Finite Group Databasebeta

← C2×#13082208 #15660835

Subgroups — C2×#13082208 #15660835

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#13082208C2132yesmaximal, direct product factor
2C2×#10623116C211yesmaximal, characteristic, complemented
3C2×#10623212C212yesmaximal, complemented
4C2×#10623252C211yesmaximal, characteristic, complemented
5C2×#10623099C212yesmaximal, complemented
6C2×#10623240C214yesmaximal, complemented
7C2×#10623061C212yesmaximal, complemented
8C2×#10623084C211yesmaximal, characteristic, complemented
9C2×#10623164C212yesmaximal, complemented
10C2×#10623256C211yesmaximal, characteristic, complemented
11C2×#10623199C212yesmaximal, complemented
12C2×#10623155C212yesmaximal, complemented
13C2×#10623237C214yesmaximal, complemented
14C2×C4×#4343C212yesmaximal, complemented
15C2×#10623053C212yesmaximal, complemented
16C2×C4×#4341C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
18C2×C11×#556C211yesmaximal, characteristic, complemented
19C22×#4343C2212yes—
20C22×Q8×D11C2211yescharacteristic
21C22×#4341C2211yescharacteristic
22C22×#4339C2212yes—
23C11×#556C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#126C2214yes—
26C2×C11×#124C2212yes—
27C2×C11×C22⋊Q8C2212yes—
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2212yes—
32C2×#67000C2212yes—
33C2×#67000C2212yes—
34C2×Q8×Dic11C2211yescharacteristic
35C2×Q8×Dic11C2212yes—
36C2×#66997C2212yes—
37C2×#66993C2212yes—
38C2×D4×Dic11C2211yescharacteristic
39C2×#66983C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C22×C4×Dic11C2212yes—
42#10623256C22116yescomplemented
43#10623252C22116yescomplemented
44#10623240C22164yescomplemented
45#10623237C22164yescomplemented
46#10623212C22132yescomplemented
47#10623199C22132yescomplemented
48#10623164C22132yescomplemented
49#10623155C22132yescomplemented
50#10623116C22116yescomplemented
51C4×#4343C22132yescomplemented
52C4×Q8×D11C22116yescomplemented
53#10623099C22132yescomplemented
54#10623084C22116yescomplemented
55C4×#4341C22116yescomplemented
56#10623061C22132yescomplemented
57#10623053C22132yescomplemented
58C2×#66951C2214yes—
59C2×#66949C2214yes—
60C2×#66948C2212yes—
61C2×#66948C2212yes—
62C2×#66947C2214yes—
63C2×#66946C2212yes—
64C2×#66946C2212yes—
65C2×#66946C2212yes—
66C2×#66946C2214yes—
67C2×#66946C2212yes—
68C2×#66945C2214yes—
69C2×#66945C2211yescharacteristic
70C2×C4⋊C4×D11C2211yescharacteristic
71C2×C4⋊C4×D11C2212yes—
72C2×#66943C2212yes—
73C2×#66942C2214yes—
74C2×#66940C2212yes—
75C2×#66940C2211yescharacteristic
76C2×#66940C2212yes—
77C2×#66940C2211yescharacteristic
78C2×#66939C2214yes—
79C2×#66938C2214yes—
80C2×#66937C2214yes—
81C2×#66937C2214yes—
82C2×#66937C2214yes—
83C2×#66936C2214yes—
84C2×(C22⋊D11)⋊C4C2214yes—
85C2×(C22⋊D11)⋊C4C2214yes—
86C2×(C22⋊D11)⋊C4C2212yes—
87C2×(C22⋊D11)⋊C4C2214yes—
88C2×#66930C2212yes—
89C2×#66929C2214yes—
90C2×#66928C2212yes—
91C2×#66927C2211yescharacteristic
92C2×C4×D44C2214yes—
93C2×C4×D44C2212yes—
94C2×#66925C2214yes—
95C2×C42×D11C2214yes—
96C2×C42×D11C2212yes—
97C2×C42×D11C2211yescharacteristic
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2314yes—
108C23×Dic11C2312yes—
109C23×Dic11C2312yes—
110C2×#4343—216no—
111C2×#4343C23116yes—
112C2×Q8×D11—28no—
113C2×Q8×D11C2318yes—
