Finite Group Databasebeta

← C2×#13082471 #15661849

Subgroups — C2×#13082471 #15661849

Order 2816.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082471C2132yesmaximal, direct product factor
2C2×#10623212C212yesmaximal, complemented
3C2×#10623100C212yesmaximal, complemented
4C2×#10623263C211yesmaximal, characteristic, complemented
5C2×#10623233C214yesmaximal, complemented
6C2×#10623110C211yesmaximal, characteristic, complemented
7C2×#10623074C211yesmaximal, characteristic, complemented
8C2×#10623173C212yesmaximal, complemented
9C2×#10623060C212yesmaximal, complemented
10C2×#10623238C214yesmaximal, complemented
11C2×#10623159C212yesmaximal, complemented
12C2×#10623259C211yesmaximal, characteristic, complemented
13C2×#10623079C211yesmaximal, characteristic
14C2×#10623111C212yesmaximal, complemented
15C2×#10623211C212yesmaximal, complemented
16C2×#10623054C212yesmaximal, complemented
17C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
18C2×C11×#556C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2211yescharacteristic
20C22×#4339C2212yes—
21C11×#556C22116yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#126C2214yes—
24C2×C11×#124C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C4×Q8×C11C2212yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2212yes—
30C2×#67000C2212yes—
31C2×#66999C2212yes—
32C2×#66999C2212yes—
33C2×Q8×Dic11C2211yescharacteristic
34C2×Q8×Dic11C2212yes—
35C2×Q8×Dic11C2212yes—
36C2×#66993C2211yescharacteristic
37C2×#66991C2211yescharacteristic
38C2×D4×Dic11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C22×C4⋊Dic11C2212yes—
41C2×#66977C2212yes—
42#10623263C22116yescomplemented
43#10623259C22116yescomplemented
44#10623238C22164yescomplemented
45#10623233C22164yescomplemented
46#10623212C22132yescomplemented
47#10623211C22132yescomplemented
48#10623173C22132yescomplemented
49#10623159C22132yescomplemented
50#10623111C22132yescomplemented
51#10623110C22116yescomplemented
52C4×Q8×D11C22116yescomplemented
53#10623100C22132yescomplemented
54#10623079C22116yes—
55#10623074C22116yescomplemented
56#10623060C22132yescomplemented
57#10623054C22132yescomplemented
58C2×#66951C2214yes—
59C2×#66951C2214yes—
60C2×#66950C2212yes—
61C2×#66950C2212yes—
62C2×#66949C2214yes—
63C2×#66948C2211yescharacteristic
64C2×#66947C2214yes—
65C2×#66945C2212yes—
66C2×#66945C2212yes—
67C2×C4⋊C4×D11C2212yes—
68C2×C4⋊C4×D11C2212yes—
69C2×C4⋊C4×D11C2211yescharacteristic
70C2×#66943C2212yes—
71C2×#66943C2214yes—
72C2×#66943C2212yes—
73C2×#66941C2211yescharacteristic
74C2×#66941C2214yes—
75C2×#66940C2211yescharacteristic
76C2×#66940C2212yes—
77C2×#66940C2212yes—
78C2×#66939C2214yes—
79C2×#66938C2212yes—
80C2×#66938C2214yes—
81C2×#66937C2212yes—
82C2×#66936C2214yes—
83C2×#66936C2214yes—
84C2×(C22⋊D11)⋊C4C2214yes—
85C2×(C22⋊D11)⋊C4C2214yes—
86C2×#66932C2214yes—
87C2×#66931C2214yes—
88C2×#66930C2214yes—
89C2×C4×D44C2212yes—
90C2×C4×D44C2214yes—
91C2×C4×D44C2211yescharacteristic
92C2×#66925C2214yes—
93C2×C42×D11C2212yes—
94C2×C42×D11C2211yescharacteristic
95C2×#66923C2214yes—
96C2×#66923C2212yes—
97C2×#66922C2211yescharacteristic
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2214yes—
