Finite Group Databasebeta

← C2×#13082517 #15662140

Subgroups — C2×#13082517 #15662140

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082517C2132yesmaximal, direct product factor
2C2×#10623202C212yesmaximal, complemented
3C2×#10623147C212yesmaximal, complemented
4C2×#10623070C212yesmaximal, complemented
5C2×#10623089C212yesmaximal, complemented
6C2×#10623145C212yesmaximal, complemented
7C2×#10623208C212yesmaximal, complemented
8C2×#10623362C212yesmaximal, complemented
9C2×#10623355C212yesmaximal, complemented
10C2×#10623134C212yesmaximal, complemented
11C2×#10623092C212yesmaximal, complemented
12C2×#10623139C212yesmaximal, complemented
13C2×#10623001C211yesmaximal, characteristic, complemented
14C2×#10623259C211yesmaximal, characteristic, complemented
15C2×#10623247C211yesmaximal, characteristic, complemented
16C2×#10623247C211yesmaximal, characteristic, complemented
17C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×#10623077C212yesmaximal, complemented
19C2×C4×#4339C211yesmaximal, characteristic, complemented
20C2×C11×#532C211yesmaximal, characteristic, complemented
21C22×C11×#41C2212yes—
22C22×Q8×D11C2212yes—
23C22×#4341C2212yes—
24C22×#4341C2212yes—
25C22×#4339C2211yescharacteristic
26C11×#532C22116yescomplemented
27C2×C11×C4⋊Q8C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C2×C11×#124C2212yes—
30C2×C11×#121C2212yes—
31C2×C11×#121C2212yes—
32C2×C4×D4×C11C2212yes—
33C2×C4×D4×C11C2212yes—
34C22×C42×C11C2211yescharacteristic
35#10623362C22132yescomplemented
36#10623355C22132yescomplemented
37C2×#66999C2212yes—
38C2×Q8×Dic11C2212yes—
39C2×#66997C2212yes—
40C2×#66992C2214yes—
41C2×#66991C2212yes—
42C2×#66991C2214yes—
43C2×#66991C2212yes—
44C2×#66991C2212yes—
45C2×#66991C2212yes—
46C2×#66989C2212yes—
47C2×#66989C2212yes—
48C2×#66989C2214yes—
49C2×#66988C2214yes—
50C2×D4×Dic11C2212yes—
51C2×D4×Dic11C2212yes—
52C2×D4×Dic11C2212yes—
53C2×D4×Dic11C2212yes—
54C2×#66982C2214yes—
55C2×C4×C22⋊D11C2211yescharacteristic
56C2×C4×C22⋊D11C2214yes—
57C2×C4×C22⋊D11C2211yescharacteristic
58C2×C4×C22⋊D11C2211yescharacteristic
59C2×C4×C22⋊D11C2211yescharacteristic
60C2×#66979C2212yes—
61C2×#66979C2211yescharacteristic
62C2×#66977C2214yes—
63C2×#66977C2212yes—
64C2×#66977C2212yes—
65C22×Dic11⋊C4C2214yes—
66#10623259C22116yescomplemented
67D11×C4⋊Q8C22116yescomplemented
68#10623247C22116yescomplemented
69#10623247C22116yescomplemented
70#10623208C22132yescomplemented
71#10623202C22132yescomplemented
72#10623147C22132yescomplemented
73#10623145C22132yescomplemented
74#10623139C22132yescomplemented
75#10623134C22132yescomplemented
76#10623092C22132yescomplemented
77#10623089C22132yescomplemented
78#10623077C22132yescomplemented
79#10623070C22132yescomplemented
80C2×#66950C2212yes—
