Finite Group Databasebeta

← C2×#13082528 #15662137

Subgroups — C2×#13082528 #15662137

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#13082528C2132yesmaximal, direct product factor
2C2×#10623099C212yesmaximal, complemented
3C2×#10623063C212yesmaximal, complemented
4C2×#10623221C212yesmaximal, complemented
5C2×#10623226C212yesmaximal, complemented
6C2×#10623061C212yesmaximal, complemented
7C2×#10623107C212yesmaximal, complemented
8C2×#10623164C212yesmaximal, complemented
9C2×#10623162C212yesmaximal, complemented
10C2×#10623174C212yesmaximal, complemented
11C2×#10623113C212yesmaximal, complemented
12C2×#10623160C212yesmaximal, complemented
13C2×#10623259C211yesmaximal, characteristic, complemented
14C2×#10623256C211yesmaximal, characteristic, complemented
15C2×#10623256C211yesmaximal, characteristic, complemented
16C2×#10623008C211yesmaximal, characteristic, complemented
17C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
18C2×#10623105C212yesmaximal, complemented
19C2×C4×#4339C211yesmaximal, characteristic, complemented
20C2×C11×#533C211yesmaximal, characteristic, complemented
21C22×#4343C2212yes—
22C22×#4343C2212yes—
23C22×Q8×D11C2212yes—
24C22×#4339C2211yescharacteristic
25C22×#4339C2212yes—
26C11×#533C22116yescomplemented
27C2×C11×C4⋊Q8C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×#125C2212yes—
30C2×C11×C22⋊Q8C2212yes—
31C2×C11×C22⋊Q8C2212yes—
32C2×C4×Q8×C11C2212yes—
33C2×C4×Q8×C11C2212yes—
34C2×C11×#117C2212yes—
35C22×C42×C11C2211yescharacteristic
36C2×#67000C2212yes—
37C2×#67000C2212yes—
38C2×#66999C2212yes—
39C2×Q8×Dic11C2212yes—
40C2×#66997C2212yes—
41C2×#66983C2212yes—
42C2×#66983C2212yes—
43C2×C4×C22⋊D11C2211yescharacteristic
44C2×C4×C22⋊D11C2211yescharacteristic
45C2×C4×C22⋊D11C2211yescharacteristic
46C2×C4×C22⋊D11C2211yescharacteristic
47C2×#66979C2211yescharacteristic
48#10623259C22116yescomplemented
49#10623256C22116yescomplemented
50#10623256C22116yescomplemented
51D11×C4⋊Q8C22116yescomplemented
52#10623226C22132yescomplemented
53#10623221C22132yescomplemented
54#10623174C22132yescomplemented
55#10623164C22132yescomplemented
56#10623162C22132yescomplemented
57#10623160C22132yescomplemented
58#10623113C22132yescomplemented
59#10623107C22132yescomplemented
60#10623105C22132yescomplemented
61#10623099C22132yescomplemented
62#10623063C22132yescomplemented
63#10623061C22132yescomplemented
64C2×#66951C2214yes—
65C2×#66950C2214yes—
66C2×#66950C2212yes—
67C2×#66949C2214yes—
68C2×#66949C2214yes—
69C2×#66948C2212yes—
70C2×#66948C2212yes—
71C2×#66948C2214yes—
72C2×#66948C2212yes—
73C2×#66948C2212yes—
74C2×#66947C2214yes—
75C2×#66946C2212yes—
76C2×#66946C2214yes—
77C2×#66946C2212yes—
78C2×#66946C2212yes—
79C2×#66946C2212yes—
80C2×#66945C2212yes—
81C2×C4⋊C4×D11C2212yes—
82C2×C4⋊C4×D11C2212yes—
83C2×C4⋊C4×D11C2214yes—
84C2×#66943C2212yes—
85C2×#66941C2212yes—
86C2×#66941C2212yes—
87C2×#66940C2212yes—
88C2×#66938C2214yes—
89C2×#66937C2214yes—
90C2×#66937C2214yes—
91C2×#66936C2214yes—
92C2×#66929C2214yes—
