Finite Group Databasebeta

← C2×#13077719 #15618739

Subgroups — C2×#13077719 #15618739

Order 2816.

1706 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13077719C2116yesmaximal, direct product factor
3C2×#10622637C211yesmaximal, characteristic, complemented
4C2×#10622292C211yesmaximal, characteristic, complemented
5C2×#10622441C211yesmaximal, characteristic, complemented
6C2×#10622441C211yesmaximal, characteristic, complemented
7C2×#10622314C211yesmaximal, characteristic, complemented
8C2×#10622314C211yesmaximal, characteristic, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622322C211yesmaximal, characteristic
11C2×#10622453C211yesmaximal, characteristic
12C2×#10622453C211yesmaximal, characteristic
13C2×#10622303C211yesmaximal, characteristic
14C2×#10622448C211yesmaximal, characteristic
15C2×#10622318C211yesmaximal, characteristic
16C2×C11×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C411yescharacteristic
19C2×#66997C411yescharacteristic
20#10623109C418yes—
21#10623109C2218yes—
22C2×#66950C411yescharacteristic
23C2×#66949C411yescharacteristic
24C2×#66949C411yescharacteristic
25C2×#66942C411yescharacteristic
26C2×#66942C411yescharacteristic
27C2×#66941C411yescharacteristic
28C2×#66925C2211yescharacteristic
29C2×#66925C2211yescharacteristic
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#446C2218yescomplemented
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×Dic11⋊C8C2211yescharacteristic
54C2×Dic11⋊C8C2211yescharacteristic
55C2×C8×Dic11C2211yescharacteristic
56C2×C8×Dic11C2211yescharacteristic
57#10622637C2218yescomplemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×C4⋊(C11⋊C8)C2211yescharacteristic
60C2×C4⋊(C11⋊C8)C2211yescharacteristic
61C2×#66867C2211yescharacteristic
62C2×#66867C2211yescharacteristic
63C2×C4×C11⋊C8C2211yescharacteristic
64#10622453C2218yes—
65#10622453C2218yes—
66#10622448C2218yes—
67#10622444C2218yescomplemented
68#10622441C2218yescomplemented
69#10622441C2218yescomplemented
70#10622322C2218yes—
71#10622318C2218yes—
72#10622314C2218yescomplemented
73#10622314C2218yescomplemented
74#10622303C2218yes—
75#10622292C2218yescomplemented
76C22×Q8×C11C2×C411yescharacteristic
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22C2×C411yescharacteristic
81C22×Dic22C2×C411yescharacteristic
82C22×Dic22C2×C411yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C4×Q8×C11C2×C414yes—
88C4×Q8×C11C2314yes—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95#66999C2×C418yes—
96#66997C2×C418yes—
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×Dic11⋊C4C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66950C2×C418yes—
124#66949C2×C418yes—
125#66949C2×C418yes—
126#66942C2×C418yes—
127#66942C2×C418yes—
128#66941C2×C418yes—
129#66925C2×C414yes—
130#66925C2×C414yes—
131#66925C2314yes—
132#66925C2314yes—
133C42×D11C2×C414yes—
134C42×D11C2314yes—
135C4×Dic22C2×C414yes—
136C4×Dic22C2×C414yes—
137C4×Dic22C2×C414yes—
138C4×Dic22C2314yes—
139C4×Dic22C2314yes—
140C4×Dic22C2314yes—
141C11×C4⋊C8C2314yes—
142C11×C4⋊C8C2314yes—
143C11×C4⋊C8C2314yes—
144C11×#97C2314yes—
145C11×#97C2314yes—
146C4×C8×C11C2314yes—
147(C2×D11)⋊C8C2314yes—
148(C2×D11)⋊C8C2314yes—
149(C2×D11)⋊C8C2314yes—
150(C2×D11)⋊C8C2314yes—
