Finite Group Databasebeta

← C2×#13082430 #15662102

Subgroups — C2×#13082430 #15662102

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082430C2132yesmaximal, direct product factor
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3C2×#10623253C211yesmaximal, characteristic, complemented
4C2×#10623216C212yesmaximal, complemented
5C2×#10623166C212yesmaximal, complemented
6C2×#10623074C211yesmaximal, characteristic, complemented
7C2×#10623042C212yesmaximal, complemented
8C2×D4×Dic22C212yesmaximal, complemented
9C2×#10623163C214yesmaximal, complemented
10C2×#10623220C212yesmaximal, complemented
11C2×#10623154C214yesmaximal, complemented
12C2×#10623109C211yesmaximal, characteristic, complemented
13C2×#10623153C212yesmaximal, complemented
14C22×#66941C212yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623077C212yesmaximal
17C2×C4×#4341C211yesmaximal, characteristic
18C2×C11×#554C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×#4341C2211yescharacteristic
21C23×Dic22C2214yes—
22C11×#554C22116yescomplemented
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×#125C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C2214yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C22×C11×C4⋊C4C2212yes—
31C2×#66999C2211yescharacteristic
32C2×Q8×Dic11C2212yes—
33C2×#66997C2212yes—
34C2×#66997C2211yescharacteristic
35C2×#66997C2214yes—
36C2×D4×Dic11C2212yes—
37C2×D4×Dic11C2211yescharacteristic
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2214yes—
40C22×C4⋊Dic11C2212yes—
41C2×#66977C2212yes—
42C2×#66977C2214yes—
43C22×Dic11⋊C4C2214yes—
44C22×C4×Dic11C2212yes—
45D11×C4⋊Q8C22116yescomplemented
46#10623253C22116yescomplemented
47#10623220C22132yescomplemented
48#10623216C22132yescomplemented
49#10623166C22132yescomplemented
50#10623163C22164yescomplemented
51#10623154C22164yescomplemented
52#10623153C22132yescomplemented
53#10623109C22116yescomplemented
54Q8×Dic22C22116yescomplemented
55#10623077C22132yes—
56#10623074C22116yescomplemented
57D4×Dic22C22132yescomplemented
58C4×#4341C22116yes—
59#10623042C22132yescomplemented
60C2×#66950C2211yescharacteristic
61C2×#66950C2214yes—
62C2×#66949C2214yes—
63C2×#66949C2212yes—
64C2×#66945C2211yescharacteristic
65C2×C4⋊C4×D11C2212yes—
66C2×C4⋊C4×D11C2212yes—
67C2×#66943C2212yes—
68C2×#66942C2214yes—
69C2×#66942C2214yes—
70C2×#66942C2214yes—
71C2×#66942C2212yes—
72C2×#66941C2212yes—
73C2×#66941C2212yes—
74C2×#66941C2212yes—
75C2×#66941C2211yescharacteristic
76C2×#66941C2212yes—
77C2×#66941C2214yes—
78C2×#66941C2214yes—
79C2×#66941C2212yes—
80C2×#66941C2214yes—
81C2×#66941C22132yescomplemented
82C2×#66940C2212yes—
83C2×#66940C2214yes—
84C2×#66940C2211yescharacteristic
85C2×#66940C2212yes—
86C2×(C22⋊D11)⋊C4C2214yes—
87C2×(C22⋊D11)⋊C4C2212yes—
88C2×#66931C2214yes—
89C2×#66931C2214yes—
90C2×#66931C2214yes—
91C2×#66930C2214yes—
92C2×#66930C2212yes—
93C2×#66925C2212yes—
94C2×C42×D11C2211yescharacteristic
95C2×#66922C2211yescharacteristic
96C2×#66922C2212yes—
97C2×C4×Dic22C2211yescharacteristic
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×Q8×C11C2312yes—
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C23×C4×C11C2314yes—
106C22×C22⋊D11C2312yes—
107C23×Dic11C2312yes—
108C23×Dic11C2314yes—
109C23×Dic11C2312yes—
