Finite Group Databasebeta

← #14780098

Subgroups — #14780098

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069415C212yesmaximal, complemented
2#13069231C212yesmaximal, complemented
3#13069182C212yesmaximal, complemented
4#13068914C212yesmaximal, complemented
5#13068914C212yesmaximal, complemented
6#13068801C212yesmaximal, complemented
7#13068684C211yesmaximal, characteristic, complemented
8#13068596C211yesmaximal, characteristic, complemented
9C4×C11×#121C211yesmaximal, characteristic
10C2×C11×#121C411yescharacteristic
11C2×C4×D4×C11C2212yes—
12C2×C4×D4×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×#4318C2212yes—
15C11×#390C411yescharacteristic
16C11×#389C411yescharacteristic
17C11×#388C412yes—
18C11×#386C412yes—
19C11×#380C411yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C22⋊C4C2212yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×C22⋊(C11⋊C8)C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×C4⋊(C11⋊C8)C2212yes—
30C2×#66867C2212yes—
31#10622162C2211yescharacteristic
32#10622162C2212yes—
33#10622162C2212yes—
34#10622162C2212yes—
35#10622162C2212yes—
36#10622162C2211yescharacteristic
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C11×#121—24no—
44C4×D4×C11—42no—
45C4×D4×C11—42no—
46C4×D4×C11—42no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4C2×C412yes—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C22⋊C4C2×C412yes—
52C2×C11×C22⋊C4C2×C412yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2×C412yes—
56C2×C42×C11—42no—
57C2×C42×C11C2×C411yescharacteristic
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×#4318—42no—
63C2×#4318—42no—
64C2×#4318—42no—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2312yes—
69C11×#95C2×C412yes—
70C11×#95C2×C412yes—
71C11×#95C2×C412yes—
72C22⋊(C11⋊C8)—42no—
73C22⋊(C11⋊C8)—42no—
74C22⋊(C11⋊C8)—41no—
75C22⋊(C11⋊C8)—42no—
76C22⋊(C11⋊C8)—42no—
77C22⋊(C11⋊C8)—41no—
78C4⋊(C11⋊C8)—42no—
79C4⋊(C11⋊C8)—42no—
80#66867—42no—
81#23334—111nomaximal, Sylow
82C24×C11C22×C412yes—
83C24×C11C22×C411yescharacteristic
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—42no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11M1614yescomplemented
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—42no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—41no—
129C42×C11—41no—
130#4318—48no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C4×#121D1111yescharacteristic
144#1955—112no—
145#1924—112no—
146#1917—112no—
147#1870—112no—
148#1870—112no—
149#1851—112no—
150#1817—111no—
151#1797—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11C2×M1612yes—
166C23×C11C23×C411yescharacteristic
167D4×C11—44no—
168D4×C11—48no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C2×M1612yes—
200C2×C4×C11C2×M1612yes—
201C2×C4×C11H(5,𝔽2)12yes—
202C2×C4×C11H(5,𝔽2)12yes—
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C11⋊C8—42no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208C11⋊C8—42no—
209C22×M16—112no—
210C2×#121Dic1111yescharacteristic
211C2×C4×D4C2×D1111yescharacteristic
212C2×C4×D4C2×D1112yes—
213C22×C42C2×D1111yescharacteristic
214C2×C4⋊C8—112no—
215C2×C4⋊C8—112no—
216C2×C22⋊C8—111no—
217C2×C22⋊C8—111no—
218C2×C22⋊C8—112no—
219C2×C22⋊C8—112no—
220C2×C22⋊C8—112no—
221C2×C22⋊C8—112no—
222C2×#97—112no—
223#390Dic1111yescharacteristic
224#389Dic1111yescharacteristic
225#388Dic1112yes—
226#386Dic1112yes—
227#380Dic1111yescharacteristic
228C4×C4⋊C4C2×D1111yescharacteristic
229C4×C22⋊C4C2×D1112yes—
230#336—112no—
231#336—111no—
232#336—112no—
233#336—111no—
234#336—112no—
235#336—112no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11#51811yescharacteristic
251C22×C11#51811yescharacteristic
252C22×C11#52011yescharacteristic
253C22×C11C22×M1611yescharacteristic
254C22×C11#56811yescharacteristic
255C22×C11#56811yescharacteristic
256C22×C11#56811yescharacteristic
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—41no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—42no—
