Finite Group Databasebeta

← #14769065

Subgroups — #14769065

Order 2816.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622342C211yesmaximal, characteristic, complemented
4C2×#10622739C211yesmaximal, characteristic, complemented
5C2×#10622339C211yesmaximal, characteristic, complemented
6#13069408C211yesmaximal, characteristic, complemented
7#13069408C211yesmaximal, characteristic, complemented
8#13068914C211yesmaximal, characteristic, complemented
9#13068912C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068595C211yesmaximal, characteristic, complemented
12#13068525C211yesmaximal, characteristic, complemented
13#13068525C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×D4×D11C411yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×D4×Dic11C411yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×#4318C2211yescharacteristic, complemented
25C22×#4313C2211yescharacteristic, complemented
26C22×#4313C2211yescharacteristic, complemented
27C4×D4×D11—24no—
28C4×D4×D11—24no—
29C2×#66946C411yescharacteristic
30C2×C4⋊C4×D11C411yescharacteristic
31C2×(C22⋊D11)⋊C4C411yescharacteristic
32C2×(C22⋊D11)⋊C4C411yescharacteristic
33C2×C22⋊C4×D11C411yescharacteristic
34C2×C22⋊C4×D11C411yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39C2×C11×C22⋊C8C2211yescharacteristic, complemented
40C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622741—24no—
44#10622739—24no—
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
55C2×Dic11⋊C8C2211yescharacteristic, complemented
56C2×Dic11⋊C8C2211yescharacteristic, complemented
57C2×C8×Dic11C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59#10622342—24no—
60#10622339—24no—
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65C24×D11C2×C411yescharacteristic
66C24×D11C2×C411yescharacteristic
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic
71C22×C22⋊D11C2×C411yescharacteristic
72C23×Dic11C2×C411yescharacteristic
73C23×Dic11C2×C411yescharacteristic
74C2×D4×D11—24no—
75C2×D4×D11—24no—
76C2×D4×D11—24no—
77C22×D44C2×C411yescharacteristic
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11C2×C411yescharacteristic
91C22×C4×D11C2×C411yescharacteristic
92C22×C4×D11C2×C411yescharacteristic
93C22×C4×D11C2×C411yescharacteristic
94C22×C4×D11C2×C411yescharacteristic
95C22×C4×D11C2×C411yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16—41no—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C2×C11×C4⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11C2×C411yescharacteristic
113C2×C22⋊Dic11C2×C411yescharacteristic
114D4×Dic11—24no—
115C4×C22⋊D11—22no—
116C4×C22⋊D11—22no—
117C4×C22⋊D11D414yes—
118C4×C22⋊D11D414yes—
119C2×(C2×D11)⋊C4C2×C411yescharacteristic
120C2×(C2×D11)⋊C4C2×C411yescharacteristic
121C2×(C2×D11)⋊C4C2×C411yescharacteristic
122C2×(C2×D11)⋊C4C2×C411yescharacteristic
123C2×C4⋊Dic11C2×C411yescharacteristic
124C2×Dic11⋊C4C2×C411yescharacteristic
125C2×Dic11⋊C4C2×C411yescharacteristic
126C2×C4×Dic11C2×C411yescharacteristic
127C2×C4×Dic11C2×C411yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129C2×#4318—22no—
130C2×#4318—22no—
131C2×#4318—41no—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4313—22no—
137C2×#4313—22no—
138C2×#4313—22no—
139C2×#4313—22no—
140C2×#4313—41no—
141C2×#4313—41no—
142#66946—24no—
143C4⋊C4×D11—24no—
144(C22⋊D11)⋊C4—24no—
145(C22⋊D11)⋊C4—24no—
146C22⋊C4×D11—24no—
147C22⋊C4×D11—24no—
148C4×D44—22no—
149C4×D44—22no—
150C42×D11—22no—
151C42×D11—22no—
152C11×C22⋊C8—22no—
153C11×C22⋊C8—22no—
154C11×C22⋊C8—41no—
155C22⋊(C11⋊C8)—22no—
156C22⋊(C11⋊C8)—22no—
