Finite Group Databasebeta

← #14780234

Subgroups — #14780234

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069557C211yesmaximal, characteristic, complemented
2#13069553C211yesmaximal, characteristic, complemented
3#13069340C211yesmaximal, characteristic, complemented
4#13069340C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic
6#13069231C211yesmaximal, characteristic
7#13069231C211yesmaximal, characteristic
8#13069224C211yesmaximal, characteristic
9#13069182C211yesmaximal, characteristic, complemented
10#13069182C211yesmaximal, characteristic, complemented
11#13069182C211yesmaximal, characteristic, complemented
12#13069175C211yesmaximal, characteristic, complemented
13#13068687C211yesmaximal, characteristic
14#13068600C211yesmaximal, characteristic
15C11×#2396C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C11×#400C411yescharacteristic
19C11×#399C411yescharacteristic
20C11×#398C411yescharacteristic
21C11×#398C411yescharacteristic
22C11×#396C411yescharacteristic
23C11×#396C411yescharacteristic
24C11×#395C411yescharacteristic
25C11×#393C411yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
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×#66867C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622162C2211yescharacteristic
46#10622162C2211yescharacteristic
47#10622162C2211yescharacteristic
48#10622162C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C4×Q8×C11—41no—
62C4×Q8×C11—41no—
63C11×#117—41no—
64C11×#117—41no—
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
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
105C11×#95C2×C411yescharacteristic
106C22⋊(C11⋊C8)—41no—
107C22⋊(C11⋊C8)—41no—
108C22⋊(C11⋊C8)—41no—
109C22⋊(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—
116#66867—41no—
117#66867—41no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#23345—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C2×Q8×C11—22no—
123C2×Q8×C11—41no—
124C2×Q8×C11—41no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C11×C4⋊C4—22no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—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—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2396D1111yescharacteristic
199#1985—111no—
200#1984—111no—
201#1940—111no—
202#1940—111no—
203#1924—111no—
204#1924—111no—
205#1924—111no—
206#1923—111no—
207#1917—111no—
208#1917—111no—
209#1917—111no—
210#1916—111no—
211#1818—111no—
212#1798—111no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11C23×C411yescharacteristic
221Q8×C11—44no—
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—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11#13112yes—
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×#117C2×D1111yescharacteristic
281C2×C4⋊C8—111no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C4⋊C8—111no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C22⋊C8—111no—
291C2×#97—111no—
292C2×#97—111no—
293C2×#97—111no—
294C2×C4×C8—111no—
295#400Dic1111yescharacteristic
296#399Dic1111yescharacteristic
297#398Dic1111yescharacteristic
298#398Dic1111yescharacteristic
299#396Dic1111yescharacteristic
300#396Dic1111yescharacteristic
301#395Dic1111yescharacteristic
302#393Dic1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304C4×C4⋊C4C2×D1111yescharacteristic
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C22⋊C4C2×D1111yescharacteristic
307C4×C22⋊C4C2×D1111yescharacteristic
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317#336—111no—
318#336—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11#51811yescharacteristic
330C22×C11#51911yescharacteristic
331C22×C11#52011yescharacteristic
332C22×C11C2×#13111yescharacteristic
333C22×C11#56811yescharacteristic
334C22×C11#56811yescharacteristic
335C22×C11#56811yescharacteristic
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11#56211yescharacteristic
350C4×C11#56211yescharacteristic
351C4×C11#56311yescharacteristic
352C4×C11#56311yescharacteristic
353C22×Q8C2×Dic1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—111no—
363C4×Q8—41no—
364C4×Q8—41no—
365#117—41no—
366#117—41no—
367C2×C4⋊C4C2×Dic1111yescharacteristic
368C2×C4⋊C4C2×Dic1111yescharacteristic
369C2×C4⋊C4C2×Dic1111yescharacteristic
