Finite Group Databasebeta

← C2×#13072279 #14921195

Subgroups — C2×#13072279 #14921195

Order 2816.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D11C211yesmaximal, characteristic
4#13072279C2116yesmaximal, direct product factor
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622563C211yesmaximal, characteristic, complemented
10C2×#10622823C211yesmaximal, characteristic, complemented
11C2×#10622602C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×C22⋊Q8—28no—
24C2×C11×C22⋊Q8C2218yescomplemented
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66999—28no—
33C2×#66999C2218yescomplemented
34C22×(C2×D11)⋊C4—28no—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2218yes—
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic, complemented
47C22×C4⋊Dic11C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×Dic11⋊C4C2211yescharacteristic, complemented
51C22×Dic11⋊C4C2211yescharacteristic, complemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yes—
54#10622844C2218yescomplemented
55#10622823C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622607C2218yescomplemented
63#10622607C2218yescomplemented
64#10622605C2218yescomplemented
65#10622602C2218yescomplemented
66#10622602C2218yescomplemented
67#10622600C2218yescomplemented
68#10622568C2218yes—
69#10622563C2218yescomplemented
70#10622555C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—42no—
77C24×D11—42no—
78C24×D11Q818yescomplemented
79C24×D11C2311yescharacteristic
80C24×D11C2314yes—
81C24×D11C2311yescharacteristic
82C22×Q8×C11—24no—
83C22×Q8×C11—24no—
84C22×Q8×C11—42no—
85C22×Q8×C11C2314yescomplemented
86C23×C4×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—42no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2314yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11—42no—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2314yes—
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C11×C22⋊Q8—232no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4C2314yescomplemented
119C2×C11×C4⋊C4C2314yescomplemented
120C2×C11×C4⋊C4C2314yescomplemented
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4D418yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66999—232no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—232no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4D418yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×C4⋊Dic11—24no—
152C2×C4⋊Dic11—42no—
153C2×C4⋊Dic11C2314yescomplemented
154C2×C4⋊Dic11C2314yescomplemented
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4—42no—
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162C2×Dic11⋊C4C2314yescomplemented
163C22⋊C4×D11—232no—
164C11⋊#95C2314yescomplemented
165C11⋊#95C2314yescomplemented
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C2×#2437—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11C2×D414yes—
176C24×C11C2×Q814yes—
177C24×C11#4114yes—
178C24×C11C2412yes—
179C24×C11C2411yescharacteristic
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—232no—
185C23×D11—28no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—28no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—232no—
194C23×D11—28no—
195C23×D11—28no—
196C23×D11—416no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—416no—
200C23×D11—416no—
201C23×D11—416no—
202C23×D11—416no—
203C23×D11C2×D414yes—
204C23×D11C2×Q814yes—
205C23×D11C2×Q814yes—
206C23×D11C2×Q8116yescomplemented
207C23×D11#4114yes—
208C23×D11C2412yes—
209C23×D11C2412yes—
210C2×Q8×C11—28no—
211C2×Q8×C11—28no—
212C2×Q8×C11—44no—
213C2×Q8×C11—416no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—28no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—28no—
231C22×C4×C11—44no—
232C22×C4×C11—416no—
233C22×C4×C11C2×D414yes—
234C22×C4×C11C2×D414yes—