157C22⋊(C11⋊C8)—41no—
158(C2×D11)⋊C8—22no—
159(C2×D11)⋊C8—22no—
160(C2×D11)⋊C8—22no—
161(C2×D11)⋊C8—22no—
162(C2×D11)⋊C8—22no—
163(C2×D11)⋊C8—22no—
164(C2×D11)⋊C8—22no—
165(C2×D11)⋊C8—41no—
166(C2×D11)⋊C8—41no—
167(C2×D11)⋊C8D414yescomplemented
168Dic11⋊C8—22no—
169Dic11⋊C8—22no—
170C8×Dic11—22no—
171C8×Dic11—22no—
172#22401—111nomaximal, Sylow
173C24×C11C22×C411yescharacteristic
174C24×C11C22×C411yescharacteristic
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—41no—
186C23×D11—41no—
187C23×D11—41no—
188C23×D11—41no—
189C23×D11C22×C411yescharacteristic
190C23×D11C22×C411yescharacteristic
191C23×D11C22×C411yescharacteristic
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—22no—
213C2×C22⋊D11—22no—
214C2×C22⋊D11—22no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11C22⋊C414yes—
217C2×C22⋊D11M1614yescomplemented
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—41no—
223C22×Dic11—41no—
224C22×Dic11C22×C411yescharacteristic
225C22×Dic11C22×C411yescharacteristic
226C22×Dic11C22×C411yescharacteristic
227C22×Dic11C22×C411yescharacteristic
228C22×Dic11C22×C411yescharacteristic
229D4×D11—232no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—21no—
259C2×C4×D11—41no—
260C2×C4×D11—41no—
261C2×C4×D11—41no—
262C2×C4×D11—41no—
263C2×C4×D11—41no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11M1614yescomplemented
273C2×C4×D11C2×D412yes—
274C2×C4×D11C2×D412yes—
275C2×C4×D11C2×D412yes—
276C2×C4×D11#4112yes—
277C11×M16—44no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C2×C8×C11—21no—
283C2×C8×C11—21no—
284C2×C8×C11—21no—
285C2×C8×C11—21no—
286C2×C8×C11—21no—
287C2×C8×C11—21no—
288C2×C8×C11—21no—
289C2×C8×C11C2×D412yescomplemented
290C11×C4⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C42×C11—21no—
294C42×C11—21no—
295C22⋊Dic11—22no—
296C22⋊Dic11C22⋊C414yes—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4C22⋊C414yes—
301C4⋊Dic11—22no—
302Dic11⋊C4—22no—
303Dic11⋊C4C22⋊C414yes—
304C4×Dic11—22no—
305C4×Dic11—22no—
306C4×Dic11C2×D412yes—
307C4×Dic11C2×D412yes—
308#4318—44no—
309C2×C11⋊C8—21no—
310C2×C11⋊C8—21no—
311C2×C11⋊C8—21no—
312C2×C11⋊C8—21no—
313C2×C11⋊C8—21no—
314C2×C11⋊C8—21no—
315C2×C11⋊C8—21no—
316C2×C11⋊C8—21no—
317C2×C11⋊C8—21no—
318C2×C11⋊C8—21no—
319C2×C11⋊C8—21no—
320C2×C11⋊C8C2×D412yescomplemented
321#4313—44no—
322#4313—44no—
323C22×C4×D4—111no—
324C2×#436—111no—
325C2×#436—111no—
326C2×#407—111no—
327C2×#407—111no—
328#1954—111no—
329#1954—111no—
330#1870—111no—
331#1870—111no—
332#1870—111no—
333#1870D1111yescharacteristic, complemented
334#1797—111no—
335#1779—111no—
336#1779—111no—
337C4×C22⋊C8—111no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—21no—
348C23×C11—21no—
349C23×C11—21no—
350C23×C11C2×C22⋊C412yes—
351C23×C11C2×M1612yes—
352C23×C11C23×C411yescharacteristic
353C22×D11—21no—
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—21no—
360C22×D11—21no—
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—21no—
364C22×D11—21no—
365C22×D11—21no—
366C22×D11—21no—
367C22×D11—21no—
368C22×D11—21no—
369C22×D11—21no—
370C22×D11—21no—
371C22×D11—44no—
372C22×D11—44no—
373C22×D11—44no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11C2×C22⋊C412yes—
384C22×D11C4×D412yes—
385C22×D11C2×M1612yes—
386C22×D11C2×M1612yes—
387C22×D11#13112yes—
388D4×C11—28no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11C2×C22⋊C412yes—
408C2×C4×C11C2×M1612yes—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C2×#4111yescharacteristic
413C2×C4×C11H(5,𝔽2)11yescharacteristic
414C2×C4×C11H(5,𝔽2)11yescharacteristic