100C2×C4×Dic22C2212yes—
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C22×C22⋊D11C2312yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C23×Dic11C2314yes—
109C2×Q8×D11—28no—
110C2×Q8×D11C2318yes—
111C2×#4339—216no—
112C2×#4339C23116yes—
113C22×D44C2311yescharacteristic
114C22×D44C2312yes—
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×C4×D11C2312yes—
119C22×C4×D11C2311yescharacteristic
120C22×C4×D11C2314yes—
121C22×C4×D11C2311yescharacteristic
122C22×Dic22C2312yes—
123C22×Dic22C2312yes—
124C22×Dic22C2311yescharacteristic
125C22×Dic22C2312yes—
126C11×C4⋊Q8C2318yes—
127C11×#126C23132yes—
128C11×#124C23116yes—
129C11×C22⋊Q8C23116yes—
130C4×Q8×C11C23116yes—
131C4×Q8×C11C2318yes—
132C4×D4×C11C2318yes—
133C11×#117C23116yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2312yes—
145C2×C42×C11C2314yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2314yes—
148#67000C23116yes—
149#66999C23116yes—
150#66999C23116yes—
151Q8×Dic11C23116yes—
152Q8×Dic11C23116yes—
153Q8×Dic11C2318yes—
154#66993C2318yes—
155#66991C2318yes—
156D4×Dic11C23116yes—
157C4×C22⋊D11C23116yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×C4⋊Dic11C2314yes—
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2314yes—
171C2×C4⋊Dic11C2314yes—
172C2×C4⋊Dic11C23116yes—
173#66977C23116yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2314yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2314yes—
185C2×C4×Dic11C2314yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190#66951C23132yes—
191#66951C23132yes—
192#66950C23116yes—
193#66950C23116yes—
194#66949C23132yes—
195#66948C2318yes—
196#66947C23132yes—
197#66945C23116yes—
198#66945C23116yes—
199C4⋊C4×D11C23116yes—
200C4⋊C4×D11C2318yes—
201C4⋊C4×D11C23116yes—
202#66943C23132yes—
203#66943C23116yes—
204#66943C23116yes—
205#66941C23132yes—
206#66941C2318yes—
207#66940C23116yes—
208#66940C23116yes—
209#66940C2318yes—
210#66939C23132yes—
211#66938C23116yes—
212#66938C23132yes—
213#66937C23116yes—
214#66936C23132yes—
215#66936C23132yes—
216(C22⋊D11)⋊C4C23132yes—
217(C22⋊D11)⋊C4C23132yes—
218#66932C23132yes—
219#66931C23132yes—
220#66930C23132yes—
221C4×D44C23132yes—
222C4×D44C2318yes—
223C4×D44C23116yes—
224#66925C23132yes—
225C42×D11C2318yes—
226C42×D11C23116yes—
227#66923C23132yes—
228#66923C23116yes—
229#66922C2318yes—
230C4×Dic22C23132yes—
231C4×Dic22C2318yes—
232C4×Dic22C23116yes—
233C2×#3507—111nomaximal, Sylow
234C24×C11C2412yes—
235C23×D11C2412yes—
236C23×D11C2411yescharacteristic
237C2×Q8×C11—24no—
238C2×Q8×C11—28no—
239C2×Q8×C11C2418yes—
240C2×Q8×C11C2414yes—
241C2×D4×C11—24no—
242C2×D4×C11C2414yes—
243C22×C4×C11—28no—
244C22×C4×C11C2414yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2412yes—
249C22×C4×C11C2418yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11C2418yes—
256C2×C22⋊D11C2418yes—
257C2×C22⋊D11C2418yes—
258C22×Dic11—48no—
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2411yescharacteristic
263C22×Dic11C2412yes—
264C22×Dic11C2414yes—
265C22×Dic11C24116yes—
266C22×Dic11C2411yescharacteristic
267Q8×D11—232no—
268#4339—264no—
269C2×D44—28no—
270C2×D44—24no—
271C2×D44C2414yes—
