Finite Group Databasebeta

← C2×#13081335 #15633449

Subgroups — C2×#13081335 #15633449

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623099C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081335C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622405C211yesmaximal, characteristic, complemented
7C2×#10622634C211yesmaximal, characteristic, complemented
8C2×#10622488C211yesmaximal, characteristic, complemented
9C2×#10622503C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic
11C2×#10622629C211yesmaximal, characteristic
12C2×#10622775C211yesmaximal, characteristic, complemented
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622369C211yesmaximal, characteristic
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C23×Dic22—21no—
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×#66977—21no—
28#10623099—24no—
29#10623099C2218yescomplemented
30D4×Dic22—24no—
31D4×Dic22C2218yescomplemented
32C2×#66951—21no—
33C2×#66949—21no—
34C2×#66946C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66931—21no—
39C2×#66931—21no—
40C2×#66929—21no—
41C2×#66928C2211yescharacteristic
42C2×#66925—21no—
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#440C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52#10622778C2218yes—
53#10622775C2218yescomplemented
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622634C2218yescomplemented
63#10622629C2218yes—
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622503C2218yescomplemented
70#10622488C2218yescomplemented
71#10622408C2218yescomplemented
72#10622405C2218yescomplemented
73#10622370C2218yescomplemented
74#10622369C2218yes—
75#10622327C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×Dic11—21no—
81C23×Dic11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22—21no—
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×Dic22—28no—
88C22×Dic22—48no—
89C22×Dic22D411yescharacteristic
90C22×Dic22C2311yescharacteristic
91C2×C11×SD16—24no—
92C2×C11×SD16C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C4×Q8×C11—22no—
96C4×Q8×C11C2314yes—
97C4×D4×C11—22no—
98C4×D4×C11C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#67000—22no—
108#67000C2314yes—
109#66997—22no—
110#66997C2314yes—
111D4×Dic11—22no—
112D4×Dic11—22no—
113D4×Dic11C2314yes—
114D4×Dic11C2314yes—
115C2×#4324—24no—
116C2×#4324C2314yes—
117C2×#4323—24no—
118C2×#4323C2314yes—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11D411yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128#66977—28no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141#66951—28no—
142#66949—28no—
143#66946—22no—
144#66946C2314yes—
145#66941—22no—
146#66941—22no—
147#66941C2314yes—
148#66941C2314yes—
149#66940—22no—
150#66940C2314yes—
151#66931—28no—
152#66931—28no—
153#66929—28no—
154#66928—22no—
155#66928C2314yes—
156#66925—28no—
157#66922—22no—
158#66922C2314yes—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×#107C2314yes—
162C11×#103C2314yes—
163C11×#102C2314yes—
164C11×#97C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66880C2314yes—
170#66880C2314yes—
171#66879C2314yes—
172Dic11⋊C8C2314yes—
173Dic11⋊C8C2314yes—
174C8×Dic11C2314yes—
175#66874C2314yes—
176#66873C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3367—111nomaximal, Sylow
181C24×C11—21no—
182C23×D11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11#4114yes—
190C2×D4×C11C2412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—24no—
195C22×C4×C11—44no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—21no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44C2412yes—
214C2×C4×D11—24no—
215C2×C4×D11—44no—
216C2×Dic22—24no—
217C2×Dic22—24no—
218C2×Dic22—24no—
219C2×Dic22—24no—
220C2×Dic22—21no—
221C2×Dic22—22no—
222C2×Dic22—22no—
223C2×Dic22—44no—
224C2×Dic22—432no—
225C2×Dic22—44no—
226C2×Dic22—44no—
227C2×Dic22C2×D414yes—
228C2×Dic22C2412yes—
229C11×SD16—28no—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245#4324—28no—
246#4323—28no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—24no—
255C4⋊Dic11C2×D414yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4C2×D414yes—
