Finite Group Databasebeta

← C2×#13078306 #15621019

Subgroups — C2×#13078306 #15621019

Order 2816.

2742 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
1C22×#66971C211yesmaximal, characteristic, complemented
2C22×#66954C211yesmaximal, characteristic, complemented
3C2×#10623160C211yesmaximal, characteristic
4C2×#10623159C211yesmaximal, characteristic, complemented
5#13078306C2116yesmaximal, direct product factor
6C2×#10622665C211yesmaximal, characteristic, complemented
7C2×#10622802C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622499C211yesmaximal, characteristic, complemented
10C2×#10622426C211yesmaximal, characteristic, complemented
11C2×#10622420C211yesmaximal, characteristic, complemented
12C2×#10622727C211yesmaximal, characteristic, complemented
13C2×#10622494C211yesmaximal, characteristic, complemented
14C2×#10622417C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#467C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×#66983C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C2×#66971—28no—
32C2×#66971C2218yescomplemented
33C22×#4314C2211yescharacteristic
34C2×#66954—28no—
35C2×#66954C2218yescomplemented
36C22×#4313C2211yescharacteristic
37C22×#4313C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623160—24no—
41#10623160C2218yes—
42#10623159—24no—
43#10623159C2218yescomplemented
44C2×#66950C2211yescharacteristic
45C2×#66949—21no—
46C2×#66948—21no—
47C2×#66948C2211yescharacteristic
48C2×#66947—21no—
49C2×#66945C2211yescharacteristic
50C2×C4⋊C4×D11C2211yescharacteristic
51C2×#66941—21no—
52C2×#66938—21no—
53C2×#66937—21no—
54C2×#66937—21no—
55C2×#66936—21no—
56C11×#467C2218yescomplemented
57C2×C11×#107C2211yescharacteristic
58C2×C11×#103C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62#10622802C2218yescomplemented
63#10622727C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67#10622665C2218yescomplemented
68#10622662C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66872C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73#10622499C2218yescomplemented
74#10622494C2218yescomplemented
75#10622426C2218yescomplemented
76#10622420C2218yescomplemented
77#10622417C2218yescomplemented
78D11×#103C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11D411yescharacteristic
84C22×C22⋊D11D411yescharacteristic
85C2×#4343—22no—
86C2×#4343—24no—
87C2×#4343—24no—
88C2×#4343C2314yes—
89C2×Q8×D11—22no—
90C2×Q8×D11—24no—
91C2×Q8×D11—24no—
92C2×Q8×D11C2314yes—
93C2×#4339—24no—
94C2×#4339—24no—
95C2×#4339D414yes—
96C2×#4339C2314yes—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44D411yescharacteristic
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×Dic22D411yescharacteristic
108C22×Dic22C2311yescharacteristic
109C2×C11×Q16—24no—
110C2×C11×Q16C2314yes—
111C22×C8×C11—24no—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2314yes—
114C22×C8×C11C2311yescharacteristic
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8C2314yes—
118C11×C22⋊Q8C2314yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126#66999—22no—
127#66999—22no—
128#66999C2314yes—
129#66999C2314yes—
130C2×#4326—24no—
131C2×#4326C2314yes—
132C2×#4325—24no—
133C2×#4325C2314yes—
134#66983—22no—
135#66983C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145#66977—22no—
146#66977C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×#4318—24no—
153C2×#4318C2314yes—
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66971—232no—
157C2×#4314—24no—
158C2×#4314C2314yes—
159#66954—232no—
160C2×#4313—24no—
161C2×#4313D418yescomplemented
162C2×#4313C2314yes—
163C2×#4313C2314yes—
164C2×C8×D11—24no—
165C2×C8×D11—24no—
166C2×C8×D11C2314yes—
167C2×C8×D11C2314yes—
168#66950—22no—
169#66950C2314yes—
170#66949—28no—
171#66948—28no—
172#66948—22no—
173#66948C2314yes—
174#66947—28no—
175#66945—22no—
176#66945C2314yes—
177C4⋊C4×D11—22no—
178C4⋊C4×D11C2314yes—
179#66941—28no—
180#66938—28no—
181#66937—28no—
182#66937—28no—
183#66936—28no—
184C11×#107C2314yes—