81C2×#66945C2212yes—
82C2×C4⋊C4×D11C2212yes—
83C2×C4⋊C4×D11C2212yes—
84C2×#66943C2212yes—
85C2×#66941C2212yes—
86C2×#66941C2212yes—
87C2×#66940C2212yes—
88C2×#66938C2214yes—
89C2×#66937C2214yes—
90C2×(C22⋊D11)⋊C4C2214yes—
91C2×#66932C2214yes—
92C2×#66932C2214yes—
93C2×#66931C2214yes—
94C2×#66931C2214yes—
95C2×#66930C2214yes—
96C4×#4339C22116yescomplemented
97C2×C4×D44C2211yescharacteristic
98C2×C4×D44C2211yescharacteristic
99C2×#66925C2211yescharacteristic
100C2×#66925C2211yescharacteristic
101C2×C42×D11C2211yescharacteristic
102C2×C42×D11C2211yescharacteristic
103#10623001C22116yescomplemented
104C2×#66923C2212yes—
105C2×#66922C2211yescharacteristic
106C2×#66922C2211yescharacteristic
107C2×C4×Dic22C2211yescharacteristic
108C2×C4×Dic22C2211yescharacteristic
109C2×C4×Dic22C2212yes—
110C2×C4×Dic22C2212yes—
111C2×C11×#41—48no—
112C2×C11×#41C23116yes—
113C22×Q8×C11C2312yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2312yes—
116C22×D4×C11C2312yes—
117C22×D4×C11C2314yes—
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2314yes—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2311yescharacteristic
124C22×C22⋊D11C2311yescharacteristic
125C22×C22⋊D11C2314yes—
126C23×Dic11C2314yes—
127C23×Dic11C2314yes—
128C2×Q8×D11—48no—
129C2×Q8×D11C23116yes—
130C2×#4341—216no—
131C2×#4341—48no—
132C2×#4341C23116yes—
133C2×#4341C23116yes—
134C2×#4339—28no—
135C2×#4339C2318yes—
136C22×D44C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2314yes—
143C22×C4×D11C2311yescharacteristic
144C22×Dic22C2311yescharacteristic
145C22×Dic22C2312yes—
146C22×Dic22C2312yes—
147C22×Dic22C2314yes—
148C11×C4⋊Q8C2318yes—
149C11×#127C2318yes—
150C11×#124C23116yes—
151C11×#121C23116yes—
152C11×#121C23116yes—
153C4×D4×C11C23116yes—
154C4×D4×C11C23116yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2314yes—
158C2×C11×C22⋊C4C2314yes—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2318yes—
164C2×C22⋊Dic11C2314yes—
165C2×C22⋊Dic11C2314yes—
166C2×C22⋊Dic11C2314yes—
167C2×C22⋊Dic11C2314yes—
168C2×C22⋊Dic11C2314yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171#66999C23116yes—
172Q8×Dic11C23116yes—
173#66997C23116yes—
174#66992C23132yes—
175#66991C23116yes—
176#66991C23116yes—
177#66991C23116yes—
178#66991C23116yes—
179#66991C23132yes—
180#66989C23116yes—
181#66989C23116yes—
182#66989C23132yes—
183#66988C23132yes—
184D4×Dic11C23116yes—
185D4×Dic11C23116yes—
186D4×Dic11C23116yes—
187D4×Dic11C23116yes—
188#66982C23132yes—
189C4×C22⋊D11C2318yes—
190C4×C22⋊D11C2318yes—
191C4×C22⋊D11C2318yes—
192C4×C22⋊D11C2318yes—
193C4×C22⋊D11C23132yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2314yes—
199#66979C23116yes—
200#66979C2318yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2314yes—
208#66977C23116yes—