151#66879C2314yes—
152#66879C2314yes—
153#66879C2314yes—
154#66879C2314yes—
155Dic11⋊C8C2314yes—
156Dic11⋊C8C2314yes—
157Dic11⋊C8C2314yes—
158Dic11⋊C8C2314yes—
159Dic11⋊C8C2314yes—
160Dic11⋊C8C2314yes—
161C8×Dic11C2314yes—
162C8×Dic11C2314yes—
163C4⋊(C11⋊C8)C2314yes—
164C4⋊(C11⋊C8)C2314yes—
165C4⋊(C11⋊C8)C2314yes—
166#66867C2314yes—
167#66867C2314yes—
168C4×C11⋊C8C2314yes—
169C2×#2987—111nomaximal, Sylow
170C23×D11C22×C411yescharacteristic
171C2×Q8×C11—42no—
172C2×Q8×C11C22×C414yes—
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11C22×C412yes—
192C2×C4×D11C22×C414yes—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C2412yes—
195C2×Dic22—42no—
196C2×Dic22—42no—
197C2×Dic22—42no—
198C2×Dic22C22×C414yes—
199C2×Dic22C22×C414yes—
200C2×Dic22C22×C414yes—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11—22no—
204C2×C8×C11—22no—
205C2×C8×C11C2412yes—
206C2×C8×C11C2412yes—
207C2×C8×C11C2412yes—
208C2×C8×C11C2412yes—
209C11×C4⋊C4C22×C414yes—
210C11×C4⋊C4C22×C414yes—
211C11×C4⋊C4C22×C414yes—
212C42×C11C22×C412yes—
213C42×C11C22×C412yes—
214C42×C11C22×C412yes—
215C42×C11C2412yes—
216C42×C11C2412yes—
217C42×C11C2412yes—
218(C2×D11)⋊C4C22×C414yes—
219(C2×D11)⋊C4C22×C414yes—
220(C2×D11)⋊C4C22×C414yes—
221(C2×D11)⋊C4C22×C414yes—
222C4⋊Dic11C22×C414yes—
223C4⋊Dic11C22×C414yes—
224C4⋊Dic11C22×C414yes—
225Dic11⋊C4C22×C414yes—
226Dic11⋊C4C22×C414yes—
227Dic11⋊C4C22×C414yes—
228Dic11⋊C4C22×C414yes—
229Dic11⋊C4C22×C414yes—
230Dic11⋊C4C22×C414yes—
231Dic11⋊C4C22×C414yes—
232Dic11⋊C4C22×C414yes—
233Dic11⋊C4C22×C414yes—
234Dic11⋊C4C22×C414yes—
235C4×Dic11C22×C412yes—
236C4×Dic11C22×C412yes—
237C4×Dic11C22×C412yes—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C414yes—
240C4×Dic11C2412yes—
241C4×Dic11C2412yes—
242C4×Dic11C2412yes—
243C2×C11⋊C8—22no—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8C2412yes—
248C2×C11⋊C8C2412yes—
249C2×C11⋊C8C2412yes—
250C2×C11⋊C8C2412yes—
251C2×#533—111no—
252#2987—1116no—
253C2×#446—111no—
254C2×#446—111no—
255C2×#446—111no—
256C2×#446—111no—
257C2×#446—111no—
258C2×#446—111no—
259C2×#446—111no—
260C2×#446D1111yescharacteristic, complemented
261C2×#433—111no—
262C2×#433—111no—
263C2×#433—111no—
264C2×#433—111no—
265C2×#432—111no—
266C2×#432—111no—
267C23×C11C23×C411yescharacteristic
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11C23×C412yes—
272Q8×C11—44no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11C23×C412yes—
280C2×C4×C11C23×C412yes—
281C2×C4×C11C23×C412yes—
282C2×C4×C11C23×C412yes—
283C2×C4×C11C23×C412yes—
284C2×C4×C11C23×C412yes—
285C2×C4×C11C23×C411yescharacteristic
286C2×C4×C112−1+412yes—
287C2×C4×C112−1+412yes—
288C2×C4×C11C2511yescharacteristic
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C412yes—
299C2×Dic11C23×C412yes—
300C2×Dic11C23×C412yes—
301C2×Dic11C23×C412yes—
302C2×Dic11C23×C412yes—
303C4×D11—24no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—44no—
307C4×D11—44no—
308Dic22—44no—
309Dic22—44no—
310Dic22—44no—
311C8×C11—22no—
312C8×C11—22no—
313C8×C11—22no—
314C8×C11—22no—
315C11⋊C8—22no—
316C11⋊C8—22no—
317C11⋊C8—22no—
318C11⋊C8—22no—
319#533—118no—
320#533—118no—
321C2×C4⋊Q8—111no—
322C2×C4⋊Q8—111no—
323C2×#125—111no—
324C2×#125—111no—
325C2×C22⋊Q8—111no—
326C2×C22⋊Q8—111no—