264Dic11⋊C4C2×D414yes—
265C4×Dic11—24no—
266C4×Dic11C2×D412yes—
267C4×Dic11C2×D412yes—
268C4×Dic11C2412yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274C2×#556—111no—
275C2×D4×Q8—111no—
276#3367—1116no—
277C2×#489—111no—
278C2×#489—111no—
279C2×#487—111no—
280C2×#477—111no—
281C2×#477—111no—
282C2×#474—111no—
283C2×#463—111no—
284C2×#463—111no—
285C2×#461—111no—
286C2×#446—111no—
287C2×#440—111no—
288C2×#440D1111yescharacteristic, complemented
289C2×C4×D8—111no—
290C23×C11—24no—
291C23×C11—22no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—42no—
302D4×C11—24no—
303D4×C11—22no—
304D4×C11C2×#4114yes—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—48no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4112yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—48no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—48no—
331C2×Dic11AGL(1,ℤ/8)14yes—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336D44—22no—
337D44—22no—
338D44—42no—
339C4×D11—48no—
340Dic22—28no—
341Dic22—22no—
342Dic22—22no—
343Dic22—48no—
344Dic22—48no—
345Dic22—42no—
346Dic22—48no—
347C8×C11—22no—
348C8×C11—22no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C23×Q8—221no—
352C22×SD16—111no—
353C22×SD16C2×D1111yescharacteristic
354C22×D8—111no—
355#556—118no—
356#556—224no—
357D4×Q8—118no—
358D4×Q8—224no—
359C2×C4⋊Q8—111no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8—111no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#124—111no—
366C2×#124—111no—
367C2×C22⋊Q8—221no—
368C2×C22⋊Q8—221no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8—221no—
371C2×C4×Q8—111no—
372C2×C4×Q8—111no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4C2×D1111yescharacteristic
378C2×#117—221no—
379#489—118no—
380#489—118no—
381#487—118no—
382#477—118no—
383#477—118no—
384#474—118no—
385#463—118no—
386#463—118no—
387#461—118no—
388#446—118no—
389#440—118no—
390#440C2×D1118yescomplemented
391C4×D8—118no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107C2×D1111yescharacteristic
395C2×C4⋊C8—111no—
396C2×C4⋊C8—111no—
397C2×C4⋊C8—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103C2×D1111yescharacteristic
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102C2×D1111yescharacteristic
408C2×#97—111no—
409C2×#97C2×D1111yescharacteristic
410C2×C4×C8—111no—
411C22×C11—24no—
412C22×C11—48no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11#54812yes—
416C22×C11C2×AGL(1,ℤ/8)12yes—
417C22×C11#57812yes—
418C22×C11C23×D411yescharacteristic
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—84no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11#54812yes—
429C4×C11C22×#4111yescharacteristic
430C4×C11C2×2−1+411yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437Dic11C2×AGL(1,ℤ/8)14yes—
438C22×Q8—111no—
439C22×Q8—111no—
440C22×Q8—221no—
441C22×Q8—221no—
442C22×Q8—228no—
443C22×Q8—221no—
444C22×Q8—448no—
445C22×Q8C22×D1111yescharacteristic
446C22×D4—111no—
447C22×D4C22×D1111yescharacteristic
448C23×C4—21no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4—221no—
452C2×SD16—24no—
453C2×SD16—114no—
454C2×SD16—224no—
455C2×SD16C22×D1114yes—
456C2×D8—114no—
457C2×D8—224no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C4⋊Q8—114no—
463C4⋊Q8—114no—
464C4⋊Q8—114no—
465C4⋊Q8—114no—
466C4⋊Q8—222no—
467C4⋊Q8—222no—
468C4⋊Q8—222no—
469C4⋊Q8—222no—
470#126—228no—
471#126—228no—
472#124—114no—
473#124—114no—
474#124—222no—
475#124—222no—
476C22⋊Q8—228no—
477C22⋊Q8—228no—
478C22⋊Q8—228no—
479C22⋊Q8—228no—
480C4×Q8—22no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—222no—
485C4×Q8C22×D1114yes—
486C4×D4—22no—
487C4×D4—114no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—222no—
491C4×D4—222no—
492C4×D4—222no—
493C4×D4C22×D1114yes—
494#117—228no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—21no—
518C2×C42—111no—
519C2×C42—111no—
520C2×C42—221no—
521C2×C42C22×D1111yescharacteristic
522#107—114no—
523#107—114no—
524#107C22×D1114yes—
525C4⋊C8—114no—
526C4⋊C8—114no—
527C4⋊C8—114no—
528#103—114no—
529#103—114no—
530#103—114no—
531#103—114no—
