Finite Group Databasebeta

← C2×#13082234 #15660867

Subgroups — C2×#13082234 #15660867

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082234C2132yesmaximal, direct product factor
2C2×#10623252C211yesmaximal, characteristic, complemented
3C2×#10623263C211yesmaximal, characteristic, complemented
4C2×#10623172C212yesmaximal, complemented
5C2×#10623170C212yesmaximal, complemented
6C2×#10623224C214yesmaximal, complemented
7C2×#10623258C211yesmaximal, characteristic, complemented
8C2×#10623164C212yesmaximal, complemented
9C2×#10623257C211yesmaximal, characteristic, complemented
10C2×#10623162C212yesmaximal, complemented
11C2×#10623109C212yesmaximal, complemented
12C2×#10623111C212yesmaximal, complemented
13C2×#10623059C214yesmaximal, complemented
14C2×C4×#4343C212yesmaximal, complemented
15C2×C4×#4339C211yesmaximal, characteristic, complemented
16C2×C4×#4339C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D11C212yesmaximal, complemented
18C2×C11×#533C211yesmaximal, characteristic, complemented
19C22×#4343C2212yes—
20C22×Q8×D11C2212yes—
21C22×#4339C2211yescharacteristic
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×#67000C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×Q8×Dic11C2212yes—
37C2×Q8×Dic11C2212yes—
38C2×#66997C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2212yes—
43C2×#66979C2211yescharacteristic
44C2×#66979C2211yescharacteristic
45#10623263C22116yescomplemented
46#10623258C22116yescomplemented
47#10623257C22116yescomplemented
48#10623252C22116yescomplemented
49#10623224C22164yescomplemented
50#10623172C22132yescomplemented
51#10623170C22132yescomplemented
52#10623164C22132yescomplemented
53#10623162C22132yescomplemented
54#10623111C22132yescomplemented
55#10623109C22132yescomplemented
56C4×#4343C22132yescomplemented
57C4×Q8×D11C22132yescomplemented
58#10623059C22164yescomplemented
59C2×#66951C2214yes—
60C2×#66951C2214yes—
61C2×#66950C2212yes—
62C2×#66949C2214yes—
63C2×#66949C2214yes—
64C2×#66948C2212yes—
65C2×#66947C2214yes—
66C2×#66947C2214yes—
67C2×#66946C2214yes—
68C2×#66946C2212yes—
69C2×#66945C2214yes—
70C2×#66945C2212yes—
71C2×C4⋊C4×D11C2214yes—
72C2×C4⋊C4×D11C2212yes—
73C2×#66943C2212yes—
74C2×#66942C2214yes—
75C2×#66942C2214yes—
76C2×#66941C2212yes—
77C2×#66940C2214yes—
78C2×#66940C2212yes—
79C2×#66938C2214yes—
80C2×#66937C2214yes—
81C2×#66936C2214yes—
82C2×#66932C2214yes—
83C4×#4339C22116yescomplemented
84C4×#4339C22116yescomplemented
85C2×C4×D44C2214yes—
86C2×C4×D44C2211yescharacteristic
87C2×C4×D44C2211yescharacteristic
88C2×C4×D44C2211yescharacteristic
89C2×C4×D44C2211yescharacteristic
90C2×#66925C2212yes—
91C2×#66925C2212yes—
92C2×#66925C2214yes—
93C2×C42×D11C2214yes—
94C2×C42×D11C2212yes—
95C2×C42×D11C2212yes—
96C2×C4×Dic22C2214yes—
97C2×C4×Dic22C2211yescharacteristic
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2312yes—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C2×#4343—216no—
109C2×#4343C23116yes—
110C2×Q8×D11—216no—
111C2×Q8×D11C23116yes—
112C2×#4339—28no—
113C2×#4339—28no—
114C2×#4339C2318yes—
115C2×#4339C2318yes—
116C22×D44C2311yescharacteristic