415C22⋊D11—28no—
416C22⋊D11—28no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—44no—
427C2×Dic11—44no—
428C2×Dic11C2×C22⋊C412yes—
429C2×Dic11C2×C22⋊C412yes—
430C2×Dic11C2×C22⋊C412yes—
431C2×Dic11C4×D412yes—
432C2×Dic11C2×M1612yes—
433C2×Dic11C2×M1612yes—
434D44—28no—
435C4×D11—22no—
436C4×D11—22no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—22no—
440C4×D11—22no—
441C4×D11—22no—
442C4×D11—22no—
443C4×D11—28no—
444C4×D11—44no—
445C4×D11—44no—
446C4×D11—44no—
447C4×D11—44no—
448C4×D11—44no—
449C4×D11—41no—
450C4×D11—41no—
451C4×D11—41no—
452C4×D11—41no—
453C8×C11—22no—
454C8×C11—41no—
455C8×C11—41no—
456C8×C11—41no—
457C11⋊C8—22no—
458C11⋊C8—41no—
459C11⋊C8—41no—
460C11⋊C8—41no—
461C23×D4—111no—
462C24×C4—111no—
463C24×C4—111no—
464C22×M16—111no—
465C22×M16—111no—
466C22×M16—111no—
467C22×M16C2×D1111yescharacteristic, complemented
468C2×C4×D4—111no—
469C2×C4×D4—111no—
470C2×C4×D4—111no—
471C2×C4×D4—111no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4—111no—
475C2×C4×D4—224no—
476C2×C4×D4—224no—
477C2×C4×D4C2×D1111yescharacteristic
478C22×C4⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C42—111no—
482#436—224no—
483#436—224no—
484C2×C4⋊C8—111no—
485C2×C4⋊C8—111no—
486#407—224no—
487#407—224no—
488C2×C22⋊C8—111no—
489C2×C22⋊C8—111no—
490C2×C22⋊C8—111no—
491C2×C22⋊C8—111no—
492C2×C22⋊C8—111no—
493C2×C22⋊C8—111no—
494C2×C22⋊C8—111no—
495C2×C22⋊C8—111no—
496C2×C22⋊C8—111no—
497C2×C22⋊C8—111no—
498C2×C22⋊C8—111no—
499C2×C22⋊C8—111no—
500C2×C22⋊C8—111no—
501C2×C22⋊C8C2×D1111yescharacteristic, complemented
502C2×C22⋊C8C2×D1111yescharacteristic, complemented
503C2×C22⋊C8C2×D1111yescharacteristic, complemented
504C2×C4×C8—111no—
505C2×C4×C8—111no—
506#336—111no—
507#336—111no—
508#336C2×D1111yescharacteristic, complemented
509#336C2×D1111yescharacteristic, complemented
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—41no—
524C22×C11C22×C22⋊C411yescharacteristic
525C22×C11C2×C4×D411yescharacteristic
526C22×C11#51811yescharacteristic
527C22×C11C22×M1611yescharacteristic
528C22×C11C22×M1611yescharacteristic
529C22×C11C2×#13111yescharacteristic
530C22×C11#56811yescharacteristic
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—22no—
534C2×D11—22no—
535C2×D11—22no—
536C2×D11—22no—
537C2×D11—22no—
538C2×D11—22no—
539C2×D11—22no—
540C2×D11—22no—
541C2×D11—22no—
542C2×D11—22no—
543C2×D11—416no—
544C2×D11—416no—
545C2×D11—41no—
546C2×D11—41no—
547C2×D11—41no—
548C2×D11—41no—
549C2×D11—41no—
550C2×D11—41no—
551C2×D11—41no—
552C2×D11—41no—
553C2×D11#43614yescomplemented
554C4×C11—22no—
555C4×C11—22no—
556C4×C11—41no—
557C4×C11—41no—
558C4×C11D4211yescharacteristic
559C4×C11D4211yescharacteristic
560C4×C11#54611yescharacteristic
561C4×C11#54611yescharacteristic
562Dic11—22no—
563Dic11—22no—
564Dic11—22no—
565Dic11—41no—
566Dic11#40714yescomplemented
567C25—111no—
568C25—111no—
569C22×D4—111no—
570C22×D4—111no—
571C22×D4—111no—
572C22×D4—224no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4C4×D1111yescharacteristic
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—441no—
596C23×C4—441no—
597C23×C4—441no—
598C23×C4—441no—
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C2×M16—22no—
602C2×M16—22no—
603C2×M16—41no—
604C2×M16—222no—
605C2×M16—222no—
606C2×M16—222no—
607C2×M16—222no—
608C2×M16—222no—
609C2×M16—222no—
610C2×M16—441no—
611C2×M16—441no—
612C2×M16—441no—
613C22×C8—111no—
614C22×C8—111no—
615C22×C8—111no—
616C22×C8—111no—
617C22×C8C22×D1111yescharacteristic
618C22×C8C22×D1111yescharacteristic
619C22×C8C22×D1111yescharacteristic