185C11×#103C2314yes—
186C11×#103C2314yes—
187#66899C2314yes—
188#66899C2314yes—
189#66885C2314yes—
190#66881C2314yes—
191#66880C2314yes—
192#66874C2314yes—
193#66873C2314yes—
194#66872C2314yes—
195#66871C2314yes—
196C2×#3063—111nomaximal, Sylow
197C24×C11C2×D411yescharacteristic
198C23×D11—21no—
199C23×D11C2×D411yescharacteristic
200C23×D11C2×D411yescharacteristic
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—22no—
206C2×Q8×C11—22no—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—82no—
223C2×C22⋊D11C2×D414yes—
224C2×C22⋊D11C2×D414yes—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4343—28no—
231#4343—28no—
232#4343—48no—
233Q8×D11—28no—
234Q8×D11—28no—
235Q8×D11—48no—
236#4339—216no—
237#4339—28no—
238#4339—28no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—21no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44C2×D414yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—82no—
257C2×C4×D11C2×D414yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2×D412yes—
260C2×C4×D11#4114yes—
261C2×C4×D11C2412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—24no—
265C2×Dic22—22no—
266C2×Dic22—21no—
267C2×Dic22—22no—
268C2×Dic22—44no—
269C2×Dic22C2×D414yes—
270C2×Dic22C2412yes—
271C11×Q16—28no—
272C2×C8×C11—28no—
273C2×C8×C11—22no—
274C2×C8×C11C2×D414yes—
275C2×C8×C11C2412yes—
276C2×C8×C11C2412yes—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4C2412yes—
282C11×C4⋊C4C2412yes—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C22⋊Dic11—24no—
286#4326—28no—
287#4325—28no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294C4⋊Dic11—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303C4×Dic11—24no—
304#4318—28no—
305C2×C11⋊C8—22no—
306C2×C11⋊C8C2×D414yes—
307C2×C11⋊C8C2412yes—
308C2×C11⋊C8C2412yes—
309#4314—28no—
310#4313—28no—
311#4313C2×D4116yescomplemented
312C8×D11—28no—
313C8×D11—28no—
314C22×#137—111no—
315C22×#131—111no—
316C2×#537—111no—
317C2×#536—111no—
318#3063—1116no—
319C2×#470—111no—
320C2×#470—111no—
321C2×#468—111no—
322C2×#468—111no—
323C2×#467—111no—
324C2×#467D1111yescharacteristic, complemented
325C2×#465—111no—
326C2×#465—111no—
327C2×#428—111no—
328C2×#416—111no—
329C22×#103—111no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11C22×D412yes—
334C23×C11C22×D411yescharacteristic
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11#12114yes—
345C22×D11C22×D412yes—
346C22×D11C22×D412yes—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—22no—
350Q8×C11—22no—
351Q8×C11—42no—
352Q8×C11—42no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D412yes—
368C2×C4×C11C2×#4112yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—28no—
371C22⋊D11—28no—
372C22⋊D11—84no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11#12114yes—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—28no—
384D44—22no—
385D44—22no—
386D44—48no—
387D44—42no—
388D44—84no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—48no—
393C4×D11—48no—
394C4×D11—84no—
395C4×D11#12118yes—
396C4×D11C22×D414yes—
397C4×D11C2×#4114yes—
398Dic22—28no—
399Dic22—22no—
400Dic22—22no—
401Dic22—42no—
402Dic22—48no—
403C8×C11—22no—
404C8×C11C22×D414yes—
405C11⋊C8—22no—
406C11⋊C8C22×D414yes—
407C22×#41—111no—
408C22×#41—111no—
409C23×Q8—111no—
410C2×#137—118no—
411C2×#137—228no—
412C22×Q16—111no—
413C22×Q16C2×D1111yescharacteristic
414C22×SD16—111no—
415C22×SD16—111no—
416C2×#131—118no—
417C2×#131—228no—
418C22×M16—111no—
419C22×M16—111no—
420C22×M16—111no—
421C23×C8—111no—
422C23×C8—111no—
423C23×C8C2×D1111yescharacteristic
424#537—118no—
425#537—224no—
426#536—118no—
427#536—224no—
428C2×C4⋊Q8—221no—
429C2×#124—221no—
430C2×#123—221no—
431C2×#123—221no—
432C2×C22⋊Q8—111no—
433C2×C22⋊Q8—111no—
434C2×C22⋊Q8—111no—
435C2×C22⋊Q8—111no—
436C2×C22⋊Q8—221no—
437C2×C22⋊Q8C2×D1111yescharacteristic
438C2×C22⋊Q8C2×D1111yescharacteristic
439C2×#121—111no—
440C2×#121—111no—
441C2×#121—221no—
442C2×#121—221no—
443C2×#121—221no—
444C2×#117—111no—
445C22×C4⋊C4—111no—
