Finite Group Databasebeta

← C2×#13080179 #15628811

Subgroups — C2×#13080179 #15628811

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×#66968C211yesmaximal, characteristic, complemented
2C23×#4326C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×#10623129C211yesmaximal, characteristic
5#13080179C2116yesmaximal, direct product factor
6C2×#10622780C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622654C211yesmaximal, characteristic, complemented
9C2×#10622779C211yesmaximal, characteristic, complemented
10C2×#10622406C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622352C211yesmaximal, characteristic, complemented
13C2×#10622421C211yesmaximal, characteristic, complemented
14C2×#10622402C211yesmaximal, characteristic, complemented
15C2×#10622343C211yesmaximal, characteristic, complemented
16C2×C11×#448C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24Q8×C22⋊D11—24no—
25Q8×C22⋊D11C2218yescomplemented
26C2×#66999—21no—
27C2×#66999C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×#66997—21no—
30C2×#66997C2211yescharacteristic
31C22×#4326—28no—
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C22×#4326C2211yescharacteristic
35C22×#4326C2211yescharacteristic
36C22×#4326C2218yescomplemented
37C2×#66992—21no—
38C2×#66989C2211yescharacteristic
39C2×D4×Dic11—21no—
40C22×#4324C2211yescharacteristic
41C2×C4×C22⋊D11—21no—
42C2×C4×C22⋊D11C2211yescharacteristic
43C2×#66977—21no—
44C2×#66977C2211yescharacteristic
45C23×C11⋊C8C2211yescharacteristic
46C2×#66968—28no—
47C2×#66968C2218yescomplemented
48C22×Dic44C2211yescharacteristic
49C22×Dic44C2211yescharacteristic
50C22×#4313C2211yescharacteristic
51#10623129—24no—
52#10623129C2218yes—
53C2×#66950C2211yescharacteristic
54C2×#66940C2211yescharacteristic
55C2×#66938—21no—
56C2×#66931—21no—
57C11×#448C2218yescomplemented
58C2×C11×#103C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62#10622786C2218yescomplemented
63#10622780C2218yescomplemented
64#10622779C2218yescomplemented
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70#10622654C2218yescomplemented
71C2×#66874C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73#10622429C2218yescomplemented
74#10622421C2218yescomplemented
75#10622406C2218yescomplemented
76#10622402C2218yescomplemented
77#10622352C2218yescomplemented
78#10622343C2218yescomplemented
79C22×Q8×C11—21no—
80C22×Q8×C11—22no—
81C22×Q8×C11—24no—
82C22×Q8×C11—42no—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2314yes—
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C23×Dic11—21no—
94C2×Q8×D11—22no—
95C2×Q8×D11—24no—
96C2×Q8×D11—42no—
97C2×Q8×D11C2314yes—
98C2×#4341—22no—
99C2×#4341—24no—
100C2×#4341—42no—
101C2×#4341C2314yes—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×Dic22—24no—
105C22×Dic22—21no—
106C22×Dic22—22no—
107C22×Dic22—21no—
108C22×Dic22—42no—
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C22×Dic22C2314yes—
112C22×Dic22C2311yescharacteristic
113C2×C11×SD16—24no—
114C2×C11×SD16—42no—
115C2×C11×SD16C2314yes—
116C2×C11×SD16C2314yes—
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2311yescharacteristic
119C11×#121—22no—
120C11×#121C2314yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#66999—22no—
128#66999—28no—
129#66999C2314yes—
130Q8×Dic11—22no—
131Q8×Dic11C2314yes—
132#66997—28no—
133#66997—22no—
134#66997C2314yes—
135C2×#4326—24no—
136C2×#4326—24no—
137C2×#4326—232no—
138C2×#4326—24no—
139C2×#4326D418yescomplemented
140C2×#4326C2314yes—
141C2×#4326C2314yes—
142C2×#4326C2314yes—
143C2×#4326C2314yes—
144#66992—28no—
145#66989—22no—
146#66989C2314yes—
147D4×Dic11—28no—
148C2×#4324—24no—
149C2×#4324C2314yes—
150C4×C22⋊D11—28no—
151C4×C22⋊D11D414yes—
152C4×C22⋊D11C2314yes—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4—21no—
155C2×(C2×D11)⋊C4D411yescharacteristic
156C2×C4⋊Dic11—21no—
157C2×C4⋊Dic11—21no—
158C2×C4⋊Dic11C2311yescharacteristic
159#66977—22no—
160#66977—28no—
161#66977C2314yes—
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4—21no—
167C2×Dic11⋊C4D411yescharacteristic
