Finite Group Databasebeta

← C2×#13082495 #15662209

Subgroups — C2×#13082495 #15662209

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082495C2132yesmaximal, direct product factor
2C2×#10623216C212yesmaximal, complemented
3C2×#10623100C212yesmaximal, complemented
4C2×#10623172C212yesmaximal, complemented
5C2×#10623064C212yesmaximal, complemented
6C2×#10623112C212yesmaximal, complemented
7C2×#10623060C212yesmaximal, complemented
8C2×#10623225C212yesmaximal, complemented
9C2×#10623170C212yesmaximal, complemented
10C2×#10623156C212yesmaximal, complemented
11C2×#10623114C212yesmaximal, complemented
12C2×#10623159C212yesmaximal
13C2×#10623001C211yesmaximal, characteristic, complemented
14C2×#10623259C211yesmaximal, characteristic, complemented
15C2×#10623259C211yesmaximal, characteristic, complemented
16C2×#10623259C211yesmaximal, characteristic, complemented
17C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×#10623103C212yesmaximal, complemented
19C2×C4×#4339C211yesmaximal, characteristic
20C2×C11×#533C211yesmaximal, characteristic, complemented
21C22×Q8×D11C2212yes—
22C22×#4339C2211yescharacteristic
23C11×#533C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#125C2212yes—
27C2×C11×C22⋊Q8C2212yes—
28C2×C11×C22⋊Q8C2212yes—
29C2×C4×Q8×C11C2212yes—
30C2×C4×Q8×C11C2212yes—
31C2×C11×#117C2212yes—
32C22×C42×C11C2211yescharacteristic
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×Q8×Dic11C2212yes—
37C2×Q8×Dic11C2212yes—
38C2×Q8×Dic11C2212yes—
39C2×#66997C2212yes—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×C4×C22⋊D11C2211yescharacteristic
43C2×C4×C22⋊D11C2211yescharacteristic
44C2×#66979C2212yes—
45C2×#66979C2211yescharacteristic
46C2×#66977C2212yes—
47C2×#66977C2212yes—
48#10623259C22116yescomplemented
49#10623259C22116yescomplemented
50#10623259C22116yescomplemented
51D11×C4⋊Q8C22116yescomplemented
52#10623225C22132yescomplemented
53#10623216C22132yescomplemented
54#10623172C22132yescomplemented
55#10623170C22132yescomplemented
56#10623159C22132yes—
57#10623156C22132yescomplemented
58#10623114C22132yescomplemented
59#10623112C22132yescomplemented
60#10623103C22132yescomplemented
61#10623100C22132yescomplemented
62#10623064C22132yescomplemented
63#10623060C22132yescomplemented
64C2×#66951C2214yes—
65C2×#66950C2212yes—
66C2×#66950C2212yes—
67C2×#66950C2212yes—
68C2×#66947C2214yes—
69C2×#66945C2214yes—
70C2×#66945C2212yes—
71C2×#66945C2212yes—
72C2×#66945C2212yes—
73C2×C4⋊C4×D11C2212yes—
74C2×C4⋊C4×D11C2212yes—
75C2×#66943C2212yes—
76C2×#66943C2214yes—
77C2×#66943C2212yes—
78C2×#66943C2212yes—
79C2×#66942C2214yes—
80C2×#66942C2214yes—
81C2×#66941C2212yes—
82C2×#66941C2212yes—
83C2×#66941C2214yes—
84C2×#66940C2212yes—
85C2×#66940C2212yes—
86C2×#66940C2212yes—
87C2×#66940C2214yes—
88C2×#66938C2214yes—
89C2×#66936C2214yes—
90C2×#66932C2214yes—
91C2×#66932C2214yes—
92C2×#66929C2214yes—
93C4×#4339C22116yes—
94C2×C4×D44C2211yescharacteristic
95C2×C4×D44C2211yescharacteristic
96C2×#66925C2214yes—
