Finite Group Databasebeta

← #14664135

Subgroups — #14664135

Order 2816.

632 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071831C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066645C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C4×C11×#100C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C2×C4×C22⋊D11—21no—
9C2×C11×#100—21no—
10C4×C11×M16—21no—
11#10622836—21no—
12C4×C22⋊Dic11C411yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14#10622604C2211yescharacteristic
15#10622592C2211yescharacteristic
16#10622573C411yescharacteristic
17#10622572—21no—
18#10622560C411yescharacteristic
19C4×(C2×D11)⋊C4—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C2×#4339—44no—
29C2×#4339—41no—
30C2×#4339—41no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—22no—
35C4×D4×C11—41no—
36C4×D4×C11—41no—
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C4×C22⋊D11—44no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—41no—
50C11×#100—24no—
51C11×#97—41no—
52C4×C8×C11—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)—41no—
59#11733—111nomaximal, Sylow
60C24×C11C22⋊C411yescharacteristic
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86#4339—44no—
87#4339—44no—
88#4339—44no—
89#4339—44no—
90C2×D44—41no—
91C2×D44—42no—
92C2×C4×D11—24no—
93C2×C4×D11—42no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×Dic22—41no—
97C2×Dic22—42no—
98C11×M16—24no—
99C11×M16—42no—
100C2×C8×C11—42no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—21no—
105C42×C11—21no—
106C22⋊Dic11—42no—
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—82no—
115#2388—111no—
116C4×#100D1111yescharacteristic, complemented
117#1459—111no—
118#1354—112no—
119#1345—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11#10412yes—
130C23×C11C2×C22⋊C411yescharacteristic
131C22×D11—22no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138D4×C11—44no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11#9911yescharacteristic
153C2×C4×C11#9911yescharacteristic
154C2×C4×C11#13512yes—
155C22⋊D11—48no—
156C22⋊D11—48no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166D44—42no—
167D44—42no—
168C4×D11—44no—
169C4×D11—44no—
170Dic22—42no—
171Dic22—42no—
172C8×C11—44no—
173C11⋊C8—82no—
174C22×#41—111no—
175C2×C4×D4—221no—
176C2×C4×D4C2×D1111yescharacteristic
177C2×#100—21no—
178C2×C22⋊C8—221no—
179C4×M16—21no—
180#395—111no—
181#394—111no—
182#394—221no—
183#393—111no—
184#392—111no—
185#392—221no—
186C4×C22⋊C4—111no—
187C4×C22⋊C4—221no—
188#343C2×D1112yes—
189#324—112no—
190#323—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—22no—
194C22×C11—42no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11C2×#9911yescharacteristic
204C22×C11#41611yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C2×D11—42no—
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11AΣL(1,𝔽16)12yes—
219Dic11—42no—
220Dic11—42no—
221Dic11—81no—
222C2×#41—441no—
223C2×#41—441no—
224C2×#41—444no—
225C22×Q8—111no—
226C22×D4—111no—
227C22×D4—221no—
228C22×D4—221no—
229C22×D4C22⋊D1111yescharacteristic
230C23×C4—221no—
231C23×C4C4×D1111yescharacteristic
232C23×C4D4411yescharacteristic
233C2×M16—22no—
234C22×C8—441no—
235C4×D4—41no—
236C4×D4—41no—
237C4×D4—444no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4C22×D1111yescharacteristic
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4C4×D1111yescharacteristic
246C2×C22⋊C4D4411yescharacteristic
247C2×C42—221no—
248C2×C42C22⋊D1111yescharacteristic
249#100—24no—
250C22⋊C8—222no—
251C22⋊C8—441no—
252#97—41no—
253C4×C8—41no—
254#95—111no—
255#95—111no—
256#95—221no—
257#95—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—42no—
261C2×C11—81no—
262C2×C11#150111yescharacteristic
263C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
264C2×C11#213211yescharacteristic
265D11—82no—
266C24—221no—
267C24(C2×D11)⋊C411yescharacteristic
268C24(C2×D11)⋊C411yescharacteristic
269#41—444no—
270#41—444no—
271#41—444no—
272#41—444no—
273C2×Q8—441no—
274C2×Q8—442no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—441no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—442no—
284C2×D4—442no—
285C2×D4—442no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—224no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—442no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4C2×D4411yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304M16—24no—
305M16—42no—
306C2×C8—42no—
307C2×C8—442no—
308C2×C8—882no—
309C4⋊C4—41no—
310C4⋊C4—442no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—442no—
314C22⋊C4—442no—
315C22⋊C4—442no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C42—21no—
319C42—21no—
320C42—442no—
321C11#1173311yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—222no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23#6686912yes—
339C23C2×(C2×D11)⋊C411yescharacteristic
340Q8—442no—
341Q8—442no—
342D4—44no—
343D4—442no—
344D4—442no—
345D4—448no—
346D4—448no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—444no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—444no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4#6687011yescharacteristic
372C2×C4#6687011yescharacteristic
373C2×C4#6700312yes—
374C8—44no—
375C8—882no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22C2×#6686911yescharacteristic
396C22C2×#6687011yescharacteristic
397C22#1062261511yescharacteristic
398C4—22no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—442no—
404C4—442no—
405C4—881no—
406C4#1062211312yes—
407C2—21no—
408C2—21no—
409C2—42no—
410C2—81no—
411C2—882no—
412C2#1306710511yescharacteristic
413C2C2×#1062211311yescharacteristic
414C2#1307029911yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#100C2
socleC22×C11C2×#99
prime radical#13071831C2
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#100D11
hypocenterC11#11733
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066645C2semidirect
4. #13066618C2semidirect
5. C4×C11×#100C2semidirect
116. C4×#100D11semidirect
321. C11#11733semidirect

Maximal subgroups

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

subgroupindex
#130718312
#130669342
#130666452
#130666182
C4×C11×#1002
#1173311