Finite Group Databasebeta

← C2×#13082195 #15660844

Subgroups — C2×#13082195 #15660844

Order 2816.

7522 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082195C2132yesmaximal, direct product factor
2C2×#10623253C211yesmaximal, characteristic, complemented
3C2×#10623098C211yesmaximal, characteristic, complemented
4C2×#10623216C212yesmaximal, complemented
5C2×#10623070C212yesmaximal, complemented
6C2×#10623042C212yesmaximal, complemented
7C2×#10623167C214yesmaximal, complemented
8C2×D4×Dic22C211yesmaximal, characteristic, complemented
9C2×#10623163C212yesmaximal, complemented
10C2×#10623219C212yesmaximal, complemented
11C2×#10623259C211yesmaximal, characteristic, complemented
12C2×#10623153C212yesmaximal, complemented
13C2×#10623153C214yesmaximal, complemented
14C2×C4×#4341C212yesmaximal
15C2×C4×#4341C211yesmaximal, characteristic
16C22×#66940C212yesmaximal, complemented
17C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
18C2×C11×#554C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2211yescharacteristic
20C22×#4341C2211yescharacteristic
21C23×Dic22C2212yes—
22C11×#554C22116yescomplemented
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×#125C2212yes—
25C2×C11×C22⋊Q8C2214yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yes—
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4C2212yes—
31C2×#66999C2212yes—
32C2×Q8×Dic11C2212yes—
33C2×Q8×Dic11C2211yescharacteristic
34C2×#66997C2214yes—
35C2×#66997C2212yes—
36C2×D4×Dic11C2211yescharacteristic
37C2×D4×Dic11C2212yes—
38C2×C4×C22⋊D11C2214yes—
39C2×C4×C22⋊D11C2212yes—
40C2×#66977C2214yes—
41C2×#66977C2212yes—
42C22×Dic11⋊C4C2214yes—
43C22×C4×Dic11C2212yes—
44C22×C4×Dic11C2214yes—
45#10623259C22116yescomplemented
46#10623253C22116yescomplemented
47#10623219C22132yescomplemented
48#10623216C22132yescomplemented
49#10623167C22164yescomplemented
50#10623163C22132yescomplemented
51#10623153C22164yescomplemented
52#10623153C22132yescomplemented
53C4×Q8×D11C22116yescomplemented
54#10623098C22116yescomplemented
55#10623070C22132yescomplemented
56D4×Dic22C22116yescomplemented
57C4×#4341C22116yes—
58C4×#4341C22132yes—
59#10623042C22132yescomplemented
60C2×#66950C2212yes—
61C2×#66949C2214yes—
62C2×#66949C2214yes—
63C2×#66945C2212yes—
64C2×#66945C2211yescharacteristic
65C2×C4⋊C4×D11C2212yes—
66C2×C4⋊C4×D11C2211yescharacteristic
67C2×#66943C2212yes—
68C2×#66942C2214yes—
69C2×#66942C2214yes—
70C2×#66942C2214yes—
71C2×#66941C2212yes—
72C2×#66941C2212yes—
73C2×#66941C2214yes—
74C2×#66941C2212yes—
75C2×#66940C2214yes—
76C2×#66940C2212yes—
77C2×#66940C2214yes—
78C2×#66940C2212yes—
79C2×#66940C2212yes—
80C2×#66940C2214yes—
81C2×#66940C2211yescharacteristic
82C2×#66940C2212yes—
83C2×#66940C2212yes—
84C2×#66940C2211yescharacteristic
85C2×#66940C22132yescomplemented
86C2×(C22⋊D11)⋊C4C2212yes—
87C2×(C22⋊D11)⋊C4C2214yes—