93#10623008C22116yescomplemented
94C2×#66928C2214yes—
95C2×#66928C2212yes—
96C2×#66927C2211yescharacteristic
97C4×#4339C22116yescomplemented
98C2×C4×D44C2214yes—
99C2×C4×D44C2211yescharacteristic
100C2×C4×D44C2212yes—
101C2×C4×D44C2212yes—
102C2×C4×D44C2211yescharacteristic
103C2×#66925C2214yes—
104C2×#66925C2211yescharacteristic
105C2×#66925C2211yescharacteristic
106C2×C42×D11C2211yescharacteristic
107C2×C42×D11C2211yescharacteristic
108C2×#66922C2211yescharacteristic
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
118C22×C22⋊D11C2314yes—
119C2×#4343—216no—
120C2×#4343—48no—
121C2×#4343C23116yes—
122C2×#4343C23116yes—
123C2×Q8×D11—48no—
124C2×Q8×D11C23116yes—
125C2×#4339—28no—
126C2×#4339—48no—
127C2×#4339C2318yes—
128C2×#4339C23116yes—
129C22×D44C2311yescharacteristic
130C22×D44C2312yes—
131C22×D44C2312yes—
132C22×D44C2314yes—
133C22×D44C2312yes—
134C22×D44C2314yes—
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2314yes—
141C22×C4×D11C2314yes—
142C22×C4×D11C2314yes—
143C22×C4×D11C2314yes—
144C22×C4×D11C2311yescharacteristic
145C22×Dic22C2311yescharacteristic
146C22×Dic22C2312yes—
147C22×Dic22C2314yes—
148C11×C4⋊Q8C2318yes—
149C11×C4⋊Q8C2318yes—
150C11×#125C23116yes—
151C11×C22⋊Q8C23116yes—
152C11×C22⋊Q8C23116yes—
153C4×Q8×C11C23116yes—
154C4×Q8×C11C23116yes—
155C11×#117C23116yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2314yes—
161C2×C11×C4⋊C4C2314yes—
162C2×C11×C22⋊C4C2314yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2314yes—
168C2×C42×C11C2318yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171#67000C23116yes—
172#67000C23116yes—
173#66999C23116yes—
174Q8×Dic11C23116yes—
175#66997C23116yes—
176#66983C23116yes—
177#66983C23116yes—
178C4×C22⋊D11C2318yes—
179C4×C22⋊D11C2318yes—
180C4×C22⋊D11C2318yes—
181C4×C22⋊D11C2318yes—
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2314yes—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2314yes—
188C2×(C2×D11)⋊C4C2314yes—
189C2×(C2×D11)⋊C4C2314yes—
190C2×(C2×D11)⋊C4C2314yes—
191C2×(C2×D11)⋊C4C2314yes—
192C2×(C2×D11)⋊C4C2314yes—
193#66979C2318yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2314yes—
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2314yes—
204C2×Dic11⋊C4C2314yes—
205C2×Dic11⋊C4C2314yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2314yes—
213#66951C23132yes—
214#66950C23116yes—
215#66950C23132yes—
216#66949C23132yes—
217#66949C23132yes—
218#66948C23116yes—
219#66948C23116yes—
220#66948C23116yes—
221#66948C23116yes—
222#66948C23132yes—
223#66947C23132yes—
224#66946C23116yes—
225#66946C23116yes—
226#66946C23116yes—
227#66946C23116yes—
228#66946C23132yes—
229#66945C23116yes—
230C4⋊C4×D11C23116yes—
231C4⋊C4×D11C23116yes—
232C4⋊C4×D11C23132yes—
233#66943C23116yes—
234#66941C23116yes—
235#66941C23116yes—
236#66940C23116yes—
237#66938C23132yes—
238#66937C23132yes—
239#66937C23132yes—
240#66936C23132yes—
241#66929C23132yes—
242#66928C23116yes—
243#66928C23132yes—
244#66927C2318yes—
245C4×D44C2318yes—