110C2×Q8×D11—48no—
111C2×Q8×D11C23116yes—
112C2×#4341Q8116yescomplemented
113C2×#4341C2318yes—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2314yes—
117C22×C4×D11C2311yescharacteristic
118C22×Dic22—416no—
119C22×Dic22C2311yescharacteristic
120C22×Dic22C2312yes—
121C22×Dic22C2314yes—
122C22×Dic22C2312yes—
123C22×Dic22C2314yes—
124C22×Dic22C2314yes—
125C22×Dic22C23132yes—
126C22×Dic22C2311yescharacteristic
127C11×C4⋊Q8C2318yes—
128C11×#125C23116yes—
129C11×C22⋊Q8C23116yes—
130C11×C22⋊Q8C23132yes—
131C4×Q8×C11C2318yes—
132C4×D4×C11C2318yes—
133C4×D4×C11C23116yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C23116yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2312yes—
148#66999C2318yes—
149Q8×Dic11C23116yes—
150#66997C23132yes—
151#66997C23116yes—
152#66997C2318yes—
153D4×Dic11C2318yes—
154D4×Dic11C23116yes—
155C4×C22⋊D11C23116yes—
156C4×C22⋊D11C23132yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2314yes—
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2314yes—
167C2×C4⋊Dic11C23116yes—
168#66977C23132yes—
169#66977C23116yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2314yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C23132yes—
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2314yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2314yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C23116yes—
194#66950C2318yes—
195#66950C23132yes—
196#66949C23132yes—
197#66949C23116yes—
198#66945C2318yes—
199C4⋊C4×D11C23116yes—
200C4⋊C4×D11C23116yes—
201#66943C23116yes—
202#66942C23132yes—
203#66942C23116yes—
204#66942C23132yes—
205#66942C23132yes—
206#66941C23116yes—
207#66941C23116yes—
208#66941C23116yes—
209#66941C23116yes—
210#66941C2318yes—
211#66941C23116yes—
212#66941C23132yes—
213#66941C23132yes—
214#66941C23132yes—
215#66940C23116yes—
216#66940C23116yes—
217#66940C2318yes—
218#66940C23132yes—
219(C22⋊D11)⋊C4C23116yes—
220(C22⋊D11)⋊C4C23132yes—
221#66931C23132yes—
222#66931C23132yes—
223#66931C23132yes—
224#66930C23116yes—
225#66930C23132yes—
226#66925C23116yes—
227C42×D11C2318yes—
228#66922C2318yes—
229#66922C23116yes—
230C4×Dic22C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C2×#3503—111nomaximal, Sylow
235C24×C11C2412yes—
236C23×D11C2411yescharacteristic
237C2×Q8×C11—24no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2414yes—
240C2×Q8×C11C2418yes—
241C2×D4×C11C2×Q818yescomplemented
242C2×D4×C11C2414yes—
243C22×C4×C11—28no—
244C22×C4×C11—48no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2418yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2414yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C24116yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11C2×Q8116yescomplemented
255C2×C22⋊D11C2418yes—
256C22×Dic11—28no—
257C22×Dic11—48no—
258C22×Dic11C2×Q8116yescomplemented
259C22×Dic11C2418yes—
260C22×Dic11C2412yes—
261C22×Dic11C2411yescharacteristic
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2414yes—
265C22×Dic11C24116yes—
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2418yes—
269C22×Dic11C2411yescharacteristic
270Q8×D11—432no—
271#4341C2×Q8164yescomplemented
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—48no—
275C2×C4×D11C2×Q818yescomplemented
276C2×C4×D11C2414yes—