97C2×#66925C2211yescharacteristic
98C2×#66925C2211yescharacteristic
99C2×C42×D11C2211yescharacteristic
100C2×C42×D11C2211yescharacteristic
101#10623001C22116yescomplemented
102C2×#66923C2214yes—
103C2×#66923C2212yes—
104C2×#66922C2211yescharacteristic
105C2×#66922C2211yescharacteristic
106C2×C4×Dic22C2212yes—
107C2×C4×Dic22C2214yes—
108C2×C4×Dic22C2212yes—
109C2×C4×Dic22C2211yescharacteristic
110C2×C4×Dic22C2211yescharacteristic
111C22×Q8×C11C2312yes—
112C22×Q8×C11C2312yes—
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C23×C4×C11C2311yescharacteristic
116C22×C22⋊D11C2311yescharacteristic
117C22×C22⋊D11C2311yescharacteristic
118C2×Q8×D11—216no—
119C2×Q8×D11C23116yes—
120C2×#4339—28no—
121C2×#4339C2318yes—
122C22×D44C2311yescharacteristic
123C22×C4×D11C2311yescharacteristic
124C22×C4×D11C2311yescharacteristic
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2314yes—
129C22×C4×D11C2311yescharacteristic
130C22×Dic22C2311yescharacteristic
131C22×Dic22C2312yes—
132C22×Dic22C2312yes—
133C22×Dic22C2314yes—
134C11×C4⋊Q8C2318yes—
135C11×C4⋊Q8C2318yes—
136C11×#125C23116yes—
137C11×C22⋊Q8C23116yes—
138C11×C22⋊Q8C23116yes—
139C4×Q8×C11C23116yes—
140C4×Q8×C11C23116yes—
141C11×#117C23116yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2314yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2314yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2314yes—
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2318yes—
155C2×C22⋊Dic11C2311yescharacteristic
156C2×C22⋊Dic11C2311yescharacteristic
157C2×C22⋊Dic11C2314yes—
158#66999C23116yes—
159#66999C23116yes—
160#66999C23116yes—
161Q8×Dic11C23116yes—
162Q8×Dic11C23116yes—
163Q8×Dic11C23116yes—
164#66997C23116yes—
165C4×C22⋊D11C2318yes—
166C4×C22⋊D11C2318yes—
167C4×C22⋊D11C2318yes—
168C4×C22⋊D11C2318yes—
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2311yescharacteristic
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yes—
176#66979C23116yes—
177#66979C2318yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2314yes—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2314yes—
186C2×C4⋊Dic11C2314yes—
187#66977C23116yes—
188#66977C23116yes—
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C2311yescharacteristic
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2311yescharacteristic
194C2×Dic11⋊C4C2311yescharacteristic
195C2×Dic11⋊C4C2314yes—
196C2×Dic11⋊C4C2314yes—
197C2×Dic11⋊C4C2314yes—
198C2×Dic11⋊C4C2314yes—
199C2×Dic11⋊C4C2314yes—
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2314yes—
206C2×C4×Dic11C2314yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2314yes—
210#66951C23132yes—
211#66950C23116yes—
212#66950C23116yes—
213#66950C23116yes—
214#66947C23132yes—
215#66945C23116yes—
216#66945C23116yes—
217#66945C23116yes—
218#66945C23132yes—
219C4⋊C4×D11C23116yes—
220C4⋊C4×D11C23116yes—
221#66943C23116yes—
222#66943C23116yes—
223#66943C23116yes—
224#66943C23132yes—
225#66942C23132yes—
226#66942C23132yes—
227#66941C23116yes—
228#66941C23116yes—