327C2×C22⋊Q8—111no—
328C2×C22⋊Q8—111no—
329C2×C4×Q8—111no—
330C2×C4×Q8—111no—
331C2×C4×Q8—111no—
332C2×C4×Q8C2×D1111yescharacteristic
333C2×#117—111no—
334C2×#117—111no—
335C22×C42—111no—
336#446—118no—
337#446—118no—
338#446—118no—
339#446—118no—
340#446—118no—
341#446—118no—
342#446—118no—
343#446C2×D1118yescomplemented
344#433—118no—
345#433—118no—
346#433—118no—
347#433—118no—
348#432—118no—
349#432—118no—
350C2×C4⋊C8—111no—
351C2×C4⋊C8—111no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358C2×C4⋊C8—111no—
359C2×C4⋊C8C2×D1111yescharacteristic
360C2×C4⋊C8C2×D1111yescharacteristic
361C2×C4⋊C8C2×D1111yescharacteristic
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×#97—111no—
369C2×#97—111no—
370C2×#97—111no—
371C2×#97—111no—
372C2×#97C2×D1111yescharacteristic
373C2×#97C2×D1111yescharacteristic
374C2×C4×C8—111no—
375C2×C4×C8—111no—
376C2×C4×C8—111no—
377C2×C4×C8C2×D1111yescharacteristic
378C22×C11#51912yes—
379C22×C11#56812yes—
380C22×C11#56812yes—
381C22×C11C24×C411yescharacteristic
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—22no—
385C2×D11—44no—
386C4×C11—22no—
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11#51912yes—
393C4×C11C2×2−1+411yescharacteristic
394C4×C11C2×2−1+411yescharacteristic
395Dic11—22no—
396Dic11—22no—
397Dic11—22no—
398Dic11—22no—
399Dic11—22no—
400Dic11—22no—
401Dic11—22no—
402C22×Q8—111no—
403C22×Q8—111no—
404C22×Q8—111no—
405C22×Q8C4×D1111yescharacteristic
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C4⋊Q8—118no—
418C4⋊Q8—118no—
419#125—118no—
420#125—118no—
421C22⋊Q8—118no—
422C22⋊Q8—118no—
423C22⋊Q8—118no—
424C22⋊Q8—118no—
425C4×Q8—114no—
426C4×Q8—114no—
427C4×Q8—114no—
428C4×Q8—114no—
429C4×Q8—114no—
430C4×Q8—114no—
431C4×Q8C4×D1114yes—
432C4×Q8C22×D1114yes—
433#117—114no—
434#117—114no—
435#117—114no—
436#117—114no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C4⋊C4—111no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4C4×D1111yescharacteristic
451C2×C4⋊C4C4×D1111yescharacteristic
452C2×C4⋊C4C4×D1111yescharacteristic
453C2×C22⋊C4—111no—
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—111no—
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—114no—
463C2×C42—114no—
464C2×C42C22×D1111yescharacteristic
465C2×C42C22×D1111yescharacteristic
466C2×C42C22×D1111yescharacteristic
467C4⋊C8—114no—
468C4⋊C8—114no—
469C4⋊C8—114no—
470C4⋊C8—114no—
471C4⋊C8—114no—
472C4⋊C8—114no—
473C4⋊C8—114no—
474C4⋊C8—114no—
475C4⋊C8—114no—
476C4⋊C8C22×D1114yes—
477C4⋊C8C22×D1114yes—
478C4⋊C8C22×D1114yes—
479C22⋊C8—114no—
480C22⋊C8—114no—
481C22⋊C8—114no—
482C22⋊C8—114no—
483#97—114no—
484#97—114no—
485#97—114no—
486#97—114no—
487#97—114no—
488#97—114no—
489#97C22×D1114yes—
490#97C22×D1114yes—
491C4×C8—114no—
492C4×C8—114no—
493C4×C8—114no—
494C4×C8C22×D1114yes—
495C2×C11#298714yescomplemented
496C2×C11C2×#51911yescharacteristic
497C2×C11C2×#56811yescharacteristic
498C2×C11C2×#56811yescharacteristic
499D11—42no—
500C24—111no—
501C2×Q8—42no—
502C2×Q8—114no—
503C2×Q8—114no—
504C2×Q8—114no—
505C2×Q8—442no—
506C2×Q8—442no—
507C2×Q8—442no—
508C2×Q8C2×C4×D1114yes—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—112no—
517C22×C4—112no—
518C22×C4—114no—