277C2×C4×D11C2414yes—
278C2×C4×D11C24116yes—
279C2×C4×D11C2414yes—
280C2×Dic22—28no—
281C2×Dic22—216no—
282C2×Dic22—24no—
283C2×Dic22—48no—
284C2×Dic22—48no—
285C2×Dic22—44no—
286C2×Dic22—464no—
287C2×Dic22C2×Q818yescomplemented
288C2×Dic22C2414yes—
289C2×Dic22C2418yes—
290C2×Dic22C24116yes—
291C2×Dic22C2418yes—
292C2×Dic22C24116yes—
293C2×Dic22C24116yes—
294C2×Dic22C2414yes—
295C11×C4⋊C4C2418yes—
296C11×C4⋊C4C2418yes—
297C11×C4⋊C4C24116yes—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C24116yes—
301C11×C4⋊C4C2418yes—
302C11×C22⋊C4C24116yes—
303C11×C22⋊C4C2418yes—
304C42×C11C2414yes—
305C42×C11C2418yes—
306C22⋊Dic11C24116yes—
307C22⋊Dic11C2418yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C2418yes—
310(C2×D11)⋊C4C2418yes—
311C4⋊Dic11C2414yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C2414yes—
314C4⋊Dic11C2418yes—
315C4⋊Dic11C24116yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C24116yes—
318Dic11⋊C4C2418yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C2418yes—
322Dic11⋊C4C24116yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C2418yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331C4×Dic11C2414yes—
332C4×Dic11C2418yes—
333C4×Dic11C24116yes—
334C4×Dic11C2418yes—
335C4×Dic11C2414yes—
336C4×Dic11C2414yes—
337C4×Dic11C24116yes—
338C4×Dic11C2418yes—
339C4×Dic11C2418yes—
340#3503—1132no—
341C2×Q82—111no—
342C2×Q82—111no—
343C2×#557—112no—
344C2×#554—112no—
345C2×#554—111no—
346C2×#554—112no—
347C2×#554D1111yescharacteristic, complemented
348C2×D4×Q8—114no—
349C2×D4×Q8—112no—
350C2×#544—112no—
351C2×#544—114no—
352C2×#533—112no—
353C2×#533—111no—
354C22×C4⋊Q8—111no—
355C22×C4⋊Q8—112no—
356C2×#520—112no—
357C2×C4×#41—111no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11C22×Q818yes—
361C23×C11C2514yes—
362C23×C11C2511yescharacteristic
363C22×D11—22no—
364C22×D11—22no—
365C22×D11C22×Q814yes—
366C22×D11C2512yes—
367Q8×C11—28no—
368Q8×C11—48no—
369D4×C11C22×Q8116yescomplemented
370C2×C4×C11—24no—
371C2×C4×C11—28no—
372C2×C4×C11—22no—
373C2×C4×C11—24no—
374C2×C4×C11—24no—
375C2×C4×C11—216no—
376C2×C4×C11—416no—
377C2×C4×C11C22×Q814yes—
378C2×C4×C112−1+414yes—
379C2×C4×C11C2514yes—
380C2×C4×C11C2514yes—
381C2×C4×C11C2512yes—
382C2×C4×C11C2518yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2512yes—
386C22⋊D11C22×Q8132yescomplemented
387C2×Dic11—28no—
388C2×Dic11—24no—
389C2×Dic11—24no—
390C2×Dic11—24no—
391C2×Dic11—22no—
392C2×Dic11—216no—
393C2×Dic11—416no—
394C2×Dic11C22×Q818yes—
395C2×Dic11C22×Q814yes—
396C2×Dic11C22×Q8132yescomplemented
397C2×Dic11H(5,𝔽2)14yes—
398C2×Dic11C2514yes—
399C2×Dic11C2512yes—
400C2×Dic11C2514yes—
401C2×Dic11C2514yes—
402C2×Dic11C2518yes—
403C2×Dic11C2514yes—
404C2×Dic11C2512yes—
405C2×Dic11C2512yes—
406C4×D11—28no—
407C4×D11—28no—
408C4×D11—416no—
409C4×D11C22×Q8116yescomplemented
410Dic22—28no—
411Dic22—216no—
412Dic22—232no—
413Dic22—416no—
414Dic22—416no—
415Dic22—48no—
416Dic22C22×Q8116yescomplemented
417C22×#41—111no—
418C23×Q8—112no—
419C23×Q8—114no—
420Q82—1116no—
421Q82—1116no—
422#557—1132no—
423#554—1132no—
424#554—1116no—
425#554—1132no—
426#554C2×D11116yescomplemented
427D4×Q8—1164no—
428D4×Q8—1132no—
429#544—1132no—
430#544—1164no—
431#533—1132no—
432#533—1116no—