229#66941C23132yes—
230#66940C23116yes—
231#66940C23116yes—
232#66940C23116yes—
233#66940C23132yes—
234#66938C23132yes—
235#66936C23132yes—
236#66932C23132yes—
237#66932C23132yes—
238#66929C23132yes—
239C4×D44C2318yes—
240C4×D44C2318yes—
241#66925C2318yes—
242#66925C2318yes—
243#66925C23132yes—
244C42×D11C2318yes—
245C42×D11C2318yes—
246#66923C23116yes—
247#66923C23132yes—
248#66922C2318yes—
249#66922C2318yes—
250C4×Dic22C23116yes—
251C4×Dic22C23116yes—
252C4×Dic22C2318yes—
253C4×Dic22C2318yes—
254C4×Dic22C23132yes—
255C2×#3509—111nomaximal, Sylow
256C24×C11C2411yescharacteristic
257C23×D11C2411yescharacteristic
258C23×D11C2411yescharacteristic
259C2×Q8×C11—28no—
260C2×Q8×C11—28no—
261C2×Q8×C11C2418yes—
262C2×Q8×C11C2418yes—
263C22×C4×C11—24no—
264C22×C4×C11—24no—
265C22×C4×C11—24no—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2414yes—
268C22×C4×C11C2414yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2414yes—
272C22×C4×C11C2414yes—
273C22×C4×C11C2414yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11C2414yes—
280C2×C22⋊D11C2414yes—
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2414yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2414yes—
288C22×Dic11C2411yescharacteristic
289Q8×D11—264no—
290#4339—232no—
291C2×D44—24no—
292C2×D44C2414yes—
293C2×C4×D11—216no—
294C2×C4×D11—24no—
295C2×C4×D11—24no—
296C2×C4×D11—24no—
297C2×C4×D11—24no—
298C2×C4×D11—24no—
299C2×C4×D11#4118yes—
300C2×C4×D11C2414yes—
301C2×C4×D11C2414yes—
302C2×C4×D11C2414yes—
303C2×C4×D11C2414yes—
304C2×C4×D11C2414yes—
305C2×C4×D11C24116yes—
306C2×C4×D11C2414yes—
307C2×Dic22—24no—
308C2×Dic22—216no—
309C2×Dic22—28no—
310C2×Dic22—28no—
311C2×Dic22C2414yes—
312C2×Dic22C2418yes—
313C2×Dic22C2418yes—
314C2×Dic22C24116yes—
315C11×C4⋊C4C2418yes—
316C11×C4⋊C4C24116yes—
317C11×C4⋊C4C2418yes—
318C11×C4⋊C4C2418yes—
319C11×C4⋊C4C24116yes—
320C11×C4⋊C4C2418yes—
321C11×C22⋊C4C24116yes—
322C42×C11C2414yes—
323C42×C11C2414yes—
324C42×C11C2414yes—
325C42×C11C24116yes—
326C42×C11C2414yes—
327C22⋊Dic11C2414yes—
328C22⋊Dic11C2414yes—
329C22⋊Dic11C24116yes—
330(C2×D11)⋊C4C2414yes—
331(C2×D11)⋊C4C2414yes—
332(C2×D11)⋊C4C2414yes—
333(C2×D11)⋊C4C2414yes—
334(C2×D11)⋊C4C24116yes—
335(C2×D11)⋊C4C24116yes—
336(C2×D11)⋊C4C24116yes—
337C4⋊Dic11C2418yes—
338C4⋊Dic11C2418yes—
339C4⋊Dic11C2414yes—
340C4⋊Dic11C2414yes—
341C4⋊Dic11C24116yes—
342C4⋊Dic11C2418yes—
343C4⋊Dic11C2418yes—
344C4⋊Dic11C24116yes—
345C4⋊Dic11C24116yes—
346Dic11⋊C4C2414yes—
347Dic11⋊C4C24116yes—
348Dic11⋊C4C2414yes—
349Dic11⋊C4C24116yes—
350Dic11⋊C4C2414yes—
351Dic11⋊C4C2414yes—
352Dic11⋊C4C24116yes—
353Dic11⋊C4C24116yes—
354Dic11⋊C4C24116yes—
355Dic11⋊C4C24116yes—
356Dic11⋊C4C24116yes—
357C4×Dic11C24116yes—
358C4×Dic11C2414yes—
359C4×Dic11C2414yes—
360C4×Dic11C2414yes—
361C4×Dic11C2414yes—
362C4×Dic11C24116yes—
363C4×Dic11C24116yes—
364C4×Dic11C2414yes—
365C4×Dic11C2414yes—
366C4×Dic11C24116yes—
367#3509—1132no—
368C2×#557—112no—
369C2×#557—112no—
370C2×#556—112no—
371C2×#556—112no—