246C4×D44C2318yes—
247C4×D44C23116yes—
248C4×D44C23116yes—
249C4×D44C23132yes—
250#66925C2318yes—
251#66925C2318yes—
252#66925C23132yes—
253C42×D11C2318yes—
254C42×D11C2318yes—
255#66922C2318yes—
256C4×Dic22C2318yes—
257C4×Dic22C2318yes—
258C2×#3511—111nomaximal, Sylow
259C24×C11C2411yescharacteristic
260C23×D11C2414yes—
261C23×D11C2411yescharacteristic
262C23×D11C2411yescharacteristic
263C2×Q8×C11—28no—
264C2×Q8×C11—28no—
265C2×Q8×C11C2418yes—
266C2×Q8×C11C2418yes—
267C22×C4×C11—24no—
268C22×C4×C11—24no—
269C22×C4×C11—24no—
270C22×C4×C11C2414yes—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2414yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2414yes—
276C22×C4×C11C2414yes—
277C22×C4×C11C2414yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—48no—
284C2×C22⋊D11C2414yes—
285C2×C22⋊D11C2414yes—
286C2×C22⋊D11C24116yes—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2414yes—
293C22×Dic11C2411yescharacteristic
294#4343—264no—
295#4343—432no—
296Q8×D11—432no—
297#4339—232no—
298#4339—432no—
299C2×D44—24no—
300C2×D44—216no—
301C2×D44—28no—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—48no—
305C2×D44C2414yes—
306C2×D44C2418yes—
307C2×D44C2418yes—
308C2×D44C24116yes—
309C2×D44C2418yes—
310C2×D44C24116yes—
311C2×C4×D11—216no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—48no—
318C2×C4×D11—48no—
319C2×C4×D11—48no—
320C2×C4×D11#4118yescomplemented
321C2×C4×D11C2414yes—
322C2×C4×D11C2414yes—
323C2×C4×D11C2414yes—
324C2×C4×D11C2414yes—
325C2×C4×D11C2414yes—
326C2×C4×D11C24116yes—
327C2×C4×D11C24116yes—
328C2×C4×D11C24116yes—
329C2×C4×D11C24116yes—
330C2×C4×D11C2414yes—
331C2×Dic22—24no—
332C2×Dic22—28no—
333C2×Dic22—48no—
334C2×Dic22C2414yes—
335C2×Dic22C2418yes—
336C2×Dic22C24116yes—
337C11×C4⋊C4C2418yes—
338C11×C4⋊C4C2418yes—
339C11×C4⋊C4C2418yes—
340C11×C4⋊C4C2418yes—
341C11×C4⋊C4C24116yes—
342C11×C4⋊C4C24116yes—
343C11×C22⋊C4C24116yes—
344C42×C11C2414yes—
345C42×C11C2414yes—
346C42×C11C2414yes—
347C42×C11C2414yes—
348C42×C11C24116yes—
349C22⋊Dic11C2414yes—
350C22⋊Dic11C2414yes—
351(C2×D11)⋊C4C2414yes—
352(C2×D11)⋊C4C24116yes—
353(C2×D11)⋊C4C2414yes—
354(C2×D11)⋊C4C2414yes—
355(C2×D11)⋊C4C2414yes—
356(C2×D11)⋊C4C24116yes—
357(C2×D11)⋊C4C24116yes—
358(C2×D11)⋊C4C24116yes—
359(C2×D11)⋊C4C24116yes—
360(C2×D11)⋊C4C24116yes—
361(C2×D11)⋊C4C24116yes—
362C4⋊Dic11C2414yes—
363C4⋊Dic11C2414yes—
364C4⋊Dic11C2418yes—
365C4⋊Dic11C2418yes—
366C4⋊Dic11C24116yes—
367Dic11⋊C4C2414yes—
368Dic11⋊C4C2414yes—
369Dic11⋊C4C2414yes—
370Dic11⋊C4C2414yes—
371Dic11⋊C4C24116yes—
372Dic11⋊C4C24116yes—
373Dic11⋊C4C24116yes—
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×#533D1111yescharacteristic, complemented
395C2×#532—111no—
396C2×#532—111no—
397C2×#532—111no—
398C22×C4⋊Q8—111no—
399C2×#520—112no—
400C2×C4×#41—111no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11C2512yes—
405C23×C11C2511yescharacteristic
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—28no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—28no—
