Finite Group Databasebeta

← #14765801

Subgroups — #14765801

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2C2×#10622613C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4#13069340C211yesmaximal, characteristic, complemented
5#13069335C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069231C211yesmaximal, characteristic
8#13069231C211yesmaximal, characteristic
9#13069224C211yesmaximal, characteristic
10#13069224C211yesmaximal, characteristic
11#13069182C211yesmaximal, characteristic, complemented
12#13069175C211yesmaximal, characteristic, complemented
13#13068600C211yesmaximal, characteristic
14#13068491C211yesmaximal, characteristic, complemented
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
35#10622637—24no—
36#10622613—24no—
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×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C11×#117—22no—
66C11×#117—22no—
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×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—41no—
111C22⋊(C11⋊C8)—41no—
112C4⋊(C11⋊C8)—22no—
113C4⋊(C11⋊C8)—22no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118C4⋊(C11⋊C8)—41no—
119C4⋊(C11⋊C8)—41no—
120#66867—22no—
121#66867—41no—
122#66867D414yes—
123C4×C11⋊C8—22no—
124C4×C11⋊C8—22no—
125C4×C11⋊C8—41no—
126#22109—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—41no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C2×D412yes—
179C42×C11#4112yes—
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—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×D412yes—
203C2×C11⋊C8C2×D412yes—
204C2×#446—111no—
205C2×#433—111no—
206#2396D1111yescharacteristic
207#1984—111no—
208#1940—111no—
209#1939—111no—
210#1939—111no—
211#1924—111no—
212#1924—111no—
213#1923—111no—
214#1923—111no—
215#1917—111no—
216#1916—111no—
217#1798—111no—
218#1771—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11C23×C411yescharacteristic
227Q8×C11—44no—
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—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C4×D412yes—
268C2×C4×C11C4×D412yes—
269C2×C4×C11#13112yes—
270C2×C4×C11#13112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C4×Q8C2×D1111yescharacteristic
286C2×#117C2×D1111yescharacteristic
287#446—224no—
288#433—224no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8—111no—
297C2×C22⋊C8—111no—
298C2×C22⋊C8—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97—111no—
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306C2×C4×C8—111no—
307#400Dic1111yescharacteristic
308#399Dic1111yescharacteristic
309#398Dic1111yescharacteristic
310#398Dic1111yescharacteristic
311#396Dic1111yescharacteristic
312#396Dic1111yescharacteristic
313#395Dic1111yescharacteristic
314#393Dic1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4C2×D1111yescharacteristic
319C4×C22⋊C4C2×D1111yescharacteristic
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329#336—111no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#51911yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11C2×#13111yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C22×C11#56811yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#53611yescharacteristic
358C4×C11#53711yescharacteristic
359C4×C11#54111yescharacteristic
360C4×C11#54211yescharacteristic
361C22×Q8C2×Dic1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C4×Q8—22no—
372C4×Q8—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4C2×Dic1111yescharacteristic
376C2×C4⋊C4C2×Dic1111yescharacteristic
377C2×C4⋊C4C2×Dic1111yescharacteristic
378C2×C4⋊C4C2×Dic1111yescharacteristic
379C2×C4⋊C4C2×Dic1111yescharacteristic
380C2×C4⋊C4C2×Dic1111yescharacteristic
381C2×C4⋊C4C2×Dic1111yescharacteristic
382C2×C4⋊C4C2×Dic1111yescharacteristic
383C2×C4⋊C4C2×Dic1111yescharacteristic
384C2×C4⋊C4C2×Dic1111yescharacteristic
385C2×C4⋊C4C2×Dic1111yescharacteristic