168C2×C4×Dic11—21no—
169C2×C4×Dic11—21no—
170C2×C4×Dic11C2311yescharacteristic
171C22×C11⋊C8—24no—
172C22×C11⋊C8C2311yescharacteristic
173C22×C11⋊C8C2314yes—
174C22×C11⋊C8C2311yescharacteristic
175#66968—232no—
176C2×Dic44—24no—
177C2×Dic44—42no—
178C2×Dic44C2314yes—
179C2×Dic44C2314yes—
180C2×#4313—24no—
181C2×#4313C2314yes—
182#66950—22no—
183#66950C2314yes—
184#66940—22no—
185#66940C2314yes—
186#66938—28no—
187#66931—28no—
188C11×#103C2314yes—
189C11×#103C2314yes—
190C11×C22⋊C8C2314yes—
191#66896C2314yes—
192(C2×D11)⋊C8C2314yes—
193#66880C2314yes—
194#66880C2314yes—
195#66879C2314yes—
196Dic11⋊C8C2314yes—
197#66874C2314yes—
198#66872C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C2×Q8×C11—21no—
204C2×Q8×C11—24no—
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—28no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11—44no—
211C2×Q8×C11—44no—
212C2×Q8×C11—48no—
213C2×Q8×C11C2×D414yes—
214C2×Q8×C11C2412yes—
215C2×Q8×C11C2412yes—
216C2×D4×C11—24no—
217C2×D4×C11—22no—
218C2×D4×C11—21no—
219C2×D4×C11—22no—
220C2×D4×C11—44no—
221C2×D4×C11C2412yes—
222C22×C4×C11—21no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—24no—
228C22×C4×C11—44no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2411yescharacteristic
233C2×C22⋊D11—24no—
234C2×C22⋊D11—24no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11C2×D414yes—
237C22×Dic11—24no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—24no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11C2×D411yescharacteristic
246C22×Dic11C2×D411yescharacteristic
247C22×Dic11C2×D411yescharacteristic
248Q8×D11—28no—
249Q8×D11—44no—
250Q8×D11—48no—
251#4341—28no—
252#4341—44no—
253#4341—48no—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—44no—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2412yes—
260C2×Dic22—28no—
261C2×Dic22—24no—
262C2×Dic22—21no—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—24no—
266C2×Dic22—21no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—22no—
271C2×Dic22—44no—
272C2×Dic22—48no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22C2×D414yes—
276C2×Dic22C2412yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×SD16—28no—
280C11×SD16—44no—
281C2×C8×C11—22no—
282C2×C8×C11—22no—
283C2×C8×C11C2412yes—
284C2×C8×C11C2412yes—
285C11×C4⋊C4—21no—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—24no—
288C22⋊Dic11—24no—
289C22⋊Dic11—24no—
290C22⋊Dic11—24no—
291C22⋊Dic11C2×D414yes—
292#4326—28no—
293#4326—28no—
294#4326—28no—
295#4326C2×D4116yescomplemented
296#4324—28no—
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⋊Dic11C2412yes—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4C2×D414yes—
310C4×Dic11—24no—
311C4×Dic11—24no—
312C4×Dic11C2×D412yes—
313C4×Dic11C2412yes—
314C2×C11⋊C8—28no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8C2×D414yes—
317C2×C11⋊C8C2412yes—
318C2×C11⋊C8C2412yes—
319Dic44—28no—
320Dic44—44no—
321#4313—28no—
322C22×#137—111no—
323C23×Q16—111no—
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×#448D1111yescharacteristic, complemented
336C2×#441—111no—
337C2×#435—111no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11#13714yescomplemented
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11C22×D412yes—
351Q8×C11—24no—
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—48no—
356Q8×C11—42no—
357Q8×C11C22×D414yes—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—48no—
361D4×C11—42no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—48no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11C22×D412yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D412yes—
376C2×C4×C11H(5,𝔽2)12yes—
377C2×C4×C11C2511yescharacteristic
378C22⋊D11—28no—
379C22⋊D11—48no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—48no—
389C2×Dic11—48no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396C4×D11—24no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400Dic22—24no—
401Dic22—22no—
402Dic22—22no—
403Dic22—22no—
404Dic22—22no—
405Dic22—22no—
406Dic22—48no—
