Finite Group Databasebeta

← C2×#13082362 #15662193

Subgroups — C2×#13082362 #15662193

Order 2816.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082362C2132yesmaximal, direct product factor
2C2×#10623172C212yesmaximal, complemented
3C2×#10623166C212yesmaximal, complemented
4C2×#10623173C212yesmaximal, complemented
5C2×#10623044C214yesmaximal, complemented
6C2×#10623170C212yesmaximal, complemented
7C2×#10623026C214yesmaximal, complemented
8C2×#10623031C211yesmaximal, characteristic, complemented
9C2×#10623174C212yesmaximal, complemented
10C2×#10623156C212yesmaximal, complemented
11C2×#10623347C211yesmaximal, characteristic, complemented
12C2×#10623153C212yesmaximal, complemented
13C2×#10623155C212yesmaximal, complemented
14C2×#10623322C211yesmaximal, characteristic
15C2×#10623035C211yesmaximal, characteristic, complemented
16C2×#10623343C211yesmaximal, characteristic, complemented
17C22×#66979C211yesmaximal, characteristic, complemented
18C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
19C23×Q8×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×C22⋊Q8C2212yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C22116yescomplemented
27C22×C11×C4⋊C4C2212yes—
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32#10623347C22116yescomplemented
33C2×#67000C2212yescomplemented
34C2×#66999C2212yescomplemented
35C2×#66999C2212yescomplemented
36#10623343C22116yescomplemented
37C2×Q8×Dic11C2212yescomplemented
38C2×Q8×Dic11C2212yescomplemented
39C2×Q8×Dic11C2212yescomplemented
40C2×Q8×Dic11C2212yescomplemented
41C2×#66997C2212yescomplemented
42#10623322C22116yes—
43C2×#66983C2211yescharacteristic
44C2×#66983C2211yescharacteristic
45C2×#66982C2214yes—
46C2×#66982C2212yes—
47C2×C4×C22⋊D11C2214yes—
48C2×C4×C22⋊D11C2212yes—
49C2×C4×C22⋊D11C2212yes—
50C2×#66979C2214yes—
51C2×#66979C2211yescharacteristic
52C2×#66979C2211yescharacteristic
53C2×#66979C2212yes—
54C2×#66979C2211yescharacteristic
55C2×#66979C2211yescharacteristic
56C2×#66979C2212yes—
57C2×#66979C2211yescharacteristic
58C2×#66979C22116yescomplemented
59C22×C4⋊Dic11C2211yescharacteristic
60C22×C4⋊Dic11C2211yescharacteristic
61C2×#66977C2214yes—
62C2×#66977C2211yescharacteristic
63C2×#66977C2211yescharacteristic
64C22×C4×Dic11C2212yes—
65#10623174C22132yescomplemented
66#10623173C22132yescomplemented
67#10623172C22132yescomplemented
68#10623170C22132yescomplemented
69#10623166C22132yescomplemented
70#10623156C22132yescomplemented
71#10623155C22132yescomplemented
72#10623153C22132yescomplemented
73#10623044C22164yescomplemented
74C2×#66951C2214yescomplemented
75C2×#66951C2214yescomplemented
76C2×#66950C2214yescomplemented
77#10623035C22116yescomplemented
78C2×#66946C2212yescomplemented
79C2×#66945C2214yescomplemented
80C2×#66945C2212yescomplemented
81C2×C4⋊C4×D11C2212yescomplemented
82#10623031C22116yescomplemented
83C2×#66943C2212yescomplemented
84C2×#66943C2214yescomplemented
85C2×#66943C2212yescomplemented
86C2×#66942C2214yescomplemented
87C2×#66942C2214yescomplemented
88C2×#66941C2212yescomplemented
89C2×#66941C2212yescomplemented
90C2×#66940C2214yescomplemented
91C2×#66940C2212yescomplemented
92#10623026C22164yescomplemented
93C2×#66939C2214yes—
94C2×#66938C2214yes—
95C2×#66936C2214yes—
96C2×(C22⋊D11)⋊C4C2214yes—
97C2×#66932C2214yes—
98C2×#66932C2214yes—
99C2×#66931C2214yes—
100C2×#66930C2214yes—
101C25×C11C2311yescharacteristic
102C22×Q8×C11—28no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2312yes—
