Finite Group Databasebeta

← C2×#13082209 #15660830

Subgroups — C2×#13082209 #15660830

Order 2816.

7802 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082209C2132yesmaximal, direct product factor
2C2×#10623116C211yesmaximal, characteristic, complemented
3C2×#10623090C212yesmaximal, complemented
4C2×#10623098C211yesmaximal, characteristic, complemented
5C2×#10623099C212yesmaximal, complemented
6C2×#10623073C211yesmaximal, characteristic, complemented
7C2×#10623071C214yesmaximal, complemented
8C2×#10623096C212yesmaximal, complemented
9C2×#10623084C211yesmaximal, characteristic, complemented
10C2×#10623083C212yesmaximal, complemented
11C2×#10623008C211yesmaximal, characteristic, complemented
12C2×#10623363C212yesmaximal, complemented
13C2×#10623010C212yesmaximal, complemented
14C2×#10623059C214yesmaximal, complemented
15C2×C4×#4339C212yesmaximal, complemented
16C2×#10623053C212yesmaximal, complemented
17C22×C4×Dic22C211yesmaximal, characteristic, complemented
18C2×C4×C11×#41C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C22×#4339C2212yes—
21C22×#4339C2212yes—
22C23×Dic22C2211yescharacteristic
23C4×C11×#41C22116yescomplemented
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2212yes—
31C2×C11×#117C2211yescharacteristic
32C22×C42×C11C2212yes—
33C22×C42×C11C2211yescharacteristic
34#10623363C22132yescomplemented
35C2×#67000C2212yes—
36C2×#66997C2212yes—
37C2×#66993C2212yes—
38C2×#66992C2214yes—
39C2×#66992C2214yes—
40C2×#66989C2212yes—
41C2×#66983C2212yes—
42C2×#66983C2212yes—
43C2×#66983C2212yes—
44C2×#66982C2214yes—
45C2×C4×C22⋊D11C2214yes—
46C2×C4×C22⋊D11C2214yes—
47C2×C4×C22⋊D11C2214yes—
48C2×#66979C2212yes—
49C22×C4⋊Dic11C2211yescharacteristic
50C2×#66977C2212yes—
51C22×Dic11⋊C4C2212yes—
52C22×C4×Dic11C2212yes—
53#10623116C22116yescomplemented
54#10623099C22132yescomplemented
55#10623098C22116yescomplemented
56#10623096C22132yescomplemented
57#10623090C22132yescomplemented
58#10623084C22116yescomplemented
59#10623083C22132yescomplemented
60#10623073C22116yescomplemented
61#10623071C22164yescomplemented
62#10623059C22164yescomplemented
63#10623053C22132yescomplemented
64C2×#66951C2214yes—
65C2×#66949C2214yes—
66C2×#66947C2214yes—
67C2×#66946C2212yes—
68C2×#66946C2212yes—
69C2×#66942C2214yes—
70C2×#66940C2212yes—
71C2×#66940C2212yes—
72C2×#66938C2214yes—
73C2×#66937C2214yes—
74C2×#66936C2214yes—
75C2×(C22⋊D11)⋊C4C2214yes—
76C2×(C22⋊D11)⋊C4C2214yes—
77C2×#66932C2214yes—
78#10623010C22132yescomplemented
79C2×#66929C2214yes—
80#10623008C22116yescomplemented
81C2×#66928C2212yes—
82C2×#66928C2212yes—
83C2×#66927C2211yescharacteristic
84C4×#4339C22132yescomplemented
85C2×C4×D44C2212yes—
86C2×C4×D44C2212yes—
87C2×C4×D44C2212yes—
88C2×#66925C2214yes—
89C2×#66925C2214yes—
90C2×C42×D11C2214yes—
91C2×#66923C2212yes—
92C2×#66922C2211yescharacteristic