412C22×D11—22no—
413C22×D11—28no—
414C22×D11C2×#4114yes—
415C22×D11C2518yes—
416C22×D11C2512yes—
417C22×D11C2512yes—
418Q8×C11—216no—
419Q8×C11—216no—
420C2×C4×C11—22no—
421C2×C4×C11—28no—
422C2×C4×C11—28no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—28no—
426C2×C4×C11—28no—
427C2×C4×C11—28no—
428C2×C4×C11C2×#4114yes—
429C2×C4×C11H(5,𝔽2)14yes—
430C2×C4×C112−1+414yes—
431C2×C4×C11C2518yes—
432C2×C4×C11C2512yes—
433C2×C4×C11C2512yes—
434C2×C4×C11C2518yes—
435C2×C4×C11C2512yes—
436C2×C4×C11C2512yes—
437C2×C4×C11C2512yes—
438C2×C4×C11C2512yes—
439C22⋊D11—28no—
440C22⋊D11—28no—
441C22⋊D11—416no—
442C2×Dic11—22no—
443C2×Dic11—28no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11C2×#4114yes—
449C2×Dic11C2512yes—
450C2×Dic11C2512yes—
451C2×Dic11C2512yes—
452C2×Dic11C2512yes—
453C2×Dic11C2512yes—
454C2×Dic11C2518yes—
455C2×Dic11C2512yes—
456D44—28no—
457D44—232no—
458D44—216no—
459D44—216no—
460D44—216no—
461D44—416no—
462C4×D11—28no—
463C4×D11—28no—
464C4×D11—28no—
465C4×D11—28no—
466C4×D11—28no—
467C4×D11—232no—
468C4×D11—416no—
469C4×D11—416no—
470C4×D11—416no—
471C4×D11C2×#41116yescomplemented
472Dic22—216no—
473Dic22—28no—
474Dic22—416no—
475C22×#41—112no—
476C22×#41—112no—
477C22×#41—111no—
478C22×#41—112no—
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#533C2×D11116yescomplemented
493#532—1116no—
494#532—1116no—
495#532—1116no—
496C2×C4⋊Q8—112no—
497C2×C4⋊Q8—1116no—
498C2×C4⋊Q8—112no—
499C2×C4⋊Q8—112no—
500C2×C4⋊Q8—111no—
501C2×C4⋊Q8C2×D1111yescharacteristic
502C2×C4⋊Q8C2×D1111yescharacteristic
503C2×#127—111no—
504C2×#126—114no—
505C2×#126—114no—
506C2×#125—112no—
507C2×#125C2×D1112yes—
508C2×#124—112no—
509C2×#124—112no—
510C2×#124—114no—
511C2×#124—112no—
512C2×#124—114no—
513C2×#123—114no—
514C2×#123—114no—
515C2×C22⋊Q8—112no—
516C2×C22⋊Q8—114no—
517C2×C22⋊Q8—114no—
518C2×C22⋊Q8—112no—
519C2×C22⋊Q8—114no—
520C2×C22⋊Q8C2×D1112yes—
521C2×C22⋊Q8C2×D1112yes—
522C2×#121—112no—
523C2×#121—112no—
524C2×#121—112no—
525C2×#121—112no—
526C2×#121—112no—
527C2×#121—112no—
528C2×#121—114no—
529C2×#121—114no—
530C2×#121—114no—
531#520—1132no—
532C4×#41—1116no—
533C2×C4×Q8—112no—
534C2×C4×Q8—112no—
535C2×C4×Q8—111no—
536C2×C4×Q8—111no—
537C2×C4×Q8C2×D1112yes—
538C2×C4×Q8C2×D1112yes—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—111no—
542C2×C4×D4—111no—
543C2×C4×D4—112no—
544C2×C4×D4—114no—
545C2×C4×D4—112no—
546C2×C4×D4—112no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4—114no—
552C2×C4×D4—112no—
553C2×#117—111no—
554C2×#117—112no—
555C2×#117—111no—
556C2×#117—111no—
557C2×#117—114no—
558C2×#117C2×D1112yes—
559C22×C4⋊C4—112no—
560C22×C4⋊C4—114no—
561C22×C4⋊C4—112no—
562C22×C42—111no—
563C22×C42—111no—
564C22×C42C2×D1111yescharacteristic
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—44no—
569C22×C11C22×#4112yes—
570C22×C11C2×H(5,𝔽2)12yes—
571C22×C11C2×2−1+412yes—
572C22×C11C2611yescharacteristic
573C2×D11—22no—
574C2×D11—22no—
575C2×D11—28no—
576C2×D11—28no—
577C2×D11—22no—