433C2×C4⋊Q8—112no—
434C2×C4⋊Q8—111no—
435C2×C4⋊Q8—114no—
436C2×C4⋊Q8—1116no—
437C2×C4⋊Q8—112no—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—114no—
440C2×C4⋊Q8—114no—
441C2×C4⋊Q8—112no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—114no—
445C2×C4⋊Q8—112no—
446C2×C4⋊Q8—1132no—
447C2×C4⋊Q8—111no—
448C2×C4⋊Q8—112no—
449C2×C4⋊Q8C2×D1111yescharacteristic
450C2×#125—112no—
451C2×#125—114no—
452C2×#125—114no—
453C2×#125—114no—
454C2×#125—112no—
455C2×#125C2×D1112yes—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—114no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—111no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8—114no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—114no—
466C2×C22⋊Q8C2×D1112yes—
467C2×C22⋊Q8C2×D1114yes—
468#520—1132no—
469C4×#41—1116no—
470C2×C4×Q8—112no—
471C2×C4×Q8—111no—
472C2×C4×Q8—112no—
473C2×C4×Q8—114no—
474C2×C4×Q8—112no—
475C2×C4×Q8—111no—
476C2×C4×Q8—112no—
477C2×C4×Q8—112no—
478C2×C4×Q8—111no—
479C2×C4×Q8C2×D1111yescharacteristic
480C2×C4×D4—111no—
481C2×C4×D4—112no—
482C2×C4×D4—112no—
483C2×C4×D4—114no—
484C2×C4×D4—112no—
485C2×C4×D4—114no—
486C2×C4×D4C2×D1111yescharacteristic
487C2×C4×D4C2×D1112yes—
488C2×#117—111no—
489C2×#117—112no—
490C2×#117—114no—
491C2×#117—112no—
492C22×C4⋊C4—114no—
493C22×C4⋊C4—112no—
494C22×C4⋊C4—112no—
495C22×C4⋊C4—112no—
496C22×C4⋊C4C2×D1112yes—
497C22×C42—112no—
498C22×C42—111no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—216no—
502C22×C11C23×Q818yes—
503C22×C11C23×Q812yes—
504C22×C11C2×H(5,𝔽2)12yes—
505C22×C11C2×2−1+412yes—
506C22×C11C2611yescharacteristic
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—28no—
510C2×D11C23×Q814yes—
511C4×C11—24no—
512C4×C11—28no—
513C4×C11—22no—
514C4×C11—24no—
515C4×C11—24no—
516C4×C11C23×Q814yes—
517C4×C11C2×2−1+414yes—
518Dic11—28no—
519Dic11—24no—
520Dic11—24no—
521Dic11—24no—
522Dic11—22no—
523Dic11C23×Q818yes—
524Dic11C23×Q814yes—
525Dic11C2×H(5,𝔽2)14yes—
526C2×#41—1116no—
527C2×#41—118no—
528C22×Q8—1116no—
529C22×Q8—111no—
530C22×Q8—111no—
531C22×Q8—114no—
532C22×Q8—112no—
533C22×Q8—114no—
534C22×Q8—114no—
535C22×Q8—112no—
536C22×Q8—1132no—
537C22×Q8—4416no—
538C22×Q8—448no—
539C22×Q8C22×D1111yescharacteristic
540C22×Q8C22×D1112yes—
541C22×D4—112no—
542C22×D4C22×D1111yescharacteristic
543C23×C4—112no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—114no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—114no—
550C23×C4C22×D1112yes—
551C23×C4C22×D1114yes—
552C4⋊Q8—1116no—
553C4⋊Q8—118no—
554C4⋊Q8—1132no—
555C4⋊Q8—1116no—
556C4⋊Q8—118no—
557C4⋊Q8—1132no—
558C4⋊Q8—1132no—
559C4⋊Q8—1116no—
560C4⋊Q8—1116no—
561C4⋊Q8—1116no—
562C4⋊Q8—1132no—
563C4⋊Q8—1116no—
564C4⋊Q8—118no—
565C4⋊Q8—1116no—
566C4⋊Q8C22×D1118yes—
567#125—1116no—
568#125—1132no—
569#125—1132no—
570#125—1132no—
571#125—1116no—
572#125C22×D11116yes—
573C22⋊Q8—118no—
574C22⋊Q8—1116no—
575C22⋊Q8—1132no—
576C22⋊Q8—1116no—
577C22⋊Q8—118no—
578C22⋊Q8—1132no—
579C22⋊Q8—1132no—
580C22⋊Q8—1132no—
581C22⋊Q8—1132no—
582C22⋊Q8—1132no—
583C22⋊Q8C22×D11116yes—
584C22⋊Q8C22×D11132yes—
585C4×Q8—1116no—
586C4×Q8—118no—
587C4×Q8—1116no—
588C4×Q8—1132no—
589C4×Q8—1116no—
590C4×Q8—118no—
591C4×Q8—1116no—
592C4×Q8—1116no—
593C4×Q8—118no—
594C4×Q8C22×D1118yes—
595C4×D4—118no—