93C2×C4×Dic22C2212yes—
94C2×C4×Dic22C2211yescharacteristic
95C2×C4×Dic22C2211yescharacteristic
96C2×C4×Dic22C2212yes—
97C2×C4×Dic22C2211yescharacteristic
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C22116yescomplemented
101C2×C11×#41—28no—
102C2×C11×#41C2318yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C23×C4×C11C2312yes—
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2312yes—
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yes—
115C23×Dic11C2312yes—
116C23×Dic11C2312yes—
117C2×#4339—216no—
118C2×#4339—216no—
119C2×#4339C23116yes—
120C2×#4339C23116yes—
121C22×D44C2312yes—
122C22×D44C2312yes—
123C22×D44C2312yes—
124C22×C4×D11C2314yes—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C22×Dic22—28no—
128C22×Dic22C2311yescharacteristic
129C22×Dic22C2312yes—
130C22×Dic22C2318yes—
131C22×Dic22C2312yes—
132C22×Dic22C2311yescharacteristic
133C4×Q8×C11C2318yes—
134C4×Q8×C11C2318yes—
135C4×D4×C11C23116yes—
136C4×D4×C11C2318yes—
137C4×D4×C11C23116yes—
138C4×D4×C11C2318yes—
139C11×#117C2318yes—
140C11×#117C23116yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2312yes—
153C2×C42×C11C2318yes—
154C2×C42×C11C2312yes—
155C2×C42×C11C2312yes—
156C2×C42×C11C23116yes—
157C2×C22⋊Dic11C2314yes—
158C2×C22⋊Dic11C2314yes—
159#67000C23116yes—
160#66997C23116yes—
161#66993C23116yes—
162#66992C23132yes—
163#66992C23132yes—
164#66989C23116yes—
165#66983C23116yes—
166#66983C23116yes—
167#66983C23116yes—
168#66982C23132yes—
169C4×C22⋊D11C23132yes—
170C4×C22⋊D11C23132yes—
171C4×C22⋊D11C23132yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yes—
176C2×(C2×D11)⋊C4C2314yes—
177C2×(C2×D11)⋊C4C2314yes—
178#66979C23116yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2318yes—
184C2×C4⋊Dic11C2312yes—
185#66977C23116yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C23116yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2314yes—
200C2×C4×Dic11C23116yes—
201C2×C4×Dic11C2314yes—
202#66951C23132yes—
203#66949C23132yes—
204#66947C23132yes—
205#66946C23116yes—
206#66946C23116yes—
207#66942C23132yes—
208#66940C23116yes—
209#66940C23116yes—
210#66938C23132yes—
211#66937C23132yes—
212#66936C23132yes—
213(C22⋊D11)⋊C4C23132yes—
214(C22⋊D11)⋊C4C23132yes—
215#66932C23132yes—
216#66929C23132yes—
217#66928C23116yes—
218#66928C23116yes—
219#66927C2318yes—
220C4×D44C23116yes—
221C4×D44C23116yes—
222C4×D44C23116yes—
223#66925C23132yes—
224#66925C23132yes—
225C42×D11C23132yes—
226#66923C23116yes—
227#66922C2318yes—
228C4×Dic22C2318yes—
229C4×Dic22C2318yes—
230C4×Dic22C23116yes—
231C4×Dic22C2318yes—
232C4×Dic22C2318yes—
233C4×Dic22C23116yes—
234C4×Dic22C23116yes—
235C2×#3480—111nomaximal, Sylow
236C24×C11C2412yes—
237C24×C11C2411yescharacteristic
238C23×D11C2414yes—
239C11×#41—232no—
240C2×Q8×C11—24no—
241C2×Q8×C11C2414yes—
242C2×D4×C11—28no—
243C2×D4×C11—24no—