272C2×D44C2418yes—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—24no—
276C2×C4×D11—42no—
277C2×C4×D11—44no—
278C2×C4×D11—48no—
279C2×C4×D11#4118yes—
280C2×C4×D11C2414yes—
281C2×C4×D11C2418yes—
282C2×C4×D11C2418yes—
283C2×C4×D11C2418yes—
284C2×C4×D11C2414yes—
285C2×C4×D11C24116yes—
286C2×C4×D11C2414yes—
287C2×Dic22—28no—
288C2×Dic22—28no—
289C2×Dic22—24no—
290C2×Dic22—44no—
291C2×Dic22C2418yes—
292C2×Dic22C2418yes—
293C2×Dic22C2414yes—
294C2×Dic22C2418yes—
295C11×C4⋊C4C2414yes—
296C11×C4⋊C4C2418yes—
297C11×C4⋊C4C2418yes—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C24116yes—
300C11×C4⋊C4C2418yes—
301C11×C22⋊C4C24116yes—
302C11×C22⋊C4C2418yes—
303C11×C22⋊C4C24116yes—
304C42×C11C2414yes—
305C42×C11C2418yes—
306C42×C11C24116yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C24116yes—
309(C2×D11)⋊C4C2418yes—
310(C2×D11)⋊C4C24116yes—
311(C2×D11)⋊C4C24116yes—
312(C2×D11)⋊C4C24116yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C24116yes—
315C4⋊Dic11C24116yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C2414yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C2418yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C24116yes—
322C4⋊Dic11C24116yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331C4×Dic11C2414yes—
332C4×Dic11C2418yes—
333C4×Dic11C24116yes—
334C4×Dic11C24116yes—
335C4×Dic11C2418yes—
336C4×Dic11C2418yes—
337C4×Dic11C2414yes—
338C4×Dic11C2414yes—
339#3507—1132no—
340C2×#559—112no—
341C2×#557—112no—
342C2×#556—111no—
343C2×#556—114no—
344C2×#556D1111yescharacteristic, complemented
345C2×#554—111no—
346C2×#554—111no—
347C2×#552—112no—
348C2×#552—112no—
349C2×#539—114no—
350C2×#536—112no—
351C2×#533—111no—
352C2×#532—111no—
353C2×#529—112no—
354C2×#529—112no—
355C2×#520—112no—
356C22×C4×Q8—111no—
357C23×C11—24no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11C2514yes—
361C23×C11C2511yescharacteristic
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—24no—
365C22×D11—24no—
366C22×D11—24no—
367C22×D11C2×#4114yes—
368C22×D11C2514yes—
369C22×D11C2512yes—
370Q8×C11—28no—
371Q8×C11—216no—
372D4×C11—28no—
373C2×C4×C11—24no—
374C2×C4×C11—24no—
375C2×C4×C11—28no—
376C2×C4×C11—22no—
377C2×C4×C11—24no—
378C2×C4×C11—216no—
379C2×C4×C11C2×#4114yes—
380C2×C4×C112−1+414yes—
381C2×C4×C11C2518yes—
382C2×C4×C11C2514yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2514yes—
386C2×C4×C11C2512yes—
387C2×C4×C11C2512yes—
388C22⋊D11—216no—
389C22⋊D11—216no—
390C22⋊D11—48no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—22no—
394C2×Dic11—28no—
395C2×Dic11—24no—
396C2×Dic11—22no—
397C2×Dic11—416no—
398C2×Dic11C2×#4114yes—
399C2×Dic11C2512yes—
400C2×Dic11C2514yes—
401C2×Dic11C2514yes—
402C2×Dic11C2512yes—
403C2×Dic11C2514yes—
404C2×Dic11C2518yes—
405C2×Dic11C2512yes—
406D44—216no—
407D44—28no—
408C4×D11—216no—
409C4×D11—216no—
410C4×D11—28no—
411C4×D11—416no—
412C4×D11—48no—
413C4×D11—44no—
414C4×D11C2×#41116yes—
415Dic22—28no—
416Dic22—216no—
417Dic22—216no—
418Dic22—48no—
419C22×#41—112no—
420C23×Q8—111no—
421#559—1132no—
422#557—1132no—
423#556—1116no—
424#556—1164no—
425#556C2×D11116yescomplemented
426#554—1116no—
427#554—1116no—
428#552—1132no—
429#552—1132no—