578C2×D11—22no—
579C2×D11—28no—
580C2×D11—22no—
581C2×D11—28no—
582C2×D11—416no—
583C2×D11—44no—
584C2×D11C22×#4114yes—
585C4×C11—22no—
586C4×C11—28no—
587C4×C11—22no—
588C4×C11—28no—
589C4×C11—22no—
590C4×C11C22×#4114yes—
591C4×C11C2×H(5,𝔽2)14yes—
592C4×C11C2×2−1+414yes—
593Dic11—22no—
594Dic11—28no—
595Dic11—22no—
596Dic11—22no—
597Dic11—22no—
598Dic11—22no—
599Dic11C22×#4114yes—
600C2×#41—1116no—
601C2×#41—1116no—
602C2×#41—118no—
603C2×#41—1116no—
604C2×#41—228no—
605C2×#41—2216no—
606C2×#41—448no—
607C2×#41—448no—
608C22×Q8—1116no—
609C22×Q8—111no—
610C22×Q8—112no—
611C22×Q8—114no—
612C22×Q8—448no—
613C22×Q8C22×D1112yes—
614C22×Q8C22×D1112yes—
615C22×D4—111no—
616C22×D4—111no—
617C22×D4—114no—
618C22×D4—112no—
619C22×D4—114no—
620C22×D4—111no—
621C22×D4—112no—
622C22×D4—112no—
623C22×D4—114no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—114no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—114no—
632C23×C4—114no—
633C23×C4—114no—
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C4⋊Q8—1116no—
638C4⋊Q8—1116no—
639C4⋊Q8—1116no—
640C4⋊Q8—118no—
641C4⋊Q8C22×D1118yes—
642C4⋊Q8C22×D1118yes—
643#127—118no—
644#126—1132no—
645#126—1132no—
646#125—1116no—
647#125C22×D11116yes—
648#124—1116no—
649#124—1116no—
650#124—1132no—
651#124—1116no—
652#124—1132no—
653#123—1132no—
654#123—1132no—
655C22⋊Q8—1116no—
656C22⋊Q8—1116no—
657C22⋊Q8—1132no—
658C22⋊Q8—1132no—
659C22⋊Q8—1132no—
660C22⋊Q8C22×D11116yes—
661C22⋊Q8C22×D11116yes—
662#121—1116no—
663#121—1116no—
664#121—1116no—
665#121—1116no—
666#121—1116no—
667#121—1116no—
668#121—1132no—
669#121—1132no—
670#121—1132no—
671C4×Q8—1116no—
672C4×Q8—1116no—
673C4×Q8—118no—
674C4×Q8—118no—
675C4×Q8C22×D11116yes—
676C4×Q8C22×D11116yes—
677C4×D4—118no—
678C4×D4—118no—
679C4×D4—118no—
680C4×D4—118no—
681C4×D4—1116no—
682C4×D4—1132no—
683C4×D4—1116no—
684C4×D4—1116no—
685C4×D4—1116no—
686C4×D4—118no—
687C4×D4—118no—
688C4×D4—1116no—
689C4×D4—1132no—
690C4×D4—1116no—
691#117—118no—
692#117—1116no—
693#117—118no—
694#117—118no—
695#117—1132no—
696#117C22×D11116yes—
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—111no—
704C2×C4⋊C4—111no—
705C2×C4⋊C4—111no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—111no—
708C2×C4⋊C4—114no—
709C2×C4⋊C4—1116no—
710C2×C4⋊C4—1132no—
711C2×C4⋊C4—1116no—
712C2×C4⋊C4C22×D1112yes—
713C2×C4⋊C4C22×D1112yes—
714C2×C4⋊C4C22×D1114yes—
715C2×C4⋊C4C22×D1112yes—
716C2×C4⋊C4C22×D1112yes—
717C2×C4⋊C4C22×D1114yes—
718C2×C22⋊C4—111no—
719C2×C22⋊C4—111no—
720C2×C22⋊C4—111no—
721C2×C22⋊C4—111no—
722C2×C22⋊C4—114no—
723C2×C22⋊C4—114no—
724C2×C22⋊C4—111no—
725C2×C22⋊C4—111no—
726C2×C22⋊C4—114no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—114no—
729C2×C22⋊C4—114no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4C22×D1114yes—
732C2×C42—111no—
733C2×C42—114no—
734C2×C42—111no—
735C2×C42—111no—
736C2×C42—111no—
737C2×C42—111no—
738C2×C42—111no—
739C2×C42—118no—
740C2×C42—118no—
741C2×C42C22×D1111yescharacteristic
742C2×C42C22×D1114yes—
