Finite Group Databasebeta

← C2×#13081384 #15633554

Subgroups — C2×#13081384 #15633554

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2#13081384C2116yesmaximal, direct product factor
3C2×#10622680C211yesmaximal, characteristic
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622681C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622679C211yesmaximal, characteristic, complemented
8C2×#10622697C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622641C211yesmaximal, characteristic, complemented
11C2×#10622640C211yesmaximal, characteristic
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622643C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4325C211yesmaximal, characteristic, complemented
16C2×C11×#557C211yesmaximal, characteristic, complemented
17C11×#557—24no—
18C11×#557C2218yescomplemented
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#125C2211yescharacteristic
25C2×C4×Q8×C11—21no—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×#67000—21no—
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34#10623116—24no—
35#10623116C2218yes—
36C2×#66947—21no—
37C2×#66947—21no—
38C2×#66946—21no—
39C2×#66928C2211yescharacteristic
40C2×#66928C2211yescharacteristic
41C2×#66927C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46#10622702C2218yescomplemented
47#10622697C2218yescomplemented
48#10622681C2218yescomplemented
49#10622680C2218yes—
50#10622679C2218yescomplemented
51#10622676C2218yescomplemented
52#10622643C2218yescomplemented
53#10622641C2218yescomplemented
54#10622641C2218yescomplemented
55#10622640C2218yes—
56#10622639C2218yescomplemented
57C4×#4325C2218yescomplemented
58#10622637C2218yescomplemented
59C2×#66874C2211yescharacteristic
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11D411yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D44—21no—
81C22×D44—21no—
82C22×D44C2311yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C11×C4⋊Q8—28no—
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8C2314yes—
90C11×#125—28no—
91C11×#125—28no—
92C11×#125—22no—
93C11×#125—22no—
94C11×#125C2314yes—
95C11×#125C2314yes—
96C4×Q8×C11—28no—
97C4×Q8×C11—22no—
98C4×Q8×C11—22no—
99C4×Q8×C11—22no—
100C4×Q8×C11D414yes—
101C4×Q8×C11C2314yes—
102C4×Q8×C11C2314yes—
103C4×Q8×C11C2314yes—
104C4×Q8×C11C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C4⋊C4D411yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125#67000—28no—
126C2×#4326—24no—
127C2×#4326C2314yes—
128C2×#4325—24no—
129C2×#4325—24no—
130C2×#4325C2314yes—
131C2×#4325C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×C4×Dic11—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66947—28no—
146#66947—28no—
147#66946—28no—
148#66928—22no—
149#66928—22no—
150#66928C2314yes—
151#66928C2314yes—
152#66927—22no—
153#66927C2314yes—
154C4×D44—22no—
155C4×D44—22no—
156C4×D44C2314yes—
157C4×D44C2314yes—
158C4×Dic22—22no—
159C4×Dic22C2314yes—
160#66899C2314yes—
161#66874C2314yes—
162#66874C2314yes—
163#66874C2314yes—
164#66873C2314yes—
165#66873C2314yes—
166#66873C2314yes—
167#66873C2314yes—
168#66873C2314yes—
169#66873C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66871C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179C2×#3371—111nomaximal, Sylow
180C23×D11—21no—
181C23×D11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—24no—
184C2×Q8×C11—22no—
185C2×Q8×C11—42no—
186C2×Q8×C11—44no—
187C2×Q8×C11C2×D414yes—
188C2×Q8×C11#4114yes—
189C2×Q8×C11C2412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—24no—
206C2×D44—24no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—44no—
212C2×D44—82no—
213C2×D44C2412yes—
214C2×D44C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—82no—
218C2×C4×D11—82no—
219C2×Dic22—21no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22C2412yes—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4C2×D414yes—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4C2×D414yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C42×C11—24no—
241C42×C11—24no—