430#539—1164no—
431#536—1132no—
432#533—1116no—
433#532—1116no—
434C2×C4⋊Q8—111no—
435C2×C4⋊Q8—114no—
436C2×C4⋊Q8—111no—
437C2×C4⋊Q8C2×D1111yescharacteristic
438C2×#127—111no—
439#529—1132no—
440#529—1132no—
441C2×#126—114no—
442C2×#126—114no—
443C2×#126—114no—
444C2×#126C2×D1114yes—
445C2×#125—112no—
446C2×#125—112no—
447C2×#125—114no—
448C2×#125—112no—
449C2×#125—114no—
450C2×#124—112no—
451C2×#124—112no—
452C2×#124—114no—
453C2×#124C2×D1112yes—
454C2×#123—114no—
455C2×#123—114no—
456C2×#123—114no—
457C2×#123—114no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8—114no—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8C2×D1112yes—
466C2×#121—111no—
467C2×#121—111no—
468C2×#121—112no—
469#520—1132no—
470C2×C4×Q8—111no—
471C2×C4×Q8—112no—
472C2×C4×Q8—112no—
473C2×C4×Q8—1116no—
474C2×C4×Q8—111no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—111no—
478C2×C4×Q8—112no—
479C2×C4×Q8—114no—
480C2×C4×Q8C2×D1111yescharacteristic
481C2×C4×Q8C2×D1112yes—
482C2×C4×D4—112no—
483C2×C4×D4—112no—
484C2×C4×D4—114no—
485C2×C4×D4—114no—
486C2×C4×D4—114no—
487C2×C4×D4—112no—
488C2×C4×D4—111no—
489C2×C4×D4C2×D1111yescharacteristic
490C2×#117—112no—
491C2×#117—112no—
492C2×#117—114no—
493C2×#117—114no—
494C2×#117C2×D1112yes—
495C22×C4⋊C4—112no—
496C22×C4⋊C4—111no—
497C22×C4⋊C4—112no—
498C22×C4⋊C4—112no—
499C22×C42—112no—
500C22×C42—111no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—48no—
505C22×C11C22×#4112yes—
506C22×C11C2×2−1+412yes—
507C22×C11#58512yes—
508C22×C11C2611yescharacteristic
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—28no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—48no—
516C2×D11C22×#4114yes—
517C4×C11—24no—
518C4×C11—24no—
519C4×C11—28no—
520C4×C11—22no—
521C4×C11—24no—
522C4×C11C22×#4114yes—
523C4×C11C2×2−1+414yes—
524Dic11—24no—
525Dic11—24no—
526Dic11—22no—
527Dic11—28no—
528Dic11—24no—
529Dic11—22no—
530Dic11C22×#4114yes—
531C2×#41—1116no—
532C2×#41—2216no—
533C22×Q8—118no—
534C22×Q8—111no—
535C22×Q8—112no—
536C22×Q8—112no—
537C22×Q8—112no—
538C22×Q8—228no—
539C22×Q8C22×D1112yes—
540C22×Q8C22×D1111yescharacteristic
541C22×D4—112no—
542C22×D4—112no—
543C22×D4—112no—
544C22×D4—111no—
545C22×D4—112no—
546C22×D4C22×D1111yescharacteristic
547C23×C4—111no—
548C23×C4—114no—
549C23×C4—112no—
550C23×C4—112no—
551C23×C4—111no—
552C23×C4—112no—
553C23×C4—111no—
554C23×C4—114no—
555C23×C4C22×D1112yes—
556C4⋊Q8—118no—
557C4⋊Q8—1132no—
558C4⋊Q8—118no—
559C4⋊Q8C22×D1118yes—
560#127—118no—
561#126—1132no—
562#126—1132no—
563#126—1132no—
564#126C22×D11132yes—
565#125—1116no—
566#125—1116no—
567#125—1132no—
568#125—1116no—
569#125—1132no—
570#124—1116no—
571#124—1116no—
572#124—1132no—
573#124C22×D11116yes—
574#123—1132no—
575#123—1132no—
576#123—1132no—
577#123—1132no—
578C22⋊Q8—1116no—
579C22⋊Q8—1116no—
580C22⋊Q8—1116no—
581C22⋊Q8—1116no—
582C22⋊Q8—1116no—
583C22⋊Q8—1132no—
584C22⋊Q8—1132no—
585C22⋊Q8C22×D11116yes—
586#121—118no—
587#121—118no—
588#121—1116no—
589C4×Q8—118no—
590C4×Q8—1116no—
591C4×Q8—1116no—
592C4×Q8—118no—
593C4×Q8—1116no—
594C4×Q8—1116no—
595C4×Q8—118no—
596C4×Q8—1116no—
597C4×Q8—1132no—
598C4×Q8C22×D1118yes—
599C4×Q8C22×D11116yes—
600C4×D4—1116no—