244C2×D4×C11C2414yes—
245C2×D4×C11C2418yes—
246C22×C4×C11—24no—
247C22×C4×C11—28no—
248C22×C4×C11—28no—
249C22×C4×C11—44no—
250C22×C4×C11—42no—
251C22×C4×C11#4118yescomplemented
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2418yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2414yes—
260C22×C4×C11C2418yes—
261C22×C4×C11C2414yes—
262C22×C4×C11C2418yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2414yes—
267C2×C22⋊D11—216no—
268C2×C22⋊D11—216no—
269C2×C22⋊D11—48no—
270C2×C22⋊D11C24116yes—
271C2×C22⋊D11C24116yes—
272C2×C22⋊D11C24116yes—
273C22×Dic11—28no—
274C22×Dic11—44no—
275C22×Dic11C2418yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2414yes—
279C22×Dic11C2412yes—
280C22×Dic11C2418yes—
281C22×Dic11C2412yes—
282#4339—264no—
283#4339—264no—
284C2×D44—28no—
285C2×D44—28no—
286C2×D44—44no—
287C2×D44C2418yes—
288C2×D44C2418yes—
289C2×D44C2418yes—
290C2×C4×D11—216no—
291C2×C4×D11—216no—
292C2×C4×D11—48no—
293C2×C4×D11C24116yes—
294C2×C4×D11C24116yes—
295C2×C4×D11C24116yes—
296C2×Dic22—28no—
297C2×Dic22—232no—
298C2×Dic22—24no—
299C2×Dic22—28no—
300C2×Dic22#4118yescomplemented
301C2×Dic22C2414yes—
302C2×Dic22C2418yes—
303C2×Dic22C2418yes—
304C2×Dic22C2414yes—
305C11×C4⋊C4C2414yes—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C2418yes—
308C11×C4⋊C4C2418yes—
309C11×C22⋊C4C2418yes—
310C11×C22⋊C4C2418yes—
311C11×C22⋊C4C2418yes—
312C42×C11C2414yes—
313C42×C11C2414yes—
314C42×C11C2414yes—
315C42×C11C2414yes—
316C42×C11C2418yes—
317C42×C11C2418yes—
318C42×C11C2418yes—
319C22⋊Dic11C24116yes—
320C22⋊Dic11C24116yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C24116yes—
323(C2×D11)⋊C4C24116yes—
324(C2×D11)⋊C4C24116yes—
325(C2×D11)⋊C4C24116yes—
326(C2×D11)⋊C4C24116yes—
327C4⋊Dic11C2414yes—
328C4⋊Dic11C2414yes—
329C4⋊Dic11C2418yes—
330C4⋊Dic11C2418yes—
331C4⋊Dic11C2418yes—
332Dic11⋊C4C2418yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C2418yes—
335Dic11⋊C4C2418yes—
336Dic11⋊C4C24116yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C24116yes—
339Dic11⋊C4C24116yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342C4×Dic11C2418yes—
343C4×Dic11C2418yes—
344C4×Dic11C24116yes—
345C4×Dic11C24116yes—
346#3480—1132no—
347C2×#559—111no—
348C2×#559—112no—
349C2×#557—111no—
350C2×#556—112no—
351C2×#556—111no—
352C2×#553—112no—
353C2×#553—114no—
354C2×#550—111no—
355C2×#548—112no—
356C2×#532—111no—
357C2×#532—112no—
358C2×#529—112no—
359C2×#529—114no—
360C2×C4×#41—112no—
361C2×C4×#41—112no—
362C2×C4×#41D1111yescharacteristic, complemented
363C22×C4×Q8—111no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—24no—
367C23×C11—24no—
368C23×C11—24no—
369C23×C11C2×#4114yes—
370C23×C11C2514yes—
371C23×C11C2512yes—
372C23×C11C2511yescharacteristic
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—28no—
376C22×D11C2518yes—
