Finite Group Databasebeta

← #14664468

Subgroups — #14664468

Order 2816.

448 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074359C211yesmaximal, characteristic
2#13068695C211yesmaximal, characteristic, complemented
3#13066944C211yesmaximal, characteristic, complemented
4#13066622C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic
9C2×#66947—21no—
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#398C2211yescharacteristic
12#10622739—21no—
13#10622607—21no—
14#10622604C2211yescharacteristic
15#10622593C411yescharacteristic
16#10622339—21no—
17#10622289—21no—
18#10622285C411yescharacteristic
19#10622280C411yescharacteristic
20#10622278—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D44—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×#4318—21no—
48C2×#4313—41no—
49#66948—41no—
50#66948—41no—
51#66947—42no—
52#66947—42no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62(C2×D11)⋊C8—41no—
63(C2×D11)⋊C8—41no—
64#11805—111nomaximal, Sylow
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×D44—41no—
77C2×D44—42no—
78C2×D44—42no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—81no—
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—21no—
89C2×C4×D11—21no—
90C2×C4×D11—41no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—81no—
107(C2×D11)⋊C4—81no—
108C4⋊Dic11—41no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—42no—
112Dic11⋊C4—81no—
113#4318—41no—
114#4318—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#4313—82no—
118#2618—111no—
119#1821—111no—
120#1463—111no—
121#1346—111no—
122#1346D1111yescharacteristic, complemented
123#1345—111no—
124#1345—111no—
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11#9911yescharacteristic
138C22×D11#9911yescharacteristic
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163D44—82no—
164D44—82no—
165D44—82no—
166C4×D11—41no—
167C4×D11—41no—
168C4×D11—41no—
169C4×D11—41no—
170C4×D11—42no—
171C4×D11—81no—
172C4×D11—81no—
173C4×D11—81no—
174C8×C11—81no—
175C8×C11—81no—
176C11⋊C8—81no—
177C11⋊C8—81no—
178C2×#123—221no—
179C2×#121—111no—
180C22×C4⋊C4—111no—
181#407—221no—
182#407—221no—
183#398—111no—
184#398C2×D1111yescharacteristic
185#396—221no—
186#396—221no—
187#394—111no—
188#394—111no—
189#386—221no—
190#380—111no—
191#343—111no—
192#343—221no—
193#343C2×D1111yescharacteristic
194#324—111no—
195#324—221no—
196#324C2×D1111yescharacteristic
197C22×C11—21no—
198C22×C11—21no—
199C22×C11C2×#9911yescharacteristic
200C22×C11#41811yescharacteristic
201C22×C11#42111yescharacteristic
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—21no—
207C2×D11—21no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—81no—
222C4×C11—81no—
223Dic11—41no—
224Dic11—41no—
225Dic11—41no—
226Dic11—81no—
227C22×D4—111no—
228C22×D4—221no—
229C23×C4—111no—
230C23×C4—111no—
231C23×C4—111no—
232C2×M16—21no—
233C2×M16—221no—
234C2×M16—441no—
235#123—442no—
236#123—442no—
237#121—441no—
238#121—441no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—441no—
246C2×C4⋊C4—441no—
247C2×C4⋊C4C4×D1111yescharacteristic
248C2×C4⋊C4C22×D1111yescharacteristic
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C22⋊C8—21no—
256C22⋊C8—221no—
257C22⋊C8—441no—
258C22⋊C8—441no—
259C22⋊C8—441no—
260#95—21no—
261#95—111no—
262#95—221no—
263#95C4×D1111yescharacteristic
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#151011yescharacteristic
267C2×C11#212111yescharacteristic
268C2×C11#213311yescharacteristic
269D11—41no—
270D11—41no—
271D11—161no—
272C24—111no—
273C24—221no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—881no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—441no—
295C22×C4—881no—
296C22×C4—881no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300M16—41no—
301M16—41no—
302M16—441no—
303M16—441no—
304M16—882no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—441no—
308C2×C8—441no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—442no—
317C4⋊C4—881no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—881no—
324C22⋊C4—881no—
325C11#1180511yescharacteristic, complemented, Sylow
326C23—111no—
327C23—111no—
328C23—221no—
329C23—221no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23C22⋊C4×D1111yescharacteristic
340D4—882no—
341D4—882no—
342D4—882no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6696411yescharacteristic
374C2×C4#6696711yescharacteristic
375C8—81no—
376C8—81no—
377C8—881no—
378C8—881no—
379C22—21no—
380C22—21no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22—442no—
388C22—442no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22D11×#9911yescharacteristic
397C22#1062238311yescharacteristic
398C22#1062243411yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—81no—
405C4—441no—
406C4—441no—
407C4—441no—
408C4—881no—
409C2—21no—
410C2—21no—
411C2—441no—
412C2—441no—
413C2—1761no—
414C2#1306714311yescharacteristic
415C2#1307026111yescharacteristic
416C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC2×#66948C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11805
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
2. #13068695C2semidirect
3. #13066944C2semidirect
4. #13066622C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1346C2semidirect
122. #1346D11semidirect
325. C11#11805semidirect

Maximal subgroups

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

subgroupindex
#130743592
#130686952
#130669442
#130666222
#130666202
#130666182
C11×#13462
#1180511