114C2×#4341—28no—
115C2×#4341C2318yes—
116C2×#4339—216no—
117C2×#4339C23116yes—
118C22×D44C2312yes—
119C22×D44C2314yes—
120C22×D44C2312yes—
121C22×D44C2312yes—
122C22×C4×D11C2314yes—
123C22×C4×D11C2314yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2314yes—
127C22×C4×D11C2312yes—
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×Dic22C2311yescharacteristic
131C22×Dic22C2312yes—
132C22×Dic22C2311yescharacteristic
133C11×C4⋊Q8C2318yes—
134C11×#126C23132yes—
135C11×#124C23116yes—
136C11×C22⋊Q8C23116yes—
137C4×Q8×C11C23116yes—
138C4×Q8×C11C2318yes—
139C4×D4×C11C2318yes—
140C11×#117C23116yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2314yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C11×C22⋊C4C2314yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2312yes—
152C2×C42×C11C2314yes—
153C2×C22⋊Dic11C2312yes—
154#67000C23116yes—
155#67000C23116yes—
156Q8×Dic11C23116yes—
157Q8×Dic11C2318yes—
158#66997C23116yes—
159#66993C23116yes—
160D4×Dic11C2318yes—
161#66983C23116yes—
162C4×C22⋊D11C23116yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2314yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2314yes—
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2312yes—
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2314yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C23116yes—
192#66951C23132yes—
193#66949C23132yes—
194#66948C23116yes—
195#66948C23116yes—
196#66947C23132yes—
197#66946C23116yes—
198#66946C23132yes—
199#66946C23116yes—
200#66946C23116yes—
201#66946C23116yes—
202#66945C23132yes—
203#66945C2318yes—
204C4⋊C4×D11C23116yes—
205C4⋊C4×D11C2318yes—
206#66943C23116yes—
207#66942C23132yes—
208#66940C23116yes—
209#66940C23116yes—
210#66940C2318yes—
211#66940C2318yes—
212#66939C23132yes—
213#66938C23132yes—
214#66937C23132yes—
215#66937C23132yes—
216#66937C23132yes—
217#66936C23132yes—
218(C22⋊D11)⋊C4C23132yes—
219(C22⋊D11)⋊C4C23132yes—
220(C22⋊D11)⋊C4C23116yes—
221(C22⋊D11)⋊C4C23132yes—
222#66930C23116yes—
223#66929C23132yes—
224#66928C23116yes—
225#66927C2318yes—
226C4×D44C23132yes—
227C4×D44C23116yes—
228#66925C23132yes—
229C42×D11C23132yes—
230C42×D11C2318yes—
231C42×D11C23116yes—
232C4×Dic22C2318yes—
233C4×Dic22C2318yes—
234C4×Dic22C23116yes—
235C2×#3480—111nomaximal, Sylow
236C24×C11C2412yes—
237C23×D11C2414yes—
238C23×D11C2411yescharacteristic
239C2×Q8×C11—24no—
240C2×Q8×C11—28no—
241C2×Q8×C11C2418yes—
242C2×Q8×C11C2414yes—
243C2×D4×C11—24no—
244C2×D4×C11C2414yes—
245C22×C4×C11—28no—
246C22×C4×C11C2412yes—
247C22×C4×C11C2418yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2414yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—216no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—48no—
257C2×C22⋊D11C24116yes—
258C2×C22⋊D11C2418yes—
259C2×C22⋊D11C24116yes—
260C22×Dic11—28no—
261C22×Dic11—44no—
262C22×Dic11C2418yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2418yes—
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2412yes—
271#4343—264no—
272Q8×D11—232no—
273#4341—232no—
274#4339—264no—
275C2×D44—216no—
276C2×D44—28no—
277C2×D44—28no—
278C2×D44—44no—
279C2×D44C2418yes—
280C2×D44C24116yes—
281C2×D44C2418yes—
282C2×D44C2418yes—
283C2×C4×D11—216no—
284C2×C4×D11—28no—
285C2×C4×D11—216no—