209#66977C23116yes—
210#66977C23132yes—
211C2×Dic11⋊C4C2314yes—
212C2×Dic11⋊C4C2314yes—
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2314yes—
218C2×Dic11⋊C4C2314yes—
219C2×Dic11⋊C4C2314yes—
220C2×Dic11⋊C4C23132yes—
221C2×C4×Dic11C2314yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2314yes—
229#66950C23116yes—
230#66945C23116yes—
231C4⋊C4×D11C23116yes—
232C4⋊C4×D11C23116yes—
233#66943C23116yes—
234#66941C23116yes—
235#66941C23116yes—
236#66940C23116yes—
237#66938C23132yes—
238#66937C23132yes—
239(C22⋊D11)⋊C4C23132yes—
240#66932C23132yes—
241#66932C23132yes—
242#66931C23132yes—
243#66931C23132yes—
244#66930C23132yes—
245C4×D44C2318yes—
246C4×D44C2318yes—
247#66925C2318yes—
248#66925C2318yes—
249C42×D11C2318yes—
250C42×D11C2318yes—
251#66923C23116yes—
252#66922C2318yes—
253#66922C2318yes—
254C4×Dic22C23116yes—
255C4×Dic22C23116yes—
256C4×Dic22C2318yes—
257C4×Dic22C2318yes—
258C2×#3511—111nomaximal, Sylow
259C24×C11C2411yescharacteristic
260C24×C11C2414yes—
261C23×D11C2411yescharacteristic
262C23×D11C2411yescharacteristic
263C11×#41—432no—
264C2×Q8×C11—28no—
265C2×Q8×C11C2418yes—
266C2×D4×C11—28no—
267C2×D4×C11—28no—
268C2×D4×C11—28no—
269C2×D4×C11—48no—
270C2×D4×C11C2418yes—
271C2×D4×C11C2418yes—
272C2×D4×C11C2418yes—
273C2×D4×C11C24116yes—
274C22×C4×C11—24no—
275C22×C4×C11—24no—
276C22×C4×C11—24no—
277C22×C4×C11—48no—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2414yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2414yes—
283C22×C4×C11C2414yes—
284C22×C4×C11C2414yes—
285C22×C4×C11C24116yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—24no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—216no—
292C2×C22⋊D11—48no—
293C2×C22⋊D11C24116yes—
294C2×C22⋊D11C2414yes—
295C2×C22⋊D11C2414yes—
296C2×C22⋊D11C24116yes—
297C22×Dic11—216no—
298C22×Dic11—48no—
299C22×Dic11C24116yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2414yes—
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2414yes—
307C22×Dic11C24116yes—
308C22×Dic11C2411yescharacteristic
309Q8×D11—432no—
310#4341—264no—
311#4341—432no—
312#4339—232no—
313C2×D44—24no—
314C2×D44C2414yes—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—48no—
321C2×C4×D11#4118yescomplemented
322C2×C4×D11C2414yes—
323C2×C4×D11C2414yes—
324C2×C4×D11C2414yes—
325C2×C4×D11C2414yes—
326C2×C4×D11C2414yes—
327C2×C4×D11C24116yes—
328C2×C4×D11C2414yes—
329C2×Dic22—24no—
330C2×Dic22—28no—
331C2×Dic22—28no—
332C2×Dic22—48no—
333C2×Dic22C2414yes—
334C2×Dic22C2418yes—
335C2×Dic22C2418yes—
336C2×Dic22C24116yes—
337C11×C4⋊C4C2418yes—
338C11×C4⋊C4C2418yes—
339C11×C22⋊C4C24116yes—
340C11×C22⋊C4C24116yes—
341C42×C11C2414yes—
342C42×C11C2414yes—
343C42×C11C2414yes—
344C42×C11C2414yes—
345C22⋊Dic11C24116yes—
346C22⋊Dic11C24116yes—
347C22⋊Dic11C24116yes—
