Finite Group Databasebeta

← #14769066

Subgroups — #14769066

Order 2816.

1908 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622741C212yesmaximal, complemented
3C2×#10622339C211yesmaximal, characteristic, complemented
4#13069408C212yesmaximal, complemented
5#13068913C212yesmaximal, complemented
6#13068910C212yesmaximal, complemented
7#13068594C211yesmaximal, characteristic, complemented
8#13068526C211yesmaximal, characteristic, complemented
9#13068525C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#407C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C411yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×M16C2212yescomplemented
16C22×C22⋊Dic11C411yescharacteristic
17C2×C4×C22⋊D11—28no—
18C2×C4×C22⋊D11C411yescharacteristic
19C2×C4×C22⋊D11C411yescharacteristic
20C2×C4×C22⋊D11C411yescharacteristic
21C2×C4×C22⋊D11C411yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×(C2×D11)⋊C4C411yescharacteristic
27C22×Dic11⋊C4C411yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×#4313C2212yescomplemented
30C11×#407—24no—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2212yescomplemented
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37C2×C22⋊(C11⋊C8)C2212yescomplemented
38#10622741—28no—
39C2×(C2×D11)⋊C8C2212yescomplemented
40C2×(C2×D11)⋊C8C2212yescomplemented
41C2×(C2×D11)⋊C8C2212yescomplemented
42C2×Dic11⋊C8C2212yescomplemented
43C2×C8×Dic11C2212yescomplemented
44#10622339—24no—
45#10622188C2212yescomplemented
46#10622188C2212yescomplemented
47C25×C11C2×C411yescharacteristic
48C24×D11C2×C411yescharacteristic
49C23×C4×C11—24no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—42no—
53C23×C4×C11C2×C411yescharacteristic
54C23×C4×C11C2×C411yescharacteristic
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C23×Dic11C2×C411yescharacteristic
67C23×Dic11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—24no—
72C22×C4×D11—42no—
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C2×C11×M16—24no—
78C2×C11×M16—24no—
79C2×C11×M16—42no—
80C22×C8×C11C2312yes—
81C22×C8×C11C2312yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C4×C22⋊D11—24no—
88C4×C22⋊D11—24no—
89C4×C22⋊D11—24no—
90C4×C22⋊D11—24no—
91C4×C22⋊D11—24no—
92C4×C22⋊D11—24no—
93C4×C22⋊D11—24no—
94C4×C22⋊D11D418yes—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×C4×Dic11—24no—
106C2×C4×Dic11C2×C411yescharacteristic
107C2×C4×Dic11C2×C411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111C22×C11⋊C8C2312yes—
112C2×#4313—24no—
113C2×#4313—24no—
114C2×#4313—42no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—24no—
117C11×C22⋊C8D414yescomplemented
118C22⋊(C11⋊C8)—24no—
119C22⋊(C11⋊C8)—22no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—42no—
122(C2×D11)⋊C8—24no—
123(C2×D11)⋊C8—24no—
124(C2×D11)⋊C8—42no—
125Dic11⋊C8—24no—
126C8×Dic11—24no—
127#22401—111nomaximal, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—41no—
134C24×C11—41no—
135C24×C11C22×C411yescharacteristic
136C24×C11C22×C411yescharacteristic
137C24×C11C22×C411yescharacteristic
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—41no—
144C23×D11—41no—
145C23×D11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—48no—
166C22×C4×C11—48no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—232no—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—22no—
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—22no—
181C2×C22⋊D11—22no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11C22⋊C414yes—
186C2×C22⋊D11M1614yescomplemented
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—41no—
194C22×Dic11—41no—
195C22×Dic11M1614yescomplemented
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C2×C4×D11—22no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—22no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—41no—
214C2×C4×D11—41no—
215C2×C4×D11—48no—
216C2×C4×D11—48no—
217C2×C4×D11C2×D414yes—
218C11×M16—48no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11C2×D414yescomplemented
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11C22⋊C414yes—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4C22⋊C414yes—
233Dic11⋊C4—22no—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4C22⋊C414yes—
237C4×Dic11—22no—
238C4×Dic11—22no—
239C4×Dic11—22no—
240C4×Dic11C2×D414yes—
241C2×C11⋊C8—22no—
242C2×C11⋊C8—22no—
243C2×C11⋊C8—22no—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247#4313—48no—
248C22×C4×D4—111no—
249C2×#436—112no—
250C2×#407—111no—