105C22×Q8×C11C2318yes—
106C23×C4×C11—28no—
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2312yes—
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2318yes—
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C23×Dic11C2312yes—
120C23×Dic11C2312yes—
121C2×#4339—28no—
122C2×#4339C2318yes—
123C22×D44C2311yescharacteristic
124C22×C4×D11C2312yes—
125C22×C4×D11C2314yes—
126C22×Dic22C2311yescharacteristic
127C22×Dic22C2314yes—
128C11×C22⋊Q8C23116yes—
129C11×C22⋊Q8C23116yes—
130C11×C22⋊Q8C23116yes—
131C11×C22⋊Q8C23116yes—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2314yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C4⋊C4C2318yes—
137C2×C11×C4⋊C4C23116yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C23116yes—
141#67006C23116yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C23116yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150#67000C23116yescomplemented
151#66999C23116yescomplemented
152#66999C23116yescomplemented
153Q8×Dic11C23116yescomplemented
154Q8×Dic11C23116yescomplemented
155Q8×Dic11C23116yescomplemented
156Q8×Dic11C23116yescomplemented
157#66997C23116yescomplemented
158#66983C2318yes—
159#66983C2318yes—
160#66982C23132yes—
161#66982C23116yes—
162C4×C22⋊D11C23132yes—
163C4×C22⋊D11C23116yes—
164C4×C22⋊D11C23116yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170#66979C23132yes—
171#66979C2318yes—
172#66979C2318yes—
173#66979C2318yes—
174#66979C23116yes—
175#66979C23116yes—
176#66979C2318yes—
177#66979C2318yes—
178C2×C4⋊Dic11C2314yes—
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2314yes—
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2318yes—
190C2×C4⋊Dic11C2318yes—
191#66977C23132yes—
192#66977C2318yes—
193#66977C2318yes—
194C2×Dic11⋊C4C2314yes—
195C2×Dic11⋊C4C2314yes—
196C2×Dic11⋊C4C2314yes—
197C2×Dic11⋊C4C2314yes—
198C2×Dic11⋊C4C2314yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×C4×Dic11C2314yes—
202C2×C4×Dic11C2314yes—
203C2×C4×Dic11C2314yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C23116yes—
210#66951C23132yescomplemented
211#66951C23132yescomplemented
212#66950C23132yescomplemented
213#66946C23116yescomplemented
214#66945C23116yescomplemented
215#66945C23132yescomplemented
216C4⋊C4×D11C23116yescomplemented
217#66943C23116yescomplemented
218#66943C23116yescomplemented
219#66943C23132yescomplemented
220#66942C23132yescomplemented
221#66942C23132yescomplemented
222#66941C23116yescomplemented
223#66941C23116yescomplemented
224#66940C23116yescomplemented
225#66940C23132yescomplemented
226#66939C23132yes—
227#66938C23132yes—
228#66936C23132yes—
229(C22⋊D11)⋊C4C23132yes—
230#66932C23132yes—
231#66932C23132yes—
232#66931C23132yes—
233#66930C23132yes—
234C2×#3495—111nomaximal, Sylow
235C24×C11—24no—
236C24×C11—24no—
237C24×C11—42no—
238C24×C11C2411yescharacteristic
239C24×C11C2414yes—
240C24×C11C2411yescharacteristic
241C24×C11C2411yescharacteristic
242C23×D11C2412yes—
243C2×Q8×C11—28no—
244C2×Q8×C11—28no—
245C2×Q8×C11—232no—
246C2×Q8×C11C2418yes—
247C2×Q8×C11C2418yes—
248C22×C4×C11—24no—
249C22×C4×C11—28no—
250C22×C4×C11—24no—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—24no—
254C22×C4×C11—232no—
255C22×C4×C11—44no—
256C22×C4×C11#4118yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2414yes—
259C22×C4×C11C2414yes—
260C22×C4×C11C2414yes—
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2414yes—
263C22×C4×C11C2414yes—
264C22×C4×C11C2414yes—
265C22×C4×C11C2418yes—