348C22⋊Dic11C24116yes—
349C22⋊Dic11C24116yes—
350C22⋊Dic11C2414yes—
351C22⋊Dic11C2414yes—
352(C2×D11)⋊C4C2414yes—
353(C2×D11)⋊C4C2414yes—
354(C2×D11)⋊C4C2414yes—
355(C2×D11)⋊C4C2414yes—
356(C2×D11)⋊C4C24116yes—
357C4⋊Dic11C2418yes—
358C4⋊Dic11C2418yes—
359C4⋊Dic11C2414yes—
360C4⋊Dic11C2414yes—
361C4⋊Dic11C2418yes—
362C4⋊Dic11C2418yes—
363C4⋊Dic11C24116yes—
364Dic11⋊C4C24116yes—
365Dic11⋊C4C24116yes—
366Dic11⋊C4C2414yes—
367Dic11⋊C4C2414yes—
368Dic11⋊C4C2414yes—
369Dic11⋊C4C2414yes—
370Dic11⋊C4C24116yes—
371Dic11⋊C4C24116yes—
372Dic11⋊C4C24116yes—
373C4×Dic11C24116yes—
374C4×Dic11C2414yes—
375C4×Dic11C2414yes—
376C4×Dic11C2414yes—
377C4×Dic11C2414yes—
378C4×Dic11C2414yes—
379C4×Dic11C2414yes—
380C4×Dic11C24116yes—
381#3511—1132no—
382C2×#556—112no—
383C2×#555—112no—
384C2×#554—112no—
385C2×#553—112no—
386C2×#553—112no—
387C2×#548—112no—
388C2×#548—112no—
389C2×#547—112no—
390C2×#542—112no—
391C2×#542—112no—
392C2×#537—112no—
393C2×#533—111no—
394C2×#533—111no—
395C2×#532—111no—
396C2×#532—111no—
397C2×#532D1111yescharacteristic, complemented
398C22×C4⋊Q8—111no—
399C2×#520—112no—
400C2×C4×#41—111no—
401C23×C11—28no—
402C23×C11—22no—
403C23×C11—28no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—28no—
407C23×C11C2512yes—
408C23×C11C2518yes—
409C23×C11C2511yescharacteristic
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11C2×#4114yes—
416C22×D11C2512yes—
417C22×D11C2512yes—
418Q8×C11—216no—
419D4×C11—216no—
420D4×C11—216no—
421D4×C11—216no—
422D4×C11—416no—
423C2×C4×C11—22no—
424C2×C4×C11—28no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—28no—
428C2×C4×C11—28no—
429C2×C4×C11—28no—
430C2×C4×C11—416no—
431C2×C4×C11C2×#4114yes—
432C2×C4×C11H(5,𝔽2)14yes—
433C2×C4×C112−1+414yes—
434C2×C4×C11C2512yes—
435C2×C4×C11C2518yes—
436C2×C4×C11C2512yes—
437C2×C4×C11C2512yes—
438C2×C4×C11C2512yes—
439C2×C4×C11C2512yes—
440C2×C4×C11C2512yes—
441C22⋊D11—28no—
442C22⋊D11—232no—
443C22⋊D11—28no—
444C22⋊D11—416no—
445C2×Dic11—22no—
446C2×Dic11—28no—
447C2×Dic11—28no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—232no—
453C2×Dic11—416no—
454C2×Dic11C2×#4114yes—
455C2×Dic11C2512yes—
456C2×Dic11C2512yes—
457C2×Dic11C2512yes—
458C2×Dic11C2518yes—
459C2×Dic11C2512yes—
460C2×Dic11C2512yes—
461C2×Dic11C2518yes—
462C2×Dic11C2512yes—
463D44—28no—
464C4×D11—28no—
465C4×D11—28no—
466C4×D11—28no—
467C4×D11—28no—
468C4×D11—28no—
469C4×D11—416no—
470C4×D11C2×#41116yescomplemented
471Dic22—216no—
472Dic22—216no—
473Dic22—28no—
474Dic22—416no—
475C22×#41—112no—
476C22×#41—112no—
477C22×#41—111no—
478C22×#41C2×D1112yes—
479C23×Q8—112no—
480#556—1132no—
481#555—1132no—
482#554—1132no—
483#553—1132no—
484#553—1132no—
485#548—1132no—
486#548—1132no—
487#547—1132no—
488#542—1132no—
489#542—1132no—