242C42×C11—24no—
243C42×C11C2×D412yes—
244C42×C11C2×D412yes—
245C42×C11C2×D412yes—
246C42×C11C2412yes—
247C42×C11C2412yes—
248C42×C11C2412yes—
249#4326—28no—
250#4325—28no—
251#4325—28no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261C4×Dic11—24no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×#559—111no—
271C2×#557D1111yescharacteristic, complemented
272#3371—1116no—
273C2×#490—111no—
274C2×#489—111no—
275C2×#488—111no—
276C2×#479—111no—
277C2×#478—111no—
278C2×#476—111no—
279C2×#464—111no—
280C2×#464—111no—
281C2×#460—111no—
282C2×#446—111no—
283C2×#441—111no—
284C2×#440—111no—
285C2×C4×SD16—111no—
286C23×C11C22×D411yescharacteristic
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295Q8×C11—24no—
296Q8×C11—22no—
297Q8×C11—44no—
298Q8×C11—48no—
299Q8×C11C2×#4114yes—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C112−1+412yes—
323C2×C4×C11C2511yescharacteristic
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—22no—
332D44—48no—
333D44—42no—
334D44—42no—
335D44—84no—
336C4×D11—84no—
337C4×D11—84no—
338Dic22—22no—
339Dic22—22no—
340Dic22—42no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C22×Q16—111no—
346C22×SD16—111no—
347C22×SD16—111no—
348#559—118no—
349#559—224no—
350#557—24no—
351#557C2×D1118yescomplemented
352C2×C4⋊Q8—21no—
353C2×C4⋊Q8C2×D1111yescharacteristic
354C2×#127—111no—
355C2×#125—21no—
356C2×#125—21no—
357C2×#125C2×D1111yescharacteristic
358C2×#125C2×D1111yescharacteristic
359C2×#124—111no—
360C2×#124—111no—
361C2×#124—221no—
362C2×#123—221no—
363C2×#123—221no—
364C2×C4×Q8—21no—
365C2×C4×Q8—111no—
366C2×C4×Q8C2×D1111yescharacteristic
367C2×C4×Q8C2×D1111yescharacteristic
368C2×C4×Q8C2×D1111yescharacteristic
369C2×C4×Q8C2×D1111yescharacteristic
370C2×C4×D4—111no—
371C2×C4×D4—111no—
372C2×C4×D4—221no—
373#490—118no—
374#489—118no—
375#488—118no—
376#479—118no—
377#478—118no—
378#476—118no—
379#464—118no—
380#464—118no—
381#460—118no—
382#446—118no—
383#441—118no—
384#440—118no—
385C4×SD16—118no—
386C2×#107—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391C2×C4⋊C8—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×#102—111no—
401C2×#102—111no—
402C2×#97—111no—
403C2×#97—111no—
404C2×C4×C8—111no—
405C22×C11#54812yes—
406C22×C11#57512yes—
407C22×C11#57712yes—
408C22×C11C23×D411yescharacteristic
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—84no—
416C2×D11—84no—
417C4×C11—24no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11#54812yes—
428C4×C11C22×#4111yescharacteristic
429C4×C11C2×2−1+411yescharacteristic
430Dic11—42no—
431Dic11—42no—
432C22×Q8—21no—
433C22×Q8—111no—
434C22×Q8C22⋊D1111yescharacteristic
435C22×Q8C22×D1111yescharacteristic
436C22×D4—111no—
437C22×D4—111no—
438C22×D4—221no—
439C22×D4—221no—
440C23×C4—221no—
441C23×C4—221no—
442C2×Q16—114no—
443C2×Q16—224no—
444C2×SD16—114no—
445C2×SD16—114no—
446C2×SD16—224no—
447C2×SD16—224no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C4⋊Q8—28no—
453C4⋊Q8—22no—
454C4⋊Q8C22×D1114yes—
455#127—114no—
456#127—222no—
457#125—28no—
458#125—28no—
459#125—22no—
460#125—22no—
461#125C22×D1114yes—
462#125C22×D1114yes—
463#124—114no—
464#124—114no—
465#124—228no—
466#124—222no—
467#124—222no—
468#123—228no—
469#123—228no—
470C4×Q8—28no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—114no—
475C4×Q8—222no—
476C4×Q8C22⋊D1114yes—
477C4×Q8C22×D1114yes—
478C4×Q8C22×D1114yes—
479C4×Q8C22×D1114yes—
480C4×Q8C22×D1114yes—
481C4×D4—114no—
482C4×D4—114no—
483C4×D4—228no—
484C4×D4—222no—
485C4×D4—222no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22⋊D1111yescharacteristic
498C2×C4⋊C4C22⋊D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—221no—
512C2×C42C22×D1111yescharacteristic
513C2×C42C22×D1111yescharacteristic
514C2×C42C22×D1111yescharacteristic
515#107—114no—
516#106—114no—
517#106—114no—
518C4⋊C8—114no—
519C4⋊C8—114no—
520C4⋊C8—114no—
521#103—114no—
522#103—114no—
523#103—114no—
524#103—114no—
525#102—114no—
526#102—114no—
527#102—114no—
528#102—114no—
529#102—114no—
530#102—114no—