407Dic22—48no—
408Dic22—42no—
409Dic22—42no—
410Dic22C22×D414yes—
411C8×C11—22no—
412C8×C11—22no—
413C11⋊C8—22no—
414C11⋊C8C22×D414yes—
415C22×#41—111no—
416C23×Q8—111no—
417C23×Q8—111no—
418C23×Q8C2×D1111yescharacteristic
419C2×#137—118no—
420C2×#137—228no—
421C22×Q16—111no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16—111no—
425C22×Q16—118no—
426C22×Q16—111no—
427C22×Q16—111no—
428C22×Q16—228no—
429C22×SD16—111no—
430C22×SD16C2×D1111yescharacteristic
431C22×SD16C2×D1111yescharacteristic
432C22×M16—111no—
433C23×C8—111no—
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—221no—
449C2×#121C2×D1111yescharacteristic
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#448C2×D1118yescomplemented
464#441—118no—
465#435—118no—
466C2×#106—111no—
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103C2×D1111yescharacteristic
472C2×#103C2×D1111yescharacteristic
473C2×#102—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8C2×D1111yescharacteristic
476C2×#97—111no—
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—22no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—84no—
484C22×C11D4212yes—
485C22×C11C2×#13712yes—
486C22×C11C2×#13714yescomplemented
487C22×C11#57812yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—44no—
493C4×C11—22no—
494C4×C11—24no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11D4212yes—
498C4×C11C23×D411yescharacteristic
499C4×C11C2×H(5,𝔽2)11yescharacteristic
500Dic11—24no—
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—22no—
513C22×Q8—24no—
514C22×Q8—42no—
515C22×Q8—114no—
516C22×Q8—111no—
517C22×Q8—111no—
518C22×Q8—111no—
519C22×Q8—114no—
520C22×Q8—221no—
521C22×Q8—224no—
522C22×Q8—222no—
523C22×Q8—221no—
524C22×Q8—222no—
525C22×Q8—224no—
526C22×Q8—442no—
527C22×Q8—442no—
528C22×Q8C22×D1111yescharacteristic
529C22×Q8C22×D1114yes—
530C22×Q8C22×D1111yescharacteristic
531C22×D4—21no—
532C22×D4—111no—
533C22×D4—221no—
534C22×D4C22×D1111yescharacteristic
535C23×C4—21no—
536C23×C4—111no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4—221no—
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542C2×Q16—118no—
543C2×Q16—114no—
544C2×Q16—114no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—114no—
549C2×Q16—224no—
550C2×Q16—224no—
551C2×Q16—2232no—
552C2×Q16—224no—
553C2×Q16—224no—
554C2×Q16—442no—
555C2×SD16—24no—
556C2×SD16—42no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16C22×D1114yes—
560C2×SD16C22×D1114yes—
561C2×M16—114no—
562C2×M16—224no—
563C22×C8—111no—
564C22×C8—111no—
565C22×C8—114no—
566C22×C8—224no—
567C22×C8C22×D1111yescharacteristic
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—22no—
585#121—228no—
586#121C22×D1114yes—
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—221no—
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⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—111no—
607C2×C22⋊C4—111no—
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#103C22×D1114yes—
622#103C22×D1114yes—
623#102—114no—
624C22⋊C8—114no—
625C22⋊C8C22×D1114yes—
626#97—114no—
627C2×C11—24no—
628C2×C11—82no—
629C2×C11#327014yescomplemented
630C2×C11C2×D4211yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57811yescharacteristic
633D11—42no—
634C24—21no—
635C24—111no—
636C24D4×D1111yescharacteristic
637#41—228no—
638#41—444no—
639#41—448no—
640C2×Q8—21no—
641C2×Q8—24no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—28no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—48no—
650C2×Q8—114no—
651C2×Q8—112no—
652C2×Q8—112no—
653C2×Q8—112no—
654C2×Q8—224no—
655C2×Q8—228no—
656C2×Q8—221no—
657C2×Q8—224no—
658C2×Q8—221no—
659C2×Q8—221no—
660C2×Q8—222no—
661C2×Q8—228no—
662C2×Q8—222no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—222no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—444no—
669C2×Q8—448no—
670C2×Q8—444no—
671C2×Q8—448no—
672C2×Q8D4×D1114yes—
673C2×Q8C23×D1112yes—
674C2×Q8C23×D1112yes—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—44no—
680C2×D4—114no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—444no—