372C2×#552—112no—
373C2×#552—112no—
374C2×#552—112no—
375C2×#552—112no—
376C2×#541—112no—
377C2×#541—112no—
378C2×#536—112no—
379C2×#533—111no—
380C2×#533—111no—
381C2×#533—111no—
382C2×#533—111no—
383C2×#533D1111yescharacteristic, complemented
384C22×C4⋊Q8—111no—
385C2×#519—112no—
386C2×C4×#41—111no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11C2512yes—
391C23×C11C2511yescharacteristic
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11C2×#4114yes—
398C22×D11C2512yes—
399C22×D11C2512yes—
400Q8×C11—216no—
401Q8×C11—216no—
402C2×C4×C11—28no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—28no—
407C2×C4×C11—28no—
408C2×C4×C11—28no—
409C2×C4×C11—28no—
410C2×C4×C11C2×#4114yes—
411C2×C4×C112−1+414yes—
412C2×C4×C112−1+414yes—
413C2×C4×C11C2512yes—
414C2×C4×C11C2518yes—
415C2×C4×C11C2518yes—
416C2×C4×C11C2512yes—
417C2×C4×C11C2512yes—
418C2×C4×C11C2512yes—
419C2×C4×C11C2512yes—
420C2×C4×C11C2512yes—
421C22⋊D11—28no—
422C22⋊D11—28no—
423C2×Dic11—28no—
424C2×Dic11—22no—
425C2×Dic11—28no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11C2×#4114yes—
431C2×Dic11C2512yes—
432C2×Dic11C2512yes—
433C2×Dic11C2518yes—
434C2×Dic11C2512yes—
435C2×Dic11C2512yes—
436C2×Dic11C2512yes—
437C2×Dic11C2518yes—
438C2×Dic11C2512yes—
439D44—28no—
440C4×D11—232no—
441C4×D11—28no—
442C4×D11—28no—
443C4×D11—28no—
444C4×D11—28no—
445C4×D11—28no—
446C4×D11C2×#41116yes—
447Dic22—216no—
448Dic22—216no—
449Dic22—28no—
450Dic22—232no—
451C22×#41—111no—
452C23×Q8—112no—
453#557—1132no—
454#557—1132no—
455#556—1132no—
456#556—1132no—
457#552—1132no—
458#552—1132no—
459#552—1132no—
460#552—1132no—
461#541—1132no—
462#541—1132no—
463#536—1132no—
464#533—1116no—
465#533—1116no—
466#533—1116no—
467#533—1116no—
468#533C2×D11116yescomplemented
469C2×C4⋊Q8—112no—
470C2×C4⋊Q8—1116no—
471C2×C4⋊Q8—112no—
472C2×C4⋊Q8—112no—
473C2×C4⋊Q8—114no—
474C2×C4⋊Q8—111no—
475C2×C4⋊Q8—111no—
476C2×C4⋊Q8C2×D1111yescharacteristic
477C2×C4⋊Q8C2×D1111yescharacteristic
478C2×#126—114no—
479C2×#126—114no—
480C2×#126—114no—
481C2×#126—114no—
482C2×#125—114no—
483C2×#125—114no—
484C2×#125—112no—
485C2×#125—112no—
486C2×#125—112no—
487C2×#125—114no—
488C2×#125—112no—
489C2×#125—114no—
490C2×#125C2×D1112yes—
491C2×#124—114no—
492C2×#123—114no—
493C2×#123—114no—
494C2×C22⋊Q8—112no—
495C2×C22⋊Q8—112no—
496C2×C22⋊Q8—112no—
497C2×C22⋊Q8—112no—
498C2×C22⋊Q8—112no—
499C2×C22⋊Q8—112no—
500C2×C22⋊Q8—112no—
501C2×C22⋊Q8—112no—
502C2×C22⋊Q8C2×D1112yes—
503C2×C22⋊Q8C2×D1112yes—
504#519—1132no—
505C4×#41—1116no—
506C2×C4×Q8—112no—
507C2×C4×Q8—112no—
508C2×C4×Q8—112no—
509C2×C4×Q8—112no—
510C2×C4×Q8—114no—
511C2×C4×Q8—112no—
512C2×C4×Q8—112no—
513C2×C4×Q8—111no—
514C2×C4×Q8—111no—
515C2×C4×Q8—112no—
516C2×C4×Q8—114no—
517C2×C4×Q8—112no—
518C2×C4×Q8C2×D1112yes—
519C2×C4×Q8C2×D1112yes—
520C2×C4×D4—111no—
521C2×C4×D4—111no—
522C2×C4×D4—111no—
523C2×C4×D4—111no—
524C2×C4×D4—111no—
525C2×C4×D4—111no—
526C2×#117—111no—
527C2×#117—112no—
528C2×#117—112no—
529C2×#117—114no—