235C22×C4×C11C2×D414yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×Dic11—28no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—28no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—44no—
262C22×Dic11—416no—
263C22×Dic11C2×D414yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—416no—
277C2×C4×D11—416no—
278C11×C4⋊C4—28no—
279C11×C4⋊C4—28no—
280C11×C4⋊C4—28no—
281C11×C22⋊C4—28no—
282C11×C22⋊C4C2×D4116yes—
283C22⋊Dic11—28no—
284C22⋊Dic11—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4C2×D4116yes—
295C4⋊Dic11—28no—
296C4⋊Dic11—44no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299Dic11⋊C4—44no—
300Dic11⋊C4—44no—
301C22×C22⋊Q8—111no—
302C22×C22⋊Q8D1111yescharacteristic, complemented
303C23×C22⋊C4—111no—
304C23×C22⋊C4—111no—
305#2437—1116no—
306C2×#399—111no—
307C2×#396—111no—
308C2×#396—111no—
309C2×#393—111no—
310C2×#385—111no—
311C2×#385—111no—
312C2×#385—111no—
313C2×#385—111no—
314C2×#380—111no—
315C2×#380—111no—
316C2×#379—111no—
317C23×C11—28no—
318C23×C11—28no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C22⋊Q8116yescomplemented
328C23×C11C22×D412yes—
329C23×C11C22×D414yes—
330C23×C11C22×D412yes—
331C23×C11C22×Q814yes—
332C23×C11C22×Q812yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—232no—
352C22×D11—28no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—232no—
360C22×D11—416no—
361C22×D11—4128no—
362C22×D11—416no—
363C22×D11—416no—
364C22×D11—416no—
365C22×D11—416no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11C22⋊Q8116yescomplemented
371C22×D11C22×D414yes—
372C22×D11C22×Q814yes—
373C22×D11C22×Q814yes—
374C22×D11C2×#4114yes—
375Q8×C11—416no—
376C2×C4×C11—28no—
377C2×C4×C11—28no—
378C2×C4×C11—28no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—416no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11C22×D414yes—
399C2×C4×C11C22×D414yes—
400C2×C4×C11C22×D414yes—
401C2×Dic11—28no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—416no—
420C2×Dic11—44no—
421C2×Dic11—44no—
422C2×Dic11—44no—
423C2×Dic11—44no—
424C2×Dic11—44no—
425C2×Dic11C22×D414yes—
426C4×D11—416no—
427C4×D11—416no—
428C26—111no—
429C23×Q8C2×D1111yescharacteristic, complemented
430C24×C4—111no—
431C24×C4—111no—
432C24×C4—111no—
433C24×C4C2×D1111yescharacteristic
434C2×C22⋊Q8—28no—
435C2×C22⋊Q8—118no—
436C2×C22⋊Q8—228no—
437C2×C22⋊Q8C2×D1118yescomplemented
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4C2×D1111yescharacteristic, complemented
445C22×C4⋊C4C2×D1111yescharacteristic, complemented
446C22×C4⋊C4C2×D1111yescharacteristic, complemented
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—118no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—118no—
461C22×C22⋊C4—228no—
462C22×C22⋊C4—228no—
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465#399—118no—
466#396—118no—
467#396—118no—
468#393—118no—
469#385—118no—
470#385—118no—
471#385—118no—
472#385—118no—
473#380—118no—
474#380—118no—
475#379—118no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—232no—
485C22×C11—24no—
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11C2×C22⋊Q814yes—
490C22×C11C2×C22⋊Q814yes—
491C22×C11C2×C22⋊Q818yescomplemented
492C22×C11#54314yes—
493C22×C11D4214yes—
494C22×C11#54614yes—
495C22×C11#54614yes—
496C22×C11#55114yes—
497C22×C11C23×D411yescharacteristic
498C22×C11C23×D411yescharacteristic
499C22×C11C23×Q811yescharacteristic
500C22×C11C22×#4111yescharacteristic
501C22×C11C22×#4111yescharacteristic
502C22×C11C2×H(5,𝔽2)11yescharacteristic
503C22×C11C2×H(5,𝔽2)11yescharacteristic
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—232no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—464no—
515C2×D11—416no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11C2×C22⋊Q818yescomplemented
521C4×C11—24no—
522C4×C11—24no—
523C4×C11—24no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533C25—111no—
534C25—111no—
535C25—118no—
536C25—114no—
537C25—224no—