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1118yes—
746C2×C42C22×D1111yescharacteristic
747C2×C11—42no—
748C2×C11#351114yescomplemented
749C2×C11C23×#4111yescharacteristic
750C2×C11C22×H(5,𝔽2)11yescharacteristic
751C2×C11C22×2−1+411yescharacteristic
752D11—24no—
753D11—48no—
754D11—42no—
755C24—111no—
756C24—111no—
757C24—114no—
758C24C23×D1111yescharacteristic
759#41—2232no—
760#41—2264no—
761#41—4432no—
762#41—4432no—
763C2×Q8—28no—
764C2×Q8—28no—
765C2×Q8—114no—
766C2×Q8—118no—
767C2×Q8—1116no—
768C2×Q8—224no—
769C2×Q8—228no—
770C2×Q8—448no—
771C2×Q8—4432no—
772C2×Q8C23×D1118yes—
773C2×Q8C23×D1118yes—
774C2×D4—114no—
775C2×D4—114no—
776C2×D4—1116no—
777C2×D4—118no—
778C2×D4—1116no—
779C2×D4—114no—
780C2×D4—118no—
781C2×D4—118no—
782C2×D4—1116no—
783C2×D4—224no—
784C2×D4—2216no—
785C2×D4—224no—
786C2×D4—224no—
787C2×D4—228no—
788C2×D4—228no—
789C2×D4—228no—
790C2×D4—448no—
791C2×D4—448no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—111no—
796C22×C4—118no—
797C22×C4—114no—
798C22×C4—111no—
799C22×C4—111no—
800C22×C4—111no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—114no—
804C22×C4—114no—
805C22×C4—114no—
806C22×C4—114no—
807C22×C4—114no—
808C22×C4—114no—
809C22×C4—1116no—
810C22×C4—1116no—
811C22×C4—1116no—
812C22×C4—1116no—
813C22×C4—2216no—
814C22×C4—224no—
815C22×C4—224no—
816C22×C4—224no—
817C22×C4—224no—
818C22×C4—224no—
819C22×C4—448no—
820C22×C4—448no—
821C22×C4—448no—
822C22×C4C23×D1114yes—
823C22×C4C23×D1114yes—
824C22×C4C23×D1114yes—
825C22×C4C23×D1114yes—
826C22×C4C23×D1111yescharacteristic
827C22×C4C23×D1111yescharacteristic
828C22×C4C23×D1111yescharacteristic
829C22×C4C23×D1114yes—
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—114no—
840C4⋊C4—114no—
841C4⋊C4—114no—
842C4⋊C4—114no—
843C4⋊C4—114no—
844C4⋊C4—1116no—
845C4⋊C4C23×D1118yes—
846C4⋊C4C23×D1118yes—
847C4⋊C4C23×D11116yes—
848C4⋊C4C23×D1118yes—
849C4⋊C4C23×D1118yes—
850C4⋊C4C23×D11116yes—
851C22⋊C4—114no—
852C22⋊C4—114no—
853C22⋊C4—114no—
854C22⋊C4—114no—
855C22⋊C4—1116no—
856C22⋊C4—1116no—
857C22⋊C4—114no—
858C22⋊C4—114no—
859C22⋊C4—1116no—
860C22⋊C4—1116no—
861C22⋊C4—1116no—
862C22⋊C4—1116no—
863C22⋊C4—1116no—
864C22⋊C4C23×D11116yes—
865C42—114no—
866C42—114no—
867C42—114no—
868C42—114no—
869C42—114no—
870C42—114no—
871C42—1116no—
872C42C23×D1114yes—
873C42C23×D1114yes—
874C42C23×D1114yes—
875C42C23×D1114yes—
876C42C23×D11116yes—
877C11C2×#351111yescharacteristic, complemented, Sylow
878C23—22no—
879C23—22no—
880C23—22no—
881C23—114no—
882C23—112no—
883C23—112no—
884C23—118no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—228no—
889C23—228no—
890C23—222no—
891C23—222no—
892C23—228no—
893C23C24×D1112yes—
894C23C24×D1111yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—228no—
898Q8—2216no—
899Q8—4416no—
900D4—228no—
901D4—2232no—
902D4—228no—
903D4—228no—
904D4—2216no—
905D4—2216no—
906D4—2216no—
907D4—4416no—
908D4—4416no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—114no—
918C2×C4—112no—
919C2×C4—1116no—