596C4×D4—1116no—
597C4×D4—1116no—
598C4×D4—1132no—
599C4×D4—1116no—
600C4×D4—1132no—
601C4×D4C22×D1118yes—
602C4×D4C22×D11116yes—
603#117—118no—
604#117—1116no—
605#117—1132no—
606#117—1116no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—112no—
614C2×C4⋊C4—1132no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—1116no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—111no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4—1116no—
630C2×C4⋊C4—1116no—
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1114yes—
635C2×C4⋊C4C22×D11116yes—
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1114yes—
638C2×C4⋊C4C22×D1112yes—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4C22×D1114yes—
645C2×C22⋊C4C22×D1112yes—
646C2×C42—111no—
647C2×C42—112no—
648C2×C42—114no—
649C2×C42—114no—
650C2×C42—112no—
651C2×C42—112no—
652C2×C42—112no—
653C2×C42—111no—
654C2×C42—1116no—
655C2×C42—111no—
656C2×C42—118no—
657C2×C42C22×D1112yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11—28no—
660C2×C11#350314yescomplemented
661C2×C11C24×Q811yescharacteristic
662C2×C11C22×H(5,𝔽2)11yescharacteristic
663C2×C11C22×2−1+411yescharacteristic
664D11—24no—
665C24—111no—
666C24C23×D1112yes—
667#41—1164no—
668C2×Q8—24no—
669C2×Q8—44no—
670C2×Q8—118no—
671C2×Q8—114no—
672C2×Q8—114no—
673C2×Q8—1116no—
674C2×Q8—118no—
675C2×Q8—1116no—
676C2×Q8—1116no—
677C2×Q8—118no—
678C2×Q8—228no—
679C2×Q8—2216no—
680C2×Q8—224no—
681C2×Q8—448no—
682C2×Q8—448no—
683C2×Q8—444no—
684C2×Q8—4464no—
685C2×Q8—4432no—
686C2×Q8C23×D1114yes—
687C2×Q8C23×D1118yes—
688C2×D4—1116no—
689C2×D4—118no—
690C2×D4Q8×D1118yescomplemented
691C2×D4C23×D1114yes—
692C22×C4—28no—
693C22×C4—48no—
694C22×C4—1116no—
695C22×C4—118no—
696C22×C4—112no—
697C22×C4—111no—
698C22×C4—111no—
699C22×C4—118no—
700C22×C4—114no—
701C22×C4—118no—
702C22×C4—112no—
703C22×C4—111no—
704C22×C4—112no—
705C22×C4—114no—
706C22×C4—112no—
707C22×C4—1116no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—1116no—
711C22×C4—224no—
712C22×C4—228no—
713C22×C4—224no—
714C22×C4—448no—
715C22×C4—448no—
716C22×C4C23×D1118yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1114yes—
721C22×C4C23×D1112yes—
722C22×C4C23×D11116yes—
723C22×C4C23×D1111yescharacteristic
724C22×C4C23×D1111yescharacteristic
725C4⋊C4—1116no—
726C4⋊C4—118no—
727C4⋊C4—114no—
728C4⋊C4—118no—
729C4⋊C4—1116no—
730C4⋊C4—1116no—
731C4⋊C4—118no—
732C4⋊C4—1116no—
733C4⋊C4—1116no—
734C4⋊C4—118no—
735C4⋊C4—118no—
736C4⋊C4—118no—
737C4⋊C4—114no—
738C4⋊C4—118no—
739C4⋊C4—1116no—
740C4⋊C4—118no—
741C4⋊C4—118no—
742C4⋊C4—1116no—
743C4⋊C4—118no—
744C4⋊C4—1116no—
745C4⋊C4C23×D1118yes—
746C4⋊C4C23×D1118yes—
747C4⋊C4C23×D1114yes—
748C4⋊C4C23×D11116yes—
749C4⋊C4C23×D1114yes—
750C4⋊C4C23×D11116yes—
751C4⋊C4C23×D1118yes—
752C22⋊C4—1116no—
753C22⋊C4—118no—
754C22⋊C4—118no—
755C22⋊C4—118no—
756C22⋊C4—118no—
757C22⋊C4C23×D11116yes—
758C22⋊C4C23×D1118yes—
759C42—114no—
760C42—114no—
761C42—118no—
762C42—118no—
763C42—118no—
764C42—114no—
765C42—1116no—
766C42—1116no—
767C42—118no—
768C42C23×D1114yes—
769C42C23×D1118yes—
770C11C2×#350311yescharacteristic, complemented, Sylow
771C23—24no—
772C23—24no—
773C23—114no—
774C23—112no—
775C23—222no—
776C23—222no—
777C23C2×Q8×D1118yes—
778C23C24×D1114yes—