490#537—1132no—
491#533—1116no—
492#533—1116no—
493#532—1116no—
494#532—1116no—
495#532C2×D11116yescomplemented
496C2×C4⋊Q8—112no—
497C2×C4⋊Q8—1116no—
498C2×C4⋊Q8—112no—
499C2×C4⋊Q8—112no—
500C2×C4⋊Q8—111no—
501C2×C4⋊Q8—111no—
502C2×C4⋊Q8C2×D1111yescharacteristic
503C2×#127C2×D1111yescharacteristic
504C2×#126—114no—
505C2×#126—114no—
506C2×#125—112no—
507C2×#125—112no—
508C2×#124—112no—
509C2×#124—112no—
510C2×#124—114no—
511C2×#124—114no—
512C2×#124C2×D1112yes—
513C2×#123—114no—
514C2×#123—114no—
515C2×C22⋊Q8—112no—
516C2×C22⋊Q8—112no—
517C2×C22⋊Q8—112no—
518C2×C22⋊Q8—114no—
519C2×C22⋊Q8—112no—
520C2×C22⋊Q8—114no—
521C2×C22⋊Q8—114no—
522C2×#121—112no—
523C2×#121—112no—
524C2×#121—112no—
525C2×#121—112no—
526C2×#121—114no—
527C2×#121—114no—
528C2×#121—114no—
529C2×#121C2×D1112yes—
530C2×#121C2×D1112yes—
531#520—1132no—
532C4×#41—1116no—
533C2×C4×Q8—112no—
534C2×C4×Q8—112no—
535C2×C4×Q8—111no—
536C2×C4×Q8—111no—
537C2×C4×Q8—112no—
538C2×C4×Q8—112no—
539C2×C4×D4—112no—
540C2×C4×D4—112no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4—111no—
544C2×C4×D4—111no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—114no—
548C2×C4×D4—114no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4C2×D1112yes—
552C2×C4×D4C2×D1112yes—
553C2×#117—111no—
554C2×#117—112no—
555C2×#117—112no—
556C2×#117—114no—
557C2×#117—111no—
558C2×#117—111no—
559C22×C4⋊C4—114no—
560C22×C4⋊C4—112no—
561C22×C4⋊C4—112no—
562C22×C42—111no—
563C22×C42—111no—
564C22×C42C2×D1111yescharacteristic
565C22×C11—22no—
566C22×C11—28no—
567C22×C11—22no—
568C22×C11—28no—
569C22×C11—22no—
570C22×C11—28no—
571C22×C11—416no—
572C22×C11—44no—
573C22×C11C22×#4112yes—
574C22×C11C2×H(5,𝔽2)12yes—
575C22×C11C2×2−1+412yes—
576C22×C11C2611yescharacteristic
577C2×D11—22no—
578C2×D11—22no—
579C2×D11—28no—
580C2×D11—22no—
581C2×D11—22no—
582C2×D11—22no—
583C2×D11—44no—
584C2×D11C22×#4114yes—
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—28no—
588C4×C11—22no—
589C4×C11C22×#4114yes—
590C4×C11C2×H(5,𝔽2)14yes—
591C4×C11C2×2−1+414yes—
592Dic11—22no—
593Dic11—28no—
594Dic11—28no—
595Dic11—22no—
596Dic11—22no—
597Dic11—22no—
598Dic11—22no—
599Dic11C22×#4114yes—
600C2×#41—48no—
601C2×#41—1116no—
602C2×#41—1116no—
603C2×#41—118no—
604C2×#41—228no—
605C2×#41—2216no—
606C2×#41—448no—
607C2×#41C22×D11116yes—
608C22×Q8—1116no—
609C22×Q8—111no—
610C22×Q8—112no—
611C22×Q8—112no—
612C22×Q8—114no—
613C22×Q8—448no—
614C22×Q8C22×D1112yes—
615C22×D4—111no—
616C22×D4—111no—
617C22×D4—114no—
618C22×D4—114no—
619C22×D4—111no—
620C22×D4C22×D1112yes—
621C22×D4C22×D1112yes—
622C22×D4C22×D1112yes—
623C22×D4C22×D1114yes—
624C23×C4—111no—
625C23×C4—114no—
626C23×C4—114no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—114no—
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1114yes—
