Finite Group Databasebeta

← #14770690

Subgroups — #14770690

Order 2816.

1280 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic, complemented
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic
3C4×C22⋊C4×D11C211yesmaximal, characteristic
4#13069223C211yesmaximal, characteristic, complemented
5#13069223C211yesmaximal, characteristic, complemented
6#13069221C211yesmaximal, characteristic, complemented
7#13069221C211yesmaximal, characteristic, complemented
8#13068796C211yesmaximal, characteristic, complemented
9#13068683C211yesmaximal, characteristic, complemented
10#13068593C211yesmaximal, characteristic, complemented
11#13068525C211yesmaximal, characteristic
12#13068390C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C22⋊C4×D11C411yescharacteristic
20C2×C22⋊C4×D11C411yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic, complemented
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic, complemented
39C2×C8×Dic11C2211yescharacteristic, complemented
40C2×C8×Dic11C2211yescharacteristic, complemented
41C2×C8×Dic11C2211yescharacteristic, complemented
42C22⋊C4×Dic11C411yescharacteristic
43C22⋊C4×Dic11C411yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
47C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
48#10622446—24no—
49#10622279C411yescharacteristic
50#10622279C411yescharacteristic
51D11×#95C411yescharacteristic
52D11×#95C411yescharacteristic
53C11×#336C2211yescharacteristic, complemented
54C11×#336C2211yescharacteristic, complemented
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—41no—
69C22×C4×D11—41no—
70C22×C4×D11C2×C411yescharacteristic
71C22×C4×D11C2×C411yescharacteristic
72C22×C4×D11C2×C411yescharacteristic
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×C4×Dic11C2×C411yescharacteristic
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2×C411yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22⋊C4×D11—24no—
109C22⋊C4×D11C818yescomplemented
110C42×D11—22no—
111C42×D11—22no—
112C42×D11—41no—
113C42×D11—41no—
114C11×C4⋊C8—22no—
115C11×C4⋊C8—41no—
116C11×C22⋊C8—22no—
117C11×#95C2×C411yescharacteristic
118C11×#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C22⋊(C11⋊C8)—22no—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—41no—
132(C2×D11)⋊C8—41no—
133(C2×D11)⋊C8D414yes—
134C8×Dic11—22no—
135C8×Dic11—22no—
136C8×Dic11—41no—
137C8×Dic11—41no—
138C4⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—41no—
140#22552—111nomaximal, Sylow
141C24×C11C22×C411yescharacteristic
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—41no—
147C23×D11—41no—
148C23×D11C2×C814yes—
149C23×D11C22×C411yescharacteristic
150C23×D11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—41no—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—22no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—41no—
193C2×C4×D11—41no—
194C2×C4×D11—41no—
195C2×C4×D11—41no—
196C2×C4×D11—41no—
197C2×C4×D11—41no—
198C2×C4×D11—44no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—44no—
202C2×C4×D11C2×C814yescomplemented
203C2×C4×D11C2×C814yescomplemented
204C2×C4×D11C2×D412yes—
205C2×C4×D11#4112yes—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—44no—
218C2×C8×C11C2×D412yes—
219C11×C22⋊C4—22no—
220C11×C22⋊C4C2×C814yes—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C22⋊Dic11C2×C814yes—
226C22⋊Dic11M1614yes—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4C2×C814yescomplemented
230(C2×D11)⋊C4C2×C814yescomplemented
231C4×Dic11—22no—
232C4×Dic11—22no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—41no—
238C4×Dic11—41no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—44no—
251C2×C11⋊C8C2×D412yes—
252C2×#431—111no—
253C22×C22⋊C8—111no—
254C2×C4×C22⋊C4—111no—
255#1923—111no—
256#1923—111no—
257#1923—111no—
258#1923—111no—
259#1850—111no—
260#1850D1111yescharacteristic, complemented
261#1817—111no—
262#1797—111no—
263#1779—111no—
264C8×C22⋊C4—111no—
265C8×C22⋊C4—111no—
266C4×C22⋊C8—111no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11#11712yes—
272C23×C11C22×C812yes—
273C23×C11C2×M1612yes—
274C23×C11C23×C411yescharacteristic
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—28no—
286C22×D11—28no—
287C22×D11—44no—
288C22×D11—44no—
289C22×D11—44no—
290C22×D11—44no—
291C22×D11—44no—
292C22×D11C4×D412yes—
