Finite Group Databasebeta

← C2×#13080361 #15629043

Subgroups — C2×#13080361 #15629043

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4326C211yesmaximal, characteristic, complemented
2C22×Q16×D11C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D11C211yesmaximal, characteristic
4C2×#10623163C211yesmaximal, characteristic
5#13080361C2116yesmaximal, direct product factor
6C2×#10622794C211yesmaximal, characteristic, complemented
7C2×#10622426C211yesmaximal, characteristic, complemented
8C2×#10622664C211yesmaximal, characteristic, complemented
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622795C211yesmaximal, characteristic, complemented
11C2×#10622352C211yesmaximal, characteristic, complemented
12C2×#10622421C211yesmaximal, characteristic, complemented
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×#10622403C211yesmaximal, characteristic, complemented
15C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
16C2×C11×#451C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24Q8×C22⋊D11—24no—
25Q8×C22⋊D11C2218yes—
26C2×#66999—21no—
27C2×#66999C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×#66997—21no—
30C2×#66997C2211yescharacteristic
31C2×#66997C2211yescharacteristic
32C22×#4326—28no—
33C22×#4326C2211yescharacteristic
34C22×#4326C2211yescharacteristic
35C22×#4326C2211yescharacteristic
36C22×#4326C2211yescharacteristic
37C22×#4326C2211yescharacteristic
38C22×#4326C2218yescomplemented
39C2×C4×C22⋊D11—21no—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×#66977—21no—
42C2×#66977C2211yescharacteristic
43C23×C11⋊C8C2211yescharacteristic
44C2×Q16×D11—28no—
45C2×Q16×D11C2218yescomplemented
46C22×Dic44C2211yescharacteristic
47C22×Dic44C2211yescharacteristic
48C22×C8×D11C2211yescharacteristic
49#10623163—24no—
50#10623163C2218yes—
51C2×#66950C2211yescharacteristic
52C2×#66949—21no—
53C2×#66941—21no—
54C2×#66940C2211yescharacteristic
55C2×(C22⋊D11)⋊C4—21no—
56C2×#66931—21no—
57C11×#451C2218yescomplemented
58C2×C11×#103C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62#10622799C2218yescomplemented
63#10622795C2218yescomplemented
64#10622794C2218yescomplemented
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×Dic11⋊C8C2211yescharacteristic
69C2×C8×Dic11C2211yescharacteristic
70#10622664C2218yescomplemented
71C2×#66874C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73#10622426C2218yescomplemented
74#10622421C2218yescomplemented
75#10622406C2218yescomplemented
76#10622403C2218yescomplemented
77#10622352C2218yescomplemented
78(C22⋊D11)⋊C8C2218yes—
79C22×Q8×C11—21no—
80C22×Q8×C11—22no—
81C22×Q8×C11—24no—
82C22×Q8×C11—42no—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2314yes—
86C22×Q8×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11D411yescharacteristic
90C23×Dic11—21no—
91C2×Q8×D11—22no—
92C2×Q8×D11—22no—
93C2×Q8×D11—24no—
94C2×Q8×D11—24no—
95C2×Q8×D11—42no—
96C2×Q8×D11—42no—
97C2×Q8×D11C2314yes—
98C2×Q8×D11C2314yes—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22—24no—
103C22×Dic22—21no—
104C22×Dic22—22no—
105C22×Dic22—21no—
106C22×Dic22—21no—
107C22×Dic22—42no—
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2314yes—
111C22×Dic22C2311yescharacteristic
112C2×C11×Q16—24no—
113C2×C11×Q16—42no—
114C2×C11×Q16C2314yes—
115C2×C11×Q16C2314yes—
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2311yescharacteristic
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8C2314yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11D411yescharacteristic
125#66999—22no—
126#66999—28no—
127#66999C2314yes—
128Q8×Dic11—22no—
