Finite Group Databasebeta

← C2×#13080186 #15628818

Subgroups — C2×#13080186 #15628818

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10623348C211yesmaximal, characteristic
4#13080186C2116yesmaximal, direct product factor
5C2×#10622803C211yesmaximal, characteristic, complemented
6C2×#10622802C211yesmaximal, characteristic, complemented
7C2×#10622727C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622795C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622841C211yesmaximal, characteristic, complemented
12C2×#10622799C211yesmaximal, characteristic, complemented
13C2×#10622840C211yesmaximal, characteristic, complemented
14C2×#10622797C211yesmaximal, characteristic, complemented
15C2×#10622724C211yesmaximal, characteristic, complemented
16C23×C11×Q16C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4343C2211yescharacteristic
20C22×Q8×D11C2211yescharacteristic
21C22×C11×Q16—28no—
22C22×C11×Q16C2211yescharacteristic
23C22×C11×Q16C2211yescharacteristic
24C22×C11×Q16C2211yescharacteristic
25C22×C11×Q16C2211yescharacteristic
26C22×C11×Q16C2218yescomplemented
27C23×C8×C11C2211yescharacteristic
28#10623348—24no—
29#10623348C2218yes—
30Q8×C22⋊D11—24no—
31Q8×C22⋊D11C2218yescomplemented
32C2×#67000—21no—
33C2×#67000C2211yescharacteristic
34C2×#66999—21no—
35C2×#66999—21no—
36C2×#66999C2211yescharacteristic
37C2×#66999C2211yescharacteristic
38C2×Q8×Dic11C2211yescharacteristic
39C2×Q8×Dic11C2211yescharacteristic
40C2×#66997—21no—
41C2×#66997C2211yescharacteristic
42C22×#4326C2211yescharacteristic
43C22×#4326C2211yescharacteristic
44C22×#4325C2211yescharacteristic
45C22×#4325C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11—21no—
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×#66977—21no—
52C2×#66977C2211yescharacteristic
53C2×#66971—28no—
54C2×#66971C2218yescomplemented
55C22×#4314C2211yescharacteristic
56C22×#4313C2211yescharacteristic
57#10622841C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62C2×#66899C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622803C2218yescomplemented
65#10622802C2218yescomplemented
66#10622800C2218yescomplemented
67#10622799C2218yescomplemented
68#10622798C2218yescomplemented
69#10622797C2218yescomplemented
70#10622795C2218yescomplemented
71#10622727C2218yescomplemented
72C2×#66885C2211yescharacteristic
73#10622724C2218yescomplemented
74C2×(C2×D11)⋊C8C2211yescharacteristic
75C2×#66881C2211yescharacteristic
76C2×#66880C2211yescharacteristic
77C2×#66879C2211yescharacteristic
78C2×Dic11⋊C8C2211yescharacteristic
79C22×Q8×C11—21no—
80C22×Q8×C11—21no—
81C22×Q8×C11—22no—
82C22×Q8×C11—22no—
83C22×Q8×C11—24no—
84C22×Q8×C11—24no—
85C22×Q8×C11—42no—
86C22×Q8×C11—42no—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2311yescharacteristic
89C22×Q8×C11C2314yes—
90C22×Q8×C11C2314yes—
91C22×Q8×C11C2311yescharacteristic
92C22×Q8×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11D411yescharacteristic
98C2×#4343—22no—
99C2×#4343—24no—
100C2×#4343—42no—
101C2×#4343C2314yes—
102C2×Q8×D11—22no—
103C2×Q8×D11—24no—
104C2×Q8×D11—42no—
105C2×Q8×D11C2314yes—
106C22×D44—21no—
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11—21no—
110C22×C4×D11C2311yescharacteristic
111C22×Dic22—21no—
112C22×Dic22C2311yescharacteristic
113C2×C11×Q16—24no—
114C2×C11×Q16—24no—
115C2×C11×Q16—232no—
116C2×C11×Q16—24no—
117C2×C11×Q16D418yescomplemented
118C2×C11×Q16C2314yes—
119C2×C11×Q16C2314yes—
120C2×C11×Q16C2314yes—
121C2×C11×Q16C2314yes—