684C2×D4C23×D1112yes—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—24no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—44no—
692C22×C4—111no—
693C22×C4—111no—
694C22×C4—111no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—224no—
698C22×C4—224no—
699C22×C4—221no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—224no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4D4×D1112yes—
710C22×C4D4×D1111yescharacteristic
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—1116no—
714Q16—228no—
715Q16—228no—
716Q16—228no—
717Q16—228no—
718Q16—444no—
719SD16—28no—
720SD16—44no—
721SD16—228no—
722M16—228no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—114no—
726C2×C8—112no—
727C2×C8—112no—
728C2×C8—228no—
729C2×C8—222no—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—21no—
733C4⋊C4—114no—
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—224no—
743C4⋊C4C23×D1112yes—
744C22⋊C4—24no—
745C22⋊C4—114no—
746C22⋊C4—114no—
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—22no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—112no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23#6696814yescomplemented
768C23C2×D4×D1112yes—
769C23C2×D4×D1111yescharacteristic
770Q8—24no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—48no—
775Q8—42no—
776Q8—114no—
777Q8—224no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—222no—
782Q8—222no—
783Q8—448no—
784Q8—448no—
785Q8—442no—
786Q8—442no—
787Q8C2×D4×D1114yes—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—228no—
793D4—448no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—224no—
812C2×C4—222no—
813C2×C4—224no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—448no—
820C2×C4—448no—
821C2×C4—448no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1111yescharacteristic
827C2×C4C2×D4×D1112yes—
828C2×C4#6703712yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—22no—
832C8—114no—
833C8—222no—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—84no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—444no—
845C22#1062312112yes—
846C22C2×#6696812yes—
847C22C2×#6696814yescomplemented
848C22#1062331012yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—222no—
855C4—224no—
856C4—222no—
857C4—222no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4#1062312112yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6703711yescharacteristic
864C2—24no—
865C2—82no—
866C2—442no—
867C2#1308017914yesdirect product factor
868C2C2×#1062312111yescharacteristic
869C2C22×#6696811yescharacteristic
870C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
prime radicalC2×#10623129C2
hypercenterC2×#448D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C23×#4326C2semidirect
3. C2×Q8×C22⋊D11C2semidirect
5. #13080179C2direct (N × H)
6. C2×#10622780C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622779C2semidirect
10. C2×#10622406C2semidirect
11. C2×#10622786C2semidirect
12. C2×#10622352C2semidirect
13. C2×#10622421C2semidirect
14. C2×#10622402C2semidirect
15. C2×#10622343C2semidirect
16. C2×C11×#448C2semidirect
25. Q8×C22⋊D11C22semidirect
36. C22×#4326C22semidirect
47. C2×#66968C22semidirect
57. C11×#448C22semidirect
62. #10622786C22semidirect
63. #10622780C22semidirect
64. #10622779C22semidirect
70. #10622654C22semidirect
73. #10622429C22semidirect
74. #10622421C22semidirect
75. #10622406C22semidirect
76. #10622402C22semidirect
77. #10622352C22semidirect
78. #10622343C22semidirect
139. C2×#4326D4semidirect
295. #4326C2×D4semidirect
335. C2×#448D11semidirect
344. C23×C11#137semidirect
463. #448C2×D11semidirect
486. C22×C11C2×#137semidirect
629. C2×C11#3270semidirect
756. C11C2×#3270semidirect
767. C23#66968semidirect
847. C22C2×#66968semidirect
867. C2#13080179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C23×#43262
C2×Q8×C22⋊D112
C2×#106231292
#130801792
C2×#106227802
C2×#106224292
C2×#106226542
C2×#106227792
C2×#106224062
C2×#106227862
C2×#106223522
C2×#106224212
C2×#106224022
C2×#106223432
C2×C11×#4482
C2×#327011