116yescomplemented
43C2×#88138C2218yes—
44C2×#88135—28no—
45C2×#88135C2218yescomplemented
46C2×C4×D52—28no—
47C2×C4×D52C2218yescomplemented
48C13×#388C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718651C2218yescomplemented
60#11718648C2218yescomplemented
61#11718619C2218yescomplemented
62#11718617C2218yescomplemented
63#11718617C2218yescomplemented
64#11718611C2218yescomplemented
65#11718594C2218yescomplemented
66#11718329C2218yescomplemented
67#11718326C2218yescomplemented
68D13×#95C2218yescomplemented
69#11718316C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—24no—
80C22×C22⋊D13—24no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13C2×C418yescomplemented
84C22×C22⋊D13C2×C418yescomplemented
85C22×C22⋊D13C2314yes—
86C22×C22⋊D13C2314yes—
87C23×Dic13—24no—
88C23×Dic13—42no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C22×D52—24no—
98C22×D52—24no—
99C22×D52C2×C418yescomplemented
100C22×D52C2314yes—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—42no—
104C22×C4×D13—42no—
105C22×C4×D13—42no—
106C22×C4×D13—42no—
107C22×C4×D13—42no—
108C22×C4×D13—42no—
109C22×C4×D13—42no—
110C22×C4×D13—42no—
111C22×C4×D13C2×C418yescomplemented
112C22×C4×D13D418yescomplemented
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C22×C4×D13C2314yes—
116C22×C4×D13C2314yes—
117C2×C13×C4⋊C4—42no—
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C22⋊C4—24no—
120C2×C13×C22⋊C4—42no—
121C2×C13×C22⋊C4C2×C418yescomplemented
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C42×C13—24no—
126C2×C42×C13C2314yes—
127C2×C22⋊Dic13—42no—
128C2×C22⋊Dic13C2314yes—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—42no—
133C2×#6103—42no—
134C2×#6103C2×C418yescomplemented
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×C4⋊Dic13—24no—
142C2×C4⋊Dic13—42no—
143C2×C4⋊Dic13C2314yes—
144C2×C4⋊Dic13C2314yes—
145C2×#6101—24no—
146C2×#6101C2×C418yescomplemented
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×C4×Dic13—24no—
150C2×C4×Dic13C2314yes—
151#88138C2×C4164yescomplemented
152#88135—232no—
153C4×D52—232no—
154C13×#95C2314yes—
155C13×#95C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2325—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C22×C414yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13—22no—
184C23×D13C22×C414yes—
185C23×D13C22×C414yes—
186C23×D13C2×D414yes—
187C23×D13#4114yes—
188C23×D13C2412yes—
189C23×D13C2412yes—
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—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13C22×C414yes—
206C22×C4×C13C22×C414yes—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C2×C22⋊D13—232no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—416no—
218C2×C22⋊D13—44no—
219C2×C22⋊D13—44no—
220C2×C22⋊D13C22×C4116yescomplemented
221C2×C22⋊D13C22×C4116yescomplemented
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×Dic13—22no—
237C22×Dic13—28no—
238C22×Dic13—44no—
239C22×Dic13—44no—
240C22×Dic13—416no—
241C22×Dic13C22×C414yes—
242C22×Dic13C22×C414yes—
243C22×Dic13C2×D414yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×D52—232no—
251C2×D52—28no—
252C2×D52—28no—
253C2×D52C22×C4116yescomplemented
254C2×C4×D13—28no—
255C2×C4×D13—28no—
256C2×C4×D13—416no—
257C2×C4×D13—416no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C2×C4×D13—416no—
267C2×C4×D13—416no—
268C2×C4×D13C22×C4116yescomplemented
269C2×C4×D13C2×D4116yescomplemented
270C13×C4⋊C4—44no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—44no—
273C13×C22⋊C4C22×C4116yescomplemented
274C42×C13—28no—
275C22⋊Dic13—44no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—44no—
280#6103—44no—
281#6103C22×C4116yescomplemented
282C4⋊Dic13—28no—
283C4⋊Dic13—44no—
284#6101—28no—
285#6101C22×C4116yescomplemented
286C4×Dic13—28no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4—131no—
290#2325—1316no—
291C2×#388—131no—
292C2×#388D1311yescharacteristic, complemented
293C2×#387—131no—
294C2×#387—131no—
295C2×#386—131no—
296C2×#386—131no—
297C2×#386—131no—
298C2×#386—131no—
299C2×#385—131no—
300C2×#385—131no—
301C2×#380—131no—
302C22×#95—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C23×C414yes—
317C23×C13C23×C412yes—
318C23×C13C22×D412yes—
319C23×C13C2×#4112yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C132−1+412yes—
324C23×C13C2511yescharacteristic
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—28no—
336C22×D13—28no—
337C22×D13—28no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13C4×D4116yes—
349C22×D13C23×C414yes—
350C22×D13C23×C414yes—
351C22×D13C22×D414yes—
352C22×D13C2×#4114yes—
353C2×C4×C13—28no—
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—22no—