122C22×C8×C11—24no—
123C22×C8×C11C2311yescharacteristic
124C22×C8×C11C2314yes—
125C22×C8×C11C2311yescharacteristic
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11D411yescharacteristic
128#67000—28no—
129#67000—22no—
130#67000C2314yes—
131#66999—22no—
132#66999—22no—
133#66999—28no—
134#66999—28no—
135#66999C2314yes—
136#66999C2314yes—
137Q8×Dic11—22no—
138Q8×Dic11—22no—
139Q8×Dic11C2314yes—
140Q8×Dic11C2314yes—
141#66997—28no—
142#66997—22no—
143#66997C2314yes—
144C2×#4326—24no—
145C2×#4326—42no—
146C2×#4326C2314yes—
147C2×#4326C2314yes—
148C2×#4325—24no—
149C2×#4325—42no—
150C2×#4325C2314yes—
151C2×#4325C2314yes—
152#66983—22no—
153#66983—28no—
154#66983C2314yes—
155C4×C22⋊D11—28no—
156C4×C22⋊D11—28no—
157C4×C22⋊D11D414yes—
158C4×C22⋊D11C2314yes—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4D411yescharacteristic
165C2×C4⋊Dic11—21no—
166C2×C4⋊Dic11—21no—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169#66977—22no—
170#66977—28no—
171#66977C2314yes—
172C2×Dic11⋊C4—21no—
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4D411yescharacteristic
178C2×C4×Dic11—21no—
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66971—232no—
184C2×#4314—24no—
185C2×#4314C2314yes—
186C2×#4313—24no—
187C2×#4313C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66899C2314yes—
191#66899C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66881C2314yes—
196#66880C2314yes—
197#66879C2314yes—
198Dic11⋊C8C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11C2×D411yescharacteristic
201C23×D11—21no—
202C23×D11C2×D411yescharacteristic
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11—24no—
206C2×Q8×C11—21no—
207C2×Q8×C11—24no—
208C2×Q8×C11—21no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—28no—
212C2×Q8×C11—28no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—22no—
217C2×Q8×C11—44no—
218C2×Q8×C11—44no—
219C2×Q8×C11—44no—
220C2×Q8×C11—44no—
221C2×Q8×C11—48no—
222C2×Q8×C11—48no—
223C2×Q8×C11C2×D414yes—
224C2×Q8×C11C2×D414yes—
225C2×Q8×C11C2412yes—
226C2×Q8×C11C2412yes—
227C2×Q8×C11C2412yes—
228C2×Q8×C11C2412yes—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11C2×D414yes—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252C22×Dic11C2×D411yescharacteristic
253#4343—28no—
254#4343—44no—
255#4343—48no—
256Q8×D11—28no—
257Q8×D11—44no—
258Q8×D11—48no—
259C2×D44—24no—
260C2×D44—21no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—44no—
264C2×D44C2412yes—
265C2×C4×D11—24no—
266C2×C4×D11—24no—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2412yes—
273C2×Dic22—24no—
274C2×Dic22—22no—
275C2×Dic22—21no—
276C2×Dic22—22no—
277C2×Dic22—44no—
278C2×Dic22C2412yes—
279C11×Q16—28no—
280C11×Q16—28no—
281C11×Q16—28no—
282C11×Q16C2×D4116yescomplemented
283C2×C8×C11—28no—
284C2×C8×C11—22no—
285C2×C8×C11C2×D414yes—
286C2×C8×C11C2412yes—
287C2×C8×C11C2412yes—
288C22⋊Dic11—24no—
289C22⋊Dic11C2×D414yes—
290#4326—28no—
291#4326—44no—
292#4325—28no—
293#4325—44no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4C2×D414yes—
300C4⋊Dic11—24no—
301C4⋊Dic11—24no—
302C4⋊Dic11—21no—
303C4⋊Dic11—21no—
304C4⋊Dic11C2412yes—
305C4⋊Dic11C2412yes—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4—24no—
311Dic11⋊C4C2×D414yes—
312C4×Dic11—24no—
313C4×Dic11—24no—
314C4×Dic11C2×D412yes—
315C4×Dic11C2412yes—
316C2×C11⋊C8—22no—
317C2×C11⋊C8—22no—
318C2×C11⋊C8C2412yes—
319C2×C11⋊C8C2412yes—
320#4314—28no—
321#4313—28no—
322C22×#137—111no—
323C23×Q16D1111yescharacteristic, complemented
