Finite Group Databasebeta

← #14780545

Subgroups — #14780545

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069340C211yesmaximal, characteristic, complemented
2#13069340C211yesmaximal, characteristic, complemented
3#13069335C211yesmaximal, characteristic, complemented
4#13069231C211yesmaximal, characteristic
5#13069231C211yesmaximal, characteristic
6#13069224C211yesmaximal, characteristic
7#13069182C211yesmaximal, characteristic, complemented
8#13069182C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068801C211yesmaximal, characteristic
11#13068801C211yesmaximal, characteristic
12#13068801C211yesmaximal, characteristic
13#13068770C211yesmaximal, characteristic, complemented
14#13068761C211yesmaximal, characteristic, complemented
15C11×#2401C211yesmaximal, characteristic
16C22×#4318C2211yescharacteristic
17C11×#401C411yescharacteristic
18C11×#400C411yescharacteristic
19C11×#400C411yescharacteristic
20C11×#400C411yescharacteristic
21C11×#397C411yescharacteristic
22C11×#397C411yescharacteristic
23C11×#397C411yescharacteristic
24C11×#396C411yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C11×#376C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622162C2211yescharacteristic
48#10622162C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×#4318—41no—
79C2×#4318—41no—
80C2×#4318—41no—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C11×#95C2×C411yescharacteristic
90C11×#95C2×C411yescharacteristic
91C11×#95C2×C411yescharacteristic
92C11×#95C2×C411yescharacteristic
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
96C11×#95C2×C411yescharacteristic
97C11×#95C2×C411yescharacteristic
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C22⋊(C11⋊C8)—41no—
106C22⋊(C11⋊C8)—41no—
107C22⋊(C11⋊C8)—41no—
108C4⋊(C11⋊C8)—41no—
109C4⋊(C11⋊C8)—41no—
110C4⋊(C11⋊C8)—41no—
111C4⋊(C11⋊C8)—41no—
112C4⋊(C11⋊C8)—41no—
113C4⋊(C11⋊C8)—41no—
114C4⋊(C11⋊C8)—41no—
115C4⋊(C11⋊C8)—41no—
116C4⋊(C11⋊C8)—41no—
117#66867—41no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#23382—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166#4318—44no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191#2401D1111yescharacteristic
192#1940—111no—
193#1940—111no—
194#1939—111no—
195#1924—111no—
196#1924—111no—
197#1923—111no—
198#1917—111no—
199#1917—111no—
200#1916—111no—
201#1851—111no—
202#1851—111no—
203#1851—111no—
204#1843—111no—
205#1840—111no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11C23×C411yescharacteristic
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#13112yes—
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C22×M16—111no—
272C2×C4⋊C8—111no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284C2×#97—111no—
285C2×#97—111no—
286C2×C4×C8—111no—
287#401Dic1111yescharacteristic
288#400Dic1111yescharacteristic
289#400Dic1111yescharacteristic
290#400Dic1111yescharacteristic
291#397Dic1111yescharacteristic
292#397Dic1111yescharacteristic
293#397Dic1111yescharacteristic
294#396Dic1111yescharacteristic
295C4×C4⋊C4C2×D1111yescharacteristic
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C4⋊C4C2×D1111yescharacteristic
298C4×C22⋊C4C2×D1111yescharacteristic
299C4×C22⋊C4C2×D1111yescharacteristic
300C4×C22⋊C4C2×D1111yescharacteristic
301#376C2×D1111yescharacteristic
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11#52011yescharacteristic
322C22×C11#52011yescharacteristic
323C22×C11#52011yescharacteristic
324C22×C11C2×#13111yescharacteristic
325C22×C11#56811yescharacteristic
326C22×C11#56811yescharacteristic
327C22×C11#56811yescharacteristic
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#56011yescharacteristic
342C4×C11#56311yescharacteristic
343C4×C11#56311yescharacteristic
344C4×C11#56311yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C2×M16—441no—
347C2×M16—441no—
348C2×M16—441no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C2×C4⋊C4C2×Dic1111yescharacteristic
358C2×C4⋊C4C2×Dic1111yescharacteristic
359C2×C4⋊C4C2×Dic1111yescharacteristic