377Q8×C11—28no—
378D4×C11—216no—
379D4×C11—28no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—24no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—28no—
387C2×C4×C11—216no—
388C2×C4×C11—216no—
389C2×C4×C11—48no—
390C2×C4×C11—44no—
391C2×C4×C11C2×#4114yes—
392C2×C4×C11C2×#4114yes—
393C2×C4×C11C2×#4114yes—
394C2×C4×C11C2×#41116yescomplemented
395C2×C4×C11C2514yes—
396C2×C4×C11C2514yes—
397C2×C4×C11C2512yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2514yes—
400C2×C4×C11C2512yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2512yes—
403C2×C4×C11C2512yes—
404C22⋊D11—232no—
405C22⋊D11—232no—
406C22⋊D11—416no—
407C2×Dic11—24no—
408C2×Dic11—28no—
409C2×Dic11—24no—
410C2×Dic11—24no—
411C2×Dic11—216no—
412C2×Dic11—48no—
413C2×Dic11C2×#4118yes—
414C2×Dic11C2514yes—
415C2×Dic11C2514yes—
416C2×Dic11C2518yes—
417C2×Dic11C2514yes—
418C2×Dic11C2514yes—
419D44—216no—
420D44—216no—
421D44—48no—
422C4×D11—232no—
423C4×D11—232no—
424C4×D11—416no—
425Dic22—28no—
426Dic22—216no—
427Dic22—216no—
428Dic22C2×#41116yescomplemented
429C22×#41—112no—
430C22×#41—112no—
431C22×#41C2×D1111yescharacteristic
432C23×Q8—111no—
433#559—1116no—
434#559—1132no—
435#557—1116no—
436#556—1132no—
437#556—1116no—
438#553—1164no—
439#553—1132no—
440#550—1116no—
441#548—1132no—
442#532—1132no—
443#532—1116no—
444C2×C4⋊Q8—112no—
445C2×C4⋊Q8—111no—
446C2×#127—112no—
447C2×#127—111no—
448#529—1164no—
449#529—1132no—
450C2×#126—114no—
451C2×#126—114no—
452C2×#126—114no—
453C2×#125—114no—
454C2×#125—112no—
455C2×#124—112no—
456C2×#124—112no—
457C2×#124—114no—
458C2×#124—112no—
459C2×#124—112no—
460C2×#123—114no—
461C2×#123—114no—
462C2×#123—114no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×#121—114no—
466C2×#121—114no—
467C2×#121—112no—
468C2×#121—112no—
469C2×#121—112no—
470C2×#121—114no—
471C4×#41—1132no—
472C4×#41—1132no—
473C4×#41C2×D11116yescomplemented
474C2×C4×Q8—112no—
475C2×C4×Q8—112no—
476C2×C4×Q8—111no—
477C2×C4×Q8—111no—
478C2×C4×Q8—112no—
479C2×C4×Q8—111no—
480C2×C4×Q8—111no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—1116no—
484C2×C4×Q8C2×D1111yescharacteristic
485C2×C4×Q8C2×D1111yescharacteristic
486C2×C4×D4—114no—
487C2×C4×D4—114no—
488C2×C4×D4—114no—
489C2×C4×D4—112no—
490C2×C4×D4—112no—
491C2×C4×D4—114no—
492C2×C4×D4—114no—
493C2×C4×D4—112no—
494C2×C4×D4—112no—
495C2×C4×D4—112no—
496C2×C4×D4C2×D1112yes—
497C2×C4×D4C2×D1111yescharacteristic
498C2×C4×D4C2×D1112yes—
499C2×C4×D4C2×D1111yescharacteristic
500C2×#117—112no—
501C2×#117—114no—
502C2×#117—114no—
503C2×#117C2×D1111yescharacteristic
504C2×#117C2×D1112yes—
505C22×C4⋊C4—112no—
506C22×C4⋊C4—111no—
507C22×C42—112no—
508C22×C42—114no—
509C22×C42C2×D1111yescharacteristic
510C22×C42C2×D1112yes—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—28no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—48no—