324C2×D4×Q8—111no—
325C2×#548—111no—
326#3270—1116no—
327C2×#497—111no—
328C2×#470—111no—
329C2×#465—111no—
330C2×#464—111no—
331C2×#462—111no—
332C2×#452—111no—
333C2×#451—111no—
334C2×#451—111no—
335C2×#448—111no—
336C2×#441—111no—
337C2×#435—111no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11#13714yescomplemented
341C23×C11C22×D412yes—
342C23×C11C22×D411yescharacteristic
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11C22×D412yes—
351Q8×C11—24no—
352Q8×C11—24no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—22no—
357Q8×C11—22no—
358Q8×C11—22no—
359Q8×C11—48no—
360Q8×C11—48no—
361Q8×C11—42no—
362Q8×C11—42no—
363Q8×C11C22×D414yes—
364Q8×C11C22×D414yes—
365C2×C4×C11—24no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—24no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—48no—
376C2×C4×C11—48no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D412yes—
382C2×C4×C11H(5,𝔽2)12yes—
383C2×C4×C11C2511yescharacteristic
384C22⋊D11—28no—
385C22⋊D11—48no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11C22×D412yes—
396C2×Dic11C22×D412yes—
397C2×Dic11C22×D412yes—
398D44—22no—
399D44—22no—
400D44—48no—
401D44—42no—
402C4×D11—24no—
403C4×D11—22no—
404C4×D11—22no—
405C4×D11—48no—
406C4×D11—48no—
407Dic22—22no—
408Dic22—22no—
409Dic22—48no—
410Dic22—42no—
411C8×C11—22no—
412C8×C11C22×D414yes—
413C11⋊C8—22no—
414C11⋊C8—22no—
415C22×#41—111no—
416C23×Q8—111no—
417C23×Q8C2×D1111yescharacteristic
418C23×Q8C2×D1111yescharacteristic
419C2×#137—118no—
420C2×#137—228no—
421C22×Q16—28no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16C2×D1111yescharacteristic
425C22×Q16C2×D1111yescharacteristic
426C22×Q16C2×D1111yescharacteristic
427C22×Q16C2×D1111yescharacteristic
428C22×Q16C2×D1118yescomplemented
429C22×SD16—111no—
430C22×SD16—111no—
431C22×SD16—111no—
432C22×M16—111no—
433C23×C8C2×D1111yescharacteristic
434D4×Q8—118no—
435D4×Q8—224no—
436#548—118no—
437#548—224no—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—221no—
440C2×#124—111no—
441C2×#124—221no—
442C2×C22⋊Q8—111no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—221no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8—221no—
448C2×#121—111no—
449C2×#121—221no—
450C2×C4×Q8—111no—
451C2×C4×Q8—111no—
452C2×C4×D4—111no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455#497—118no—
456#470—118no—
457#465—118no—
458#464—118no—
459#462—118no—
460#452—118no—
461#451—118no—
462#451—118no—
463#448—118no—
464#441—118no—
465#435—118no—
466C2×#106—111no—
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#102—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×#97—111no—
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—22no—
480C22×C11D4212yes—
481C22×C11C2×#13712yes—
482C22×C11C2×#13714yescomplemented
483C22×C11#57812yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—22no—
488C2×D11—44no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—84no—
493C4×C11—22no—
494C4×C11—24no—
495C4×C11—24no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11D4212yes—
499C4×C11C23×D411yescharacteristic
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501Dic11—22no—
502Dic11—22no—
503Dic11—22no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C2×#41—114no—
508C2×#41—222no—
509C2×#41—224no—
510C2×#41—442no—
511C22×Q8—21no—
512C22×Q8—21no—
513C22×Q8—22no—
514C22×Q8—22no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—42no—
518C22×Q8—42no—
519C22×Q8—114no—
520C22×Q8—111no—