266C22×C4×C11C2414yes—
267C22×C4×C11C2418yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2414yes—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11C2418yes—
275C2×C22⋊D11C2418yes—
276C2×C22⋊D11C2418yes—
277C22×Dic11—28no—
278C22×Dic11—44no—
279C22×Dic11C2418yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2418yes—
288#4339—232no—
289C2×D44—24no—
290C2×D44C2414yes—
291C2×C4×D11—28no—
292C2×C4×D11—48no—
293C2×C4×D11C2418yes—
294C2×C4×D11C24116yes—
295C2×Dic22—24no—
296C2×Dic22—48no—
297C2×Dic22C2414yes—
298C2×Dic22C24116yes—
299C11×C4⋊C4C2418yes—
300C11×C4⋊C4C24116yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C24116yes—
303C11×C22⋊C4C24116yes—
304C11×C22⋊C4C24116yes—
305C22⋊Dic11C2418yes—
306C22⋊Dic11C2418yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C2418yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C2418yes—
311C22⋊Dic11C2418yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C24116yes—
314(C2×D11)⋊C4C24116yes—
315(C2×D11)⋊C4C2418yes—
316(C2×D11)⋊C4C2418yes—
317C4⋊Dic11C24116yes—
318C4⋊Dic11C24116yes—
319C4⋊Dic11C24116yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C2414yes—
322C4⋊Dic11C2418yes—
323C4⋊Dic11C2418yes—
324C4⋊Dic11C2414yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C2414yes—
327C4⋊Dic11C2414yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C2418yes—
335C4×Dic11C24116yes—
336C4×Dic11C24116yes—
337C4×Dic11C24116yes—
338C4×Dic11C2418yes—
339C4×Dic11C2418yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342C4×Dic11C2418yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—112no—
347C2×#552—112no—
348C2×#552—114no—
349C2×#551—114no—
350C2×#544—111no—
351C2×#542—112no—
352C2×#541—112no—
353C2×#536—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#525—111no—
357C22×C22⋊Q8D1111yescharacteristic, complemented
358C2×#520—111no—
359C2×#519—111no—
360C22×#117—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—28no—
366C23×C11—22no—
367C23×C11—28no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—44no—
371C23×C11—416no—
372C23×C11C2×#4114yes—
373C23×C112−1+414yes—
374C23×C11C2512yes—
375C23×C11C2512yes—
376C23×C11C2512yes—
377C23×C11C2511yescharacteristic
378C22×D11—24no—
379C22×D11—24no—
380C22×D11—24no—
381C22×D11C2514yes—
382Q8×C11—216no—
383Q8×C11—216no—
384C2×C4×C11—28no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—216no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
391C2×C4×C11—28no—
392C2×C4×C11—28no—
393C2×C4×C11—28no—
394C2×C4×C11—48no—
395C2×C4×C11C2×#4114yes—
396C2×C4×C11C2×#4114yes—
397C2×C4×C11C2×#41116yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2518yes—
400C2×C4×C11C2518yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2512yes—
403C2×C4×C11C2512yes—
404C22⋊D11—216no—
405C22⋊D11—216no—
406C22⋊D11—48no—
407C2×Dic11—24no—
408C2×Dic11—216no—
409C2×Dic11—24no—
410C2×Dic11—24no—
411C2×Dic11—24no—
412C2×Dic11—24no—
413C2×Dic11—24no—
414C2×Dic11—24no—
415C2×Dic11—48no—
416C2×Dic11C2514yes—
417C2×Dic11C2514yes—
418C2×Dic11C2514yes—
419C2×Dic11C2514yes—
420C2×Dic11C2514yes—
421C2×Dic11C2514yes—
422C2×Dic11C2514yes—
423D44—28no—
424C4×D11—216no—
425C4×D11—416no—
426Dic22—28no—
427Dic22—416no—
428C22×#41—111no—
429C23×Q8C2×D1111yescharacteristic
430C24×C4C2×D1111yescharacteristic
431#556—1132no—
432#554—1132no—
433#552—1132no—
434#552—1132no—
435#552—1164no—
436#551—1164no—
437#544—1116no—
438#542—1132no—
439#541—1132no—
440#536—1116no—