530C2×#117—112no—
531C2×#117—112no—
532C2×#117—111no—
533C2×#117—111no—
534C2×#117—114no—
535C2×#117C2×D1112yes—
536C22×C4⋊C4—112no—
537C22×C4⋊C4—112no—
538C22×C42—111no—
539C22×C42—111no—
540C22×C42C2×D1111yescharacteristic
541C22×C11—22no—
542C22×C11—22no—
543C22×C11—22no—
544C22×C11—44no—
545C22×C11C22×#4112yes—
546C22×C11C2×2−1+412yes—
547C22×C11C2×2−1+412yes—
548C22×C11C2611yescharacteristic
549C2×D11—22no—
550C2×D11—22no—
551C2×D11—28no—
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—22no—
555C2×D11—44no—
556C2×D11C22×#4114yes—
557C4×C11—22no—
558C4×C11—28no—
559C4×C11—22no—
560C4×C11—22no—
561C4×C11—28no—
562C4×C11C22×#4114yes—
563C4×C11C2×2−1+414yes—
564C4×C11C2×2−1+414yes—
565Dic11—28no—
566Dic11—22no—
567Dic11—28no—
568Dic11—22no—
569Dic11—22no—
570Dic11—22no—
571Dic11—22no—
572Dic11C22×#4114yes—
573C2×#41—118no—
574C2×#41—228no—
575C22×Q8—1116no—
576C22×Q8—112no—
577C22×Q8—112no—
578C22×Q8—114no—
579C22×Q8—111no—
580C22×Q8—2216no—
581C22×Q8C22×D1112yes—
582C22×Q8C22×D1112yes—
583C22×D4—111no—
584C22×D4—111no—
585C22×D4—111no—
586C23×C4—111no—
587C23×C4—114no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595C23×C4C22×D1111yescharacteristic
596C4⋊Q8—1116no—
597C4⋊Q8—1116no—
598C4⋊Q8—1116no—
599C4⋊Q8—1132no—
600C4⋊Q8—118no—
601C4⋊Q8—118no—
602C4⋊Q8C22×D1118yes—
603C4⋊Q8C22×D1118yes—
604#126—1132no—
605#126—1132no—
606#126—1132no—
607#126—1132no—
608#125—1116no—
609#125—1116no—
610#125—1116no—
611#125—1132no—
612#125—1132no—
613#125—1132no—
614#125—1116no—
615#125—1132no—
616#125C22×D11116yes—
617#124—1132no—
618#123—1132no—
619#123—1132no—
620C22⋊Q8—1116no—
621C22⋊Q8—1116no—
622C22⋊Q8—1116no—
623C22⋊Q8—1116no—
624C22⋊Q8—1116no—
625C22⋊Q8—1116no—
626C22⋊Q8—1116no—
627C22⋊Q8—1116no—
628C22⋊Q8C22×D11116yes—
629C22⋊Q8C22×D11116yes—
630C4×Q8—1116no—
631C4×Q8—1116no—
632C4×Q8—1116no—
633C4×Q8—1116no—
634C4×Q8—1132no—
635C4×Q8—1116no—
636C4×Q8—1116no—
637C4×Q8—118no—
638C4×Q8—118no—
639C4×Q8—1116no—
640C4×Q8—1132no—
641C4×Q8—1116no—
642C4×Q8C22×D11116yes—
643C4×Q8C22×D11116yes—
644C4×D4—118no—
645C4×D4—118no—
646C4×D4—118no—
647C4×D4—118no—
648C4×D4—118no—
649C4×D4—118no—
650#117—118no—
651#117—1116no—
652#117—1116no—
653#117—1132no—
654#117—1116no—
655#117—1116no—
656#117—118no—
657#117—118no—
658#117—1132no—
659#117C22×D11116yes—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—114no—
663C2×C4⋊C4—114no—
664C2×C4⋊C4—112no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—111no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—114no—
673C2×C4⋊C4—114no—
674C2×C4⋊C4—114no—
675C2×C4⋊C4—114no—
676C2×C4⋊C4—114no—
677C2×C4⋊C4—114no—
678C2×C4⋊C4—114no—
679C2×C4⋊C4—114no—
680C2×C4⋊C4—1116no—
681C2×C4⋊C4—1116no—
682C2×C4⋊C4C22×D1112yes—
683C2×C4⋊C4C22×D1112yes—
684C2×C4⋊C4C22×D1112yes—
685C2×C4⋊C4C22×D1112yes—
686C2×C4⋊C4C22×D1114yes—
687C2×C4⋊C4C22×D1114yes—
688C2×C22⋊C4—111no—
689C2×C22⋊C4—111no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—111no—
692C2×C22⋊C4—111no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—111no—