129Q8×Dic11C2314yes—
130#66997—28no—
131#66997—22no—
132#66997—22no—
133#66997C2314yes—
134#66997C2314yes—
135C2×#4326—24no—
136C2×#4326—24no—
137C2×#4326—232no—
138C2×#4326—24no—
139C2×#4326—24no—
140C2×#4326D418yescomplemented
141C2×#4326C2314yes—
142C2×#4326C2314yes—
143C2×#4326C2314yes—
144C2×#4326C2314yes—
145C2×#4326C2314yes—
146C4×C22⋊D11—28no—
147C4×C22⋊D11D414yes—
148C4×C22⋊D11C2314yes—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4D411yescharacteristic
152C2×C4⋊Dic11—21no—
153C2×C4⋊Dic11—21no—
154C2×C4⋊Dic11C2311yescharacteristic
155#66977—22no—
156#66977—28no—
157#66977C2314yes—
158C2×Dic11⋊C4—21no—
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4D411yescharacteristic
166C2×C4×Dic11—21no—
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C22×C11⋊C8—24no—
170C22×C11⋊C8C2311yescharacteristic
171C22×C11⋊C8C2314yes—
172C22×C11⋊C8C2311yescharacteristic
173Q16×D11—232no—
174C2×Dic44—24no—
175C2×Dic44—42no—
176C2×Dic44C2314yes—
177C2×Dic44C2314yes—
178C2×C8×D11—24no—
179C2×C8×D11C2314yes—
180#66950—22no—
181#66950C2314yes—
182#66949—28no—
183#66941—28no—
184#66940—22no—
185#66940C2314yes—
186(C22⋊D11)⋊C4—28no—
187#66931—28no—
188C11×#103C2314yes—
189C11×#103C2314yes—
190C11×C22⋊C8C2314yes—
191#66899C2314yes—
192(C2×D11)⋊C8C2314yes—
193#66880C2314yes—
194#66880C2314yes—
195Dic11⋊C8C2314yes—
196C8×Dic11C2314yes—
197#66874C2314yes—
198#66871C2314yes—
199C2×D4×Q16—111nomaximal, Sylow
200C24×C11C2×D411yescharacteristic
201C23×D11C2×D411yescharacteristic
202C2×Q8×C11—21no—
203C2×Q8×C11—24no—
204C2×Q8×C11—21no—
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—28no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11—44no—
213C2×Q8×C11—44no—
214C2×Q8×C11—48no—
215C2×Q8×C11C2×D414yes—
216C2×Q8×C11C2412yes—
217C2×Q8×C11C2412yes—
218C2×Q8×C11C2412yes—
219C22×C4×C11—21no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—24no—
226C22×C4×C11—44no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11Q1618yescomplemented
232C2×C22⋊D11C2×D414yes—
233C22×Dic11—21no—
234C22×Dic11—24no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—44no—
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242Q8×D11—28no—
243Q8×D11—28no—
244Q8×D11—44no—
245Q8×D11—44no—
246Q8×D11—48no—
247Q8×D11—48no—
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11C2×D412yes—
255C2×C4×D11C2412yes—
256C2×Dic22—28no—
257C2×Dic22—24no—
258C2×Dic22—24no—
259C2×Dic22—21no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—24no—
263C2×Dic22—21no—
264C2×Dic22—21no—
265C2×Dic22—22no—
266C2×Dic22—22no—
267C2×Dic22—22no—
268C2×Dic22—44no—
269C2×Dic22—48no—
270C2×Dic22—44no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C2×Dic22C2×D414yes—
274C2×Dic22C2412yes—
275C2×Dic22C2412yes—
276C2×Dic22C2412yes—
277C11×Q16—28no—
278C11×Q16—44no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11C2×D414yes—
289#4326—28no—
290#4326—28no—
291#4326—28no—
292#4326—28no—
293#4326C2×D4116yescomplemented
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4C2×D414yes—
297C4⋊Dic11—24no—
298C4⋊Dic11—24no—
299C4⋊Dic11—21no—
300C4⋊Dic11C2412yes—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4C2×D414yes—
309C4×Dic11—24no—
310C4×Dic11—24no—
311C4×Dic11C2×D412yes—
312C4×Dic11C2412yes—
313C2×C11⋊C8—28no—
314C2×C11⋊C8—22no—
315C2×C11⋊C8C2×D414yes—
316C2×C11⋊C8C2412yes—
317C2×C11⋊C8C2412yes—
318Dic44—28no—
319Dic44—44no—
320C8×D11—28no—
321C23×Q16—111no—
322C23×Q16—111no—
323C2×D4×Q8—111no—
324C2×D4×Q8—111no—
325D4×Q16—1116no—
326C2×#494—111no—
327C2×#467—111no—
328C2×#467—111no—
329C2×#462—111no—
330C2×#462—111no—