293C22×D11C22×C812yes—
294C22×D11C22×C812yes—
295C22×D11#13112yes—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11#11712yes—
313C2×C4×C11C22×C812yes—
314C2×C4×C11C22×C812yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—44no—
335C2×Dic11C4×D412yes—
336C2×Dic11C22×C812yes—
337C2×Dic11C22×C812yes—
338C2×Dic11C2×M1612yes—
339C2×Dic11C2×M1612yes—
340C4×D11—28no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—44no—
346C4×D11—44no—
347C4×D11—44no—
348C4×D11—44no—
349C4×D11—44no—
350C4×D11—41no—
351C4×D11—41no—
352C4×D11—41no—
353C4×D11—41no—
354C8×C11—22no—
355C8×C11—41no—
356C8×C11—41no—
357C8×C11—41no—
358C11⋊C8—22no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C24×C4—111no—
363C23×C8—111no—
364C23×C8C2×D1111yescharacteristic
365C22×C22⋊C4—111no—
366C22×C22⋊C4—111no—
367C22×C42—111no—
368C22×C42—111no—
369#431—224no—
370C2×C4⋊C8—111no—
371C2×C4⋊C8—111no—
372C2×C4⋊C8C2×D1111yescharacteristic, complemented
373C2×C4⋊C8C2×D1111yescharacteristic, complemented
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×C22⋊C8—111no—
377C2×C22⋊C8—111no—
378C2×C22⋊C8—111no—
379C2×C22⋊C8—111no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8—224no—
384C2×C22⋊C8C2×D1111yescharacteristic
385C2×C4×C8—111no—
386C2×C4×C8—111no—
387C2×C4×C8—111no—
388C2×C4×C8—111no—
389C4×C22⋊C4—111no—
390C4×C22⋊C4—111no—
391C4×C22⋊C4—111no—
392C4×C22⋊C4—111no—
393C4×C22⋊C4—111no—
394C4×C22⋊C4—111no—
395C4×C22⋊C4—111no—
396C4×C22⋊C4C2×D1111yescharacteristic
397C2×#95—111no—
398C2×#95—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336C2×D1111yescharacteristic, complemented
406#336C2×D1111yescharacteristic, complemented
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11#43114yescomplemented
414C22×C11C2×#11711yescharacteristic
415C22×C11C2×C4×D411yescharacteristic
416C22×C11#51811yescharacteristic
417C22×C11C23×C811yescharacteristic
418C22×C11C22×M1611yescharacteristic
419C22×C11C2×#13111yescharacteristic
420C22×C11#56811yescharacteristic
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—416no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11C8×D414yes—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11#54611yescharacteristic
442C4×C11#54611yescharacteristic
443C4×C11#55111yescharacteristic
444C4×C11#55111yescharacteristic
445Dic11—22no—
446Dic11—22no—
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—41no—
451C25—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—222no—
462C23×C4—222no—
463C23×C4—222no—
464C23×C4—222no—
465C23×C4—441no—
466C23×C4—441no—
467C23×C4C22×D1111yescharacteristic
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—41no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475C22×C8—222no—
476C22×C8—222no—
477C22×C8—441no—
478C22×C8C22×D1111yescharacteristic
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4—118no—
487C2×C22⋊C4—111no—
488C2×C22⋊C4—111no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4C4×D1111yescharacteristic
491C2×C22⋊C4C4×D1111yescharacteristic
492C2×C42—111no—
493C2×C42—111no—
494C2×C42—111no—
495C2×C42—111no—
496C2×C42—111no—
497C2×C42—111no—
498C2×C42—222no—
499C2×C42—222no—
500C2×C42—441no—
501C2×C42—441no—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504C4⋊C8—22no—
505C4⋊C8—41no—
506C4⋊C8—222no—
507C4⋊C8—441no—
508C22⋊C8—22no—
509C22⋊C8—114no—
510C22⋊C8—222no—
511C22⋊C8—222no—
512C22⋊C8—222no—
513C22⋊C8—222no—
514C22⋊C8—222no—
515C22⋊C8—222no—
516C22⋊C8—441no—
517C22⋊C8—441no—
518C4×C8—222no—
519C4×C8—222no—
520C4×C8—441no—
521C4×C8—441no—
522#95—111no—
523#95—111no—
524#95—111no—
525#95—111no—
526#95—111no—
527#95—111no—
528#95C4×D1111yescharacteristic
529#95C4×D1111yescharacteristic
530C2×C11—24no—
531C2×C11#234211yescharacteristic
532C2×C11C2×#43111yescharacteristic
533C2×C11#292411yescharacteristic
534C2×C11C2×C8×D411yescharacteristic
535C2×C11D4×M1611yescharacteristic
536C2×C11#297211yescharacteristic
537C2×C11#297411yescharacteristic
538D11—24no—
539D11—42no—
540C24—111no—
541C24—111no—
542C24—114no—
543C24—222no—
544C24—222no—
545C24—222no—
546C24—222no—
547C24—441no—
548C24—441no—
549C24C2×C4×D1111yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—114no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—114no—
563C22×C4—111no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—441no—