446#470—118no—
447#470—118no—
448#468—118no—
449#468—118no—
450#467—118no—
451#467C2×D1118yescomplemented
452#465—118no—
453#465—118no—
454#428—118no—
455C2×#107—111no—
456C2×#107C2×D1111yescharacteristic
457C2×#106—111no—
458C2×#106—111no—
459#416—118no—
460C2×#103—111no—
461C2×#103—111no—
462C2×#103—111no—
463C2×#103—111no—
464C2×#103—118no—
465C2×#103C2×D1111yescharacteristic
466C2×#103C2×D1111yescharacteristic
467C2×#102—111no—
468C2×#102—111no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—44no—
473C22×C11C2×#12112yes—
474C22×C11#57712yes—
475C22×C11#57812yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—28no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—44no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—84no—
488C2×D11C2×#12114yes—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11C2×#12112yes—
495C4×C11C23×D411yescharacteristic
496C4×C11C22×#4111yescharacteristic
497Dic11—22no—
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501Dic11C2×#12114yes—
502C2×#41—114no—
503C2×#41—114no—
504C2×#41—114no—
505C2×#41—224no—
506C2×#41—224no—
507C2×#41—222no—
508C2×#41—224no—
509C2×#41—224no—
510C22×Q8—111no—
511C22×Q8—114no—
512C22×Q8—111no—
513C22×Q8—221no—
514C22×Q8—222no—
515C22×Q8—224no—
516C22×Q8—224no—
517C22×Q8C22×D1111yescharacteristic
518C22×Q8C22×D1111yescharacteristic
519C22×D4—111no—
520C22×D4—111no—
521C22×D4—111no—
522C22×D4—111no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—221no—
529C23×C4—221no—
530C23×C4—221no—
531C23×C4C22×D1111yescharacteristic
532#137—2232no—
533C2×Q16—24no—
534C2×Q16—114no—
535C2×Q16—224no—
536C2×Q16C22×D1114yes—
537C2×SD16—114no—
538C2×SD16—114no—
539C2×SD16—224no—
540C2×SD16—224no—
541#131—2232no—
542C2×M16—114no—
543C2×M16—118no—
544C2×M16—114no—
545C2×M16—114no—
546C2×M16—224no—
547C2×M16—224no—
548C22×C8—24no—
549C22×C8—111no—
550C22×C8—111no—
551C22×C8—114no—
552C22×C8—114no—
553C22×C8—224no—
554C22×C8—224no—
555C22×C8C22×D1111yescharacteristic
556C22×C8C22×D1114yes—
557C22×C8C22×D1111yescharacteristic
558C4⋊Q8—228no—
559#124—228no—
560#123—228no—
561#123—228no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—114no—
565C22⋊Q8—114no—
566C22⋊Q8—114no—
567C22⋊Q8—114no—
568C22⋊Q8—222no—
569C22⋊Q8—228no—
570C22⋊Q8—222no—
571C22⋊Q8—222no—
572C22⋊Q8—222no—
573C22⋊Q8C22×D1114yes—
574C22⋊Q8C22×D1114yes—
575#121—114no—
576#121—114no—
577#121—228no—
578#121—228no—
579#121—222no—
580#121—228no—
581#121—222no—
582#117—114no—
583#117—222no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—111no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—221no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—221no—
607#107—114no—
608#107C22×D1114yes—
609#106—114no—
610#106—114no—
611#103—114no—
612#103—114no—
613#103—114no—
614#103—114no—
615#103C22×D1114yes—
616#103C22×D1114yes—
617#102—114no—
618#102—114no—
619C2×C11—42no—
620C2×C11#306314yescomplemented
621C2×C11C22×#12111yescharacteristic
622C2×C11C2×#57711yescharacteristic
623C2×C11C2×#57811yescharacteristic
624D11—24no—
625D11—42no—
626D11—82no—
627C24—111no—
628C24—111no—
629C24—221no—
630C24D4×D1111yescharacteristic
631#41—228no—
632#41—2216no—
633#41—228no—
634#41—228no—
635#41—228no—
636#41—448no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—114no—
644C2×Q8—112no—
645C2×Q8—224no—
646C2×Q8—224no—
647C2×Q8—228no—
648C2×Q8—228no—
649C2×Q8—221no—
650C2×Q8—222no—
651C2×Q8—222no—
652C2×Q8—444no—
653C2×Q8—448no—
654C2×Q8C23×D1112yes—
655C2×Q8C23×D1112yes—
656C2×D4—114no—
657C2×D4—114no—
658C2×D4—114no—
659C2×D4—112no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—224no—
663C2×D4—224no—
664C2×D4—224no—
665C2×D4—224no—
666C2×D4—222no—
667C2×D4—221no—
668C2×D4—222no—
669C2×D4—444no—
670C2×D4—882no—
671C2×D4—882no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—111no—
679C22×C4—112no—
680C22×C4—114no—
681C22×C4—114no—
682C22×C4—112no—
683C22×C4—111no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—224no—
687C22×C4—224no—