88C2×#66931C2214yes—
89C2×#66931C2214yes—
90C2×#66931C2214yes—
91C2×#66930C2214yes—
92C2×#66930C2212yes—
93C2×C42×D11C2211yescharacteristic
94C2×C42×D11C2212yes—
95C2×#66923C2212yes—
96C2×#66922C2211yescharacteristic
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×Q8×C11C2312yes—
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2312yes—
105C23×C4×C11C2314yes—
106C22×C22⋊D11C2312yes—
107C23×Dic11C2314yes—
108C23×Dic11C2312yes—
109C23×Dic11C2312yes—
110C2×Q8×D11—28no—
111C2×Q8×D11C2318yes—
112C2×#4341Q8116yescomplemented
113C2×#4341C2318yes—
114C22×C4×D11C2312yes—
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2312yes—
118C22×C4×D11C2311yescharacteristic
119C22×Dic22—216no—
120C22×Dic22C2312yes—
121C22×Dic22C2312yes—
122C22×Dic22C2314yes—
123C22×Dic22C23116yes—
124C22×Dic22C2314yes—
125C22×Dic22C2311yescharacteristic
126C22×Dic22C2311yescharacteristic
127C11×C4⋊Q8C2318yes—
128C11×#125C23116yes—
129C11×C22⋊Q8C23116yes—
130C11×C22⋊Q8C23132yes—
131C4×Q8×C11C2318yes—
132C4×D4×C11C2318yes—
133C4×D4×C11C23116yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C23116yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2314yes—
148#66999C23116yes—
149Q8×Dic11C23116yes—
150Q8×Dic11C2318yes—
151#66997C23132yes—
152#66997C23116yes—
153D4×Dic11C23116yes—
154D4×Dic11C2318yes—
155C4×C22⋊D11C23116yes—
156C4×C22⋊D11C23132yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2314yes—
165#66977C23116yes—
166#66977C23132yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2314yes—
173C2×Dic11⋊C4C2314yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2314yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C23132yes—
180C2×C4×Dic11C2312yes—
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2312yes—
183C2×C4×Dic11C2314yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2314yes—
190C2×C4×Dic11C2314yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C23116yes—
193C2×C4×Dic11C23132yes—
194#66950C23116yes—
195#66949C23132yes—
196#66949C23132yes—
197#66945C23116yes—
198#66945C2318yes—
199C4⋊C4×D11C2318yes—
200C4⋊C4×D11C23116yes—
201#66943C23116yes—
202#66942C23132yes—
203#66942C23132yes—
204#66942C23132yes—
205#66941C23116yes—
206#66941C23116yes—
207#66941C23116yes—
208#66941C23132yes—
209#66940C23116yes—
210#66940C23116yes—
211#66940C23116yes—
212#66940C2318yes—
213#66940C23116yes—
214#66940C23132yes—
215#66940C23132yes—
216#66940C2318yes—
217#66940C23116yes—
218#66940C23132yes—
219(C22⋊D11)⋊C4C23132yes—
220(C22⋊D11)⋊C4C23116yes—
221#66931C23132yes—
222#66931C23132yes—
223#66931C23132yes—
224#66930C23132yes—
225#66930C23116yes—
226C42×D11C2318yes—
227C42×D11C23116yes—
228#66923C23116yes—
229#66922C2318yes—
230C4×Dic22C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C2×Q8×#41—111nomaximal, Sylow
235C24×C11C2412yes—
236C23×D11C2411yescharacteristic
237C2×Q8×C11—24no—
