Finite Group Databasebeta

← #14664693

Subgroups — #14664693

Order 2816.

438 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074090C211yesmaximal, characteristic
2#13068695C211yesmaximal, characteristic, complemented
3D11×#324C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#394C2211yescharacteristic
11#10622835C411yescharacteristic
12#10622739—21no—
13#10622599C2211yescharacteristic
14#10622569—21no—
15#10622569—21no—
16#10622564—21no—
17#10622557—21no—
18D11×C22⋊C8—21no—
19#10622279C411yescharacteristic
20#10622272C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66991—41no—
40#66991—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—21no—
47C2×#4318—21no—
48C2×C8×D11—41no—
49C4⋊C4×D11—41no—
50C4⋊C4×D11—41no—
51C11×C22⋊C8—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—41no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11852—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11C22⋊C411yescharacteristic
65C2×D4×C11—41no—
66C2×D4×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—42no—
72C2×C22⋊D11—42no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—41no—
89C2×C4×D11—81no—
90C2×C4×D11—81no—
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—81no—
99C22⋊Dic11—42no—
100C22⋊Dic11—42no—
101C22⋊Dic11—81no—
102(C2×D11)⋊C4—42no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—81no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C8×D11—82no—
113#2591—111no—
114#1821—111no—
115C2×#324—111no—
116#1353—111no—
117#1353—111no—
118#1345—111no—
119#1345D1111yescharacteristic, complemented
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—22no—
131C22×D11—41no—
132C22×D11#9911yescharacteristic
133C22×D11#9911yescharacteristic
134D4×C11—82no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C22⋊D11—82no—
147C22⋊D11—82no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C4×D11—41no—
162C4×D11—41no—
163C4×D11—41no—
164C4×D11—41no—
165C4×D11—42no—
166C4×D11—81no—
167C4×D11—81no—
168C4×D11—81no—
169C8×C11—81no—
170C8×C11—81no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173C2×#121—111no—
174C22×C4⋊C4—111no—
175#407—221no—
176C2×C22⋊C8—221no—
177#400—111no—
178#400—111no—
179#394—111no—
180#394C2×D1111yescharacteristic
181#388—221no—
182#388—221no—
183#386—221no—
184#386—221no—
185C4×C22⋊C4—111no—
186#343—111no—
187#343—221no—
188#343C2×D1111yescharacteristic
189#324—111no—
190#324—221no—
191#324C2×D1111yescharacteristic
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11C2×#9911yescharacteristic
202C22×C11#41611yescharacteristic
203C22×C11#42111yescharacteristic
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—21no—
207C2×D11—21no—
208C2×D11—21no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11#35512yes—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—81no—
217Dic11—41no—
218Dic11—41no—
219Dic11—41no—
220Dic11—81no—
221Dic11—81no—
222C22×D4—221no—
223C22×D4C4×D1111yescharacteristic
224C23×C4—111no—
225C23×C4—111no—
226C23×C4—111no—
227C2×M16—21no—
228C2×M16—221no—
229C22×C8—441no—
230#121—441no—
231#121—441no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—441no—
237C2×C4⋊C4—441no—
238C2×C4⋊C4C22×D1111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C42—221no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C22⋊C8—441no—
249C22⋊C8—441no—
250C22⋊C8—441no—
251#95—111no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95C4×D1111yescharacteristic
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—161no—
260C2×C11#151611yescharacteristic
261C2×C11#212111yescharacteristic
262C2×C11C2×#35511yescharacteristic
263D11—22no—
264D11—41no—
265C24—21no—
266C24—111no—
267C2×D4—41no—
268C2×D4—81no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4—442no—
272C2×D4—442no—
273C22×C4—21no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—441no—
288C22×C4—881no—
289C22×C4—881no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293M16—41no—
294M16—41no—
295M16—441no—
296M16—441no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—441no—
300C2×C8—441no—
301C2×C8—882no—
302C4⋊C4—41no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—81no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4—881no—
314C42—881no—
315C11#1185211yescharacteristic, complemented, Sylow
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—111no—
324C23—111no—
325C23—222no—
326C23—221no—
327C23—221no—
328C23—441no—
329C23C22⋊C4×D1111yescharacteristic
330D4—82no—
331D4—882no—
332D4—882no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4#6696511yescharacteristic
364C2×C4#6696911yescharacteristic
365C8—81no—
366C8—81no—
367C8—881no—
368C8—881no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—112no—
379C22—221no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—442no—
385C22—442no—
386C22D11×#9911yescharacteristic
387C22#1062238511yescharacteristic
388C22#1062243411yescharacteristic
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—81no—
394C4—441no—
395C4—441no—
396C4—441no—
397C4—881no—
398C4—881no—
399C2—21no—
400C2—21no—
401C2—161no—
402C2—222no—
403C2—441no—
404C2#1306716911yescharacteristic
405C2#1307025911yescharacteristic
406C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radicalC2×#66991C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11852
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068695C2semidirect
3. D11×#324C2semidirect
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
119. #1345D11semidirect
315. C11#11852semidirect

Maximal subgroups

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

subgroupindex
#130740902
#130686952
D11×#3242
#130666442
#130666422
#130666192
C11×#13452
#1185211