620C22×C8C22×D1111yescharacteristic
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—114no—
624C4×D4—114no—
625C4×D4—222no—
626C4×D4—222no—
627C4×D4—222no—
628C4×D4—222no—
629C4×D4—224no—
630C4×D4—224no—
631C4×D4—224no—
632C4×D4—224no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—224no—
637C2×C4⋊C4C4×D1111yescharacteristic
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—111no—
642C2×C22⋊C4—111no—
643C2×C22⋊C4—111no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4C4×D1111yescharacteristic
647C2×C22⋊C4C4×D1111yescharacteristic
648C2×C42—111no—
649C2×C42—111no—
650C2×C42—111no—
651C2×C42—222no—
652C2×C42—222no—
653C2×C42C22×D1111yescharacteristic
654C4⋊C8—222no—
655C4⋊C8—222no—
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659C22⋊C8—114no—
660C22⋊C8—222no—
661C22⋊C8—222no—
662C22⋊C8—222no—
663C22⋊C8—222no—
664C22⋊C8—222no—
665C22⋊C8—222no—
666C22⋊C8—222no—
667C22⋊C8—222no—
668C22⋊C8—222no—
669C22⋊C8—441no—
670C22⋊C8—441no—
671C22⋊C8—441no—
672C4×C8—222no—
673C4×C8—222no—
674C2×C11—42no—
675C2×C11—42no—
676C2×C11D4×C22⋊C411yescharacteristic
677C2×C11C2×#40711yescharacteristic
678C2×C11#288011yescharacteristic
679C2×C11C2×#43611yescharacteristic
680C2×C11D4×M1611yescharacteristic
681C2×C11#297411yescharacteristic
682C2×C11#297511yescharacteristic
683D11—24no—
684D11—42no—
685D11—42no—
686C24—111no—
687C24—111no—
688C24—111no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—441no—
700C24—441no—
701C24—441no—
702C24—441no—
703C24C2×C4×D1111yescharacteristic
704C24C2×C4×D1111yescharacteristic
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—114no—
709C2×D4—114no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—2232no—
717C2×D4—222no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—111no—
729C22×C4—111no—
730C22×C4—111no—
731C22×C4—111no—
732C22×C4—114no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—111no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—441no—
769C22×C4—441no—
770C22×C4—441no—
771C22×C4—441no—
772C22×C4—441no—
773C22×C4—444no—
774C22×C4—444no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—441no—
782C22×C4—441no—
783C22×C4C2×C4×D1111yescharacteristic
784C22×C4C2×C4×D1111yescharacteristic
785C22×C4C2×C4×D1111yescharacteristic
786C22×C4C2×C4×D1111yescharacteristic
787C22×C4D4×D1112yes—
788C22×C4D4×D1112yes—
789C22×C4C23×D1111yescharacteristic
790M16—44no—
791M16—444no—
792M16—444no—
793M16—444no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—112no—
806C2×C8—221no—
807C2×C8—221no—
808C2×C8—221no—
809C2×C8—221no—
810C2×C8—221no—
811C2×C8—221no—
812C2×C8—221no—
813C2×C8—221no—
814C2×C8—221no—
815C2×C8—221no—
816C2×C8—221no—
817C2×C8D4×D1112yescomplemented
818C4⋊C4—22no—
819C4⋊C4—114no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—114no—
825C22⋊C4—114no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C42—21no—
831C42—21no—
832C42—112no—
833C42—112no—
834C42—222no—
835C42—222no—
836C11#2240111yescharacteristic, complemented, Sylow
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—112no—
850C23—112no—
851C23—112no—
852C23—112no—
853C23—112no—
854C23—228no—
855C23—228no—
856C23—221no—
857C23—221no—
858C23—221no—
859C23—221no—
860C23—221no—
861C23—221no—
862C23—221no—
863C23—221no—
864C23—221no—
865C23—221no—
866C23—221no—
867C23—221no—
868C23—221no—
869C23—221no—
870C23—221no—
871C23—221no—
872C23—444no—
873C23—444no—
874C23—444no—
875C23—444no—
876C23—444no—
877C23—444no—
878C23—444no—
879C23—444no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23C22⋊C4×D1112yes—