441#533—1132no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—112no—
445#529—1132no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#125—114no—
451C2×#125—114no—
452C2×#125—112no—
453C2×#125—114no—
454C2×#125—112no—
455C2×#124—112no—
456C2×#124—114no—
457#525—1116no—
458C2×#123—112no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123—114no—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—111no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8—114no—
467C2×C22⋊Q8—114no—
468C2×C22⋊Q8—114no—
469C2×C22⋊Q8C2×D1112yes—
470C2×C22⋊Q8C2×D1112yes—
471C2×C22⋊Q8C2×D1112yes—
472C2×C22⋊Q8C2×D1112yes—
473C2×C22⋊Q8C2×D11116yescomplemented
474C2×#121—111no—
475C2×#121—111no—
476C2×#120—112no—
477#520—1116no—
478#519—1116no—
479C2×C4×Q8—112no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×Q8—114no—
485C2×C4×D4—114no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4—114no—
490C2×#117—111no—
491C2×#117—111no—
492C2×#117—112no—
493C2×#117—111no—
494C2×#117—112no—
495C2×#117—111no—
496C2×#117—111no—
497C2×#117—114no—
498C2×#117—1116no—
499C2×#117—112no—
500C2×#117—114no—
501C2×#117—114no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—112no—
505C22×C4⋊C4C2×D1111yescharacteristic
506C22×C4⋊C4C2×D1112yes—
507C22×C22⋊C4—112no—
508C22×C22⋊C4C2×D1112yes—
509C22×C42—112no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—28no—
515C22×C11—28no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—22no—
519C22×C11—416no—
520C22×C11—44no—
521C22×C11C22×#4114yes—
522C22×C11C22×#4112yes—
523C22×C11C2×2−1+414yes—
524C22×C11C2×2−1+412yes—
525C22×C11#58512yes—
526C22×C11C2611yescharacteristic
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—48no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—28no—
534C4×C11—28no—
535C4×C11C22×#4114yes—
536C4×C11C22×#4114yes—
537Dic11—24no—
538Dic11—24no—
539Dic11—24no—
540Dic11—24no—
541Dic11—24no—
542Dic11—24no—
543Dic11—24no—
544C25C22×D1111yescharacteristic
545C2×#41—118no—
546C2×#41—228no—
547C22×Q8—28no—
548C22×Q8—111no—
549C22×Q8—114no—
550C22×Q8C22×D1112yes—
551C22×Q8C22×D1112yes—
552C22×Q8C22×D1118yes—
553C22×D4—112no—
554C22×D4—112no—
555C22×D4—112no—
556C22×D4—111no—
557C23×C4—28no—
558C23×C4—112no—
559C23×C4—112no—
560C23×C4—112no—
561C23×C4—114no—
562C23×C4C22×D1112yes—
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1118yes—
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C4⋊Q8—1116no—
572C4⋊Q8—1116no—
573C4⋊Q8—1116no—
574#126—1132no—
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#125—1116no—
579#125—1132no—
580#125—1132no—
581#125—1132no—
582#125—1116no—
583#124—1116no—
584#124—1132no—
585#123—1116no—
586#123—1132no—
587#123—1132no—
588#123—1132no—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—118no—
592C22⋊Q8—118no—
593C22⋊Q8—1132no—
594C22⋊Q8—1132no—
595C22⋊Q8—1132no—
596C22⋊Q8C22×D11116yes—
597C22⋊Q8C22×D11116yes—
598C22⋊Q8C22×D11116yes—
599C22⋊Q8C22×D11116yes—
600#121—118no—
601#121—118no—
602#120—1116no—
603C4×Q8—1116no—
604C4×Q8—1116no—
605C4×Q8—1116no—
606C4×Q8—1116no—
607C4×Q8—1116no—
608C4×Q8—1132no—
609C4×D4—1132no—
610C4×D4—1116no—
611C4×D4—1116no—
612C4×D4—1116no—
613C4×D4—1132no—
614#117—118no—
615#117—118no—
616#117—1116no—
617#117—118no—
618#117—1116no—
619#117—118no—
620#117—118no—
621#117—1132no—
622#117—1116no—
623#117—1132no—
624#117—1132no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—118no—
632C2×C4⋊C4—118no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—1116no—