286C2×C4×D11—24no—
287C2×C4×D11—44no—
288C2×C4×D11—48no—
289C2×C4×D11—42no—
290C2×C4×D11#4118yescomplemented
291C2×C4×D11C24116yes—
292C2×C4×D11C24116yes—
293C2×C4×D11C2418yes—
294C2×C4×D11C2414yes—
295C2×C4×D11C24116yes—
296C2×C4×D11C2418yes—
297C2×C4×D11C2414yes—
298C2×C4×D11C2414yes—
299C2×Dic22—28no—
300C2×Dic22—24no—
301C2×Dic22#4118yescomplemented
302C2×Dic22C2414yes—
303C2×Dic22C2418yes—
304C2×Dic22C2414yes—
305C11×C4⋊C4C2418yes—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C2418yes—
308C11×C4⋊C4C2414yes—
309C11×C4⋊C4C2418yes—
310C11×C4⋊C4C24116yes—
311C11×C22⋊C4C2418yes—
312C11×C22⋊C4C24116yes—
313C11×C22⋊C4C24116yes—
314C42×C11C2414yes—
315C42×C11C2418yes—
316C42×C11C24116yes—
317C22⋊Dic11C2418yes—
318(C2×D11)⋊C4C24116yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C2418yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C24116yes—
323(C2×D11)⋊C4C24116yes—
324(C2×D11)⋊C4C24116yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C2418yes—
327C4⋊Dic11C2414yes—
328C4⋊Dic11C24116yes—
329Dic11⋊C4C2418yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C2418yes—
332Dic11⋊C4C2418yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C2418yes—
335Dic11⋊C4C24116yes—
336C4×Dic11C2414yes—
337C4×Dic11C2418yes—
338C4×Dic11C2418yes—
339C4×Dic11C2418yes—
340C4×Dic11C2418yes—
341C4×Dic11C2414yes—
342C4×Dic11C2418yes—
343C4×Dic11C24116yes—
344C4×Dic11C2414yes—
345C4×Dic11C2418yes—
346#3480—1132no—
347C2×#559—112no—
348C2×#559—111no—
349C2×#557—111no—
350C2×#556—112no—
351C2×#556D1111yescharacteristic, complemented
352C2×#553—114no—
353C2×#553—112no—
354C2×#550—111no—
355C2×#548—112no—
356C2×#532—111no—
357C2×#532—112no—
358C2×#529—114no—
359C2×#529—112no—
360C2×C4×#41—112no—
361C2×C4×#41—111no—
362C2×C4×#41—112no—
363C22×C4×Q8—111no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11—24no—
367C23×C11C2514yes—
368C23×C11C2511yescharacteristic
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—28no—
374C22×D11C2×#4114yes—
375C22×D11C2518yes—
376C22×D11C2512yes—
377Q8×C11—28no—
378Q8×C11—216no—
379D4×C11—28no—
380C2×C4×C11—24no—
381C2×C4×C11—24no—
382C2×C4×C11—28no—
383C2×C4×C11—24no—
384C2×C4×C11—22no—
385C2×C4×C11—216no—
386C2×C4×C11C2×#4114yes—
387C2×C4×C11C2×#4114yes—
388C2×C4×C11C2514yes—
389C2×C4×C11C2512yes—
390C2×C4×C11C2518yes—
391C2×C4×C11C2514yes—
392C2×C4×C11C2514yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C22⋊D11—216no—
396C22⋊D11—232no—
397C22⋊D11—416no—
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—24no—
401C2×Dic11—22no—
402C2×Dic11—24no—
403C2×Dic11—216no—
404C2×Dic11—48no—
405C2×Dic11C2×#4118yes—
406C2×Dic11C2×#4114yes—
407C2×Dic11C2512yes—
408C2×Dic11C2514yes—
409C2×Dic11C2514yes—
410C2×Dic11C2514yes—
411C2×Dic11C2512yes—
412C2×Dic11C2512yes—
413C2×Dic11C2514yes—
414D44—232no—
415D44—216no—
416D44—216no—
417D44—48no—
418C4×D11—28no—
419C4×D11—232no—
420C4×D11—216no—
421C4×D11—232no—
422C4×D11—416no—
423C4×D11—44no—
424C4×D11—48no—
425C4×D11C2×#41116yescomplemented
426Dic22—28no—
427Dic22—216no—
428Dic22C2×#41116yescomplemented
429C22×#41—112no—
430C22×#41—111no—
431C22×#41—112no—
432C23×Q8—111no—
433#559—1132no—
434#559—1116no—
435#557—1116no—
436#556—1132no—
437#556C2×D11116yescomplemented