601C4×D4—1116no—
602C4×D4—1132no—
603C4×D4—1132no—
604C4×D4—1132no—
605C4×D4—1116no—
606C4×D4—118no—
607C4×D4C22×D1118yes—
608#117—1116no—
609#117—1116no—
610#117—1132no—
611#117—1132no—
612#117C22×D11116yes—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—114no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—1116no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—118no—
631C2×C4⋊C4—1116no—
632C2×C4⋊C4—1116no—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1112yes—
635C2×C4⋊C4C22×D1112yes—
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1114yes—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4C22×D1114yes—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1112yes—
650C2×C42—114no—
651C2×C42—112no—
652C2×C42—112no—
653C2×C42—114no—
654C2×C42—111no—
655C2×C42—112no—
656C2×C42—111no—
657C2×C42—111no—
658C2×C42—1116no—
659C2×C42—118no—
660C2×C42C22×D1114yes—
661C2×C42C22×D1111yescharacteristic
662C2×C42C22×D1112yes—
663C2×C11—44no—
664C2×C11#350714yescomplemented
665C2×C11C23×#4111yescharacteristic
666C2×C11C22×2−1+411yescharacteristic
667C2×C11C2×#58511yescharacteristic
668D11—24no—
669D11—44no—
670C24—111no—
671C24—112no—
672C24C23×D1112yes—
673#41—2264no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—114no—
677C2×Q8—118no—
678C2×Q8—118no—
679C2×Q8—118no—
680C2×Q8—228no—
681C2×Q8—228no—
682C2×Q8—2232no—
683C2×Q8—224no—
684C2×Q8—444no—
685C2×Q8C23×D1118yes—
686C2×Q8C23×D1114yes—
687C2×D4—24no—
688C2×D4—118no—
689C2×D4—118no—
690C2×D4—118no—
691C2×D4—114no—
692C2×D4—118no—
693C2×D4—228no—
694C2×D4—228no—
695C2×D4—228no—
696C2×D4—224no—
697C2×D4—444no—
698C2×D4C23×D1114yes—
699C22×C4—28no—
700C22×C4—111no—
701C22×C4—118no—
702C22×C4—114no—
703C22×C4—111no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—111no—
708C22×C4—114no—
709C22×C4—1116no—
710C22×C4—114no—
711C22×C4—118no—
712C22×C4—118no—
713C22×C4—118no—
714C22×C4—114no—
715C22×C4—1116no—
716C22×C4—228no—
717C22×C4—228no—
718C22×C4—224no—
719C22×C4—444no—
720C22×C4—448no—
721C22×C4—442no—
722C22×C4—448no—
723C22×C4C23×D1118yes—
724C22×C4C23×D1114yes—
725C22×C4C23×D1112yes—
726C22×C4C23×D1112yes—
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1112yes—
729C22×C4C23×D1111yescharacteristic
730C22×C4C23×D1111yescharacteristic
731C4⋊C4—114no—
732C4⋊C4—118no—
733C4⋊C4—118no—
734C4⋊C4—1116no—
735C4⋊C4—1116no—
736C4⋊C4—118no—
737C4⋊C4—118no—
738C4⋊C4—118no—
739C4⋊C4—1116no—
740C4⋊C4—1116no—
741C4⋊C4—1116no—
742C4⋊C4—118no—
743C4⋊C4—114no—
744C4⋊C4—118no—
745C4⋊C4—1116no—
746C4⋊C4—1116no—
747C4⋊C4C23×D1114yes—
748C4⋊C4C23×D1118yes—
749C4⋊C4C23×D1118yes—
750C4⋊C4C23×D1114yes—
751C4⋊C4C23×D1118yes—
752C4⋊C4C23×D11116yes—
753C22⋊C4—118no—
754C22⋊C4—1116no—
755C22⋊C4—118no—
756C22⋊C4—1116no—
757C22⋊C4—1116no—
758C22⋊C4—1116no—
759C22⋊C4—118no—
760C22⋊C4—1116no—
761C22⋊C4C23×D11116yes—
762C22⋊C4C23×D11116yes—
763C22⋊C4C23×D1118yes—
764C42—118no—
765C42—118no—
766C42—114no—
767C42—118no—
768C42—114no—
769C42—114no—
770C42—1116no—
771C42—1116no—
772C42C23×D1114yes—
773C42C23×D1118yes—
774C42C23×D11116yes—
775C11C2×#350711yescharacteristic, complemented, Sylow
776C23—24no—
777C23—24no—