521C22×Q8—221no—
522C22×Q8—222no—
523C22×Q8—224no—
524C22×Q8—442no—
525C22×Q8C22×D1111yescharacteristic
526C22×Q8C22×D1111yescharacteristic
527C22×Q8C22×D1114yes—
528C22×Q8C22×D1114yes—
529C22×Q8C22×D1111yescharacteristic
530C22×Q8C22×D1111yescharacteristic
531C22×D4—111no—
532C22×D4—111no—
533C22×D4—221no—
534C22×D4—221no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—111no—
538C23×C4—221no—
539C23×C4—221no—
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542C2×Q16—24no—
543C2×Q16—24no—
544C2×Q16—232no—
545C2×Q16—24no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—224no—
549C2×Q16—442no—
550C2×Q16C22⋊D1118yescomplemented
551C2×Q16C22×D1114yes—
552C2×Q16C22×D1114yes—
553C2×Q16C22×D1114yes—
554C2×Q16C22×D1114yes—
555C2×SD16—114no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16—224no—
560C2×SD16—442no—
561C2×M16—114no—
562C2×M16—224no—
563C22×C8—24no—
564C22×C8—111no—
565C22×C8—111no—
566C22×C8C22×D1111yescharacteristic
567C22×C8C22×D1114yes—
568C22×C8C22×D1111yescharacteristic
569C4⋊Q8—114no—
570C4⋊Q8—222no—
571C4⋊Q8—228no—
572#124—114no—
573#124—222no—
574#124—228no—
575C22⋊Q8—114no—
576C22⋊Q8—114no—
577C22⋊Q8—114no—
578C22⋊Q8—228no—
579C22⋊Q8—228no—
580C22⋊Q8—228no—
581C22⋊Q8—222no—
582C22⋊Q8—222no—
583C22⋊Q8—222no—
584#121—114no—
585#121—228no—
586#121—222no—
587C4×Q8—114no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×D4—114no—
592C4×D4—114no—
593C4×D4—228no—
594C4×D4—228no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C22⋊C4—111no—
606C2×C22⋊C4—111no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C42—111no—
614C2×C42—221no—
615C2×C42—221no—
616#106—114no—
617C4⋊C8—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103—114no—
623#102—114no—
624C22⋊C8—114no—
625C22⋊C8—114no—
626#97—114no—
627C2×C11—24no—
628C2×C11#327014yescomplemented
629C2×C11C2×D4211yescharacteristic
630C2×C11C22×#13711yescharacteristic
631C2×C11C2×#57811yescharacteristic
632D11—42no—
633D11—82no—
634C24—111no—
635C24—221no—
636C24D4×D1111yescharacteristic
637#41—228no—
638#41—444no—
639#41—448no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—21no—
644C2×Q8—24no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—44no—
658C2×Q8—48no—
659C2×Q8—48no—
660C2×Q8—112no—
661C2×Q8—224no—
662C2×Q8—221no—
663C2×Q8—228no—
664C2×Q8—222no—
665C2×Q8—222no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—448no—
669C2×Q8C2×C22⋊D1114yes—
670C2×Q8C2×C22⋊D1114yes—
671C2×Q8C23×D1112yes—
672C2×Q8C23×D1112yes—
673C2×Q8C23×D1112yes—
674C2×Q8C23×D1112yes—
675C2×D4—114no—
676C2×D4—112no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—221no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—444no—
684C2×D4—444no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—111no—
696C22×C4—111no—
697C22×C4—111no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—224no—
701C22×C4—224no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4D4×D1112yes—
710C22×C4D4×D1111yescharacteristic
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—28no—
714Q16—28no—
715Q16—28no—
716Q16—228no—
717Q16—444no—
718Q16C2×C22⋊D11116yescomplemented
719SD16—228no—
720SD16—228no—
721SD16—444no—
722M16—228no—
723C2×C8—22no—
724C2×C8—28no—
725C2×C8—112no—
726C2×C8—112no—
727C2×C8—222no—
728C2×C8—222no—
729C2×C8C2×C22⋊D1114yes—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—114no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—224no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—224no—