331C2×#451—111no—
332C2×#451—111no—
333C2×#451—111no—
334C2×#451D1111yescharacteristic, complemented
335C2×C4×Q16—111no—
336C2×C8×D4—111no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11C2×Q1614yescomplemented
340C23×C11C22×D412yes—
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C22×D11—22no—
344C22×D11C2×Q1614yescomplemented
345C22×D11C22×D412yes—
346Q8×C11—24no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—22no—
350Q8×C11—22no—
351Q8×C11—22no—
352Q8×C11—48no—
353Q8×C11—42no—
354Q8×C11—42no—
355Q8×C11C22×D414yes—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—24no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—48no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D412yes—
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11C2×Q16116yescomplemented
375C2×Dic11—24no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—48no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11C2×Q1614yescomplemented
387C2×Dic11C22×D412yes—
388C2×Dic11C22×D412yes—
389C2×Dic11C22×D412yes—
390C4×D11—24no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—48no—
394C4×D11—48no—
395Dic22—24no—
396Dic22—22no—
397Dic22—22no—
398Dic22—22no—
399Dic22—22no—
400Dic22—22no—
401Dic22—48no—
402Dic22—48no—
403Dic22—48no—
404Dic22—42no—
405Dic22—42no—
406Dic22C22×D414yes—
407C8×C11—22no—
408C8×C11—22no—
409C11⋊C8—22no—
410C11⋊C8C22×D414yes—
411C23×Q8—111no—
412C23×Q8—111no—
413C23×Q8—111no—
414C23×Q8C2×D1111yescharacteristic
415C22×Q16—111no—
416C22×Q16—111no—
417C22×Q16—111no—
418C22×Q16—111no—
419C22×Q16—111no—
420C22×Q16—118no—
421C22×Q16—118no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16—228no—
425C22×Q16—228no—
426C22×Q16C2×D1111yescharacteristic
427C22×Q16C2×D1111yescharacteristic
428C23×C8—111no—
429C23×C8—111no—
430D4×Q8—118no—
431D4×Q8—118no—
432D4×Q8—224no—
433D4×Q8—224no—
434C2×C4⋊Q8—111no—
435C2×C4⋊Q8—111no—
436C2×C4⋊Q8—221no—
437C2×C4⋊Q8—221no—
438C2×C22⋊Q8—111no—
439C2×C22⋊Q8—111no—
440C2×C22⋊Q8—111no—
441C2×C22⋊Q8—221no—
442C2×C22⋊Q8—221no—
443C2×C22⋊Q8—221no—
444C2×C22⋊Q8—221no—
445C2×C22⋊Q8C2×D1111yescharacteristic
446C2×C4×Q8—111no—
447C2×C4×Q8—111no—
448C2×C4×D4—111no—
449C2×C4×D4—221no—
450C2×C4×D4—221no—
451#494—118no—
452#467—118no—
453#467—118no—
454#462—118no—
455#462—118no—
456#451—118no—
457#451—118no—
458#451—118no—
459#451C2×D1118yescomplemented
460C4×Q16—118no—
461C8×D4—118no—
462C2×#107—111no—
463C2×C4⋊C8—111no—
464C2×#103—111no—
465C2×#103—111no—
466C2×#103—111no—
467C2×#103—111no—
468C2×#103C2×D1111yescharacteristic
469C2×#103C2×D1111yescharacteristic
470C2×C22⋊C8—111no—
471C2×C22⋊C8C2×D1111yescharacteristic
472C2×C4×C8—111no—
473C22×C11—22no—
474C22×C11—28no—
475C22×C11—22no—
476C22×C11D4212yes—
477C22×C11C22×Q1612yes—
478C22×C11C22×Q1614yescomplemented
479C22×C11#57812yes—
480C22×C11C23×D411yescharacteristic
481C2×D11—22no—
482C2×D11—28no—
483C2×D11—22no—
484C2×D11C22×Q1614yescomplemented
485C4×C11—22no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11D4212yes—
491C4×C11C23×D411yescharacteristic
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493Dic11—24no—
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499Dic11C22×Q1614yescomplemented
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—24no—
503C22×Q8—42no—
504C22×Q8—114no—
505C22×Q8—114no—
506C22×Q8—111no—
507C22×Q8—111no—
508C22×Q8—111no—
509C22×Q8—114no—
510C22×Q8—221no—
511C22×Q8—221no—
512C22×Q8—224no—
513C22×Q8—222no—
514C22×Q8—222no—
515C22×Q8—221no—
516C22×Q8—222no—
517C22×Q8—224no—
518C22×Q8—224no—
519C22×Q8—442no—
520C22×Q8—442no—
521C22×Q8—442no—