251C2×#407D1111yescharacteristic, complemented
252#1954—112no—
253#1870—112no—
254#1870—112no—
255#1797—111no—
256#1779—111no—
257#1779—111no—
258C4×C22⋊C8—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—28no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11C2×C22⋊C412yes—
283C23×C11C4×D412yes—
284C23×C11C2×M1612yes—
285C23×C11C2×M1612yes—
286C23×C11#13112yes—
287C23×C11C23×C411yescharacteristic
288C22×D11—28no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11C2×C22⋊C412yes—
308C22×D11C2×M1612yes—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—24no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11C2×C22⋊C412yes—
326C2×C4×C11C4×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11H(5,𝔽2)12yes—
331C22⋊D11—28no—
332C22⋊D11—28no—
333C22⋊D11—28no—
334C22⋊D11—28no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—28no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—44no—
349C2×Dic11—44no—
350C2×Dic11C2×C22⋊C412yes—
351C2×Dic11C2×C22⋊C412yes—
352C2×Dic11C2×C22⋊C412yes—
353C2×Dic11C2×M1612yes—
354C2×Dic11C2×M1612yes—
355C2×Dic11C2×M1612yes—
356C4×D11—24no—
357C4×D11—24no—
358C4×D11—44no—
359C4×D11—44no—
360C4×D11—42no—
361C4×D11—42no—
362C8×C11—24no—
363C8×C11—42no—
364C11⋊C8—42no—
365C11⋊C8—42no—
366C23×D4—111no—
367C24×C4—111no—
368C24×C4C2×D1111yescharacteristic
369C22×M16—112no—
370C22×M16C2×D1112yescomplemented
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—228no—
380C22×C4⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C42—111no—
384#436—228no—
385C2×C4⋊C8—112no—
386#407—24no—
387#407—224no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—112no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—112no—
392C2×C22⋊C8—112no—
393C2×C22⋊C8—112no—
394C2×C22⋊C8—112no—
395C2×C22⋊C8C2×D1111yescharacteristic
396C2×C22⋊C8C2×D1111yescharacteristic
397C2×C22⋊C8C2×D1112yescomplemented
398C2×C4×C8—112no—
399#336—112no—
400#336—112no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—416no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11#43614yescomplemented
423C22×C11C22×C22⋊C411yescharacteristic
424C22×C11C2×C4×D411yescharacteristic
425C22×C11#51811yescharacteristic
426C22×C11C22×M1611yescharacteristic
427C22×C11C22×M1611yescharacteristic
428C22×C11C2×#13111yescharacteristic
429C22×C11#56811yescharacteristic
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—416no—
437C2×D11—41no—
438C2×D11—41no—
439C2×D11—41no—
440C2×D11—41no—
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11—41no—
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—41no—
448C4×C11D4212yes—
449C4×C11#54612yes—
450Dic11—22no—
451Dic11—22no—
452Dic11—22no—
453Dic11—41no—
454Dic11—41no—
455Dic11#40714yescomplemented
456C25—111no—
457C25C4×D1111yescharacteristic
458C22×D4—111no—
459C22×D4—111no—
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—224no—
463C22×D4—224no—
464C22×D4—224no—
465C23×C4—22no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—42no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—111no—
476C23×C4—224no—
477C23×C4—222no—
478C23×C4—222no—
479C23×C4—442no—
480C23×C4C4×D1111yescharacteristic
481C23×C4C4×D1111yescharacteristic
482C23×C4C4×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486C2×M16—24no—
487C2×M16—24no—
488C2×M16—42no—
489C2×M16—224no—
490C2×M16—224no—
491C2×M16—442no—
492C22×C8—112no—
493C22×C8—112no—
494C22×C8C22×D1112yes—
495C22×C8C22×D1112yes—
496C4×D4—118no—
497C4×D4—224no—
498C4×D4—224no—
499C4×D4—224no—
500C4×D4—224no—
501C4×D4—224no—
502C4×D4—224no—
503C4×D4—224no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—224no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—111no—
522C2×C42—111no—
523C2×C42—224no—
524C4⋊C8—224no—
525C22⋊C8—22no—
526C22⋊C8—24no—
527C22⋊C8—224no—
528C22⋊C8—222no—
529C22⋊C8—224no—
530C22⋊C8—222no—
531C22⋊C8—224no—
532C22⋊C8—442no—
533C22⋊C8—442no—
534C22⋊C8C22⋊D1114yescomplemented
535C4×C8—224no—
536C2×C11—24no—
537C2×C11—42no—
538C2×C11—42no—
539C2×C11D4×C22⋊C411yescharacteristic
540C2×C11C2×#40711yescharacteristic
541C2×C11#288011yescharacteristic
542C2×C11C2×#43611yescharacteristic
543C2×C11D4×M1611yescharacteristic
544C2×C11#297411yescharacteristic
545C2×C11#297511yescharacteristic
546D11—42no—
547D11—42no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—41no—
554C24—41no—
555C24—111no—
556C24—111no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—441no—
563C24—441no—
564C24C2×C4×D1111yescharacteristic
565C24C2×C4×D1111yescharacteristic