778C23—24no—
779C23—114no—
780C23—112no—
781C23—114no—
782C23—222no—
783C23—222no—
784C23—224no—
785C23—224no—
786C23—224no—
787C23C24×D1114yes—
788C23C24×D1111yescharacteristic
789Q8—28no—
790Q8—216no—
791Q8—2216no—
792Q8—2216no—
793Q8—228no—
794Q8—448no—
795D4—28no—
796D4—2216no—
797D4—2216no—
798D4—2216no—
799D4—228no—
800D4—448no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—216no—
807C2×C4—114no—
808C2×C4—112no—
809C2×C4—1116no—
810C2×C4—112no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—112no—
815C2×C4—118no—
816C2×C4—2216no—
817C2×C4—224no—
818C2×C4—224no—
819C2×C4—222no—
820C2×C4—224no—
821C2×C4—228no—
822C2×C4—222no—
823C2×C4—2216no—
824C2×C4—228no—
825C2×C4—448no—
826C2×C4—4416no—
827C2×C4—444no—
828C2×C4—4416no—
829C2×C4#41×D1114yes—
830C2×C4#6704314yes—
831C2×C4C24×D1118yes—
832C2×C4C24×D1114yes—
833C2×C4C24×D1114yes—
834C2×C4C24×D1112yes—
835C2×C4C24×D1114yes—
836C2×C4C24×D1112yes—
837C2×C4C24×D1112yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—114no—
843C22—222no—
844C22—222no—
845C22—228no—
846C22—224no—
847C22—224no—
848C22—224no—
849C22—448no—
850C22C2×#41×D1112yes—
851C22C2×#6704312yes—
852C22#1062345712yes—
853C22C25×D1111yescharacteristic
854C4—24no—
855C4—24no—
856C4—28no—
857C4—24no—
858C4—22no—
859C4—114no—
860C4—224no—
861C4—224no—
862C4—222no—
863C4—224no—
864C4—228no—
865C4—222no—
866C4C2×#41×D1114yes—
867C4C2×#6704314yes—
868C2—44no—
869C2—224no—
870C2—444no—
871C2#1308247114yesdirect product factor
872C2C22×#41×D1111yescharacteristic
873C2C22×#6704311yescharacteristic
874C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#556C2
socleC23×C11C25
prime radicalC2×#10623079C2
hypercenterC2×#556D11
hypocenterC11C2×#3507
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13082471C2direct (N × H)
2. C2×#10623212C2semidirect
3. C2×#10623100C2semidirect
4. C2×#10623263C2semidirect
5. C2×#10623233C2semidirect
6. C2×#10623110C2semidirect
7. C2×#10623074C2semidirect
8. C2×#10623173C2semidirect
9. C2×#10623060C2semidirect
10. C2×#10623238C2semidirect
11. C2×#10623159C2semidirect
12. C2×#10623259C2semidirect
14. C2×#10623111C2semidirect
15. C2×#10623211C2semidirect
16. C2×#10623054C2semidirect
17. C2×C4×Q8×D11C2semidirect
18. C2×C11×#556C2semidirect
21. C11×#556C22semidirect
42. #10623263C22semidirect
43. #10623259C22semidirect
44. #10623238C22semidirect
45. #10623233C22semidirect
46. #10623212C22semidirect
47. #10623211C22semidirect
48. #10623173C22semidirect
49. #10623159C22semidirect
50. #10623111C22semidirect
51. #10623110C22semidirect
52. C4×Q8×D11C22semidirect
53. #10623100C22semidirect
55. #10623074C22semidirect
56. #10623060C22semidirect
57. #10623054C22semidirect
344. C2×#556D11semidirect
425. #556C2×D11semidirect
664. C2×C11#3507semidirect
775. C11C2×#3507semidirect
871. C2#13082471direct (N × H)

Maximal subgroups

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

subgroupindex
#130824712
C2×#106232122
C2×#106231002
C2×#106232632
C2×#106232332
C2×#106231102
C2×#106230742
C2×#106231732
C2×#106230602
C2×#106232382
C2×#106231592
C2×#106232592
C2×#106230792
C2×#106231112
C2×#106232112
C2×#106230542
C2×C4×Q8×D112
C2×C11×#5562
C2×#350711