438#553—1164no—
439#553—1132no—
440#550—1116no—
441#548—1132no—
442#532—1116no—
443#532—1132no—
444C2×C4⋊Q8—112no—
445C2×C4⋊Q8C2×D1111yescharacteristic
446C2×#127—112no—
447C2×#127—111no—
448#529—1164no—
449#529—1132no—
450C2×#126—114no—
451C2×#126—114no—
452C2×#126C2×D1114yes—
453C2×#125—114no—
454C2×#125—112no—
455C2×#124—112no—
456C2×#124—112no—
457C2×#124—114no—
458C2×#124—112no—
459C2×#124C2×D1112yes—
460C2×#123—114no—
461C2×#123—114no—
462C2×#123—114no—
463C2×C22⋊Q8—114no—
464C2×C22⋊Q8C2×D1112yes—
465C2×#121—112no—
466C2×#121—112no—
467C2×#121—112no—
468C2×#121—114no—
469C2×#121—114no—
470C2×#121—114no—
471C4×#41—1132no—
472C4×#41—1116no—
473C4×#41—1132no—
474C2×C4×Q8—111no—
475C2×C4×Q8—112no—
476C2×C4×Q8—1116no—
477C2×C4×Q8—111no—
478C2×C4×Q8—112no—
479C2×C4×Q8—112no—
480C2×C4×Q8—111no—
481C2×C4×Q8—111no—
482C2×C4×Q8—112no—
483C2×C4×Q8—111no—
484C2×C4×Q8C2×D1111yescharacteristic
485C2×C4×Q8C2×D1112yes—
486C2×C4×D4—111no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4—114no—
490C2×C4×D4—112no—
491C2×C4×D4—112no—
492C2×C4×D4—112no—
493C2×C4×D4—114no—
494C2×C4×D4—112no—
495C2×C4×D4—114no—
496C2×C4×D4—114no—
497C2×C4×D4—114no—
498C2×C4×D4—112no—
499C2×C4×D4C2×D1111yescharacteristic
500C2×#117—111no—
501C2×#117—114no—
502C2×#117—112no—
503C2×#117—114no—
504C2×#117C2×D1112yes—
505C22×C4⋊C4—112no—
506C22×C4⋊C4—111no—
507C22×C42—112no—
508C22×C42—111no—
509C22×C42—112no—
510C22×C42—114no—
511C22×C11—24no—
512C22×C11—24no—
513C22×C11—24no—
514C22×C11—48no—
515C22×C11C22×#4112yes—
516C22×C11C22×#4112yes—
517C22×C11#58512yes—
518C22×C11C2611yescharacteristic
519C2×D11—22no—
520C2×D11—22no—
521C2×D11—28no—
522C2×D11—28no—
523C2×D11—28no—
524C2×D11—28no—
525C2×D11—416no—
526C2×D11C22×#4114yes—
527C4×C11—24no—
528C4×C11—24no—
529C4×C11—28no—
530C4×C11—24no—
531C4×C11—22no—
532C4×C11C22×#4114yes—
533C4×C11C22×#4114yes—
534Dic11—22no—
535Dic11—24no—
536Dic11—24no—
537Dic11—22no—
538Dic11—24no—
539Dic11C22×#4118yes—
540Dic11C22×#4114yes—
541C2×#41—1116no—
542C2×#41—118no—
543C2×#41—1116no—
544C2×#41—2216no—
545C2×#41—228no—
546C2×#41—2216no—
547C22×Q8—118no—
548C22×Q8—111no—
549C22×Q8—112no—
550C22×Q8—111no—
551C22×Q8—228no—
552C22×Q8C22×D1111yescharacteristic
553C22×Q8C22×D1112yes—
554C22×D4—112no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—112no—
559C22×D4—112no—
560C22×D4—112no—
561C22×D4C22×D1111yescharacteristic
562C23×C4—111no—
563C23×C4—112no—
564C23×C4—112no—
565C23×C4—112no—
566C23×C4—111no—
567C23×C4—114no—
568C23×C4—114no—
569C23×C4—111no—
570C23×C4—112no—
571C23×C4—114no—
572C23×C4C22×D1112yes—
573C4⋊Q8—1116no—
574C4⋊Q8C22×D1118yes—
575#127—1116no—
576#127—118no—
577#126—1132no—
578#126—1132no—
579#126C22×D11132yes—
580#125—1132no—
581#125—1116no—
582#124—1116no—
583#124—1116no—
584#124—1132no—
585#124—1116no—
586#124C22×D11116yes—
587#123—1132no—
588#123—1132no—
589#123—1132no—
590C22⋊Q8—1132no—
591C22⋊Q8C22×D11116yes—
592#121—1116no—
593#121—1116no—
594#121—1116no—
595#121—1132no—
596#121—1132no—
597#121—1132no—
598C4×Q8—118no—
599C4×Q8—1116no—
600C4×Q8—118no—
601C4×Q8—1116no—
602C4×Q8—1116no—
603C4×Q8—118no—
604C4×Q8—118no—
605C4×Q8—1116no—
606C4×Q8—118no—
607C4×Q8C22×D1118yes—
608C4×Q8C22×D11116yes—
609C4×D4—118no—