538C25—224no—
539C25—224no—
540C25—224no—
541C25—442no—
542C25—442no—
543C25C22×D1111yescharacteristic
544C22×Q8—24no—
545C22×Q8—24no—
546C22×Q8—42no—
547C22×Q8C22×D1114yescomplemented
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—42no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—114no—
558C23×C4—114no—
559C23×C4—114no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—224no—
565C23×C4—224no—
566C23×C4—442no—
567C23×C4—442no—
568C23×C4—442no—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1114yes—
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C22⋊Q8—232no—
577C22⋊Q8—2232no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—224no—
590C2×C4⋊C4—442no—
591C2×C4⋊C4—442no—
592C2×C4⋊C4—442no—
593C2×C4⋊C4C22×D1114yescomplemented
594C2×C4⋊C4C22×D1114yescomplemented
595C2×C4⋊C4C22×D1114yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—118no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—2232no—
611C2×C22⋊C4—224no—
612C2×C22⋊C4—224no—
613C2×C22⋊C4—224no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—224no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—2232no—
621C2×C22⋊C4—442no—
622C2×C22⋊C4—442no—
623C2×C22⋊C4C22⋊D1118yes—
624C2×C22⋊C4C22×D1114yes—
625C2×C22⋊C4C22×D1114yes—
626#95—114no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—114no—
631#95—114no—
632C2×C11—28no—
633C2×C11#243718yescomplemented
634C2×C11C22×C22⋊Q811yescharacteristic
635C2×C11C22×C22⋊Q811yescharacteristic
636C2×C11C2×#54311yescharacteristic
637C2×C11C2×D4211yescharacteristic
638C2×C11C2×#54611yescharacteristic
639C2×C11C2×#54611yescharacteristic
640C2×C11C2×#55111yescharacteristic
641D11—28no—
642D11—44no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—114no—
648C24—114no—
649C24—114no—
650C24—112no—
651C24—114no—
652C24—112no—
653C24—1116no—
654C24—228no—
655C24—2232no—
656C24—228no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—2232no—
662C24—222no—
663C24—222no—
664C24—228no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—228no—
669C24—222no—
670C24—4416no—
671C24—444no—
672C24—444no—
673C24—4416no—
674C24—4416no—
675C24—4416no—
676C24—4416no—
677C24Q8×D1114yes—
678C24#434314yes—
679C24C2×C22⋊D1114yes—
680C24C23×D1112yes—
681C24C23×D1111yescharacteristic
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—416no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—44no—
704C22×C4—416no—
705C22×C4—114no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—228no—
713C22×C4—228no—
714C22×C4—228no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—228no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—228no—
734C22×C4—228no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4—4416no—
738C22×C4—4416no—
739C22×C4—444no—
740C22×C4—4416no—
741C22×C4D4×D1114yes—
742C22×C4C2×C22⋊D1114yes—
743C22×C4C2×C22⋊D1114yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—228no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—444no—
757C4⋊C4—444no—
758C4⋊C4—444no—
759C22⋊C4—28no—
760C22⋊C4—1116no—
761C22⋊C4—228no—
762C22⋊C4—228no—
763C22⋊C4—228no—
764C22⋊C4—228no—
765C22⋊C4—228no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—228no—
770C22⋊C4—444no—
771C22⋊C4—444no—
772C22⋊C4C2×C22⋊D11116yes—
773C11C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—1116no—
785C23—114no—
786C23—114no—
787C23—114no—
788C23—114no—
789C23—2232no—
790C23—228no—
791C23—228no—
792C23—228no—
793C23—228no—
794C23—228no—
795C23—228no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—228no—
801C23—2232no—
802C23—228no—
803C23—228no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—4416no—
811C23—4416no—
812C23—44128no—
813C23—4416no—
814C23—4416no—
815C23—4416no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23#66999116yescomplemented
821C23C2×D4×D1112yes—
822C23#6703712yes—
823C23C2×Q8×D1114yes—
824C23C2×Q8×D1112yes—