779C23C24×D1111yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—1116no—
783Q8—2216no—
784Q8—2232no—
785Q8—228no—
786Q8—4416no—
787Q8—4416no—
788Q8—448no—
789D4—1132no—
790D4C2×Q8×D11116yescomplemented
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—114no—
799C2×C4—118no—
800C2×C4—1132no—
801C2×C4—114no—
802C2×C4—114no—
803C2×C4—112no—
804C2×C4—112no—
805C2×C4—1116no—
806C2×C4—114no—
807C2×C4—112no—
808C2×C4—114no—
809C2×C4—118no—
810C2×C4—114no—
811C2×C4—228no—
812C2×C4—2216no—
813C2×C4—222no—
814C2×C4—224no—
815C2×C4—224no—
816C2×C4—228no—
817C2×C4—224no—
818C2×C4—228no—
819C2×C4—4416no—
820C2×C4—4416no—
821C2×C4C2×Q8×D1114yes—
822C2×C4#6704314yes—
823C2×C4C24×D1114yes—
824C2×C4C24×D1114yes—
825C2×C4C24×D1112yes—
826C2×C4C24×D1118yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—114no—
834C22—222no—
835C22—222no—
836C22—228no—
837C22C22×Q8×D1118yes—
838C22C22×Q8×D1112yes—
839C22C2×#6704312yes—
840C22D11×H(5,𝔽2)12yes—
841C22C25×D1111yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—114no—
848C4—118no—
849C4—114no—
850C4—224no—
851C4—228no—
852C4—224no—
853C4—222no—
854C4—224no—
855C4C22×Q8×D1114yes—
856C4C2×#6704314yes—
857C2—28no—
858C2—224no—
859C2#1308243014yesdirect product factor
860C2C23×Q8×D1111yescharacteristic
861C2C2×D11×H(5,𝔽2)11yescharacteristic
862C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#554C2
socleC23×C11C25
prime radicalC22×#4341C22
hypercenterC2×#554D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13082430C2direct (N × H)
2. C2×Q8×Dic22C2semidirect
3. C2×#10623253C2semidirect
4. C2×#10623216C2semidirect
5. C2×#10623166C2semidirect
6. C2×#10623074C2semidirect
7. C2×#10623042C2semidirect
8. C2×D4×Dic22C2semidirect
9. C2×#10623163C2semidirect
10. C2×#10623220C2semidirect
11. C2×#10623154C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623153C2semidirect
14. C22×#66941C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
18. C2×C11×#554C2semidirect
22. C11×#554C22semidirect
45. D11×C4⋊Q8C22semidirect
46. #10623253C22semidirect
47. #10623220C22semidirect
48. #10623216C22semidirect
49. #10623166C22semidirect
50. #10623163C22semidirect
51. #10623154C22semidirect
52. #10623153C22semidirect
53. #10623109C22semidirect
54. Q8×Dic22C22semidirect
56. #10623074C22semidirect
57. D4×Dic22C22semidirect
59. #10623042C22semidirect
81. C2×#66941C22semidirect
112. C2×#4341Q8semidirect
241. C2×D4×C11C2×Q8semidirect
254. C2×C22⋊D11C2×Q8semidirect
258. C22×Dic11C2×Q8semidirect
271. #4341C2×Q8semidirect
275. C2×C4×D11C2×Q8semidirect
287. C2×Dic22C2×Q8semidirect
347. C2×#554D11semidirect
369. D4×C11C22×Q8semidirect
386. C22⋊D11C22×Q8semidirect
396. C2×Dic11C22×Q8semidirect
409. C4×D11C22×Q8semidirect
416. Dic22C22×Q8semidirect
426. #554C2×D11semidirect
660. C2×C11#3503semidirect
690. C2×D4Q8×D11semidirect
770. C11C2×#3503semidirect
790. D4C2×Q8×D11semidirect
859. C2#13082430direct (N × H)

Maximal subgroups

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

subgroupindex
#130824302
C2×Q8×Dic222
C2×#106232532
C2×#106232162
C2×#106231662
C2×#106230742
C2×#106230422
C2×D4×Dic222
C2×#106231632
C2×#106232202
C2×#106231542
C2×#106231092
C2×#106231532
C22×#669412
C2×D11×C4⋊Q82
C2×#106230772
C2×C4×#43412
C2×C11×#5542
C2×#350311