522C22×Q8C22×D1111yescharacteristic
523C22×Q8C22×D1111yescharacteristic
524C22×Q8C22×D1114yes—
525C22×Q8C22×D1111yescharacteristic
526C22×D4—111no—
527C23×C4—21no—
528C23×C4—111no—
529C23×C4—221no—
530C23×C4—221no—
531C23×C4—221no—
532C23×C4C22×D1111yescharacteristic
533C2×Q16—24no—
534C2×Q16—42no—
535C2×Q16—118no—
536C2×Q16—114no—
537C2×Q16—114no—
538C2×Q16—114no—
539C2×Q16—114no—
540C2×Q16—114no—
541C2×Q16—114no—
542C2×Q16—114no—
543C2×Q16—224no—
544C2×Q16—224no—
545C2×Q16—224no—
546C2×Q16—2232no—
547C2×Q16—2232no—
548C2×Q16—224no—
549C2×Q16—224no—
550C2×Q16—442no—
551C2×Q16C22×D1114yes—
552C2×Q16C22×D1114yes—
553C22×C8—111no—
554C22×C8—111no—
555C22×C8—114no—
556C22×C8—114no—
557C22×C8—224no—
558C22×C8—224no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561C4⋊Q8—114no—
562C4⋊Q8—114no—
563C4⋊Q8—222no—
564C4⋊Q8—222no—
565C4⋊Q8—228no—
566C4⋊Q8—228no—
567C22⋊Q8—22no—
568C22⋊Q8—114no—
569C22⋊Q8—114no—
570C22⋊Q8—114no—
571C22⋊Q8—228no—
572C22⋊Q8—228no—
573C22⋊Q8—228no—
574C22⋊Q8—228no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577C22⋊Q8—222no—
578C22⋊Q8C22×D1114yes—
579C4×Q8—114no—
580C4×Q8—114no—
581C4×Q8—222no—
582C4×Q8—222no—
583C4×D4—114no—
584C4×D4—114no—
585C4×D4—228no—
586C4×D4—228no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—221no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4—221no—
597C2×C4⋊C4—221no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4C22×D1111yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—111no—
602C2×C22⋊C4—111no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—111no—
607C2×C42—221no—
608C2×C42—221no—
609#107—114no—
610C4⋊C8—114no—
611#103—114no—
612#103—114no—
613#103—114no—
614#103—114no—
615#103C22×D1114yes—
616#103C22×D1114yes—
617C22⋊C8—114no—
618C22⋊C8C22×D1114yes—
619C4×C8—114no—
620C2×C11—24no—
621C2×C11D4×Q1614yescomplemented
622C2×C11C2×D4211yescharacteristic
623C2×C11C23×Q1611yescharacteristic
624C2×C11C2×#57811yescharacteristic
625D11—24no—
626C24—111no—
627C24D4×D1111yescharacteristic
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—24no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—28no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—44no—
639C2×Q8—44no—
640C2×Q8—48no—
641C2×Q8—114no—
642C2×Q8—112no—
643C2×Q8—112no—
644C2×Q8—112no—
645C2×Q8—224no—
646C2×Q8—224no—
647C2×Q8—228no—
648C2×Q8—221no—
649C2×Q8—224no—
650C2×Q8—221no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—228no—
654C2×Q8—228no—
655C2×Q8—222no—
656C2×Q8—222no—
657C2×Q8—222no—
658C2×Q8—222no—
659C2×Q8—444no—
660C2×Q8—444no—
661C2×Q8—444no—
662C2×Q8—448no—
663C2×Q8—444no—
664C2×Q8—444no—
665C2×Q8—444no—
666C2×Q8—448no—
667C2×Q8—448no—
668C2×Q8D4×D1114yes—
669C2×Q8C23×D1112yes—
670C2×Q8C23×D1112yes—
671C2×Q8C23×D1112yes—
672C2×D4—118no—
673C2×D4—114no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—44no—
682C22×C4—111no—
683C22×C4—111no—
684C22×C4—111no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—224no—
688C22×C4—224no—
689C22×C4—221no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—224no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—444no—
697C22×C4—444no—
698C22×C4—444no—
699C22×C4D4×D1112yes—
700C22×C4D4×D1111yescharacteristic
701C22×C4C23×D1112yes—
702C22×C4C23×D1111yescharacteristic
703Q16—28no—
704Q16—44no—
705Q16—1116no—
706Q16—228no—
707Q16—228no—
708Q16—228no—
709Q16—228no—
710Q16—228no—
711Q16—444no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—114no—
715C2×C8—112no—
716C2×C8—112no—
717C2×C8—228no—
718C2×C8—228no—
719C2×C8—222no—
720C2×C8C23×D1112yes—
721C2×C8C23×D1112yes—