532#103—114no—
533#103C22×D1114yes—
534#102—114no—
535#102—114no—
536#102—114no—
537#102C22×D1114yes—
538#97—114no—
539#97C22×D1114yes—
540C4×C8—114no—
541C2×C11—44no—
542C2×C11#336714yescomplemented
543C2×C11C2×#54811yescharacteristic
544C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
545C2×C11C2×#57811yescharacteristic
546D11—82no—
547C24—21no—
548C24—221no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—114no—
553C2×Q8—112no—
554C2×Q8—224no—
555C2×Q8—224no—
556C2×Q8—224no—
557C2×Q8—221no—
558C2×Q8—224no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—444no—
562C2×Q8—444no—
563C2×Q8—444no—
564C2×Q8—4432no—
565C2×Q8C23×D1112yes—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—112no—
569C2×D4—222no—
570C2×D4—221no—
571C2×D4—222no—
572C2×D4#433914yes—
573C2×D4C23×D1112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4D4×D1111yescharacteristic
593C22×C4D4×D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595SD16—28no—
596SD16—228no—
597D8—228no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—222no—
603C2×C8—222no—
604C2×C8C23×D1112yes—
605C2×C8C23×D1112yes—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—114no—
610C4⋊C4—114no—
611C4⋊C4—114no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—224no—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—24no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C42—24no—
633C42—112no—
634C42—112no—
635C42—112no—
636C42—112no—
637C42—224no—
638C42D4×D1112yes—
639C42C23×D1112yes—
640C11C2×#336711yescharacteristic, complemented, Sylow
641C23—24no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—222no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—228no—
654Q8—222no—
655Q8—222no—
656Q8—448no—
657Q8—448no—
658Q8—448no—
659Q8—442no—
660D4—24no—
661D4—22no—
662D4—222no—
663D4—222no—
664D4—442no—
665D4C2×#433914yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—48no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—114no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—448no—
687C2×C4—448no—
688C2×C4—448no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4C2×#433912yes—
693C2×C4C2×D4×D1112yes—
694C2×C4C2×D4×D1112yes—
695C2×C4C2×D4×D1111yescharacteristic
696C2×C4#6704312yes—
697C2×C4C24×D1111yescharacteristic
698C8—22no—
699C8—22no—
700C8—222no—
701C8—222no—
702C22—24no—
703C22—42no—
704C22—42no—
705C22—48no—
706C22—442no—
707C22—442no—
708C22—442no—
709C22—884no—
710C22#1062308312yes—
711C22D11×AGL(1,ℤ/8)12yes—
712C22#1062331012yes—
713C22C22×D4×D1111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—114no—
720C4—222no—
721C4—222no—
722C4—222no—
723C4—442no—
724C4—442no—
725C4—442no—
726C4#1062308312yes—
727C4C22×#433911yescharacteristic
728C4C2×#6704311yescharacteristic
729C2—44no—
730C2—882no—
731C2#1308133514yesdirect product factor
732C2C2×#1062308311yescharacteristic
733C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
734C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#440D11
hypocenterC11C2×#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623099C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081335C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622634C2semidirect
8. C2×#10622488C2semidirect
9. C2×#10622503C2semidirect
12. C2×#10622775C2semidirect
13. C2×#10622314C2semidirect
14. C2×#10622370C2semidirect
16. C2×C11×#440C2semidirect
29. #10623099C22semidirect
31. D4×Dic22C22semidirect
45. C11×#440C22semidirect
53. #10622775C22semidirect
62. #10622634C22semidirect
69. #10622503C22semidirect
70. #10622488C22semidirect
71. #10622408C22semidirect
72. #10622405C22semidirect
73. #10622370C22semidirect
75. #10622327C22semidirect
76. #10622314C22semidirect
288. C2×#440D11semidirect
390. #440C2×D11semidirect
542. C2×C11#3367semidirect
640. C11C2×#3367semidirect
731. C2#13081335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230992
C2×D4×Dic222
#130813352
C2×#106224082
C2×#106223272
C2×#106224052
C2×#106226342
C2×#106224882
C2×#106225032
C2×#106227782
C2×#106226292
C2×#106227752
C2×#106223142
C2×#106223702
C2×#106223692
C2×C11×#4402
C2×#336711