637C4⋊Q8—1116no—
638C4⋊Q8—1116no—
639C4⋊Q8—1116no—
640C4⋊Q8—118no—
641C4⋊Q8—118no—
642C4⋊Q8C22×D1118yes—
643#127C22×D1118yes—
644#126—1132no—
645#126—1132no—
646#125—1116no—
647#125—1116no—
648#124—1116no—
649#124—1116no—
650#124—1132no—
651#124—1132no—
652#124C22×D11116yes—
653#123—1132no—
654#123—1132no—
655C22⋊Q8—1116no—
656C22⋊Q8—1116no—
657C22⋊Q8—1116no—
658C22⋊Q8—1132no—
659C22⋊Q8—1116no—
660C22⋊Q8—1132no—
661C22⋊Q8—1132no—
662#121—1116no—
663#121—1116no—
664#121—1116no—
665#121—1116no—
666#121—1132no—
667#121—1132no—
668#121—1132no—
669#121C22×D11116yes—
670#121C22×D11116yes—
671C4×Q8—1116no—
672C4×Q8—1116no—
673C4×Q8—118no—
674C4×Q8—118no—
675C4×Q8—1116no—
676C4×Q8—1116no—
677C4×D4—1116no—
678C4×D4—1116no—
679C4×D4—1116no—
680C4×D4—1116no—
681C4×D4—118no—
682C4×D4—118no—
683C4×D4—118no—
684C4×D4—118no—
685C4×D4—1132no—
686C4×D4—1132no—
687C4×D4—118no—
688C4×D4—118no—
689C4×D4C22×D11116yes—
690C4×D4C22×D11116yes—
691#117—118no—
692#117—1116no—
693#117—1116no—
694#117—1132no—
695#117—118no—
696#117—118no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—114no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—114no—
702C2×C4⋊C4—114no—
703C2×C4⋊C4—1132no—
704C2×C4⋊C4—114no—
705C2×C4⋊C4—111no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—111no—
708C2×C4⋊C4—111no—
709C2×C4⋊C4—111no—
710C2×C4⋊C4—111no—
711C2×C4⋊C4—112no—
712C2×C4⋊C4—114no—
713C2×C4⋊C4—114no—
714C2×C4⋊C4—1116no—
715C2×C4⋊C4—1116no—
716C2×C4⋊C4C22×D1112yes—
717C2×C4⋊C4C22×D1112yes—
718C2×C22⋊C4—114no—
719C2×C22⋊C4—111no—
720C2×C22⋊C4—111no—
721C2×C22⋊C4—114no—
722C2×C22⋊C4—114no—
723C2×C22⋊C4—114no—
724C2×C22⋊C4—114no—
725C2×C22⋊C4—111no—
726C2×C22⋊C4—111no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—114no—
730C2×C22⋊C4C22×D1114yes—
731C2×C22⋊C4C22×D1114yes—
732C2×C42—111no—
733C2×C42—114no—
734C2×C42—114no—
735C2×C42—111no—
736C2×C42—111no—
737C2×C42—111no—
738C2×C42—111no—
739C2×C42—111no—
740C2×C42—118no—
741C2×C42—118no—
742C2×C42C22×D1111yescharacteristic
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1118yes—
746C2×C42C22×D1111yescharacteristic
747C2×C11—42no—
748C2×C11—48no—
749C2×C11#351114yescomplemented
750C2×C11C23×#4111yescharacteristic
751C2×C11C22×H(5,𝔽2)11yescharacteristic
752C2×C11C22×2−1+411yescharacteristic
753D11—24no—
754D11—42no—
755C24—111no—
756C24—111no—
757C24C23×D1111yescharacteristic
758C24C23×D1114yes—
759#41—432no—
760#41—2232no—
761#41—2264no—
762#41—4432no—
763C2×Q8—28no—
764C2×Q8—114no—
765C2×Q8—118no—
766C2×Q8—118no—
767C2×Q8—1116no—
768C2×Q8—224no—
769C2×Q8—228no—
770C2×Q8—228no—
771C2×Q8—448no—
772C2×Q8—4432no—
773C2×Q8C23×D1118yes—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—48no—
778C2×D4—114no—
779C2×D4—114no—
780C2×D4—1116no—