722C4⋊C4—24no—
723C4⋊C4—21no—
724C4⋊C4—114no—
725C4⋊C4—112no—
726C4⋊C4—224no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—224no—
730C4⋊C4—224no—
731C4⋊C4—224no—
732C4⋊C4—224no—
733C4⋊C4—224no—
734C4⋊C4—221no—
735C4⋊C4—224no—
736C4⋊C4C23×D1112yes—
737C22⋊C4—24no—
738C22⋊C4—114no—
739C22⋊C4—114no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C42—112no—
744C42—112no—
745C42—224no—
746C42—224no—
747C11C2×D4×Q1611yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—114no—
751C23—112no—
752C23—222no—
753C23—222no—
754C23Q16×D1114yescomplemented
755C23C2×D4×D1112yes—
756C23C2×D4×D1111yescharacteristic
757Q8—24no—
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—22no—
763Q8—48no—
764Q8—42no—
765Q8—42no—
766Q8—114no—
767Q8—224no—
768Q8—222no—
769Q8—222no—
770Q8—222no—
771Q8—222no—
772Q8—222no—
773Q8—448no—
774Q8—448no—
775Q8—448no—
776Q8—442no—
777Q8—442no—
778Q8C2×D4×D1114yes—
779D4—1116no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—114no—
794C2×C4—112no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—224no—
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—448no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4C2×D4×D1112yes—
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×D4×D1112yes—
816C2×C4#6703712yes—
817C2×C4C24×D1111yescharacteristic
818C8—22no—
819C8—22no—
820C8—114no—
821C8—222no—
822C22—28no—
823C22—22no—
824C22—22no—
825C22—114no—
826C22—228no—
827C22—222no—
828C22—222no—
829C22#1062312112yes—
830C22C2×Q16×D1112yes—
831C22C2×Q16×D1114yescomplemented
832C22#1062331012yes—
833C22C22×D4×D1111yescharacteristic
834C4—22no—
835C4—24no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—114no—
840C4—222no—
841C4—224no—
842C4—222no—
843C4—442no—
844C4—442no—
845C4—442no—
846C4#1062312112yes—
847C4C22×D4×D1111yescharacteristic
848C4C2×#6703711yescharacteristic
849C2—24no—
850C2—224no—
851C2#1308036114yesdirect product factor
852C2C2×#1062312111yescharacteristic
853C2C22×Q16×D1111yescharacteristic
854C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#451D11
hypocenterC11C2×D4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C23×#4326C2semidirect
2. C22×Q16×D11C2semidirect
5. #13080361C2direct (N × H)
6. C2×#10622794C2semidirect
7. C2×#10622426C2semidirect
8. C2×#10622664C2semidirect
9. C2×#10622406C2semidirect
10. C2×#10622795C2semidirect
11. C2×#10622352C2semidirect
12. C2×#10622421C2semidirect
13. C2×#10622799C2semidirect
14. C2×#10622403C2semidirect
16. C2×C11×#451C2semidirect
38. C22×#4326C22semidirect
45. C2×Q16×D11C22semidirect
57. C11×#451C22semidirect
62. #10622799C22semidirect
63. #10622795C22semidirect
64. #10622794C22semidirect
70. #10622664C22semidirect
73. #10622426C22semidirect
74. #10622421C22semidirect
75. #10622406C22semidirect
76. #10622403C22semidirect
77. #10622352C22semidirect
140. C2×#4326D4semidirect
231. C2×C22⋊D11Q16semidirect
293. #4326C2×D4semidirect
334. C2×#451D11semidirect
339. C23×C11C2×Q16semidirect
344. C22×D11C2×Q16semidirect
374. C22⋊D11C2×Q16semidirect
386. C2×Dic11C2×Q16semidirect
459. #451C2×D11semidirect
478. C22×C11C22×Q16semidirect
484. C2×D11C22×Q16semidirect
499. Dic11C22×Q16semidirect
621. C2×C11D4×Q16semidirect
747. C11C2×D4×Q16semidirect
754. C23Q16×D11semidirect
831. C22C2×Q16×D11semidirect
851. C2#13080361direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43262
C22×Q16×D112
C2×Q8×C22⋊D112
C2×#106231632
#130803612
C2×#106227942
C2×#106224262
C2×#106226642
C2×#106224062
C2×#106227952
C2×#106223522
C2×#106224212
C2×#106227992
C2×#106224032
C2×(C22⋊D11)⋊C82
C2×C11×#4512
C2×D4×Q1611