920C2×C4—112no—
921C2×C4—112no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—112no—
925C2×C4—118no—
926C2×C4—2232no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—228no—
933C2×C4—228no—
934C2×C4—228no—
935C2×C4—228no—
936C2×C4—228no—
937C2×C4—228no—
938C2×C4—4416no—
939C2×C4—4416no—
940C2×C4—4416no—
941C2×C4#6704014yes—
942C2×C4#41×D1114yes—
943C2×C4#6704214yes—
944C2×C4C24×D1118yes—
945C2×C4C24×D1112yes—
946C2×C4C24×D1112yes—
947C2×C4C24×D1112yes—
948C2×C4C24×D1118yes—
949C2×C4C24×D1112yes—
950C2×C4C24×D1112yes—
951C2×C4C24×D1112yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—114no—
957C22—222no—
958C22—222no—
959C22—228no—
960C22—228no—
961C22—222no—
962C22—222no—
963C22—228no—
964C22—222no—
965C22—228no—
966C22—444no—
967C22—4416no—
968C22C2×#6704012yes—
969C22C2×#41×D1112yes—
970C22C2×#6704212yes—
971C22C25×D1111yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—114no—
978C4—222no—
979C4—222no—
980C4—222no—
981C4—228no—
982C4—222no—
983C4—222no—
984C4C2×#6704014yes—
985C4C2×#41×D1114yes—
986C4C2×#6704214yes—
987C2—42no—
988C2—224no—
989C2—442no—
990C2—448no—
991C2#1308252814yesdirect product factor
992C2C22×#41×D1111yescharacteristic
993C2C22×#6704211yescharacteristic
994C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
hypercenterC2×#533D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082528C2direct (N × H)
2. C2×#10623099C2semidirect
3. C2×#10623063C2semidirect
4. C2×#10623221C2semidirect
5. C2×#10623226C2semidirect
6. C2×#10623061C2semidirect
7. C2×#10623107C2semidirect
8. C2×#10623164C2semidirect
9. C2×#10623162C2semidirect
10. C2×#10623174C2semidirect
11. C2×#10623113C2semidirect
12. C2×#10623160C2semidirect
13. C2×#10623259C2semidirect
14. C2×#10623256C2semidirect
15. C2×#10623256C2semidirect
16. C2×#10623008C2semidirect
17. C2×D11×C4⋊Q8C2semidirect
18. C2×#10623105C2semidirect
19. C2×C4×#4339C2semidirect
20. C2×C11×#533C2semidirect
26. C11×#533C22semidirect
48. #10623259C22semidirect
49. #10623256C22semidirect
50. #10623256C22semidirect
51. D11×C4⋊Q8C22semidirect
52. #10623226C22semidirect
53. #10623221C22semidirect
54. #10623174C22semidirect
55. #10623164C22semidirect
56. #10623162C22semidirect
57. #10623160C22semidirect
58. #10623113C22semidirect
59. #10623107C22semidirect
60. #10623105C22semidirect
61. #10623099C22semidirect
62. #10623063C22semidirect
63. #10623061C22semidirect
93. #10623008C22semidirect
97. C4×#4339C22semidirect
320. C2×C4×D11#41semidirect
394. C2×#533D11semidirect
471. C4×D11C2×#41semidirect
492. #533C2×D11semidirect
748. C2×C11#3511semidirect
877. C11C2×#3511semidirect
991. C2#13082528direct (N × H)

Maximal subgroups

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

subgroupindex
#130825282
C2×#106230992
C2×#106230632
C2×#106232212
C2×#106232262
C2×#106230612
C2×#106231072
C2×#106231642
C2×#106231622
C2×#106231742
C2×#106231132
C2×#106231602
C2×#106232592
C2×#106232562
C2×#106230082
C2×D11×C4⋊Q82
C2×#106231052
C2×C4×#43392
C2×C11×#5332
C2×#351111