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1114yes—
648C2×C4⋊C4C22×D1112yes—
649C2×C4⋊C4C22×D1118yes—
650C2×C4⋊C4C22×D1114yes—
651C2×C4⋊C4C22×D11116yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—1116no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4C22×D1114yes—
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D11116yes—
668C2×C42—112no—
669C2×C42—112no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—114no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—1116no—
676C2×C42—112no—
677C2×C11—24no—
678C2×C11—24no—
679C2×C11—42no—
680C2×C11#349514yescomplemented
681C2×C11C23×#4111yescharacteristic
682C2×C11C22×2−1+411yescharacteristic
683C2×C11C2×#58511yescharacteristic
684D11—44no—
685C24—24no—
686C24—24no—
687C24—42no—
688C24—112no—
689C24C23×D1111yescharacteristic
690C24C23×D1114yes—
691C24C23×D1111yescharacteristic
692C24C23×D1111yescharacteristic
693#41—2232no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—232no—
697C2×Q8—114no—
698C2×Q8—1116no—
699C2×Q8—224no—
700C2×Q8—448no—
701C2×Q8C23×D1118yes—
702C2×Q8C23×D1118yes—
703C2×D4—118no—
704C2×D4—118no—
705C2×D4—118no—
706C2×D4—114no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—224no—
710C2×D4—444no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—232no—
718C22×C4—44no—
719C22×C4—118no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—118no—
728C22×C4—118no—
729C22×C4—1116no—
730C22×C4—228no—
731C22×C4—228no—
732C22×C4—448no—
733C22×C4—444no—
734C22×C4#434118yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1118yes—
737C22×C4C23×D1114yes—
738C22×C4C23×D1114yes—
739C22×C4C23×D1114yes—
740C22×C4C23×D1114yes—
741C22×C4C23×D1111yescharacteristic
742C22×C4C23×D1114yes—
743C22×C4C23×D1114yes—
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1118yes—
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—114no—
750C4⋊C4—114no—
751C4⋊C4—118no—
752C4⋊C4—114no—
753C4⋊C4—114no—
754C4⋊C4—118no—
755C4⋊C4—1116no—
756C4⋊C4—114no—
757C4⋊C4—114no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4—118no—
764C4⋊C4—118no—
765C4⋊C4—1116no—
766C4⋊C4—1116no—
767C4⋊C4C23×D1118yes—
768C4⋊C4C23×D11116yes—
769C4⋊C4C23×D1118yes—
770C4⋊C4C23×D11116yes—
771C22⋊C4—118no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—118no—
775C22⋊C4—118no—
776C22⋊C4—118no—
777C22⋊C4—118no—
778C22⋊C4—118no—
779C22⋊C4—1116no—
780C22⋊C4—1116no—
781C22⋊C4—118no—
782C22⋊C4—1116no—
783C22⋊C4C23×D11116yes—
784C22⋊C4C23×D11116yes—
785C42—118no—
786C42—118no—
787C42—118no—
788C42—118no—
789C42—1116no—
790C42—1116no—
791C42—1116no—
792C42—118no—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—28no—
801C23—22no—
802C23—22no—
803C23—44no—
804C23—416no—
805C23—114no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23C2×#434114yes—
810C23#6704014yes—
811C23C24×D1112yes—
812C23C24×D1112yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—228no—
818Q8—4416no—
819D4—2216no—
820D4—2216no—
821D4—228no—
822D4—448no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—216no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—48no—
834C2×C4—114no—
835C2×C4—114no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—224no—
842C2×C4—2216no—
843C2×C4—224no—
844C2×C4—224no—
845C2×C4—224no—
846C2×C4—224no—
847C2×C4—224no—
848C2×C4—224no—
849C2×C4—2216no—
850C2×C4—4416no—
851C2×C4—448no—
852C2×C4C2×#434114yes—
853C2×C4C2×#434114yes—
854C2×C4C2×#4341116yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1118yes—