370C2×C4×C13—22no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13C23×C414yes—
375C2×C4×C13C23×C414yes—
376C2×C4×C13C22×D414yes—
377C22⋊D13—232no—
378C22⋊D13—416no—
379C2×Dic13—28no—
380C2×Dic13—28no—
381C2×Dic13—28no—
382C2×Dic13—22no—
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—416no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13—44no—
401C2×Dic13C23×C414yes—
402C2×Dic13C23×C414yes—
403C2×Dic13C22×D414yes—
404D52—232no—
405C4×D13—416no—
406C4×D13—416no—
407C4×D13—416no—
408C4×D13—416no—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4—131no—
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4—131no—
416C24×C4—131no—
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×C4⋊C4—131no—
427C22×C4⋊C4C2×D1311yescharacteristic
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C22⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4C2×D1311yescharacteristic
438C22×C42—131no—
439C22×C42C2×D1311yescharacteristic
440#388—138no—
441#388C2×D1318yescomplemented
442#387—138no—
443#387—138no—
444#386—138no—
445#386—138no—
446#386—138no—
447#386—138no—
448#385—138no—
449#385—138no—
450#380—138no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—138no—
460C2×#95C2×D1311yescharacteristic
461C2×#95C2×D1311yescharacteristic
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—416no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13C2×C4×D414yes—
471C22×C13#51814yes—
472C22×C13#52014yes—
473C22×C13#53414yes—
474C22×C13#53714yes—
475C22×C13#53814yes—
476C22×C13#53914yes—
477C22×C13C24×C411yescharacteristic
478C22×C13C23×D411yescharacteristic
479C22×C13C22×#4111yescharacteristic
480C22×C13C2×H(5,𝔽2)11yescharacteristic
481C22×C13C2×H(5,𝔽2)11yescharacteristic
482C22×C13C2×H(5,𝔽2)11yescharacteristic
483C22×C13C2×2−1+411yescharacteristic
484C2×D13—232no—
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—24no—
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—416no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13C2×C4×D418yes—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—42no—
504C4×C13—42no—
505C4×C13—42no—
506Dic13—24no—
507Dic13—24no—
508Dic13—24no—
509Dic13—42no—
510Dic13—42no—
511Dic13—42no—
512C25—131no—
513C25—131no—
514C25C22×D1311yescharacteristic
515C22×D4—138no—
516C22×D4—134no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—138no—
520C22×D4—134no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—522no—
526C22×D4—522no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—138no—
531C23×C4—138no—
532C23×C4—134no—
533C23×C4—134no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—134no—
538C23×C4—134no—
539C23×C4—134no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4—264no—
543C23×C4—522no—
544C23×C4—522no—
545C23×C4—522no—
546C23×C4—522no—
547C23×C4—522no—
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×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559#121—1364no—
560C4×D4—2632no—
561C4×D4—2632no—
562C2×C4⋊C4—42no—
563C2×C4⋊C4—138no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—264no—
570C2×C4⋊C4—522no—
571C2×C4⋊C4C22×D1314yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—138no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—522no—
586C2×C22⋊C4—522no—
587C2×C22⋊C4—522no—
588C2×C22⋊C4C4×D1318yescomplemented
589C2×C22⋊C4C22×D1314yes—
590C2×C22⋊C4C22×D1314yes—
591C2×C22⋊C4C22×D1314yes—
592C2×C42—24no—
593C2×C42—134no—
594C2×C42—264no—
595C2×C42C22×D1314yes—
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—44no—
607C2×C13#232518yescomplemented
608C2×C13C22×C4×D411yescharacteristic
609C2×C13C2×#51811yescharacteristic
610C2×C13C2×#52011yescharacteristic
611C2×C13C2×#53411yescharacteristic
612C2×C13C2×#53711yescharacteristic
613C2×C13C2×#53811yescharacteristic
614C2×C13C2×#53911yescharacteristic
615D13—28no—
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—134no—
624C24—134no—
625C24—134no—
626C24—132no—
627C24—134no—
628C24—132no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24C2×C4×D1314yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—1316no—
643C2×D4—1316no—
644C2×D4—1316no—
645C2×D4—268no—
646C2×D4—2632no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—2632no—
650C2×D4—268no—
651C2×D4—5216no—
652C2×D4—524no—
653C2×D4—524no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
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—22no—
669C22×C4—134no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—1316no—
676C22×C4—1316no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—268no—
681C22×C4—268no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
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—268no—