741C4⋊C4—221no—
742C4⋊C4—221no—
743C4⋊C4—224no—
744C22⋊C4—114no—
745C22⋊C4—114no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C42—112no—
753C42—112no—
754C42—224no—
755C42—224no—
756C11C2×#327011yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—112no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23#6697114yescomplemented
768C23C2×D4×D1112yes—
769C23C2×D4×D1111yescharacteristic
770Q8—24no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—48no—
779Q8—48no—
780Q8—42no—
781Q8—42no—
782Q8—222no—
783Q8—222no—
784Q8—448no—
785Q8—442no—
786Q8C22×C22⋊D1114yes—
787Q8C22×C22⋊D1114yes—
788D4—228no—
789D4—222no—
790D4—222no—
791D4—448no—
792D4—448no—
793D4—442no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—48no—
805C2×C4—48no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—112no—
809C2×C4—112no—
810C2×C4—112no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—224no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—448no—
821C2×C4—448no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1111yescharacteristic
827C2×C4#6703712yes—
828C2×C4C22×C22⋊D1112yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—222no—
832C8—222no—
833C8C22×C22⋊D1114yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—444no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—884no—
845C22C2×#6697112yes—
846C22C2×#6697114yescomplemented
847C22#1062329712yes—
848C22D4×C22⋊D1112yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—24no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—222no—
856C4—222no—
857C4—222no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4D4×C22⋊D1112yes—
862C4C2×#6703711yescharacteristic
863C4C23×C22⋊D1111yescharacteristic
864C2—24no—
865C2—442no—
866C2—882no—
867C2#1308018614yesdirect product factor
868C2C2×D4×C22⋊D1111yescharacteristic
869C2C22×#6697111yescharacteristic
870C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC23×C11×Q16C2
socleC23×C11C22×D4
prime radicalC2×#10623348C2
hypercenterC23×Q16D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C2×Q8×C22⋊D11C2semidirect
4. #13080186C2direct (N × H)
5. C2×#10622803C2semidirect
6. C2×#10622802C2semidirect
7. C2×#10622727C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622795C2semidirect
10. C2×#10622800C2semidirect
11. C2×#10622841C2semidirect
12. C2×#10622799C2semidirect
13. C2×#10622840C2semidirect
14. C2×#10622797C2semidirect
15. C2×#10622724C2semidirect
16. C23×C11×Q16C2semidirect
26. C22×C11×Q16C22semidirect
31. Q8×C22⋊D11C22semidirect
54. C2×#66971C22semidirect
57. #10622841C22semidirect
58. #10622840C22semidirect
64. #10622803C22semidirect
65. #10622802C22semidirect
66. #10622800C22semidirect
67. #10622799C22semidirect
68. #10622798C22semidirect
69. #10622797C22semidirect
70. #10622795C22semidirect
71. #10622727C22semidirect
73. #10622724C22semidirect
117. C2×C11×Q16D4semidirect
282. C11×Q16C2×D4semidirect
323. C23×Q16D11semidirect
340. C23×C11#137semidirect
428. C22×Q16C2×D11semidirect
482. C22×C11C2×#137semidirect
550. C2×Q16C22⋊D11semidirect
628. C2×C11#3270semidirect
718. Q16C2×C22⋊D11semidirect
756. C11C2×#3270semidirect
767. C23#66971semidirect
846. C22C2×#66971semidirect
867. C2#13080186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×Q8×C22⋊D112
C2×#106233482
#130801862
C2×#106228032
C2×#106228022
C2×#106227272
C2×#106227982
C2×#106227952
C2×#106228002
C2×#106228412
C2×#106227992
C2×#106228402
C2×#106227972
C2×#106227242
C23×C11×Q162
C2×#327011