Finite Group Databasebeta

← #14648969

Subgroups — #14648969

Order 2816.

544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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#13078616C211yesmaximal, characteristic
2#13077335C211yesmaximal, characteristic, complemented
3#13067266C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic, complemented
5#13066513C211yesmaximal, characteristic, complemented
6#13066461C211yesmaximal, characteristic, complemented
7C11×#1955C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66954—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C11×#97C2211yescharacteristic
15#10622830C412yes—
16#10622723—21no—
17#10622628—21no—
18C4×#4323—22no—
19#10622620—21no—
20#10622580C412yes—
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622319—22no—
25#10622319—22no—
26D4⋊(C11⋊C8)—22no—
27#10622123—21no—
28#10622120—21no—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4323—22no—
43#66983—21no—
44#66983C2×C412yes—
45C2×#4318—21no—
46#66954—42no—
47#66954—42no—
48C2×#4313—22no—
49C2×C8×D11—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—42no—
58C11×C22⋊C8—42no—
59C11×#97—21no—
60C11×#97—21no—
61#66896—22no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)C2×C412yes—
64(C2×D11)⋊C8—24no—
65#66873—22no—
66#66871—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#9049—111nomaximal, Sylow
74C24×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—42no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×C22⋊D11—22no—
89#4339—41no—
90#4339—41no—
91#4339—41no—
92#4339—41no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44C22⋊C412yes—
96C2×C4×D11—22no—
97C2×Dic22—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11D812yescomplemented
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4323—44no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22⋊C412yes—
120#4318—41no—
121#4318—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#4313—44no—
126C8×D11—44no—
127#3100—111no—
128#2932—111no—
129#1955D1111yescharacteristic, complemented
130#1540—111no—
131#1486—111no—
132#1301—111no—
133#1281—111no—
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11C4×D411yescharacteristic
142C22×D11—22no—
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—41no—
146D4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C22⋊D11—42no—
167C22⋊D11—42no—
168C2×Dic11—22no—
169D44—42no—
170D44—41no—
171D44—41no—
172D44—81no—
173C4×D11—42no—
174C4×D11—42no—
175Dic22—41no—
176Dic22—41no—
177C8×C11—22no—
178C8×C11—41no—
179C8×C11—81no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C11⋊C8—81no—
183C2×#131—221no—
184#532—111no—
185C2×C4×D4C2×D1111yescharacteristic
186#480—112no—
187#474—221no—
188#459—221no—
189#447—112no—
190C4×D8—222no—
191#435—222no—
192#435—222no—
193#431—111no—
194#431—111no—
195#423—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197#408—221no—
198C2×C22⋊C8—21no—
199C2×C22⋊C8—21no—
200C2×#97C2×D1111yescharacteristic
201#332—221no—
202#331—221no—
203D4⋊C8—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#38611yescharacteristic
214C22×C11C4×D811yescharacteristic
215C22×C11#44211yescharacteristic
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—81no—
224C4×C11#44711yescharacteristic
225C4×C11#44911yescharacteristic
226C4×C11#45911yescharacteristic
227C4×C11#46311yescharacteristic
228Dic11—42no—
229C2×#41—221no—
230C22×D4C4×D1111yescharacteristic
231C23×C4—21no—
232C2×D8—222no—
233#131—442no—
234#131—442no—
235C2×M16—222no—
236C2×M16—221no—
237C22×C8—21no—
238C22×C8—222no—
239C22×C8C22⋊D1111yescharacteristic
240C22×C8C22⋊D1111yescharacteristic
241C4⋊Q8—111no—
242#127—111no—
243#124—221no—
244#121—112no—
245#121—221no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—112no—
251C4×D4—221no—
252C2×C4⋊C4C4×D1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D1111yescharacteristic
255#107—222no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#102—222no—
263#102—222no—
264C22⋊C8—42no—
265C22⋊C8—42no—
266C22⋊C8—112no—
267C22⋊C8—224no—
268C22⋊C8—221no—
269#97—21no—
270#97—21no—
271C4×C8—221no—
272C4×C8—221no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—82no—
276C2×C11#187911yescharacteristic
277C2×C11#188111yescharacteristic
278C2×C11#189111yescharacteristic
279D11—82no—
280C24—21no—
281#41—441no—
282#41—441no—
283#41—441no—
284#41—441no—
285C2×Q8—221no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—42no—
289C2×D4—112no—
290C2×D4—222no—
291C2×D4—221no—
292C2×D4—221no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—222no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4#433911yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304D8—444no—
305M16—444no—
306M16—441no—
307M16—441no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—444no—
319C2×C8—441no—
320C2×C8#432312yescomplemented
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—112no—
324C4⋊C4—221no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C42D4×D1111yescharacteristic
330C42D4×D1111yescharacteristic
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C11#904911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—222no—
342C23C4×C22⋊D1111yescharacteristic
343Q8—441no—
344Q8—441no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—442no—
350D4—442no—
351D4—442no—
352D4—441no—
353D4—441no—
354D4—881no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—222no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4C22⋊C4×D1111yescharacteristic
368C2×C4(C22⋊D11)⋊C411yescharacteristic
369C2×C4#6693611yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4C2×#432311yescharacteristic
372C2×C4#6698511yescharacteristic
373C2×C4#6699011yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4#6700211yescharacteristic
376C2×C4#6700311yescharacteristic
377C8—22no—
378C8—41no—
379C8—81no—
380C8—442no—
381C8—442no—
382C8—881no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—442no—
393C22—442no—
394C22—442no—
395C22#1062256911yescharacteristic
396C22C4×#432311yescharacteristic
397C22#1062262711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—442no—
404C4#1062264911yescharacteristic
405C4#1062265011yescharacteristic
406C4#1062267011yescharacteristic
407C4#1062268511yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—882no—
412C2#1306896711yescharacteristic
413C2#1306898111yescharacteristic
414C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1955C2
socleC22×C11#386
prime radical#13078616C2
cosocleC2×C42×C11C23
hypercenter#1955D11
hypocenterC11#9049
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13077335C2semidirect
3. #13067266C2semidirect
4. #13067041C2semidirect
5. #13066513C2semidirect
6. #13066461C2semidirect
7. C11×#1955C2semidirect
106. C2×C8×C11D8semidirect
129. #1955D11semidirect
320. C2×C8#4323semidirect
333. C11#9049semidirect

Maximal subgroups

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

subgroupindex
#130786162
#130773352
#130672662
#130670412
#130665132
#130664612
C11×#19552
#904911