238C2×Q8×C11—44no—
239C2×Q8×C11C2414yes—
240C2×Q8×C11C2418yes—
241C2×D4×C11C2×Q818yescomplemented
242C2×D4×C11C2414yes—
243C22×C4×C11—28no—
244C22×C4×C11—48no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2414yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2418yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2412yes—
251C22×C4×C11C24116yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11C2×Q8116yescomplemented
255C2×C22⋊D11C2418yes—
256C22×Dic11—216no—
257C22×Dic11—44no—
258C22×Dic11C2×Q8116yescomplemented
259C22×Dic11C24116yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2414yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2418yes—
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2412yes—
268C22×Dic11C2418yes—
269C22×Dic11C2412yes—
270Q8×D11—232no—
271#4341C2×Q8164yescomplemented
272C2×C4×D11—28no—
273C2×C4×D11—24no—
274C2×C4×D11—44no—
275C2×C4×D11—42no—
276C2×C4×D11C2×Q818yescomplemented
277C2×C4×D11C2418yes—
278C2×C4×D11C2414yes—
279C2×C4×D11C2414yes—
280C2×C4×D11C2418yes—
281C2×C4×D11C2414yes—
282C2×Dic22—216no—
283C2×Dic22—28no—
284C2×Dic22—264no—
285C2×Dic22—28no—
286C2×Dic22—48no—
287C2×Dic22C2×Q818yescomplemented
288C2×Dic22#4118yescomplemented
289C2×Dic22C2418yes—
290C2×Dic22C2418yes—
291C2×Dic22C24116yes—
292C2×Dic22C24116yes—
293C2×Dic22C2414yes—
294C2×Dic22C2414yes—
295C11×C4⋊C4C2414yes—
296C11×C4⋊C4C2418yes—
297C11×C4⋊C4C24116yes—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C24116yes—
300C11×C4⋊C4C2418yes—
301C11×C4⋊C4C2418yes—
302C11×C22⋊C4C24116yes—
303C11×C22⋊C4C2418yes—
304C42×C11C2414yes—
305C42×C11C2418yes—
306C22⋊Dic11C2418yes—
307C22⋊Dic11C24116yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C24116yes—
310C4⋊Dic11C2418yes—
311C4⋊Dic11C2414yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C2414yes—
314C4⋊Dic11C2418yes—
315C4⋊Dic11C24116yes—
316Dic11⋊C4C24116yes—
317Dic11⋊C4C2418yes—
318Dic11⋊C4C2418yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C24116yes—
322Dic11⋊C4C24116yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C24116yes—
328C4×Dic11C2418yes—
329C4×Dic11C2414yes—
330C4×Dic11C2418yes—
331C4×Dic11C24116yes—
332C4×Dic11C2418yes—
333C4×Dic11C2414yes—
334C4×Dic11C2418yes—
335C4×Dic11C2414yes—
336C4×Dic11C2418yes—
337C4×Dic11C24116yes—
338C4×Dic11C24116yes—
339C4×Dic11C2418yes—
340Q8×#41—1132no—
341C2×Q82—111no—
342C2×#557—112no—
343C2×#557—111no—
344C2×#554—114no—
345C2×#554—112no—
346C2×#554—112no—
347C2×#554D1111yescharacteristic, complemented
348C2×D4×Q8—112no—
349C2×D4×Q8—111no—
350C2×#533—111no—
351C2×#533—112no—
352C2×#533—112no—
353C2×#533—114no—
354C2×C4×#41—112no—
355C2×C4×#41—111no—
356C22×C4×Q8—111no—
357C22×C4×Q8—112no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11C22×Q818yes—
361C23×C11C2514yes—
362C23×C11C2511yescharacteristic
363C22×D11—22no—
364C22×D11—22no—