519C22×C4—114no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×C4×D1111yescharacteristic
526C22×C4C2×C4×D1111yescharacteristic
527C22×C4C2×C4×D1111yescharacteristic
528C22×C4C2×C4×D1111yescharacteristic
529C22×C4C2×C4×D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—112no—
536C2×C8—112no—
537C2×C8—112no—
538C2×C8—112no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—222no—
542C2×C8—222no—
543C2×C8C23×D1112yes—
544C2×C8C23×D1112yes—
545C2×C8C23×D1112yes—
546C2×C8C23×D1112yes—
547C4⋊C4—114no—
548C4⋊C4—114no—
549C4⋊C4—114no—
550C4⋊C4—114no—
551C4⋊C4—114no—
552C4⋊C4—114no—
553C4⋊C4—114no—
554C4⋊C4—114no—
555C4⋊C4—114no—
556C4⋊C4—114no—
557C4⋊C4—114no—
558C4⋊C4—114no—
559C4⋊C4—114no—
560C4⋊C4C2×C4×D1114yes—
561C4⋊C4C2×C4×D1114yes—
562C4⋊C4C2×C4×D1114yes—
563C22⋊C4—114no—
564C22⋊C4—114no—
565C22⋊C4—114no—
566C22⋊C4—114no—
567C42—112no—
568C42—114no—
569C42—114no—
570C42—112no—
571C42—112no—
572C42—112no—
573C42—112no—
574C42—112no—
575C42C2×C4×D1112yes—
576C42C2×C4×D1112yes—
577C42C2×C4×D1112yes—
578C42C23×D1112yes—
579C42C23×D1112yes—
580C42C23×D1112yes—
581C11C2×#298711yescharacteristic, complemented, Sylow
582C23—112no—
583C23—222no—
584C23—222no—
585C23—222no—
586C23C22×C4×D1111yescharacteristic
587Q8—44no—
588Q8—444no—
589Q8—444no—
590Q8—444no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—444no—
615C2×C4—444no—
616C2×C4C22×C4×D1112yes—
617C2×C4C22×C4×D1112yes—
618C2×C4C22×C4×D1112yes—
619C2×C4C22×C4×D1112yes—
620C2×C4C22×C4×D1112yes—
621C2×C4C22×C4×D1112yes—
622C2×C4C22×C4×D1111yescharacteristic
623C2×C4#6704012yes—
624C2×C4#6704312yes—
625C2×C4C24×D1111yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—222no—
631C8—222no—
632C8—222no—
633C8—222no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—444no—
638C22#1062310312yes—
639C22#1062327612yes—
640C22#1062328112yes—
641C22C23×C4×D1111yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—222no—
649C4—222no—
650C4—222no—
651C4—222no—
652C4—222no—
653C4—222no—
654C4—222no—
655C4#1062310312yes—
656C4C2×#6704011yescharacteristic
657C4C2×#6704311yescharacteristic
658C2—442no—
659C2#1307771914yesdirect product factor
660C2C2×#1062310311yescharacteristic
661C2C2×#1062328111yescharacteristic
662C2C2×#1062327611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#446C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenterC2×#446D11
hypocenterC11C2×#2987
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13077719C2direct (N × H)
3. C2×#10622637C2semidirect
4. C2×#10622292C2semidirect
5. C2×#10622441C2semidirect
6. C2×#10622441C2semidirect
7. C2×#10622314C2semidirect
8. C2×#10622314C2semidirect
9. C2×#10622444C2semidirect
16. C2×C11×#446C2semidirect
34. C11×#446C22semidirect
57. #10622637C22semidirect
67. #10622444C22semidirect
68. #10622441C22semidirect
69. #10622441C22semidirect
72. #10622314C22semidirect
73. #10622314C22semidirect
75. #10622292C22semidirect
260. C2×#446D11semidirect
343. #446C2×D11semidirect
495. C2×C11#2987semidirect
581. C11C2×#2987semidirect
659. C2#13077719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
#130777192
C2×#106226372
C2×#106222922
C2×#106224412
C2×#106223142
C2×#106224442
C2×#106223222
C2×#106224532
C2×#106223032
C2×#106224482
C2×#106223182
C2×C11×#4462
C2×#298711