518C22×C11C22×#4114yes—
519C22×C11C22×#4112yes—
520C22×C11C22×#4112yes—
521C22×C11#58512yes—
522C22×C11C2611yescharacteristic
523C2×D11—28no—
524C2×D11—28no—
525C2×D11—28no—
526C2×D11—416no—
527C4×C11—24no—
528C4×C11—22no—
529C4×C11—24no—
530C4×C11—22no—
531C4×C11—24no—
532C4×C11—22no—
533C4×C11C22×#4114yes—
534C4×C11C22×#4114yes—
535C4×C11C22×#4114yes—
536Dic11—24no—
537Dic11—28no—
538Dic11—24no—
539Dic11—24no—
540Dic11C22×#4118yes—
541C2×#41—28no—
542C2×#41—1116no—
543C2×#41—1116no—
544C2×#41—2216no—
545C2×#41—2216no—
546C2×#41C22×D1118yes—
547C22×Q8—111no—
548C22×Q8—112no—
549C22×Q8—111no—
550C22×Q8—112no—
551C22×Q8—118no—
552C22×Q8—228no—
553C22×Q8C22×D1111yescharacteristic
554C22×D4—114no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—112no—
558C22×D4—112no—
559C22×D4—112no—
560C22×D4C22×D1112yes—
561C22×D4C22×D1111yescharacteristic
562C23×C4—112no—
563C23×C4—112no—
564C23×C4—114no—
565C23×C4—114no—
566C23×C4—114no—
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1112yes—
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1112yes—
572C23×C4C22×D1111yescharacteristic
573C4⋊Q8—1116no—
574C4⋊Q8—118no—
575#127—1116no—
576#127—118no—
577#126—1132no—
578#126—1132no—
579#126—1132no—
580#125—1132no—
581#125—1116no—
582#124—1116no—
583#124—1116no—
584#124—1132no—
585#124—1116no—
586#124—1116no—
587#123—1132no—
588#123—1132no—
589#123—1132no—
590C22⋊Q8—1116no—
591C22⋊Q8—1132no—
592#121—1132no—
593#121—1132no—
594#121—1116no—
595#121—1116no—
596#121—1116no—
597#121—1132no—
598C4×Q8—1116no—
599C4×Q8—1116no—
600C4×Q8—118no—
601C4×Q8—1116no—
602C4×Q8—118no—
603C4×Q8—118no—
604C4×Q8—118no—
605C4×Q8—1116no—
606C4×Q8—1116no—
607C4×Q8C22×D1118yes—
608C4×Q8C22×D1118yes—
609C4×D4—1132no—
610C4×D4—1132no—
611C4×D4—1132no—
612C4×D4—1116no—
613C4×D4—1116no—
614C4×D4—1132no—
615C4×D4—1132no—
616C4×D4—1116no—
617C4×D4—1116no—
618C4×D4—1116no—
619C4×D4C22×D11116yes—
620C4×D4C22×D1118yes—
621C4×D4C22×D11116yes—
622C4×D4C22×D1118yes—
623#117—1116no—
624#117—1132no—
625#117—1132no—
626#117C22×D1118yes—
627#117C22×D11116yes—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—1116no—
636C2×C4⋊C4—118no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C4⋊C4C22×D1112yes—
646C2×C4⋊C4C22×D1112yes—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4C22×D1112yes—
656C2×C22⋊C4C22×D1112yes—
657C2×C22⋊C4C22×D1112yes—
658C2×C42—114no—
659C2×C42—114no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42—1116no—
663C2×C42—112no—
664C2×C42—112no—
665C2×C42—1132no—
666C2×C42C22×D1112yes—
667C2×C42C22×D1112yes—
668C2×C42C22×D1111yescharacteristic
669C2×C42C22×D1111yescharacteristic
670C2×C42C22×D1118yes—
671C2×C42C22×D11116yes—
672C2×C42C22×D1112yes—
673C2×C42C22×D1111yescharacteristic
674C2×C42C22×D1111yescharacteristic
675C2×C11—24no—
676C2×C11—44no—