365C22×D11C22×Q814yes—
366C22×D11C2512yes—
367Q8×C11—28no—
368Q8×C11—48no—
369D4×C11C22×Q8116yescomplemented
370C2×C4×C11—24no—
371C2×C4×C11—24no—
372C2×C4×C11—28no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—216no—
376C2×C4×C11—416no—
377C2×C4×C11C22×Q814yes—
378C2×C4×C11C2×#4114yes—
379C2×C4×C11C2514yes—
380C2×C4×C11C2518yes—
381C2×C4×C11C2514yes—
382C2×C4×C11C2512yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2512yes—
386C22⋊D11C22×Q8132yescomplemented
387C2×Dic11—22no—
388C2×Dic11—28no—
389C2×Dic11—24no—
390C2×Dic11—24no—
391C2×Dic11—22no—
392C2×Dic11—232no—
393C2×Dic11—48no—
394C2×Dic11C22×Q818yes—
395C2×Dic11C22×Q814yes—
396C2×Dic11C22×Q8132yescomplemented
397C2×Dic11C2×#4118yes—
398C2×Dic11C2512yes—
399C2×Dic11C2514yes—
400C2×Dic11C2514yes—
401C2×Dic11C2518yes—
402C2×Dic11C2512yes—
403C2×Dic11C2512yes—
404C2×Dic11C2514yes—
405C2×Dic11C2514yes—
406C4×D11—28no—
407C4×D11—216no—
408C4×D11—48no—
409C4×D11—44no—
410C4×D11C22×Q8116yescomplemented
411Dic22—216no—
412Dic22—232no—
413Dic22—216no—
414Dic22—416no—
415Dic22C22×Q8116yescomplemented
416Dic22C2×#41116yescomplemented
417C22×#41—111no—
418C23×Q8—111no—
419C23×Q8—112no—
420Q82—1116no—
421#557—1132no—
422#557—1116no—
423#554—1164no—
424#554—1132no—
425#554—1132no—
426#554C2×D11116yescomplemented
427D4×Q8—1132no—
428D4×Q8—1116no—
429#533—1116no—
430#533—1132no—
431#533—1132no—
432#533—1164no—
433C2×C4⋊Q8—112no—
434C2×C4⋊Q8—114no—
435C2×C4⋊Q8—114no—
436C2×C4⋊Q8—112no—
437C2×C4⋊Q8—112no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—111no—
440C2×C4⋊Q8C2×D1111yescharacteristic
441C2×#125—114no—
442C2×#125—114no—
443C2×#125—114no—
444C2×#125—112no—
445C2×#125—112no—
446C2×#125C2×D1112yes—
447C2×C22⋊Q8—112no—
448C2×C22⋊Q8—112no—
449C2×C22⋊Q8—114no—
450C2×C22⋊Q8—114no—
451C2×C22⋊Q8—114no—
452C2×C22⋊Q8—112no—
453C2×C22⋊Q8—114no—
454C2×C22⋊Q8—114no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8C2×D1112yes—
457C2×C22⋊Q8C2×D1114yes—
458C4×#41—1132no—
459C4×#41—1116no—
460C2×C4×Q8—111no—
461C2×C4×Q8—112no—
462C2×C4×Q8—1116no—
463C2×C4×Q8—111no—
464C2×C4×Q8—112no—
465C2×C4×Q8—112no—
466C2×C4×Q8—114no—
467C2×C4×Q8—112no—
468C2×C4×Q8—114no—
469C2×C4×Q8—112no—
470C2×C4×Q8—111no—
471C2×C4×Q8—112no—
472C2×C4×Q8—114no—
473C2×C4×Q8—1132no—
474C2×C4×Q8—111no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—111no—
478C2×C4×Q8C2×D1111yescharacteristic
479C2×C4×D4—112no—
480C2×C4×D4—111no—
481C2×C4×D4—112no—
482C2×C4×D4—114no—
483C2×C4×D4—114no—
484C2×C4×D4—112no—
485C2×C4×D4C2×D1111yescharacteristic
486C2×C4×D4C2×D1112yes—
487C2×#117—112no—
488C2×#117—111no—
489C2×#117—114no—
490C2×#117—112no—
491C22×C4⋊C4—114no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—111no—
494C22×C4⋊C4C2×D1112yes—
495C22×C42—114no—
496C22×C42—112no—
497C22×C42—111no—
498C22×C42—112no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—216no—