695C2×C22⋊C4—111no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4C22×D1114yes—
699C2×C42—111no—
700C2×C42—114no—
701C2×C42—114no—
702C2×C42—114no—
703C2×C42—111no—
704C2×C42—114no—
705C2×C42—111no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—118no—
710C2×C42—118no—
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1114yes—
713C2×C42C22×D1111yescharacteristic
714C2×C42C22×D1111yescharacteristic
715C2×C42C22×D1118yes—
716C2×C42C22×D1111yescharacteristic
717C2×C11—42no—
718C2×C11#350914yescomplemented
719C2×C11C23×#4111yescharacteristic
720C2×C11C22×2−1+411yescharacteristic
721C2×C11C22×2−1+411yescharacteristic
722D11—24no—
723D11—42no—
724C24—111no—
725C24—111no—
726C24C23×D1111yescharacteristic
727#41—2232no—
728C2×Q8—28no—
729C2×Q8—28no—
730C2×Q8—118no—
731C2×Q8—118no—
732C2×Q8—1116no—
733C2×Q8—114no—
734C2×Q8—2216no—
735C2×Q8—224no—
736C2×Q8—2264no—
737C2×Q8—228no—
738C2×Q8—228no—
739C2×Q8C23×D1118yes—
740C2×Q8C23×D1118yes—
741C2×D4—114no—
742C2×D4—114no—
743C2×D4—114no—
744C2×D4—224no—
745C2×D4—224no—
746C2×D4—224no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—111no—
751C22×C4—118no—
752C22×C4—114no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—114no—
756C22×C4—111no—
757C22×C4—111no—
758C22×C4—114no—
759C22×C4—111no—
760C22×C4—114no—
761C22×C4—114no—
762C22×C4—114no—
763C22×C4—114no—
764C22×C4—114no—
765C22×C4—1116no—
766C22×C4—2216no—
767C22×C4—224no—
768C22×C4—224no—
769C22×C4—224no—
770C22×C4—224no—
771C22×C4—224no—
772C22×C4C23×D1114yes—
773C22×C4C23×D1114yes—
774C22×C4C23×D1114yes—
775C22×C4C23×D1111yescharacteristic
776C22×C4C23×D1114yes—
777C22×C4C23×D1114yes—
778C22×C4C23×D1111yescharacteristic
779C22×C4C23×D1111yescharacteristic
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783C4⋊C4—118no—
784C4⋊C4—118no—
785C4⋊C4—1116no—
786C4⋊C4—1116no—
787C4⋊C4—118no—
788C4⋊C4—114no—
789C4⋊C4—114no—
790C4⋊C4—114no—
791C4⋊C4—114no—
792C4⋊C4—114no—
793C4⋊C4—114no—
794C4⋊C4—118no—
795C4⋊C4—1116no—
796C4⋊C4—1116no—
797C4⋊C4—1116no—
798C4⋊C4—1116no—
799C4⋊C4—1116no—
800C4⋊C4—1116no—
801C4⋊C4—1116no—
802C4⋊C4—1116no—
803C4⋊C4C23×D1118yes—
804C4⋊C4C23×D1118yes—
805C4⋊C4C23×D1118yes—
806C4⋊C4C23×D1118yes—
807C4⋊C4C23×D11116yes—
808C4⋊C4C23×D11116yes—
809C22⋊C4—114no—
810C22⋊C4—114no—
811C22⋊C4—1116no—
812C22⋊C4—114no—
813C22⋊C4—114no—
814C22⋊C4—1116no—
815C22⋊C4—114no—
816C22⋊C4—114no—
817C22⋊C4—1116no—
818C22⋊C4—1116no—
819C22⋊C4C23×D11116yes—
820C42—114no—
821C42—114no—
822C42—114no—
823C42—114no—
824C42—114no—
825C42—114no—
826C42—1116no—
827C42—1116no—
828C42—1116no—
829C42—1116no—
830C42C23×D1114yes—
831C42C23×D1114yes—
832C42C23×D1114yes—
833C42C23×D1114yes—
834C42C23×D11116yes—
835C11C2×#350911yescharacteristic, complemented, Sylow
836C23—22no—
837C23—22no—
838C23—22no—
839C23—114no—
840C23—112no—
841C23—112no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23C24×D1112yes—
848C23C24×D1111yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—2232no—