386C2×C22⋊C4C2×Dic1111yescharacteristic
387C2×C22⋊C4C2×Dic1111yescharacteristic
388C2×C22⋊C4C2×Dic1111yescharacteristic
389C2×C22⋊C4C2×Dic1111yescharacteristic
390C2×C22⋊C4C2×Dic1111yescharacteristic
391C2×C22⋊C4C2×Dic1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—222no—
399C4⋊C8—222no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402C4⋊C8—222no—
403C4⋊C8—222no—
404C4⋊C8—441no—
405C4⋊C8—441no—
406C22⋊C8—222no—
407C22⋊C8—222no—
408C22⋊C8—441no—
409C22⋊C8—441no—
410#97—114no—
411#97—222no—
412#97—441no—
413C4×C8—222no—
414C4×C8—222no—
415C4×C8—441no—
416#95C2×Dic1111yescharacteristic
417#95C2×Dic1111yescharacteristic
418#95C2×Dic1111yescharacteristic
419#95C2×Dic1111yescharacteristic
420#95C2×Dic1111yescharacteristic
421#95C2×Dic1111yescharacteristic
422#95C2×Dic1111yescharacteristic
423#95C2×Dic1111yescharacteristic
424#95C2×Dic1111yescharacteristic
425#95C2×Dic1111yescharacteristic
426C2×C11—81no—
427C2×C11#232311yescharacteristic
428C2×C11#293311yescharacteristic
429C2×C11#293511yescharacteristic
430C2×C11#298611yescharacteristic
431C2×C11#298711yescharacteristic
432C2×C11#299211yescharacteristic
433C2×C11#299311yescharacteristic
434C24C22×Dic1111yescharacteristic
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—41no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C22×Dic1111yescharacteristic
446C22×C4C22×Dic1111yescharacteristic
447C22×C4C22×Dic1111yescharacteristic
448C22×C4C22×Dic1111yescharacteristic
449C22×C4C22×Dic1111yescharacteristic
450C22×C4C22×Dic1111yescharacteristic
451C22×C4C22×Dic1111yescharacteristic
452C22×C4C22×Dic1111yescharacteristic
453C22×C4C22×Dic1111yescharacteristic
454C22×C4C22×Dic1111yescharacteristic
455C22×C4C22×Dic1111yescharacteristic
456C22×C4C22×Dic1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—112no—
459C2×C8—112no—
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—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42D4×D1112yes—
510C42#434112yes—
511C11#2210911yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C23×Dic1111yescharacteristic
520Q8—44no—
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—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4D4×Dic1112yes—
561C2×C4D4×Dic1112yes—
562C2×C4#6700112yes—
563C2×C4#6700112yes—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4#6704011yescharacteristic
567C2×C4#6704011yescharacteristic
568C2×C4#6704211yescharacteristic
569C2×C4#6704311yescharacteristic
570C8—222no—
571C8—222no—
572C8—441no—
573C8—441no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8—441no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×D4×Dic1111yescharacteristic
586C22#1062334311yescharacteristic
587C22C2×#6700111yescharacteristic
588C22C2×#6700111yescharacteristic
589C22#1062335011yescharacteristic
590C22#1062335011yescharacteristic
591C22#1062335811yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4#1062315611yescharacteristic
606C4#1062315911yescharacteristic
607C4#1062316011yescharacteristic
608C4#1062317411yescharacteristic
609C2—81no—
610C2#1307130011yescharacteristic
611C2#1307734311yescharacteristic
612C2#1307736011yescharacteristic
613C2#1307771811yescharacteristic
614C2#1307772211yescharacteristic
615C2#1307775511yescharacteristic
616C2#1307776511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2396C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2396D11
hypocenterC11#22109
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2396

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
3. #13069553C2semidirect
4. #13069340C2semidirect
5. #13069335C2semidirect
6. #13069335C2semidirect
11. #13069182C2semidirect
12. #13069175C2semidirect
14. #13068491C2semidirect
511. C11#22109semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
C2×#106226132
#130695532
#130693402
#130693352
#130692312
#130692242
#130691822
#130691752
#130686002
#130684912
C11×#23962
#2210911