117C22×D44C2314yes—
118C22×D44C2311yescharacteristic
119C22×C4×D11C2312yes—
120C22×C4×D11C2312yes—
121C22×C4×D11C2312yes—
122C22×C4×D11C2312yes—
123C22×C4×D11C2312yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C22×Dic22C2311yescharacteristic
128C22×Dic22C2314yes—
129C22×Dic22C2311yescharacteristic
130C11×C4⋊Q8C2318yes—
131C11×C4⋊Q8C2318yes—
132C11×#125C23116yes—
133C11×C22⋊Q8C23116yes—
134C11×C22⋊Q8C23116yes—
135C4×Q8×C11C23116yes—
136C4×Q8×C11C23116yes—
137C11×#117C23116yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2314yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2314yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2318yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153#67000C23116yes—
154#66999C23116yes—
155#66999C23116yes—
156Q8×Dic11C23116yes—
157Q8×Dic11C23116yes—
158#66997C23116yes—
159C4×C22⋊D11C23116yes—
160C4×C22⋊D11C23116yes—
161C4×C22⋊D11C23116yes—
162C4×C22⋊D11C23116yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171#66979C2318yes—
172#66979C2318yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2314yes—
178C2×C4⋊Dic11C2314yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2314yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2314yes—
194C2×C4×Dic11C2314yes—
195#66951C23132yes—
196#66951C23132yes—
197#66950C23116yes—
198#66949C23132yes—
199#66949C23132yes—
200#66948C23116yes—
201#66947C23132yes—
202#66947C23132yes—
203#66946C23116yes—
204#66946C23132yes—
205#66945C23116yes—
206#66945C23132yes—
207C4⋊C4×D11C23116yes—
208C4⋊C4×D11C23132yes—
209#66943C23116yes—
210#66942C23132yes—
211#66942C23132yes—
212#66941C23116yes—
213#66940C23116yes—
214#66940C23132yes—
215#66938C23132yes—
216#66937C23132yes—
217#66936C23132yes—
218#66932C23132yes—
219C4×D44C2318yes—
220C4×D44C2318yes—
221C4×D44C2318yes—
222C4×D44C2318yes—
223C4×D44C23132yes—
224#66925C23116yes—
225#66925C23116yes—
226#66925C23132yes—
227C42×D11C23116yes—
228C42×D11C23116yes—
229C42×D11C23132yes—
230C4×Dic22C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C2318yes—
233C4×Dic22C2318yes—
234C4×Dic22C23132yes—
235C2×#3482—111nomaximal, Sylow
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C23×D11C2412yes—
239C2×Q8×C11—28no—
240C2×Q8×C11—28no—
241C2×Q8×C11C2418yes—
242C2×Q8×C11C2418yes—
243C22×C4×C11—24no—
244C22×C4×C11—24no—
245C22×C4×C11—24no—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2414yes—
249C22×C4×C11C2414yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2414yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—28no—
258C2×C22⋊D11—28no—
259C2×C22⋊D11C2418yes—
260C2×C22⋊D11C2418yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267#4343—264no—
268Q8×D11—264no—
269#4339—232no—
270#4339—232no—
271C2×D44—216no—
272C2×D44—24no—
273C2×D44#4118yescomplemented
274C2×D44C2414yes—
275C2×D44C24116yes—
276C2×D44C2414yes—
277C2×C4×D11—28no—
278C2×C4×D11—216no—
279C2×C4×D11—28no—
280C2×C4×D11—216no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11C2418yes—
286C2×C4×D11C2418yes—
287C2×C4×D11C2418yes—
288C2×C4×D11C2418yes—
289C2×C4×D11C2418yes—
290C2×C4×D11C2418yes—