852Q8—228no—
853Q8—2216no—
854Q8—2216no—
855D4—228no—
856D4—228no—
857D4—228no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—22no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—114no—
867C2×C4—112no—
868C2×C4—1116no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—118no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—118no—
875C2×C4—112no—
876C2×C4—2232no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—228no—
880C2×C4—222no—
881C2×C4—228no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—228no—
885C2×C4—228no—
886C2×C4—228no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4#6704014yes—
890C2×C4#41×D1114yes—
891C2×C4#6704314yes—
892C2×C4C24×D1112yes—
893C2×C4C24×D1118yes—
894C2×C4C24×D1118yes—
895C2×C4C24×D1112yes—
896C2×C4C24×D1112yes—
897C2×C4C24×D1112yes—
898C2×C4C24×D1112yes—
899C2×C4C24×D1112yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—114no—
905C22—222no—
906C22—222no—
907C22—228no—
908C22—222no—
909C22—222no—
910C22—222no—
911C22—444no—
912C22C2×#6704012yes—
913C22C2×#41×D1112yes—
914C22C2×#6704312yes—
915C22C25×D1111yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—114no—
922C4—222no—
923C4—228no—
924C4—222no—
925C4—222no—
926C4—222no—
927C4—222no—
928C4—228no—
929C4C2×#6704014yes—
930C4C2×#41×D1114yes—
931C4C2×#6704314yes—
932C2—42no—
933C2—224no—
934C2—442no—
935C2#1308249514yesdirect product factor
936C2C22×#41×D1111yescharacteristic
937C2C22×#6704311yescharacteristic
938C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082495C2direct (N × H)
2. C2×#10623216C2semidirect
3. C2×#10623100C2semidirect
4. C2×#10623172C2semidirect
5. C2×#10623064C2semidirect
6. C2×#10623112C2semidirect
7. C2×#10623060C2semidirect
8. C2×#10623225C2semidirect
9. C2×#10623170C2semidirect
10. C2×#10623156C2semidirect
11. C2×#10623114C2semidirect
13. C2×#10623001C2semidirect
14. C2×#10623259C2semidirect
15. C2×#10623259C2semidirect
16. C2×#10623259C2semidirect
17. C2×D11×C4⋊Q8C2semidirect
18. C2×#10623103C2semidirect
20. C2×C11×#533C2semidirect
23. C11×#533C22semidirect
48. #10623259C22semidirect
49. #10623259C22semidirect
50. #10623259C22semidirect
51. D11×C4⋊Q8C22semidirect
52. #10623225C22semidirect
53. #10623216C22semidirect
54. #10623172C22semidirect
55. #10623170C22semidirect
57. #10623156C22semidirect
58. #10623114C22semidirect
59. #10623112C22semidirect
60. #10623103C22semidirect
61. #10623100C22semidirect
62. #10623064C22semidirect
63. #10623060C22semidirect
101. #10623001C22semidirect
383. C2×#533D11semidirect
468. #533C2×D11semidirect
718. C2×C11#3509semidirect
835. C11C2×#3509semidirect
935. C2#13082495direct (N × H)

Maximal subgroups

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

subgroupindex
#130824952
C2×#106232162
C2×#106231002
C2×#106231722
C2×#106230642
C2×#106231122
C2×#106230602
C2×#106232252
C2×#106231702
C2×#106231562
C2×#106231142
C2×#106231592
C2×#106230012
C2×#106232592
C2×D11×C4⋊Q82
C2×#106231032
C2×C4×#43392
C2×C11×#5332
C2×#350911