677C2×C11#348014yescomplemented
678C2×C11C23×#4111yescharacteristic
679C2×C11C23×#4111yescharacteristic
680C2×C11C2×#58511yescharacteristic
681D11—48no—
682C24—114no—
683C24C23×D1112yes—
684C24C23×D1111yescharacteristic
685#41—232no—
686#41—2264no—
687#41—2264no—
688C2×Q8—24no—
689C2×Q8—118no—
690C2×Q8—114no—
691C2×Q8—118no—
692C2×Q8—114no—
693C2×Q8—118no—
694C2×Q8—228no—
695C2×Q8—2232no—
696C2×Q8—228no—
697C2×Q8—224no—
698C2×Q8C23×D1114yes—
699C2×D4—28no—
700C2×D4—24no—
701C2×D4—1116no—
702C2×D4—1116no—
703C2×D4—1116no—
704C2×D4—118no—
705C2×D4—118no—
706C2×D4—118no—
707C2×D4—2216no—
708C2×D4—2216no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—444no—
712C2×D4—448no—
713C2×D4C23×D1118yes—
714C2×D4C23×D1114yes—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—44no—
719C22×C4—42no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—114no—
724C22×C4—112no—
725C22×C4—118no—
726C22×C4—118no—
727C22×C4—1116no—
728C22×C4—1116no—
729C22×C4—1116no—
730C22×C4—2216no—
731C22×C4—228no—
732C22×C4—2216no—
733C22×C4—448no—
734C22×C4—444no—
735C22×C4#433918yescomplemented
736C22×C4C23×D1112yes—
737C22×C4C23×D1112yes—
738C22×C4C23×D1111yescharacteristic
739C22×C4C23×D1111yescharacteristic
740C22×C4C23×D1112yes—
741C22×C4C23×D1111yescharacteristic
742C22×C4C23×D1114yes—
743C22×C4C23×D1118yes—
744C22×C4C23×D1118yes—
745C22×C4C23×D1114yes—
746C22×C4C23×D1118yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1114yes—
749C22×C4C23×D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751C4⋊C4—118no—
752C4⋊C4—114no—
753C4⋊C4—118no—
754C4⋊C4—114no—
755C4⋊C4—118no—
756C4⋊C4—118no—
757C4⋊C4—118no—
758C4⋊C4—1116no—
759C4⋊C4—118no—
760C4⋊C4—1116no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4—118no—
764C4⋊C4C23×D1114yes—
765C4⋊C4C23×D1114yes—
766C4⋊C4C23×D1118yes—
767C4⋊C4C23×D1118yes—
768C22⋊C4—1116no—
769C22⋊C4—1116no—
770C22⋊C4—1116no—
771C22⋊C4—1116no—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4—1116no—
775C22⋊C4—1116no—
776C22⋊C4C23×D1118yes—
777C22⋊C4C23×D1118yes—
778C22⋊C4C23×D1118yes—
779C42—118no—
780C42—118no—
781C42—1116no—
782C42—1116no—
783C42—118no—
784C42—118no—
785C42C23×D1118yes—
786C42C23×D1114yes—
787C42C23×D1118yes—
788C42C23×D1114yes—
789C42C23×D1118yes—
790C42C23×D1114yes—
791C42C23×D1114yes—
792C11C2×#348011yescharacteristic, complemented, Sylow
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—118no—
799C23—228no—
800C23—228no—
801C23—228no—
802C23C2×#433914yes—
803C23C24×D1114yes—
804C23C24×D1112yes—
805C23C24×D1111yescharacteristic
806Q8—28no—
807Q8—1116no—
808Q8—2216no—
809Q8—2216no—
810Q8—228no—
811D4—216no—
812D4—28no—
813D4—2232no—
814D4—2232no—
815D4—2216no—
816D4—2216no—
817D4—448no—
818D4—4416no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—48no—
829C2×C4—44no—
830C2×C4—118no—
831C2×C4—114no—