291C2×C4×D11C24116yes—
292C2×C4×D11C24116yes—
293C2×Dic22—216no—
294C2×Dic22—24no—
295C2×Dic22#4118yescomplemented
296C2×Dic22C2414yes—
297C2×Dic22C24116yes—
298C2×Dic22C2414yes—
299C11×C4⋊C4C2418yes—
300C11×C4⋊C4C24116yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2418yes—
303C11×C4⋊C4C24116yes—
304C11×C4⋊C4C2418yes—
305C11×C22⋊C4C24116yes—
306C42×C11C2414yes—
307C42×C11C2414yes—
308C42×C11C2414yes—
309C42×C11C24116yes—
310C42×C11C2414yes—
311C22⋊Dic11C2418yes—
312C22⋊Dic11C2418yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C2418yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C24116yes—
318(C2×D11)⋊C4C24116yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C24116yes—
321C4⋊Dic11C2414yes—
322C4⋊Dic11C2414yes—
323C4⋊Dic11C2414yes—
324C4⋊Dic11C2414yes—
325C4⋊Dic11C24116yes—
326C4⋊Dic11C24116yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C2418yes—
329Dic11⋊C4C2418yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C24116yes—
335C4×Dic11C2418yes—
336C4×Dic11C2418yes—
337C4×Dic11C2418yes—
338C4×Dic11C2418yes—
339C4×Dic11C2418yes—
340C4×Dic11C2418yes—
341C4×Dic11C24116yes—
342C4×Dic11C24116yes—
343#3482—1132no—
344C2×#557—111no—
345C2×#556—111no—
346C2×#556—112no—
347C2×#552—114no—
348C2×#552—112no—
349C2×D4×Q8—111no—
350C2×#548—112no—
351C2×#547—111no—
352C2×#547—112no—
353C2×#533—112no—
354C2×#533D1111yescharacteristic, complemented
355C2×#529—112no—
356C2×#529—114no—
357C2×C4×#41—111no—
358C2×C4×#41—111no—
359C2×C4×#41—112no—
360C22×C4×Q8—112no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11C2512yes—
365C23×C11C2511yescharacteristic
366C22×D11—24no—
367C22×D11—24no—
368C22×D11—24no—
369C22×D11—24no—
370C22×D11—24no—
371C22×D11C2×#4118yes—
372C22×D11C2514yes—
373C22×D11C2514yes—
374Q8×C11—216no—
375Q8×C11—216no—
376C2×C4×C11—28no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—28no—
380C2×C4×C11—22no—
381C2×C4×C11—28no—
382C2×C4×C11—28no—
383C2×C4×C11—28no—
384C2×C4×C11C2×#4114yes—
385C2×C4×C11C2×#4114yes—
386C2×C4×C112−1+414yes—
387C2×C4×C11C2512yes—
388C2×C4×C11C2512yes—
389C2×C4×C11C2518yes—
390C2×C4×C11C2518yes—
391C2×C4×C11C2512yes—
392C2×C4×C11C2512yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C22⋊D11—216no—
396C22⋊D11—216no—
397C2×Dic11—24no—
398C2×Dic11—24no—
399C2×Dic11—24no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11C2×#4118yes—
403C2×Dic11C2514yes—
404C2×Dic11C2514yes—
405C2×Dic11C2514yes—
406C2×Dic11C2514yes—
407C2×Dic11C2514yes—
408C2×Dic11C2514yes—
409D44—232no—
410D44—28no—
411D44C2×#41116yescomplemented
412C4×D11—216no—
413C4×D11—232no—
414C4×D11—216no—
415C4×D11—216no—
416C4×D11—216no—
417C4×D11—216no—
418C4×D11—216no—
419C4×D11—232no—
420Dic22—28no—
421Dic22—232no—
422Dic22C2×#41116yescomplemented
423C22×#41—112no—
424C22×#41—111no—
425C22×#41—111no—
426C23×Q8—112no—
427#557—1116no—
428#556—1116no—
429#556—1132no—
430#552—1164no—
431#552—1132no—
432D4×Q8—1116no—
433#548—1132no—
434#547—1116no—
435#547—1132no—
436#533—1132no—
437#533C2×D11116yescomplemented
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—112no—
440C2×C4⋊Q8C2×D1111yescharacteristic