857C2×C4C24×D1118yes—
858C2×C4C24×D1112yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—28no—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—224no—
873C22—224no—
874C22—224no—
875C22—448no—
876C22C22×#434114yes—
877C22C22×#434112yes—
878C22C2×#6704014yes—
879C22C2×#6704012yes—
880C22#1062345312yes—
881C22C25×D1111yescharacteristic
882C4—22no—
883C4—22no—
884C4—28no—
885C4—28no—
886C4—224no—
887C4—224no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4C22×#434114yes—
894C4C22×#434114yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—444no—
899C2#1308236214yesdirect product factor
900C2C23×#434111yescharacteristic
901C2C22×#6704011yescharacteristic
902C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13082362C2direct (N × H)
2. C2×#10623172C2semidirect
3. C2×#10623166C2semidirect
4. C2×#10623173C2semidirect
5. C2×#10623044C2semidirect
6. C2×#10623170C2semidirect
7. C2×#10623026C2semidirect
8. C2×#10623031C2semidirect
9. C2×#10623174C2semidirect
10. C2×#10623156C2semidirect
11. C2×#10623347C2semidirect
12. C2×#10623153C2semidirect
13. C2×#10623155C2semidirect
15. C2×#10623035C2semidirect
16. C2×#10623343C2semidirect
17. C22×#66979C2semidirect
18. C22×C11×C22⋊Q8C2semidirect
26. C2×C11×C22⋊Q8C22semidirect
32. #10623347C22semidirect
33. C2×#67000C22semidirect
34. C2×#66999C22semidirect
35. C2×#66999C22semidirect
36. #10623343C22semidirect
37. C2×Q8×Dic11C22semidirect
38. C2×Q8×Dic11C22semidirect
39. C2×Q8×Dic11C22semidirect
40. C2×Q8×Dic11C22semidirect
41. C2×#66997C22semidirect
58. C2×#66979C22semidirect
65. #10623174C22semidirect
66. #10623173C22semidirect
67. #10623172C22semidirect
68. #10623170C22semidirect
69. #10623166C22semidirect
70. #10623156C22semidirect
71. #10623155C22semidirect
72. #10623153C22semidirect
73. #10623044C22semidirect
74. C2×#66951C22semidirect
75. C2×#66951C22semidirect
76. C2×#66950C22semidirect
77. #10623035C22semidirect
78. C2×#66946C22semidirect
79. C2×#66945C22semidirect
80. C2×#66945C22semidirect
81. C2×C4⋊C4×D11C22semidirect
82. #10623031C22semidirect
83. C2×#66943C22semidirect
84. C2×#66943C22semidirect
85. C2×#66943C22semidirect
86. C2×#66942C22semidirect
87. C2×#66942C22semidirect
88. C2×#66941C22semidirect
89. C2×#66941C22semidirect
90. C2×#66940C22semidirect
91. C2×#66940C22semidirect
92. #10623026C22semidirect
150. #67000C23semidirect
151. #66999C23semidirect
152. #66999C23semidirect
153. Q8×Dic11C23semidirect
154. Q8×Dic11C23semidirect
155. Q8×Dic11C23semidirect
156. Q8×Dic11C23semidirect
157. #66997C23semidirect
210. #66951C23semidirect
211. #66951C23semidirect
212. #66950C23semidirect
213. #66946C23semidirect
214. #66945C23semidirect
215. #66945C23semidirect
216. C4⋊C4×D11C23semidirect
217. #66943C23semidirect
218. #66943C23semidirect
219. #66943C23semidirect
220. #66942C23semidirect
221. #66942C23semidirect
222. #66941C23semidirect
223. #66941C23semidirect
224. #66940C23semidirect
225. #66940C23semidirect
357. C22×C22⋊Q8D11semidirect
473. C2×C22⋊Q8C2×D11semidirect
680. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082362direct (N × H)

Maximal subgroups

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

subgroupindex
#130823622
C2×#106231722
C2×#106231662
C2×#106231732
C2×#106230442
C2×#106231702
C2×#106230262
C2×#106230312
C2×#106231742
C2×#106231562
C2×#106233472
C2×#106231532
C2×#106231552
C2×#106233222
C2×#106230352
C2×#106233432
C22×#669792
C22×C11×C22⋊Q82
C2×#349511