370C2×C4⋊C4C2×Dic1111yescharacteristic
371C2×C4⋊C4C2×Dic1111yescharacteristic
372C2×C4⋊C4C2×Dic1111yescharacteristic
373C2×C4⋊C4C2×Dic1111yescharacteristic
374C2×C4⋊C4C2×Dic1111yescharacteristic
375C2×C4⋊C4C2×Dic1111yescharacteristic
376C2×C4⋊C4C2×Dic1111yescharacteristic
377C2×C4⋊C4C2×Dic1111yescharacteristic
378C2×C22⋊C4C2×Dic1111yescharacteristic
379C2×C22⋊C4C2×Dic1111yescharacteristic
380C2×C22⋊C4C2×Dic1111yescharacteristic
381C2×C22⋊C4C2×Dic1111yescharacteristic
382C2×C22⋊C4C2×Dic1111yescharacteristic
383C2×C22⋊C4C2×Dic1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C2×C42C22×D1111yescharacteristic
390C4⋊C8—441no—
391C4⋊C8—441no—
392C4⋊C8—441no—
393C4⋊C8—441no—
394C4⋊C8—441no—
395C4⋊C8—441no—
396C22⋊C8—441no—
397C22⋊C8—441no—
398C22⋊C8—441no—
399C22⋊C8—441no—
400#97—441no—
401#97—441no—
402#97—441no—
403C4×C8—441no—
404#95C2×Dic1111yescharacteristic
405#95C2×Dic1111yescharacteristic
406#95C2×Dic1111yescharacteristic
407#95C2×Dic1111yescharacteristic
408#95C2×Dic1111yescharacteristic
409#95C2×Dic1111yescharacteristic
410#95C2×Dic1111yescharacteristic
411#95C2×Dic1111yescharacteristic
412#95C2×Dic1111yescharacteristic
413#95C2×Dic1111yescharacteristic
414C2×C11—81no—
415C2×C11#237811yescharacteristic
416C2×C11#297611yescharacteristic
417C2×C11#298011yescharacteristic
418C2×C11#298511yescharacteristic
419C2×C11#298711yescharacteristic
420C2×C11#299311yescharacteristic
421C2×C11#299511yescharacteristic
422C24C22×Dic1111yescharacteristic
423C2×Q8—22no—
424C2×Q8—41no—
425C2×Q8—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4C22×Dic1111yescharacteristic
433C22×C4C22×Dic1111yescharacteristic
434C22×C4C22×Dic1111yescharacteristic
435C22×C4C22×Dic1111yescharacteristic
436C22×C4C22×Dic1111yescharacteristic
437C22×C4C22×Dic1111yescharacteristic
438C22×C4C22×Dic1111yescharacteristic
439C22×C4C22×Dic1111yescharacteristic
440C22×C4C22×Dic1111yescharacteristic
441C22×C4C22×Dic1111yescharacteristic
442C22×C4C22×Dic1111yescharacteristic
443C22×C4C22×Dic1111yescharacteristic
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
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—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C4⋊C4—22no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C22⋊C4—22no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C11#2334511yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23C23×Dic1111yescharacteristic
508Q8—44no—
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—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4#6700112yes—
552C2×C4#6703711yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#6704011yescharacteristic
555C2×C4#6704011yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—441no—
559C8—441no—
560C8—441no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1062332911yescharacteristic
574C22#1062334311yescharacteristic
575C22C2×#6700111yescharacteristic
576C22#1062335011yescharacteristic
577C22#1062335011yescharacteristic
578C22#1062335011yescharacteristic
579C22#1062335811yescharacteristic
580C4—22no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4#1062317711yescharacteristic
594C4#1062317711yescharacteristic
595C4#1062317811yescharacteristic
596C4#1062317811yescharacteristic
597C2—81no—
598C2#1307178211yescharacteristic
599C2#1307766411yescharacteristic
600C2#1307768711yescharacteristic
601C2#1307771111yescharacteristic
602C2#1307772211yescharacteristic
603C2#1307776511yescharacteristic
604C2#1307778611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2396C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2396D11
hypocenterC11#23345
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2396

Complements

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

NH ≅ G/Ntype
1. #13069557C2semidirect
2. #13069553C2semidirect
3. #13069340C2semidirect
4. #13069340C2semidirect
9. #13069182C2semidirect
10. #13069182C2semidirect
11. #13069182C2semidirect
12. #13069175C2semidirect
499. C11#23345semidirect

Maximal subgroups

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

subgroupindex
#130695572
#130695532
#130693402
#130692312
#130692242
#130691822
#130691752
#130686872
#130686002
C11×#23962
#2334511