441C2×C4⋊Q8C2×D1111yescharacteristic
442#529—1132no—
443#529—1164no—
444C2×#126—114no—
445C2×#126—114no—
446C2×#126—114no—
447C2×#125—114no—
448C2×#125—114no—
449C2×#125—112no—
450C2×#125C2×D1112yes—
451C2×#124—112no—
452C2×#124—114no—
453C2×#123—114no—
454C2×#123—114no—
455C2×#123—114no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—114no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8C2×D1112yes—
462C2×C22⋊Q8C2×D1112yes—
463C2×#121—112no—
464C2×#121—114no—
465C4×#41—1132no—
466C4×#41—1116no—
467C4×#41—1116no—
468C2×C4×Q8—112no—
469C2×C4×Q8—112no—
470C2×C4×Q8—1132no—
471C2×C4×Q8—112no—
472C2×C4×Q8—114no—
473C2×C4×Q8—111no—
474C2×C4×Q8—114no—
475C2×C4×Q8—111no—
476C2×C4×Q8—111no—
477C2×C4×Q8—111no—
478C2×C4×Q8C2×D1112yes—
479C2×C4×Q8C2×D1112yes—
480C2×C4×D4—112no—
481C2×C4×D4—112no—
482C2×C4×D4—112no—
483C2×C4×D4—112no—
484C2×C4×D4—112no—
485C2×C4×D4—114no—
486C2×C4×D4—111no—
487C2×C4×D4—114no—
488C2×C4×D4—111no—
489C2×C4×D4—111no—
490C2×C4×D4—111no—
491C2×#117—111no—
492C2×#117—111no—
493C2×#117—114no—
494C2×#117—112no—
495C2×#117—112no—
496C2×#117—112no—
497C2×#117—114no—
498C2×#117C2×D1112yes—
499C22×C4⋊C4—114no—
500C22×C4⋊C4—112no—
501C22×C42—112no—
502C22×C42—114no—
503C22×C42—112no—
504C22×C42C2×D1111yescharacteristic
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—44no—
509C22×C11C22×#4112yes—
510C22×C11C22×#4112yes—
511C22×C11C2×2−1+412yes—
512C22×C11C2611yescharacteristic
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—216no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—48no—
520C2×D11C22×#4118yes—
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—28no—
524C4×C11—28no—
525C4×C11—22no—
526C4×C11C22×#4114yes—
527C4×C11C22×#4114yes—
528C4×C11C2×2−1+414yes—
529Dic11—24no—
530Dic11—24no—
531Dic11—24no—
532Dic11—24no—
533Dic11—24no—
534Dic11C22×#4118yes—
535C2×#41—1116no—
536C2×#41—118no—
537C2×#41—118no—
538C2×#41—228no—
539C2×#41—228no—
540C2×#41—2216no—
541C22×Q8—1116no—
542C22×Q8—111no—
543C22×Q8—114no—
544C22×Q8—111no—
545C22×Q8—2216no—
546C22×Q8C22×D1112yes—
547C22×Q8C22×D1112yes—
548C22×D4—112no—
549C22×D4—112no—
550C22×D4—111no—
551C22×D4—114no—
552C22×D4—111no—
553C23×C4—114no—
554C23×C4—112no—
555C23×C4—114no—
556C23×C4—112no—
557C23×C4—112no—
558C23×C4—112no—
559C23×C4—112no—
560C23×C4—112no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C4⋊Q8—1116no—
565C4⋊Q8—1116no—
566C4⋊Q8C22×D1118yes—
567C4⋊Q8C22×D1118yes—
568#126—1132no—
569#126—1132no—
570#126—1132no—
571#125—1132no—
572#125—1116no—
573#125—1132no—
574#125C22×D11116yes—
575#124—1116no—
576#124—1132no—
577#123—1132no—
578#123—1132no—
579#123—1132no—
580C22⋊Q8—1116no—
581C22⋊Q8—1116no—
582C22⋊Q8—1132no—
583C22⋊Q8—1116no—
584C22⋊Q8—1132no—
585C22⋊Q8C22×D11116yes—
586C22⋊Q8C22×D11116yes—
587#121—1116no—
588#121—1132no—
589C4×Q8—1116no—
590C4×Q8—1116no—
591C4×Q8—1116no—
592C4×Q8—1132no—
593C4×Q8—118no—
594C4×Q8—1132no—
595C4×Q8—118no—
596C4×Q8—118no—
597C4×Q8—118no—
598C4×Q8C22×D11116yes—
599C4×Q8C22×D11116yes—
600C4×D4—1116no—
601C4×D4—1116no—
602C4×D4—1116no—
603C4×D4—1116no—
604C4×D4—1116no—