265C4×C11#56012yes—
266C4×C11#56212yes—
267C22×D4C2×Dic1112yes—
268C22×D4C2×Dic1111yescharacteristic
269C23×C4C2×Dic1111yescharacteristic
270C23×C4C2×Dic1111yescharacteristic
271C23×C4C22×D1112yes—
272C23×C4C22×D1111yescharacteristic
273C2×M16—442no—
274C2×M16—442no—
275C2×M16—442no—
276C22×C8—112no—
277C22×C8—112no—
278C22×C8—112no—
279C22×C8—112no—
280#121—24no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C2×C4⋊C4C2×Dic1111yescharacteristic
285C2×C4⋊C4C2×Dic1111yescharacteristic
286C2×C4⋊C4C2×Dic1112yes—
287C2×C4⋊C4C2×Dic1111yescharacteristic
288C2×C22⋊C4C2×Dic1112yes—
289C2×C22⋊C4C2×Dic1112yes—
290C2×C22⋊C4C2×Dic1112yes—
291C2×C22⋊C4C2×Dic1112yes—
292C2×C22⋊C4C2×Dic1112yes—
293C2×C42—42no—
294C2×C42C2×Dic1111yescharacteristic
295C2×C42C2×Dic1111yescharacteristic
296C2×C42C22×D1111yescharacteristic
297C2×C42C22×D1112yes—
298C2×C42C22×D1111yescharacteristic
299C4⋊C8—442no—
300C4⋊C8—442no—
301C22⋊C8—442no—
302C22⋊C8—442no—
303C22⋊C8—442no—
304C22⋊C8—441no—
305C22⋊C8—442no—
306C22⋊C8—441no—
307#97—442no—
308#95C2×Dic1112yes—
309#95C2×Dic1112yes—
310#95C2×Dic1112yes—
311C2×C11—42no—
312C2×C11—82no—
313C2×C11#237711yescharacteristic
314C2×C11#297311yescharacteristic
315C2×C11#297511yescharacteristic
316C2×C11#297811yescharacteristic
317C2×C11#298011yescharacteristic
318C2×C11#298911yescharacteristic
319C2×C11#299511yescharacteristic
320C24C22×Dic1112yes—
321C24C22×Dic1111yescharacteristic
322C2×D4—24no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—41no—
327C2×D4—42no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4#431814yescomplemented
344C22×C4C22×Dic1111yescharacteristic
345C22×C4C22×Dic1111yescharacteristic
346C22×C4C22×Dic1112yes—
347C22×C4C22×Dic1112yes—
348C22×C4C22×Dic1112yes—
349C22×C4C22×Dic1111yescharacteristic
350C22×C4C22×Dic1111yescharacteristic
351C22×C4C22×Dic1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353M16—448no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—222no—
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—42no—
369C4⋊C4—41no—
370C22⋊C4—24no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—22no—
379C42—41no—
380C42—41no—
381C11#2333411yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23C2×#431812yes—
396C23C23×Dic1111yescharacteristic
397D4—44no—
398D4—48no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4C2×#431812yes—
430C2×C4C2×#431812yes—
431C2×C4#6703712yes—
432C2×C4#6703712yes—
433C2×C4#6704211yescharacteristic
434C2×C4#6704311yescharacteristic
435C8—442no—
436C8—442no—
437C8—442no—
438C8—442no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22C22×#431811yescharacteristic
454C22#1062332911yescharacteristic
455C22#1062332911yescharacteristic
456C22#1062335011yescharacteristic
457C22#1062335011yescharacteristic
458C22#1062335011yescharacteristic
459C22#1062335811yescharacteristic
460C4—22no—
461C4—22no—
462C4—42no—
463C4—41no—
464C4—42no—
465C4—41no—
466C4—41no—
467C4—42no—
468C4#1062315112yes—
469C4#1062315212yes—
470C2—42no—
471C2—82no—
472C2#1307177311yescharacteristic
473C2#1307764511yescharacteristic
474C2#1307765711yescharacteristic
475C2#1307767811yescharacteristic
476C2#1307768711yescharacteristic
477C2#1307773311yescharacteristic
478C2#1307778611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#121C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#23334
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13069415C2semidirect
2. #13069231C2semidirect
3. #13069182C2semidirect
4. #13068914C2semidirect
5. #13068914C2semidirect
6. #13068801C2semidirect
7. #13068684C2semidirect
8. #13068596C2semidirect
105. C22×C4×C11M16semidirect
343. C22×C4#4318semidirect
381. C11#23334semidirect

Maximal subgroups

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

subgroupindex
#130694152
#130692312
#130691822
#130689142
#130688012
#130686842
#130685962
C4×C11×#1212
#2333411