688C22×C4—224no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—444no—
695C22×C4—444no—
696C22×C4—882no—
697C22×C4D4×D1112yes—
698C22×C4D4×D1111yescharacteristic
699C22×C4C23×D1112yes—
700C22×C4C23×D1111yescharacteristic
701Q16—28no—
702Q16—228no—
703SD16—228no—
704SD16—228no—
705M16—1116no—
706M16—228no—
707M16—228no—
708C2×C8—22no—
709C2×C8—28no—
710C2×C8—114no—
711C2×C8—112no—
712C2×C8—112no—
713C2×C8—228no—
714C2×C8—228no—
715C2×C8—222no—
716C2×C8D4×D1114yes—
717C2×C8C23×D1112yes—
718C2×C8C23×D1112yes—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—112no—
724C4⋊C4—112no—
725C4⋊C4—224no—
726C4⋊C4—224no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—221no—
730C4⋊C4—221no—
731C4⋊C4—224no—
732C4⋊C4C23×D1112yes—
733C4⋊C4C23×D1112yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—224no—
737C22⋊C4—224no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C42—224no—
744C11C2×#306311yescharacteristic, complemented, Sylow
745C23—22no—
746C23—22no—
747C23—22no—
748C23—114no—
749C23—112no—
750C23—112no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—442no—
758C23—442no—
759C23—442no—
760C23C2×D4×D1112yes—
761C23C2×D4×D1111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—42no—
767Q8—42no—
768Q8—228no—
769Q8—222no—
770Q8—222no—
771Q8—448no—
772Q8—442no—
773D4—228no—
774D4—228no—
775D4—228no—
776D4—222no—
777D4—222no—
778D4—448no—
779D4—442no—
780D4—884no—
781D4—884no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—114no—
795C2×C4—112no—
796C2×C4—118no—
797C2×C4—114no—
798C2×C4—114no—
799C2×C4—112no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—448no—
808C2×C4—448no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—884no—
813C2×C4C2×D4×D1112yes—
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×D4×D1112yes—
816C2×C4#41×D1112yes—
817C2×C4C24×D1111yescharacteristic
818C8—22no—
819C8—114no—
820C8—222no—
821C8C2×D4×D1114yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—114no—
827C22—228no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—222no—
833C22—444no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—884no—
838C22D11×#12112yes—
839C22#1062329712yes—
840C22#1062330112yes—
841C22C22×D4×D1111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—114no—
848C4—222no—
849C4—442no—
850C4—442no—
851C4—442no—
852C4D11×#12112yes—
853C4C22×D4×D1111yescharacteristic
854C4C2×#41×D1111yescharacteristic
855C2—42no—
856C2—224no—
857C2—442no—
858C2—882no—
859C2#1307830614yesdirect product factor
860C2C2×D11×#12111yescharacteristic
861C2C2×#1062330111yescharacteristic
862C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC2×#10623160C2
hypercenterC2×#467D11
hypocenterC11C2×#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C22×#66954C2semidirect
4. C2×#10623159C2semidirect
5. #13078306C2direct (N × H)
6. C2×#10622665C2semidirect
7. C2×#10622802C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622499C2semidirect
10. C2×#10622426C2semidirect
11. C2×#10622420C2semidirect
12. C2×#10622727C2semidirect
13. C2×#10622494C2semidirect
14. C2×#10622417C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#467C2semidirect
32. C2×#66971C22semidirect
35. C2×#66954C22semidirect
43. #10623159C22semidirect
56. C11×#467C22semidirect
62. #10622802C22semidirect
63. #10622727C22semidirect
67. #10622665C22semidirect
68. #10622662C22semidirect
73. #10622499C22semidirect
74. #10622494C22semidirect
75. #10622426C22semidirect
76. #10622420C22semidirect
77. #10622417C22semidirect
78. D11×#103C22semidirect
161. C2×#4313D4semidirect
311. #4313C2×D4semidirect
324. C2×#467D11semidirect
451. #467C2×D11semidirect
620. C2×C11#3063semidirect
744. C11C2×#3063semidirect
859. C2#13078306direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C22×#669542
C2×#106231602
C2×#106231592
#130783062
C2×#106226652
C2×#106228022
C2×#106226622
C2×#106224992
C2×#106224262
C2×#106224202
C2×#106227272
C2×#106224942
C2×#106224172
C2×D11×#1032
C2×C11×#4672
C2×#306311