605C4×D4—1132no—
606C4×D4—118no—
607C4×D4—118no—
608C4×D4—1132no—
609C4×D4—118no—
610C4×D4—118no—
611#117—118no—
612#117—118no—
613#117—1132no—
614#117—1116no—
615#117—1116no—
616#117—1116no—
617#117—1132no—
618#117C22×D11116yes—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—1132no—
634C2×C4⋊C4—1116no—
635C2×C4⋊C4C22×D1112yes—
636C2×C4⋊C4C22×D1114yes—
637C2×C4⋊C4C22×D1114yes—
638C2×C4⋊C4C22×D1112yes—
639C2×C4⋊C4C22×D1112yes—
640C2×C4⋊C4C22×D1112yes—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4C22×D1114yes—
652C2×C42—112no—
653C2×C42—114no—
654C2×C42—112no—
655C2×C42—112no—
656C2×C42—114no—
657C2×C42—112no—
658C2×C42—112no—
659C2×C42—112no—
660C2×C42—1132no—
661C2×C42—1116no—
662C2×C42—1116no—
663C2×C42C22×D1111yescharacteristic
664C2×C42C22×D1111yescharacteristic
665C2×C42C22×D1118yes—
666C2×C42C22×D1114yes—
667C2×C42C22×D1111yescharacteristic
668C2×C42C22×D1111yescharacteristic
669C2×C11—42no—
670C2×C11#348214yescomplemented
671C2×C11C23×#4111yescharacteristic
672C2×C11C23×#4111yescharacteristic
673C2×C11C22×2−1+411yescharacteristic
674D11—28no—
675D11—44no—
676C24—112no—
677C24—112no—
678C24C23×D1111yescharacteristic
679#41—2232no—
680#41—2232no—
681#41—2264no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—118no—
685C2×Q8—114no—
686C2×Q8—1116no—
687C2×Q8—114no—
688C2×Q8—2216no—
689C2×Q8—2264no—
690C2×Q8—224no—
691C2×Q8C23×D1118yes—
692C2×Q8C23×D1118yes—
693C2×D4—118no—
694C2×D4—118no—
695C2×D4—118no—
696C2×D4—114no—
697C2×D4—1116no—
698C2×D4—114no—
699C2×D4—2216no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—224no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—118no—
713C22×C4—1116no—
714C22×C4—118no—
715C22×C4—1116no—
716C22×C4—118no—
717C22×C4—118no—
718C22×C4—118no—
719C22×C4—118no—
720C22×C4—2216no—
721C22×C4—228no—
722C22×C4—228no—
723C22×C4—2216no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4C23×D1111yescharacteristic
729C22×C4C23×D1111yescharacteristic
730C22×C4C23×D1114yes—
731C22×C4C23×D1114yes—
732C22×C4C23×D1111yescharacteristic
733C22×C4C23×D1114yes—
734C22×C4C23×D1114yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739C4⋊C4—118no—
740C4⋊C4—114no—
741C4⋊C4—1116no—
742C4⋊C4—1116no—
743C4⋊C4—1116no—
744C4⋊C4—114no—
745C4⋊C4—118no—
746C4⋊C4—118no—
747C4⋊C4—114no—
748C4⋊C4—114no—
749C4⋊C4—118no—
750C4⋊C4—1116no—
751C4⋊C4—1116no—
752C4⋊C4—1116no—
753C4⋊C4C23×D1118yes—
754C4⋊C4C23×D11116yes—
755C4⋊C4C23×D11116yes—
756C4⋊C4C23×D1118yes—
757C4⋊C4C23×D1118yes—
758C4⋊C4C23×D1118yes—
759C22⋊C4—118no—
760C22⋊C4—118no—
761C22⋊C4—118no—
762C22⋊C4—1116no—
763C22⋊C4—118no—
764C22⋊C4—118no—
765C22⋊C4—118no—
766C22⋊C4—1116no—
767C22⋊C4—1116no—
768C22⋊C4—1116no—
769C22⋊C4C23×D11116yes—
770C42—118no—
771C42—118no—
772C42—118no—
773C42—1116no—
774C42—118no—
775C42—118no—
776C42—1116no—
777C42—118no—
778C42C23×D1114yes—
779C42C23×D1114yes—
780C42C23×D11116yes—
781C42C23×D1114yes—
782C42C23×D1114yes—
783C11C2×#348211yescharacteristic, complemented, Sylow
784C23—22no—
785C23—22no—
786C23—22no—
787C23—118no—
788C23—114no—
789C23—114no—
790C23—224no—
791C23—224no—
792C23—224no—