566C24C2×C4×D1111yescharacteristic
567C2×D4—114no—
568C2×D4—114no—
569C2×D4—222no—
570C2×D4—222no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—2232no—
578C2×D4—222no—
579C2×D4—222no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—111no—
601C22×C4—114no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—114no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—221no—
615C22×C4—222no—
616C22×C4—221no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—221no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—221no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4—448no—
628C22×C4—448no—
629C22×C4—441no—
630C22×C4—441no—
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4#433912yes—
635C22×C4D4×D1114yes—
636C22×C4C2×C22⋊D1112yes—
637C22×C4C23×D1111yescharacteristic
638M16—48no—
639M16—448no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8—222no—
650C2×C8—222no—
651C2×C8C2×C22⋊D1114yescomplemented
652C4⋊C4—114no—
653C4⋊C4—222no—
654C4⋊C4—222no—
655C4⋊C4—222no—
656C22⋊C4—114no—
657C22⋊C4—114no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—222no—
661C22⋊C4—222no—
662C22⋊C4—222no—
663C22⋊C4—222no—
664C42—114no—
665C42—222no—
666C42—222no—
667C42—222no—
668C11#2240111yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—28no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—112no—
693C23—112no—
694C23—228no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—221no—
699C23—221no—
700C23—221no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—444no—
708C23—444no—
709C23—444no—
710C23—444no—
711C23—444no—
712C23—444no—
713C23C22⋊C4×D1112yes—
714C23M16×D1112yes—
715C23M16×D1112yes—
716C23#6696012yes—
717C23C4×C22⋊D1112yes—
718C23C22×C4×D1111yescharacteristic
719D4—228no—
720D4—228no—
721D4—228no—
722D4—228no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—228no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—444no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4C22⋊C4×D1112yes—
767C2×C4C4×C22⋊D1112yes—
768C2×C4C2×#433911yescharacteristic
769C2×C4C2×D4×D1112yes—
770C2×C4#6703712yes—
771C2×C4C22×C22⋊D1111yescharacteristic
772C8—24no—
773C8—42no—
774C8—442no—
775C8—442no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—222no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—4416no—
804C22—441no—
805C22—441no—
806C22—441no—
807C22—441no—
808C22—441no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22#1062274114yescomplemented
813C22C2×C22⋊C4×D1111yescharacteristic
814C22#1062301711yescharacteristic
815C22C2×M16×D1111yescharacteristic
816C22C2×M16×D1111yescharacteristic
817C22C2×#6696011yescharacteristic
818C22#1062327611yescharacteristic
819C22C2×C4×C22⋊D1111yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—114no—
824C4—222no—
825C4—222no—
826C4—222no—
827C4—441no—
828C4—441no—
829C4#1062302112yes—
830C4D4×C22⋊D1112yes—
831C2—24no—
832C2—42no—
833C2—42no—
834C2—442no—
835C2—442no—
836C2C22⋊C4×C22⋊D1111yescharacteristic
837C2D11×#40711yescharacteristic
838C2#1307706611yescharacteristic
839C2C2×#1062274111yescharacteristic
840C2M16×C22⋊D1111yescharacteristic
841C2#1307765211yescharacteristic
842C2#1307765511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#407C2
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#22401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622339C2semidirect
4. #13069408C2semidirect
5. #13068913C2semidirect
6. #13068910C2semidirect
7. #13068594C2semidirect
8. #13068526C2semidirect
9. #13068525C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C2×C11×#407C2semidirect
15. C22×C11×M16C22semidirect
29. C22×#4313C22semidirect
33. C2×C11×C22⋊C8C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
39. C2×(C2×D11)⋊C8C22semidirect
40. C2×(C2×D11)⋊C8C22semidirect
41. C2×(C2×D11)⋊C8C22semidirect
42. C2×Dic11⋊C8C22semidirect
43. C2×C8×Dic11C22semidirect
45. #10622188C22semidirect
46. #10622188C22semidirect
117. C11×C22⋊C8D4semidirect
186. C2×C22⋊D11M16semidirect
195. C22×Dic11M16semidirect
224. C2×C8×C11C2×D4semidirect
251. C2×#407D11semidirect
370. C22×M16C2×D11semidirect
397. C2×C22⋊C8C2×D11semidirect
422. C22×C11#436semidirect
455. Dic11#407semidirect
534. C22⋊C8C22⋊D11semidirect
651. C2×C8C2×C22⋊D11semidirect
668. C11#22401semidirect
812. C22#10622741semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106227412
C2×#106223392
#130694082
#130689132
#130689102
#130685942
#130685262
#130685252
C22⋊C8×Dic112
C2×C11×#4072
#2240111