832C2×C4—114no—
833C2×C4—114no—
834C2×C4—118no—
835C2×C4—114no—
836C2×C4—2232no—
837C2×C4—2216no—
838C2×C4—228no—
839C2×C4—224no—
840C2×C4—224no—
841C2×C4—224no—
842C2×C4—2232no—
843C2×C4—4416no—
844C2×C4—448no—
845C2×C4C2×#433914yes—
846C2×C4C2×#433914yes—
847C2×C4C2×#4339116yescomplemented
848C2×C4#41×D1114yes—
849C2×C4C24×D1114yes—
850C2×C4C24×D1114yes—
851C2×C4C24×D1112yes—
852C2×C4C24×D1112yes—
853C2×C4C24×D1114yes—
854C2×C4C24×D1112yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C22—22no—
859C22—22no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—48no—
865C22—228no—
866C22—228no—
867C22—228no—
868C22—4416no—
869C22C22×#433914yes—
870C22C22×#433912yes—
871C22C2×#41×D1112yes—
872C22#1062345312yes—
873C22C25×D1111yescharacteristic
874C4—24no—
875C4—22no—
876C4—24no—
877C4—22no—
878C4—24no—
879C4—22no—
880C4—118no—
881C4—224no—
882C4—228no—
883C4—224no—
884C4—224no—
885C4C22×#433914yes—
886C4C22×#433914yes—
887C4C2×#41×D1114yes—
888C2—24no—
889C2—44no—
890C2—448no—
891C2#1308220914yesdirect product factor
892C2C22×#41×D1111yescharacteristic
893C2C23×#433911yescharacteristic
894C2C2×#1062345311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082209C2direct (N × H)
2. C2×#10623116C2semidirect
3. C2×#10623090C2semidirect
4. C2×#10623098C2semidirect
5. C2×#10623099C2semidirect
6. C2×#10623073C2semidirect
7. C2×#10623071C2semidirect
8. C2×#10623096C2semidirect
9. C2×#10623084C2semidirect
10. C2×#10623083C2semidirect
11. C2×#10623008C2semidirect
12. C2×#10623363C2semidirect
13. C2×#10623010C2semidirect
14. C2×#10623059C2semidirect
15. C2×C4×#4339C2semidirect
16. C2×#10623053C2semidirect
17. C22×C4×Dic22C2semidirect
18. C2×C4×C11×#41C2semidirect
23. C4×C11×#41C22semidirect
34. #10623363C22semidirect
53. #10623116C22semidirect
54. #10623099C22semidirect
55. #10623098C22semidirect
56. #10623096C22semidirect
57. #10623090C22semidirect
58. #10623084C22semidirect
59. #10623083C22semidirect
60. #10623073C22semidirect
61. #10623071C22semidirect
62. #10623059C22semidirect
63. #10623053C22semidirect
78. #10623010C22semidirect
80. #10623008C22semidirect
84. C4×#4339C22semidirect
100. C2×C4×Dic22C22semidirect
251. C22×C4×C11#41semidirect
300. C2×Dic22#41semidirect
362. C2×C4×#41D11semidirect
394. C2×C4×C11C2×#41semidirect
428. Dic22C2×#41semidirect
473. C4×#41C2×D11semidirect
677. C2×C11#3480semidirect
735. C22×C4#4339semidirect
792. C11C2×#3480semidirect
847. C2×C4C2×#4339semidirect
891. C2#13082209direct (N × H)

Maximal subgroups

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

subgroupindex
#130822092
C2×#106231162
C2×#106230902
C2×#106230982
C2×#106230992
C2×#106230732
C2×#106230712
C2×#106230962
C2×#106230842
C2×#106230832
C2×#106230082
C2×#106233632
C2×#106230102
C2×#106230592
C2×C4×#43392
C2×#106230532
C22×C4×Dic222
C2×C4×C11×#412
C2×#348011