610C4×D4—1116no—
611C4×D4—1116no—
612C4×D4—1132no—
613C4×D4—1116no—
614C4×D4—1116no—
615C4×D4—1116no—
616C4×D4—1132no—
617C4×D4—1116no—
618C4×D4—1132no—
619C4×D4—1132no—
620C4×D4—1132no—
621C4×D4—1116no—
622C4×D4C22×D1118yes—
623#117—118no—
624#117—1132no—
625#117—1116no—
626#117—1132no—
627#117C22×D11116yes—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—1116no—
640C2×C4⋊C4—118no—
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C4⋊C4C22×D1112yes—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1114yes—
645C2×C4⋊C4C22×D1112yes—
646C2×C4⋊C4C22×D1112yes—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—112no—
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×D1114yes—
657C2×C22⋊C4C22×D1114yes—
658C2×C42—112no—
659C2×C42—111no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42—114no—
663C2×C42—112no—
664C2×C42—112no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—112no—
668C2×C42—1116no—
669C2×C42—118no—
670C2×C42—1116no—
671C2×C42—1132no—
672C2×C42C22×D1114yes—
673C2×C42C22×D1112yes—
674C2×C42C22×D1111yescharacteristic
675C2×C11—44no—
676C2×C11#348014yescomplemented
677C2×C11C23×#4111yescharacteristic
678C2×C11C23×#4111yescharacteristic
679C2×C11C2×#58511yescharacteristic
680D11—24no—
681D11—48no—
682C24—111no—
683C24—114no—
684C24C23×D1112yes—
685#41—2264no—
686#41—2232no—
687#41—2264no—
688C2×Q8—24no—
689C2×Q8—28no—
690C2×Q8—118no—
691C2×Q8—114no—
692C2×Q8—118no—
693C2×Q8—114no—
694C2×Q8—228no—
695C2×Q8—2232no—
696C2×Q8—224no—
697C2×Q8C23×D1114yes—
698C2×Q8C23×D1118yes—
699C2×D4—24no—
700C2×D4—118no—
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—228no—
712C2×D4—444no—
713C2×D4—448no—
714C2×D4C23×D1114yes—
715C22×C4—28no—
716C22×C4—111no—
717C22×C4—112no—
718C22×C4—118no—
719C22×C4—114no—
720C22×C4—118no—
721C22×C4—112no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—118no—
727C22×C4—118no—
728C22×C4—114no—
729C22×C4—1116no—
730C22×C4—1116no—
731C22×C4—114no—
732C22×C4—118no—
733C22×C4—1116no—
734C22×C4—228no—
735C22×C4—2216no—
736C22×C4—2216no—
737C22×C4—228no—
738C22×C4—224no—
739C22×C4—448no—
740C22×C4—444no—
741C22×C4—442no—
742C22×C4—444no—
743C22×C4C23×D1118yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1114yes—
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1111yescharacteristic
750C22×C4C23×D1111yescharacteristic
751C4⋊C4—118no—
752C4⋊C4—118no—
753C4⋊C4—114no—
754C4⋊C4—118no—
755C4⋊C4—118no—
756C4⋊C4—114no—
757C4⋊C4—1116no—
758C4⋊C4—118no—
759C4⋊C4—118no—
760C4⋊C4—1116no—
761C4⋊C4—1116no—
762C4⋊C4C23×D1114yes—
763C4⋊C4C23×D1118yes—
764C4⋊C4C23×D1114yes—
765C4⋊C4C23×D11116yes—
766C4⋊C4C23×D1118yes—
767C4⋊C4C23×D1118yes—
768C22⋊C4—118no—
769C22⋊C4—118no—
770C22⋊C4—1116no—
771C22⋊C4—1116no—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4—1116no—
775C22⋊C4—1116no—
776C22⋊C4C23×D1118yes—
777C22⋊C4C23×D11116yes—
778C22⋊C4C23×D11116yes—
779C42—118no—
780C42—118no—
781C42—114no—
782C42—114no—
783C42—118no—
784C42—118no—
785C42—1116no—
786C42—118no—
787C42—114no—
788C42—118no—
789C42C23×D11116yes—
790C42C23×D1118yes—
791C42C23×D1114yes—
792C11C2×#348011yescharacteristic, complemented, Sylow
793C23—24no—
794C23—24no—
795C23—24no—
796C23—114no—
797C23—112no—
798C23—118no—
799C23—222no—