698C22×C4—5216no—
699C22×C4—5216no—
700C22×C4—524no—
701C22×C4—524no—
702C22×C4—524no—
703C22×C4—524no—
704C22×C4—524no—
705C22×C4—524no—
706C22×C4—524no—
707C22×C4—524no—
708C22×C4—5216no—
709C22×C4—5216no—
710C22×C4—524no—
711C22×C4—524no—
712C22×C4—5216no—
713C22×C4C2×C4×D1314yes—
714C22×C4C2×C4×D1314yes—
715C22×C4D4×D1314yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1312yes—
722C4⋊C4—44no—
723C4⋊C4—1316no—
724C4⋊C4—268no—
725C4⋊C4—268no—
726C4⋊C4—524no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—1316no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C22⋊C4—524no—
736C22⋊C4C2×C4×D13116yescomplemented
737C42—28no—
738C42—268no—
739C13C2×#232511yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—1316no—
754C23—134no—
755C23—134no—
756C23—134no—
757C23—134no—
758C23—268no—
759C23—268no—
760C23—268no—
761C23—268no—
762C23—268no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—268no—
768C23—268no—
769C23—268no—
770C23—268no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—524no—
778C23—524no—
779C23—524no—
780C23—524no—
781C23C22×C4×D1314yes—
782C23C22×C4×D1312yes—
783C23C2×D4×D1312yes—
784C23#8825112yes—
785C23#41×D1312yes—
786C23#8825612yes—
787C23#8825612yes—
788C23#8825712yes—
789C23C24×D1311yescharacteristic
790D4—2632no—
791D4—2632no—
792D4—5216no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—268no—
818C2×C4—268no—
819C2×C4—268no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
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—5216no—
836C2×C4—5216no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—5216no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4—524no—
843C2×C4C22×C4×D1314yes—
844C2×C4C22×C4×D1314yes—
845C2×C4C2×D4×D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—138no—
855C22—264no—
856C22—264no—
857C22—2632no—
858C22—264no—
859C22—264no—
860C22—264no—
861C22—264no—
862C22—264no—
863C22—264no—
864C22—264no—
865C22—5216no—
866C22—522no—
867C22—522no—
868C22—522no—
869C22—522no—
870C22#1171922814yes—
871C22C4×D4×D1314yes—
872C22#1171925014yes—
873C22#1171931314yes—
874C22#1171935814yes—
875C22#1171938314yes—
876C22#1171941214yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×D4×D1311yescharacteristic
879C22C2×#8825111yescharacteristic
880C22C2×#41×D1311yescharacteristic
881C22C2×#8825611yescharacteristic
882C22C2×#8825611yescharacteristic
883C22C2×#8825711yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—44no—
897C2—268no—
898C2—524no—
899C2#1311754018yesdirect product factor
900C2C2×C4×D4×D1311yescharacteristic
901C2C2×#1171925011yescharacteristic
902C2C2×#1171922811yescharacteristic
903C2C2×#1171935811yescharacteristic
904C2C2×#1171931311yescharacteristic
905C2C2×#1171938311yescharacteristic
906C2C2×#1171941211yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2325
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D52C2semidirect
3. C22×#88135C2semidirect
4. #13117540C2direct (N × H)
5. C2×#11718651C2semidirect
6. C2×#11718316C2semidirect
7. C2×#11718594C2semidirect
8. C2×#11718326C2semidirect
9. C2×#11718619C2semidirect
10. C2×#11718617C2semidirect
11. C2×#11718617C2semidirect
12. C2×#11718611C2semidirect
13. C2×#11718329C2semidirect
14. C2×#11718648C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#388C2semidirect
42. C2×#88138C4semidirect
45. C2×#88135C22semidirect
47. C2×C4×D52C22semidirect
48. C13×#388C22semidirect
59. #11718651C22semidirect
60. #11718648C22semidirect
61. #11718619C22semidirect
62. #11718617C22semidirect
63. #11718617C22semidirect
64. #11718611C22semidirect
65. #11718594C22semidirect
66. #11718329C22semidirect
67. #11718326C22semidirect
68. D13×#95C22semidirect
69. #11718316C22semidirect
83. C22×C22⋊D13C2×C4semidirect
84. C22×C22⋊D13C2×C4semidirect
99. C22×D52C2×C4semidirect
111. C22×C4×D13C2×C4semidirect
112. C22×C4×D13D4semidirect
121. C2×C13×C22⋊C4C2×C4semidirect
134. C2×#6103C2×C4semidirect
146. C2×#6101C2×C4semidirect
151. #88138C2×C4semidirect
220. C2×C22⋊D13C22×C4semidirect
221. C2×C22⋊D13C22×C4semidirect
253. C2×D52C22×C4semidirect
268. C2×C4×D13C22×C4semidirect
269. C2×C4×D13C2×D4semidirect
273. C13×C22⋊C4C22×C4semidirect
281. #6103C22×C4semidirect
285. #6101C22×C4semidirect
292. C2×#388D13semidirect
441. #388C2×D13semidirect
588. C2×C22⋊C4C4×D13semidirect
607. C2×C13#2325semidirect
736. C22⋊C4C2×C4×D13semidirect
739. C13C2×#2325semidirect
899. C2#13117540direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
C22×C4×D522
C22×#881352
#131175402
C2×#117186512
C2×#117183162
C2×#117185942
C2×#117183262
C2×#117186192
C2×#117186172
C2×#117186112
C2×#117183292
C2×#117186482
C2×D13×#952
C2×C13×#3882
C2×#232513