793C23—224no—
794C23—224no—
795C23C24×D1112yes—
796C23C24×D1111yescharacteristic
797Q8—216no—
798Q8—216no—
799Q8—1116no—
800Q8—2232no—
801Q8—228no—
802D4—1116no—
803D4—2232no—
804D4—2216no—
805D4—2216no—
806D4—228no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—118no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—2232no—
823C2×C4—2216no—
824C2×C4—2216no—
825C2×C4—2232no—
826C2×C4—224no—
827C2×C4—224no—
828C2×C4—224no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—2216no—
832C2×C4—2216no—
833C2×C4—2216no—
834C2×C4—2216no—
835C2×C4#6704014yes—
836C2×C4#41×D1114yes—
837C2×C4#41×D1114yes—
838C2×C4C24×D1112yes—
839C2×C4C24×D1112yes—
840C2×C4C24×D1118yes—
841C2×C4C24×D1118yes—
842C2×C4C24×D1112yes—
843C2×C4C24×D1112yes—
844C2×C4C24×D1112yes—
845C2×C4C24×D1112yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—118no—
851C22—224no—
852C22—224no—
853C22—2216no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—448no—
858C22C2×#6704012yes—
859C22C2×#41×D1112yes—
860C22C2×#41×D1112yes—
861C22C25×D1111yescharacteristic
862C4—22no—
863C4—22no—
864C4—28no—
865C4—28no—
866C4—22no—
867C4—118no—
868C4—224no—
869C4—224no—
870C4—224no—
871C4—224no—
872C4—224no—
873C4C2×#6704014yes—
874C4C2×#41×D1114yes—
875C4C2×#41×D1114yes—
876C2—42no—
877C2—228no—
878C2—444no—
879C2#1308223414yesdirect product factor
880C2C22×#41×D1111yescharacteristic
881C2C22×#41×D1111yescharacteristic
882C2C22×#6704011yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
hypercenterC2×#533D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082234C2direct (N × H)
2. C2×#10623252C2semidirect
3. C2×#10623263C2semidirect
4. C2×#10623172C2semidirect
5. C2×#10623170C2semidirect
6. C2×#10623224C2semidirect
7. C2×#10623258C2semidirect
8. C2×#10623164C2semidirect
9. C2×#10623257C2semidirect
10. C2×#10623162C2semidirect
11. C2×#10623109C2semidirect
12. C2×#10623111C2semidirect
13. C2×#10623059C2semidirect
14. C2×C4×#4343C2semidirect
15. C2×C4×#4339C2semidirect
16. C2×C4×#4339C2semidirect
17. C2×C4×Q8×D11C2semidirect
18. C2×C11×#533C2semidirect
23. C11×#533C22semidirect
45. #10623263C22semidirect
46. #10623258C22semidirect
47. #10623257C22semidirect
48. #10623252C22semidirect
49. #10623224C22semidirect
50. #10623172C22semidirect
51. #10623170C22semidirect
52. #10623164C22semidirect
53. #10623162C22semidirect
54. #10623111C22semidirect
55. #10623109C22semidirect
56. C4×#4343C22semidirect
57. C4×Q8×D11C22semidirect
58. #10623059C22semidirect
83. C4×#4339C22semidirect
84. C4×#4339C22semidirect
273. C2×D44#41semidirect
295. C2×Dic22#41semidirect
354. C2×#533D11semidirect
411. D44C2×#41semidirect
422. Dic22C2×#41semidirect
437. #533C2×D11semidirect
670. C2×C11#3482semidirect
783. C11C2×#3482semidirect
879. C2#13082234direct (N × H)

Maximal subgroups

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

subgroupindex
#130822342
C2×#106232522
C2×#106232632
C2×#106231722
C2×#106231702
C2×#106232242
C2×#106232582
C2×#106231642
C2×#106232572
C2×#106231622
C2×#106231092
C2×#106231112
C2×#106230592
C2×C4×#43432
C2×C4×#43392
C2×C4×Q8×D112
C2×C11×#5332
C2×#348211