825C23C2×#434314yes—
826C23C2×#434312yes—
827C23#41×D1112yes—
828C23#6704212yes—
829C23C22×C22⋊D1114yes—
830C23C22×C22⋊D1112yes—
831C23C24×D1111yescharacteristic
832Q8—416no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—114no—
856C2×C4—228no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—4416no—
875C2×C4—4416no—
876C2×C4—4416no—
877C2×C4—444no—
878C2×C4—444no—
879C2×C4—444no—
880C2×C4—444no—
881C2×C4—444no—
882C2×C4C2×D4×D1114yes—
883C2×C4C22×C22⋊D1114yes—
884C2×C4C22×C22⋊D1114yes—
885C22—24no—
886C22—232no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—118no—
893C22—224no—
894C22—2232no—
895C22—224no—
896C22—224no—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—224no—
901C22—224no—
902C22—224no—
903C22—4464no—
904C22—442no—
905C22—4416no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22D11×C22⋊Q814yes—
910C22#1062316114yes—
911C22#1062316514yes—
912C22#1062316814yes—
913C22D4×C22⋊D1114yes—
914C22C2×#6699914yes—
915C22C2×#6699918yescomplemented
916C22#1062336014yes—
917C22C22×D4×D1111yescharacteristic
918C22C2×#6703711yescharacteristic
919C22C22×Q8×D1111yescharacteristic
920C22C22×#434311yescharacteristic
921C22C2×#41×D1111yescharacteristic
922C22C2×#6704211yescharacteristic
923C22C23×C22⋊D1111yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—224no—
931C4—442no—
932C4—442no—
933C4—442no—
934C4—442no—
935C4—442no—
936C2—28no—
937C2—228no—
938C2—444no—
939C2#1307227918yesdirect product factor
940C2C2×D11×C22⋊Q811yescharacteristic
941C2C22×#6699911yescharacteristic
942C2C2×#1062316511yescharacteristic
943C2C2×D4×C22⋊D1111yescharacteristic
944C2C2×#1062336011yescharacteristic
945C2C2×#1062316111yescharacteristic
946C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
4. #13072279C2direct (N × H)
5. C2×#10622605C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622823C2semidirect
11. C2×#10622602C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622555C2semidirect
14. C2×#10622600C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
18. C23×Q8×C11C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
25. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C4⋊C4C22semidirect
33. C2×#66999C22semidirect
46. C22×C4⋊Dic11C22semidirect
47. C22×C4⋊Dic11C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×Dic11⋊C4C22semidirect
54. #10622844C22semidirect
55. #10622823C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622607C22semidirect
63. #10622607C22semidirect
64. #10622605C22semidirect
65. #10622602C22semidirect
66. #10622602C22semidirect
67. #10622600C22semidirect
69. #10622563C22semidirect
70. #10622555C22semidirect
78. C24×D11Q8semidirect
85. C22×Q8×C11C23semidirect
118. C2×C11×C4⋊C4C23semidirect
119. C2×C11×C4⋊C4C23semidirect
120. C2×C11×C4⋊C4C23semidirect
153. C2×C4⋊Dic11C23semidirect
154. C2×C4⋊Dic11C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
161. C2×Dic11⋊C4C23semidirect
162. C2×Dic11⋊C4C23semidirect
164. C11⋊#95C23semidirect
165. C11⋊#95C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
206. C23×D11C2×Q8semidirect
302. C22×C22⋊Q8D11semidirect
327. C23×C11C22⋊Q8semidirect
370. C22×D11C22⋊Q8semidirect
429. C23×Q8C2×D11semidirect
437. C2×C22⋊Q8C2×D11semidirect
444. C22×C4⋊C4C2×D11semidirect
445. C22×C4⋊C4C2×D11semidirect
446. C22×C4⋊C4C2×D11semidirect
491. C22×C11C2×C22⋊Q8semidirect
520. C2×D11C2×C22⋊Q8semidirect
547. C22×Q8C22×D11semidirect
593. C2×C4⋊C4C22×D11semidirect
594. C2×C4⋊C4C22×D11semidirect
595. C2×C4⋊C4C22×D11semidirect
633. C2×C11#2437semidirect
773. C11C2×#2437semidirect
820. C23#66999semidirect
915. C22C2×#66999semidirect
939. C2#13072279direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
#130722792
C2×#106226052
C2×#106226072
C2×#106228442
C2×#106225632
C2×#106228232
C2×#106226022
C2×#106225552
C2×#106226002
C2×#106225682
C22×C11×C22⋊Q82
C2×#243711