502C22×C11C23×Q818yes—
503C22×C11C23×Q812yes—
504C22×C11C22×#4112yes—
505C22×C11#58512yes—
506C22×C11C2611yescharacteristic
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—28no—
510C2×D11C23×Q814yes—
511C4×C11—24no—
512C4×C11—24no—
513C4×C11—24no—
514C4×C11—28no—
515C4×C11—22no—
516C4×C11C23×Q814yes—
517C4×C11C22×#4114yes—
518Dic11—22no—
519Dic11—28no—
520Dic11—24no—
521Dic11—24no—
522Dic11—22no—
523Dic11C23×Q818yes—
524Dic11C23×Q814yes—
525Dic11C22×#4118yes—
526C2×#41—1116no—
527C2×#41—118no—
528C22×Q8—118no—
529C22×Q8—111no—
530C22×Q8—111no—
531C22×Q8—114no—
532C22×Q8—112no—
533C22×Q8—112no—
534C22×Q8—1116no—
535C22×Q8—114no—
536C22×Q8—2216no—
537C22×Q8—228no—
538C22×Q8C22×D1111yescharacteristic
539C22×Q8C22×D1112yes—
540C22×D4—112no—
541C22×D4C22×D1111yescharacteristic
542C23×C4—112no—
543C23×C4—111no—
544C23×C4—114no—
545C23×C4—112no—
546C23×C4—112no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—112no—
550C23×C4C22×D1112yes—
551C23×C4C22×D1114yes—
552C4⋊Q8—1116no—
553C4⋊Q8—1132no—
554C4⋊Q8—1132no—
555C4⋊Q8—1116no—
556C4⋊Q8—1116no—
557C4⋊Q8—1116no—
558C4⋊Q8—118no—
559C4⋊Q8C22×D1118yes—
560#125—1132no—
561#125—1132no—
562#125—1132no—
563#125—1116no—
564#125—1116no—
565#125C22×D11116yes—
566C22⋊Q8—1116no—
567C22⋊Q8—1116no—
568C22⋊Q8—1132no—
569C22⋊Q8—1132no—
570C22⋊Q8—1116no—
571C22⋊Q8—1132no—
572C22⋊Q8—1132no—
573C22⋊Q8—1132no—
574C22⋊Q8—1132no—
575C22⋊Q8C22×D11116yes—
576C22⋊Q8C22×D11132yes—
577C4×Q8—118no—
578C4×Q8—1116no—
579C4×Q8—118no—
580C4×Q8—1116no—
581C4×Q8—1116no—
582C4×Q8—1132no—
583C4×Q8—1116no—
584C4×Q8—1132no—
585C4×Q8—1116no—
586C4×Q8—118no—
587C4×Q8—1116no—
588C4×Q8—1132no—
589C4×Q8—118no—
590C4×Q8—1116no—
591C4×Q8—1116no—
592C4×Q8—118no—
593C4×Q8C22×D1118yes—
594C4×D4—1116no—
595C4×D4—118no—
596C4×D4—1116no—
597C4×D4—1132no—
598C4×D4—1132no—
599C4×D4—1116no—
600C4×D4C22×D1118yes—
601C4×D4C22×D11116yes—
602#117—1116no—
603#117—118no—
604#117—1132no—
605#117—1116no—
606C2×C4⋊C4—112no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—1132no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4—118no—
627C2×C4⋊C4C22×D1111yescharacteristic
628C2×C4⋊C4C22×D1112yes—
629C2×C4⋊C4C22×D1114yes—
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D11116yes—
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1114yes—
635C2×C22⋊C4—114no—
636C2×C22⋊C4—112no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1112yes—
641C2×C42—114no—
642C2×C42—112no—
643C2×C42—111no—
644C2×C42—112no—
645C2×C42—112no—
646C2×C42—114no—
647C2×C42—111no—
648C2×C42—114no—
649C2×C42—112no—
650C2×C42—112no—
651C2×C42—112no—
652C2×C42—111no—
653C2×C42—1132no—
654C2×C42—1116no—
655C2×C42—118no—
656C2×C42—1116no—
657C2×C42C22×D1112yes—
658C2×C42C22×D1111yescharacteristic
659C2×C11—28no—
660C2×C11Q8×#4114yescomplemented
661C2×C11C24×Q811yescharacteristic