781C2×D4—1116no—
782C2×D4—114no—
783C2×D4—224no—
784C2×D4—224no—
785C2×D4—224no—
786C2×D4—2216no—
787C2×D4—448no—
788C2×D4C23×D1118yes—
789C2×D4C23×D1118yes—
790C2×D4C23×D1118yes—
791C2×D4C23×D11116yes—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—48no—
796C22×C4—111no—
797C22×C4—118no—
798C22×C4—114no—
799C22×C4—1116no—
800C22×C4—111no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—114no—
804C22×C4—111no—
805C22×C4—111no—
806C22×C4—114no—
807C22×C4—1116no—
808C22×C4—114no—
809C22×C4—114no—
810C22×C4—114no—
811C22×C4—114no—
812C22×C4—114no—
813C22×C4—1116no—
814C22×C4—2216no—
815C22×C4—224no—
816C22×C4—224no—
817C22×C4—224no—
818C22×C4—224no—
819C22×C4—224no—
820C22×C4—448no—
821C22×C4—448no—
822C22×C4C23×D1114yes—
823C22×C4C23×D1114yes—
824C22×C4C23×D1114yes—
825C22×C4C23×D1111yescharacteristic
826C22×C4C23×D1114yes—
827C22×C4C23×D1111yescharacteristic
828C22×C4C23×D1111yescharacteristic
829C22×C4C23×D11116yes—
830C22×C4C23×D1111yescharacteristic
831C22×C4C23×D1111yescharacteristic
832C22×C4C23×D1111yescharacteristic
833C4⋊C4—114no—
834C4⋊C4—1116no—
835C4⋊C4—118no—
836C4⋊C4—118no—
837C4⋊C4—1116no—
838C4⋊C4—1116no—
839C4⋊C4—1116no—
840C4⋊C4—114no—
841C4⋊C4—118no—
842C4⋊C4—114no—
843C4⋊C4—114no—
844C4⋊C4—114no—
845C4⋊C4—114no—
846C4⋊C4—118no—
847C4⋊C4—1116no—
848C4⋊C4—1116no—
849C4⋊C4C23×D1118yes—
850C4⋊C4C23×D1118yes—
851C22⋊C4—1116no—
852C22⋊C4—114no—
853C22⋊C4—114no—
854C22⋊C4—1116no—
855C22⋊C4—1116no—
856C22⋊C4—1116no—
857C22⋊C4—1116no—
858C22⋊C4—114no—
859C22⋊C4—114no—
860C22⋊C4—114no—
861C22⋊C4—114no—
862C22⋊C4—1116no—
863C22⋊C4C23×D11116yes—
864C22⋊C4C23×D11116yes—
865C42—114no—
866C42—114no—
867C42—114no—
868C42—114no—
869C42—114no—
870C42—114no—
871C42—1116no—
872C42—1116no—
873C42C23×D1114yes—
874C42C23×D1114yes—
875C42C23×D1114yes—
876C42C23×D1114yes—
877C11C2×#351111yescharacteristic, complemented, Sylow
878C23—22no—
879C23—28no—
880C23—22no—
881C23—28no—
882C23—22no—
883C23—28no—
884C23—114no—
885C23—112no—
886C23—112no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23C24×D1112yes—
893C23C24×D1118yes—
894C23C24×D1111yescharacteristic
895Q8—216no—
896Q8—228no—
897Q8—2216no—
898Q8—2216no—
899Q8—4416no—
900D4—216no—
901D4—216no—
902D4—216no—
903D4—416no—
904D4—228no—
905D4—228no—
906D4—228no—
907D4—2232no—
908D4—4416no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—416no—
917C2×C4—114no—
918C2×C4—112no—
919C2×C4—1116no—
920C2×C4—112no—
921C2×C4—112no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—118no—
925C2×C4—112no—
926C2×C4—118no—
927C2×C4—2232no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—228no—
931C2×C4—228no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—228no—
936C2×C4—228no—
937C2×C4—228no—
938C2×C4—228no—
939C2×C4—228no—