531#97—114no—
532#97—114no—
533C4×C8—114no—
534C2×C11#337114yescomplemented
535C2×C11C2×#54811yescharacteristic
536C2×C11C2×#57511yescharacteristic
537C2×C11C2×#57711yescharacteristic
538D11—82no—
539D11—82no—
540C24—221no—
541C24—221no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—42no—
546C2×Q8—44no—
547C2×Q8—112no—
548C2×Q8—221no—
549C2×Q8—222no—
550C2×Q8—222no—
551C2×Q8#434314yes—
552C2×Q8C2×C22⋊D1114yes—
553C2×Q8C23×D1112yes—
554C2×D4—112no—
555C2×D4—112no—
556C2×D4—222no—
557C2×D4—222no—
558C2×D4—222no—
559C2×D4—222no—
560C2×D4—224no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—224no—
564C2×D4—444no—
565C2×D4—882no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—224no—
573C22×C4—224no—
574C22×C4—882no—
575C22×C4—882no—
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583Q16—228no—
584SD16—228no—
585SD16—228no—
586C2×C8—112no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—112no—
590C2×C8—222no—
591C2×C8—222no—
592C2×C8—222no—
593C2×C8—222no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—112no—
606C4⋊C4—221no—
607C4⋊C4—224no—
608C4⋊C4C2×C22⋊D1114yes—
609C4⋊C4C2×C22⋊D1114yes—
610C4⋊C4C2×C22⋊D1114yes—
611C4⋊C4C23×D1112yes—
612C4⋊C4C23×D1112yes—
613C4⋊C4C23×D1112yes—
614C22⋊C4—224no—
615C22⋊C4—224no—
616C22⋊C4—224no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C42—24no—
621C42—24no—
622C42—24no—
623C42—224no—
624C42C2×C22⋊D1112yes—
625C42C2×C22⋊D1112yes—
626C42C2×C22⋊D1112yes—
627C42C23×D1112yes—
628C42C23×D1112yes—
629C42C23×D1112yes—
630C11C2×#337111yescharacteristic, complemented, Sylow
631C23—222no—
632C23—222no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23C22×C22⋊D1111yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—222no—
645Q8—222no—
646Q8—442no—
647Q8C2×#434314yes—
648D4—222no—
649D4—222no—
650D4—222no—
651D4—222no—
652D4—448no—
653D4—442no—
654D4—442no—
655D4—884no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—884no—
675C2×C4—884no—
676C2×C4C2×#434312yes—
677C2×C4#6704012yes—
678C2×C4C22×C22⋊D1112yes—
679C2×C4C22×C22⋊D1112yes—
680C2×C4C22×C22⋊D1112yes—
681C2×C4C22×C22⋊D1112yes—
682C2×C4C22×C22⋊D1112yes—
683C2×C4C22×C22⋊D1112yes—
684C2×C4C22×C22⋊D1111yescharacteristic
685C2×C4C24×D1111yescharacteristic
686C8—222no—
687C8—222no—
688C8—222no—
689C8—222no—
690C22—442no—
691C22—442no—
692C22—442no—
693C22—442no—
694C22—442no—
695C22—442no—
696C22—884no—
697C22—884no—
698C22#1062334812yes—
699C22#1062335312yes—
700C22#1062336812yes—
701C22C23×C22⋊D1111yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—442no—
713C4—442no—
714C4#1062334812yes—
715C4C22×#434311yescharacteristic
716C4C2×#6704011yescharacteristic
717C2—882no—
718C2—882no—
719C2#1308138414yesdirect product factor
720C2C2×#1062334811yescharacteristic
721C2C2×#1062335311yescharacteristic
722C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#557D11
hypocenterC11C2×#3371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081384C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622681C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622679C2semidirect
8. C2×#10622697C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622641C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622643C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4325C2semidirect
16. C2×C11×#557C2semidirect
18. C11×#557C22semidirect
46. #10622702C22semidirect
47. #10622697C22semidirect
48. #10622681C22semidirect
50. #10622679C22semidirect
51. #10622676C22semidirect
52. #10622643C22semidirect
53. #10622641C22semidirect
54. #10622641C22semidirect
56. #10622639C22semidirect
57. C4×#4325C22semidirect
58. #10622637C22semidirect
271. C2×#557D11semidirect
351. #557C2×D11semidirect
534. C2×C11#3371semidirect
630. C11C2×#3371semidirect
719. C2#13081384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130813842
C2×#106226802
C2×#106227022
C2×#106226812
C2×#106226762
C2×#106226792
C2×#106226972
C2×#106226412
C2×#106226402
C2×#106226372
C2×#106226432
C2×#106226392
C2×C4×#43252
C2×C11×#5572
C2×#337111