662C2×C11C23×#4111yescharacteristic
663C2×C11C2×#58511yescharacteristic
664D11—24no—
665C24—111no—
666C24C23×D1112yes—
667#41—1164no—
668C2×Q8—24no—
669C2×Q8—44no—
670C2×Q8—118no—
671C2×Q8—118no—
672C2×Q8—114no—
673C2×Q8—114no—
674C2×Q8—1116no—
675C2×Q8—118no—
676C2×Q8—118no—
677C2×Q8—1116no—
678C2×Q8—2216no—
679C2×Q8—228no—
680C2×Q8—2264no—
681C2×Q8—2232no—
682C2×Q8—228no—
683C2×Q8—448no—
684C2×Q8C23×D1114yes—
685C2×Q8C23×D1118yes—
686C2×D4—1116no—
687C2×D4—118no—
688C2×D4Q8×D1118yescomplemented
689C2×D4C23×D1114yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—1116no—
693C22×C4—118no—
694C22×C4—111no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—118no—
698C22×C4—114no—
699C22×C4—1116no—
700C22×C4—111no—
701C22×C4—111no—
702C22×C4—114no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—118no—
706C22×C4—118no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—118no—
710C22×C4—228no—
711C22×C4—2216no—
712C22×C4—224no—
713C22×C4—444no—
714C22×C4—442no—
715C22×C4—444no—
716C22×C4C23×D1118yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1114yes—
719C22×C4C23×D1112yes—
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1112yes—
722C22×C4C23×D11116yes—
723C22×C4C23×D1111yescharacteristic
724C22×C4C23×D1111yescharacteristic
725C4⋊C4—118no—
726C4⋊C4—1116no—
727C4⋊C4—1116no—
728C4⋊C4—118no—
729C4⋊C4—118no—
730C4⋊C4—1116no—
731C4⋊C4—118no—
732C4⋊C4—114no—
733C4⋊C4—1116no—
734C4⋊C4—118no—
735C4⋊C4—118no—
736C4⋊C4—1116no—
737C4⋊C4—118no—
738C4⋊C4—114no—
739C4⋊C4—1116no—
740C4⋊C4—1116no—
741C4⋊C4—1116no—
742C4⋊C4—118no—
743C4⋊C4C23×D1114yes—
744C4⋊C4C23×D1118yes—
745C4⋊C4C23×D11116yes—
746C4⋊C4C23×D1118yes—
747C4⋊C4C23×D1118yes—
748C4⋊C4C23×D1114yes—
749C4⋊C4C23×D11116yes—
750C22⋊C4—1116no—
751C22⋊C4—118no—
752C22⋊C4—1116no—
753C22⋊C4—118no—
754C22⋊C4C23×D11116yes—
755C22⋊C4C23×D1118yes—
756C42—118no—
757C42—114no—
758C42—1116no—
759C42—118no—
760C42—114no—
761C42—118no—
762C42—118no—
763C42—1116no—
764C42—114no—
765C42—1116no—
766C42—118no—
767C42—118no—
768C42C23×D1118yes—
769C42C23×D1114yes—
770C11C2×Q8×#4111yescharacteristic, complemented, Sylow
771C23—24no—
772C23—24no—
773C23—114no—
774C23—112no—
775C23—222no—
776C23—222no—
777C23C2×Q8×D1118yes—
778C23C24×D1114yes—
779C23C24×D1111yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—1116no—
783Q8—1116no—
784Q8—2232no—
785Q8—2216no—
786Q8—2216no—
787Q8—4416no—
788D4—1132no—
789D4C2×Q8×D11116yescomplemented
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—216no—
796C2×C4—416no—
797C2×C4—114no—
798C2×C4—118no—
799C2×C4—1132no—
800C2×C4—118no—
801C2×C4—112no—
802C2×C4—114no—
803C2×C4—114no—
804C2×C4—1116no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—118no—
808C2×C4—114no—
809C2×C4—114no—
810C2×C4—2216no—
811C2×C4—2232no—
812C2×C4—228no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—224no—