940C2×C4—4416no—
941C2×C4—4416no—
942C2×C4#6703714yes—
943C2×C4#41×D1114yes—
944C2×C4#6704314yes—
945C2×C4C24×D1112yes—
946C2×C4C24×D1118yes—
947C2×C4C24×D1112yes—
948C2×C4C24×D1112yes—
949C2×C4C24×D1112yes—
950C2×C4C24×D1112yes—
951C2×C4C24×D1112yes—
952C22—22no—
953C22—28no—
954C22—22no—
955C22—28no—
956C22—22no—
957C22—28no—
958C22—44no—
959C22—416no—
960C22—114no—
961C22—222no—
962C22—222no—
963C22—228no—
964C22—222no—
965C22—222no—
966C22—222no—
967C22—444no—
968C22C2×#6703712yes—
969C22C2×#41×D1112yes—
970C22C2×#6704312yes—
971C22C25×D1111yescharacteristic
972C4—22no—
973C4—22no—
974C4—28no—
975C4—22no—
976C4—114no—
977C4—228no—
978C4—222no—
979C4—222no—
980C4—222no—
981C4—228no—
982C4—222no—
983C4—222no—
984C4C2×#6703714yes—
985C4C2×#41×D1114yes—
986C4C2×#6704314yes—
987C2—42no—
988C2—48no—
989C2—224no—
990C2—442no—
991C2#1308251714yesdirect product factor
992C2C22×#41×D1111yescharacteristic
993C2C22×#6703711yescharacteristic
994C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#532C2
socleC23×C11C25
hypercenterC2×#532D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13082517C2direct (N × H)
2. C2×#10623202C2semidirect
3. C2×#10623147C2semidirect
4. C2×#10623070C2semidirect
5. C2×#10623089C2semidirect
6. C2×#10623145C2semidirect
7. C2×#10623208C2semidirect
8. C2×#10623362C2semidirect
9. C2×#10623355C2semidirect
10. C2×#10623134C2semidirect
11. C2×#10623092C2semidirect
12. C2×#10623139C2semidirect
13. C2×#10623001C2semidirect
14. C2×#10623259C2semidirect
15. C2×#10623247C2semidirect
16. C2×#10623247C2semidirect
17. C2×D11×C4⋊Q8C2semidirect
18. C2×#10623077C2semidirect
19. C2×C4×#4339C2semidirect
20. C2×C11×#532C2semidirect
26. C11×#532C22semidirect
35. #10623362C22semidirect
36. #10623355C22semidirect
66. #10623259C22semidirect
67. D11×C4⋊Q8C22semidirect
68. #10623247C22semidirect
69. #10623247C22semidirect
70. #10623208C22semidirect
71. #10623202C22semidirect
72. #10623147C22semidirect
73. #10623145C22semidirect
74. #10623139C22semidirect
75. #10623134C22semidirect
76. #10623092C22semidirect
77. #10623089C22semidirect
78. #10623077C22semidirect
79. #10623070C22semidirect
96. C4×#4339C22semidirect
103. #10623001C22semidirect
321. C2×C4×D11#41semidirect
397. C2×#532D11semidirect
470. C4×D11C2×#41semidirect
495. #532C2×D11semidirect
749. C2×C11#3511semidirect
877. C11C2×#3511semidirect
991. C2#13082517direct (N × H)

Maximal subgroups

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

subgroupindex
#130825172
C2×#106232022
C2×#106231472
C2×#106230702
C2×#106230892
C2×#106231452
C2×#106232082
C2×#106233622
C2×#106233552
C2×#106231342
C2×#106230922
C2×#106231392
C2×#106230012
C2×#106232592
C2×#106232472
C2×D11×C4⋊Q82
C2×#106230772
C2×C4×#43392
C2×C11×#5322
C2×#351111