587C22×C4—441no—
588C22×C4—441no—
589C22×C4—441no—
590C22×C4—441no—
591C22×C4—441no—
592C22×C4—444no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—441no—
597C22×C4C2×C4×D1111yescharacteristic
598C22×C4C2×C4×D1111yescharacteristic
599C22×C4C2×C4×D1111yescharacteristic
600C22×C4C2×C4×D1111yescharacteristic
601C22×C4C2×C4×D1111yescharacteristic
602C22×C4#434112yes—
603C22×C4#434312yes—
604C22×C4C23×D1111yescharacteristic
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8—112no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—444no—
630C2×C8D4×D1112yes—
631C22⋊C4—22no—
632C22⋊C4—114no—
633C22⋊C4—114no—
634C22⋊C4—114no—
635C22⋊C4—114no—
636C22⋊C4—222no—
637C22⋊C4—222no—
638C22⋊C4C8×D1114yes—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—222no—
644C42—222no—
645C42—221no—
646C42—221no—
647C42—221no—
648C42—221no—
649C42—441no—
650C42—441no—
651C11#2255211yescharacteristic, complemented, Sylow
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—112no—
657C23—112no—
658C23—112no—
659C23—112no—
660C23—228no—
661C23—221no—
662C23—221no—
663C23—221no—
664C23—221no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—228no—
672C23—444no—
673C23—444no—
674C23—444no—
675C23—444no—
676C23—444no—
677C23#6694512yes—
678C23C2×C8×D1112yes—
679C23M16×D1112yes—
680C23C22×C4×D1111yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—228no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4—444no—
723C2×C4—444no—
724C2×C4—444no—
725C2×C4—444no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4#6694512yes—
731C2×C4C2×C8×D1112yes—
732C2×C4C2×C8×D1112yes—
733C2×C4C2×D4×D1111yescharacteristic
734C2×C4C2×#434111yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4C2×#434311yescharacteristic
737C2×C4#41×D1111yescharacteristic
738C2×C4#6704211yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—222no—
744C8—441no—
745C8—441no—
746C8—441no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—114no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—4416no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22#1062244614yescomplemented
769C22C2×#6694511yescharacteristic
770C22C4×D4×D1111yescharacteristic
771C22#1062307611yescharacteristic
772C22C22×C8×D1111yescharacteristic
773C22C2×M16×D1111yescharacteristic
774C22D11×#13111yescharacteristic
775C22#1062328111yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—222no—
782C4—222no—
783C4—222no—
784C4—222no—
785C4—222no—
786C4—441no—
787C4#1062312211yescharacteristic
788C4#1062316111yescharacteristic
789C4#1062316811yescharacteristic
790C4#1062318911yescharacteristic
791C2—24no—
792C2—224no—
793C2—442no—
794C2#1307146311yescharacteristic
795C2C2×#1062244611yescharacteristic
796C2#1307727311yescharacteristic
797C2C8×D4×D1111yescharacteristic
798C2#1307734911yescharacteristic
799C2#1307763711yescharacteristic
800C2#1307764611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1850C2
socleC23×C11C23×C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#22552
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622446C2semidirect
4. #13069223C2semidirect
5. #13069223C2semidirect
6. #13069221C2semidirect
7. #13069221C2semidirect
8. #13068796C2semidirect
9. #13068683C2semidirect
10. #13068593C2semidirect
12. #13068390C2semidirect
13. C8×C22⋊Dic11C2semidirect
14. #13068373C2semidirect
15. C11×#1850C2semidirect
23. C2×C11×C4⋊C8C22semidirect
24. C2×C11×C4⋊C8C22semidirect
38. C2×C8×Dic11C22semidirect
39. C2×C8×Dic11C22semidirect
40. C2×C8×Dic11C22semidirect
41. C2×C8×Dic11C22semidirect
46. C2×C4⋊(C11⋊C8)C22semidirect
47. C2×C4⋊(C11⋊C8)C22semidirect
53. C11×#336C22semidirect
54. C11×#336C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
109. C22⋊C4×D11C8semidirect
202. C2×C4×D11C2×C8semidirect
203. C2×C4×D11C2×C8semidirect
229. (C2×D11)⋊C4C2×C8semidirect
230. (C2×D11)⋊C4C2×C8semidirect
260. #1850D11semidirect
372. C2×C4⋊C8C2×D11semidirect
373. C2×C4⋊C8C2×D11semidirect
405. #336C2×D11semidirect
406. #336C2×D11semidirect
413. C22×C11#431semidirect
651. C11#22552semidirect
768. C22#10622446semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
C22×(C2×D11)⋊C82
C4×C22⋊C4×D112
#130692232
#130692212
#130687962
#130686832
#130685932
#130685252
#130683902
C8×C22⋊Dic112
#130683732
C11×#18502
#2255211