800C23—222no—
801C23—228no—
802C23—228no—
803C23—228no—
804C23C24×D1114yes—
805C23C24×D1111yescharacteristic
806Q8—28no—
807Q8—216no—
808Q8—1116no—
809Q8—2216no—
810Q8—228no—
811D4—28no—
812D4—2232no—
813D4—2232no—
814D4—2216no—
815D4—2216no—
816D4—2216no—
817D4—448no—
818D4—4416no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—216no—
825C2×C4—114no—
826C2×C4—118no—
827C2×C4—112no—
828C2×C4—114no—
829C2×C4—1116no—
830C2×C4—114no—
831C2×C4—112no—
832C2×C4—112no—
833C2×C4—114no—
834C2×C4—114no—
835C2×C4—2216no—
836C2×C4—2232no—
837C2×C4—2232no—
838C2×C4—2216no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—224no—
842C2×C4—222no—
843C2×C4—224no—
844C2×C4—228no—
845C2×C4—4416no—
846C2×C4—448no—
847C2×C4—444no—
848C2×C4—448no—
849C2×C4#41×D1114yes—
850C2×C4#41×D1114yes—
851C2×C4C24×D1114yes—
852C2×C4C24×D1114yes—
853C2×C4C24×D1114yes—
854C2×C4C24×D1118yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—48no—
862C22—114no—
863C22—222no—
864C22—222no—
865C22—228no—
866C22—228no—
867C22—228no—
868C22—228no—
869C22—4416no—
870C22C2×#41×D1112yes—
871C22C2×#41×D1112yes—
872C22#1062345712yes—
873C22C25×D1111yescharacteristic
874C4—24no—
875C4—28no—
876C4—24no—
877C4—24no—
878C4—22no—
879C4—114no—
880C4—118no—
881C4—224no—
882C4—222no—
883C4—224no—
884C4—222no—
885C4—224no—
886C4C2×#41×D1114yes—
887C4C2×#41×D1114yes—
888C2—44no—
889C2—224no—
890C2—448no—
891C2#1308220814yesdirect product factor
892C2C22×#41×D1111yescharacteristic
893C2C22×#41×D1111yescharacteristic
894C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#556C2
socleC23×C11C25
hypercenterC2×#556D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13082208C2direct (N × H)
2. C2×#10623116C2semidirect
3. C2×#10623212C2semidirect
4. C2×#10623252C2semidirect
5. C2×#10623099C2semidirect
6. C2×#10623240C2semidirect
7. C2×#10623061C2semidirect
8. C2×#10623084C2semidirect
9. C2×#10623164C2semidirect
10. C2×#10623256C2semidirect
11. C2×#10623199C2semidirect
12. C2×#10623155C2semidirect
13. C2×#10623237C2semidirect
14. C2×C4×#4343C2semidirect
15. C2×#10623053C2semidirect
16. C2×C4×#4341C2semidirect
17. C2×C4×Q8×D11C2semidirect
18. C2×C11×#556C2semidirect
23. C11×#556C22semidirect
42. #10623256C22semidirect
43. #10623252C22semidirect
44. #10623240C22semidirect
45. #10623237C22semidirect
46. #10623212C22semidirect
47. #10623199C22semidirect
48. #10623164C22semidirect
49. #10623155C22semidirect
50. #10623116C22semidirect
51. C4×#4343C22semidirect
52. C4×Q8×D11C22semidirect
53. #10623099C22semidirect
54. #10623084C22semidirect
55. C4×#4341C22semidirect
56. #10623061C22semidirect
57. #10623053C22semidirect
290. C2×C4×D11#41semidirect
301. C2×Dic22#41semidirect
351. C2×#556D11semidirect
425. C4×D11C2×#41semidirect
428. Dic22C2×#41semidirect
437. #556C2×D11semidirect
676. C2×C11#3480semidirect
792. C11C2×#3480semidirect
891. C2#13082208direct (N × H)

Maximal subgroups

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

subgroupindex
#130822082
C2×#106231162
C2×#106232122
C2×#106232522
C2×#106230992
C2×#106232402
C2×#106230612
C2×#106230842
C2×#106231642
C2×#106232562
C2×#106231992
C2×#106231552
C2×#106232372
C2×C4×#43432
C2×#106230532
C2×C4×#43412
C2×C4×Q8×D112
C2×C11×#5562
C2×#348011