816C2×C4—224no—
817C2×C4—228no—
818C2×C4—448no—
819C2×C4—444no—
820C2×C4—448no—
821C2×C4C2×Q8×D1114yes—
822C2×C4#41×D1114yes—
823C2×C4C24×D1114yes—
824C2×C4C24×D1118yes—
825C2×C4C24×D1114yes—
826C2×C4C24×D1112yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1112yes—
829C2×C4C24×D1112yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—114no—
834C22—222no—
835C22—222no—
836C22—228no—
837C22C22×Q8×D1118yes—
838C22C22×Q8×D1112yes—
839C22C2×#41×D1112yes—
840C22#1062345512yes—
841C22C25×D1111yescharacteristic
842C4—24no—
843C4—24no—
844C4—24no—
845C4—28no—
846C4—22no—
847C4—114no—
848C4—118no—
849C4—118no—
850C4—228no—
851C4—222no—
852C4—222no—
853C4—224no—
854C4—224no—
855C4C22×Q8×D1114yes—
856C4C2×#41×D1114yes—
857C2—28no—
858C2—224no—
859C2#1308219514yesdirect product factor
860C2C23×Q8×D1111yescharacteristic
861C2C22×#41×D1111yescharacteristic
862C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#554C2
socleC23×C11C25
prime radicalC22×#4341C22
hypercenterC2×#554D11
hypocenterC11C2×Q8×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13082195C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623098C2semidirect
4. C2×#10623216C2semidirect
5. C2×#10623070C2semidirect
6. C2×#10623042C2semidirect
7. C2×#10623167C2semidirect
8. C2×D4×Dic22C2semidirect
9. C2×#10623163C2semidirect
10. C2×#10623219C2semidirect
11. C2×#10623259C2semidirect
12. C2×#10623153C2semidirect
13. C2×#10623153C2semidirect
16. C22×#66940C2semidirect
17. C2×C4×Q8×D11C2semidirect
18. C2×C11×#554C2semidirect
22. C11×#554C22semidirect
45. #10623259C22semidirect
46. #10623253C22semidirect
47. #10623219C22semidirect
48. #10623216C22semidirect
49. #10623167C22semidirect
50. #10623163C22semidirect
51. #10623153C22semidirect
52. #10623153C22semidirect
53. C4×Q8×D11C22semidirect
54. #10623098C22semidirect
55. #10623070C22semidirect
56. D4×Dic22C22semidirect
59. #10623042C22semidirect
85. C2×#66940C22semidirect
112. C2×#4341Q8semidirect
241. C2×D4×C11C2×Q8semidirect
254. C2×C22⋊D11C2×Q8semidirect
258. C22×Dic11C2×Q8semidirect
271. #4341C2×Q8semidirect
276. C2×C4×D11C2×Q8semidirect
287. C2×Dic22C2×Q8semidirect
288. C2×Dic22#41semidirect
347. C2×#554D11semidirect
369. D4×C11C22×Q8semidirect
386. C22⋊D11C22×Q8semidirect
396. C2×Dic11C22×Q8semidirect
410. C4×D11C22×Q8semidirect
415. Dic22C22×Q8semidirect
416. Dic22C2×#41semidirect
426. #554C2×D11semidirect
660. C2×C11Q8×#41semidirect
688. C2×D4Q8×D11semidirect
770. C11C2×Q8×#41semidirect
789. D4C2×Q8×D11semidirect
859. C2#13082195direct (N × H)

Maximal subgroups

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

subgroupindex
#130821952
C2×#106232532
C2×#106230982
C2×#106232162
C2×#106230702
C2×#106230422
C2×#106231672
C2×D4×Dic222
C2×#106231632
C2×#106232192
C2×#106232592
C2×#106231532
C2×C4×#43412
C22×#669402
C2×C4×Q8×D112
C2×C11×#5542
C2×Q8×#4111