885C23M16×D1112yes—
886C23C22×C4×D1111yescharacteristic
887D4—28no—
888D4—228no—
889D4—228no—
890D4—228no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—112no—
910C2×C4—112no—
911C2×C4—112no—
912C2×C4—112no—
913C2×C4—112no—
914C2×C4—112no—
915C2×C4—228no—
916C2×C4—221no—
917C2×C4—221no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4—444no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4C22⋊C4×D1112yes—
945C2×C4M16×D1112yes—
946C2×C4C2×D4×D1111yescharacteristic
947C2×C4C2×D4×D1111yescharacteristic
948C2×C4C2×D4×D1111yescharacteristic
949C2×C4#6703711yescharacteristic
950C2×C4#41×D1111yescharacteristic
951C2×C4#6704211yescharacteristic
952C8—22no—
953C8—41no—
954C8—41no—
955C8—41no—
956C8—222no—
957C8—441no—
958C8—441no—
959C8—441no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—114no—
975C22—222no—
976C22—222no—
977C22—222no—
978C22—222no—
979C22—222no—
980C22—222no—
981C22—222no—
982C22—222no—
983C22—222no—
984C22—222no—
985C22—222no—
986C22—222no—
987C22—4416no—
988C22—4416no—
989C22—441no—
990C22—441no—
991C22—441no—
992C22—441no—
993C22—441no—
994C22—441no—
995C22—441no—
996C22—441no—
997C22C2×C22⋊C4×D1111yescharacteristic
998C22C4×D4×D1111yescharacteristic
999C22#1062307611yescharacteristic
1000C22C2×M16×D1111yescharacteristic
1001C22C2×M16×D1111yescharacteristic
1002C22D11×#13111yescharacteristic
1003C22#1062328111yescharacteristic
1004C4—22no—
1005C4—22no—
1006C4—41no—
1007C4—41no—
1008C4—114no—
1009C4—222no—
1010C4—222no—
1011C4—222no—
1012C4—441no—
1013C4#1062312111yescharacteristic
1014C4#1062314011yescharacteristic
1015C4#1062314111yescharacteristic
1016C4#1062318511yescharacteristic
1017C2—42no—
1018C2—42no—
1019C2—224no—
1020C2—442no—
1021C2—442no—
1022C2#1307143411yescharacteristic
1023C2D11×#40711yescharacteristic
1024C2#1307706411yescharacteristic
1025C2D11×#43611yescharacteristic
1026C2#1307734911yescharacteristic
1027C2#1307764611yescharacteristic
1028C2#1307765411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622342C2semidirect
4. C2×#10622739C2semidirect
5. C2×#10622339C2semidirect
6. #13069408C2semidirect
7. #13069408C2semidirect
8. #13068914C2semidirect
9. #13068912C2semidirect
10. #13068912C2semidirect
11. #13068595C2semidirect
12. #13068525C2semidirect
13. #13068525C2semidirect
14. #13068373C2semidirect
15. C11×#1870C2semidirect
19. C22×C11×M16C22semidirect
24. C22×#4318C22semidirect
25. C22×#4313C22semidirect
26. C22×#4313C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C2×C11×C22⋊C8C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×(C2×D11)⋊C8C22semidirect
50. C2×(C2×D11)⋊C8C22semidirect
51. C2×(C2×D11)⋊C8C22semidirect
52. C2×(C2×D11)⋊C8C22semidirect
53. C2×(C2×D11)⋊C8C22semidirect
54. C2×(C2×D11)⋊C8C22semidirect
55. C2×Dic11⋊C8C22semidirect
56. C2×Dic11⋊C8C22semidirect
57. C2×C8×Dic11C22semidirect
58. C2×C8×Dic11C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
167. (C2×D11)⋊C8D4semidirect
217. C2×C22⋊D11M16semidirect
272. C2×C4×D11M16semidirect
289. C2×C8×C11C2×D4semidirect
320. C2×C11⋊C8C2×D4semidirect
333. #1870D11semidirect
467. C22×M16C2×D11semidirect
501. C2×C22⋊C8C2×D11semidirect
502. C2×C22⋊C8C2×D11semidirect
503. C2×C22⋊C8C2×D11semidirect
508. #336C2×D11semidirect
509. #336C2×D11semidirect
553. C2×D11#436semidirect
566. Dic11#407semidirect
817. C2×C8D4×D11semidirect
836. C11#22401semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×#106227412
C2×#106223422
C2×#106227392
C2×#106223392
#130694082
#130689142
#130689122
#130685952
#130685252
#130683732
C11×#18702
#2240111