360C2×C4⋊C4C2×Dic1111yescharacteristic
361C2×C4⋊C4C2×Dic1111yescharacteristic
362C2×C4⋊C4C2×Dic1111yescharacteristic
363C2×C22⋊C4C2×Dic1111yescharacteristic
364C2×C22⋊C4C2×Dic1111yescharacteristic
365C2×C22⋊C4C2×Dic1111yescharacteristic
366C2×C22⋊C4C2×Dic1111yescharacteristic
367C2×C22⋊C4C2×Dic1111yescharacteristic
368C2×C22⋊C4C2×Dic1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C2×C42C22×D1111yescharacteristic
371C2×C42C22×D1111yescharacteristic
372C2×C42C22×D1111yescharacteristic
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—441no—
376C4⋊C8—441no—
377C4⋊C8—441no—
378C4⋊C8—441no—
379C4⋊C8—441no—
380C4⋊C8—441no—
381C4⋊C8—441no—
382C4⋊C8—441no—
383C4⋊C8—441no—
384C22⋊C8—441no—
385C22⋊C8—441no—
386C22⋊C8—441no—
387#97—441no—
388#97—441no—
389C4×C8—441no—
390#95C2×Dic1111yescharacteristic
391#95C2×Dic1111yescharacteristic
392#95C2×Dic1111yescharacteristic
393#95C2×Dic1111yescharacteristic
394#95C2×Dic1111yescharacteristic
395#95C2×Dic1111yescharacteristic
396#95C2×Dic1111yescharacteristic
397#95C2×Dic1111yescharacteristic
398#95C2×Dic1111yescharacteristic
399#95C2×Dic1111yescharacteristic
400#95C2×Dic1111yescharacteristic
401#95C2×Dic1111yescharacteristic
402#95C2×Dic1111yescharacteristic
403#95C2×Dic1111yescharacteristic
404#95C2×Dic1111yescharacteristic
405#95C2×Dic1111yescharacteristic
406C2×C11—81no—
407C2×C11#238311yescharacteristic
408C2×C11#299211yescharacteristic
409C2×C11#299311yescharacteristic
410C2×C11#299311yescharacteristic
411C2×C11#299511yescharacteristic
412C2×C11#299511yescharacteristic
413C2×C11#299511yescharacteristic
414C24C22×Dic1111yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4C22×Dic1111yescharacteristic
422C22×C4C22×Dic1111yescharacteristic
423C22×C4C22×Dic1111yescharacteristic
424C22×C4C22×Dic1111yescharacteristic
425C22×C4C22×Dic1111yescharacteristic
426C22×C4C22×Dic1111yescharacteristic
427C22×C4C22×Dic1111yescharacteristic
428C22×C4C22×Dic1111yescharacteristic
429C22×C4C22×Dic1111yescharacteristic
430C22×C4C22×Dic1111yescharacteristic
431C22×C4C22×Dic1111yescharacteristic
432C22×C4C22×Dic1111yescharacteristic
433C22×C4C22×Dic1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435M16—444no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C22⋊C4—22no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C11#2338211yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C23×Dic1111yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4#6700112yes—
536C2×C4#6704211yescharacteristic
537C2×C4#6704211yescharacteristic
538C2×C4#6704211yescharacteristic
539C2×C4#6704311yescharacteristic
540C2×C4#6704311yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—441no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×#6700111yescharacteristic
558C22#1062335011yescharacteristic
559C22#1062335011yescharacteristic
560C22#1062335011yescharacteristic
561C22#1062335811yescharacteristic
562C22#1062335811yescharacteristic
563C22#1062335811yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4#1062324211yescharacteristic
578C4#1062324311yescharacteristic
579C4#1062324311yescharacteristic
580C4#1062324311yescharacteristic
581C2—81no—
582C2#1307180811yescharacteristic
583C2#1307775511yescharacteristic
584C2#1307776511yescharacteristic
585C2#1307776511yescharacteristic
586C2#1307778611yescharacteristic
587C2#1307778611yescharacteristic
588C2#1307778611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2401C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2401D11
hypocenterC11#23382
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #13069340C2semidirect
2. #13069340C2semidirect
3. #13069335C2semidirect
7. #13069182C2semidirect
8. #13069182C2semidirect
9. #13069175C2semidirect
13. #13068770C2semidirect
14. #13068761C2semidirect
484. C11#23382semidirect

Maximal subgroups

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

subgroupindex
#130693402
#130693352
#130692312
#130692242
#130691822
#130691752
#130688012
#130687702
#130687612
C11×#24012
#2338211