Finite Group Databasebeta

← #14658369

Subgroups — #14658369

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069542C211yesmaximal, characteristic
2#13069422C211yesmaximal, characteristic
3#13069380C211yesmaximal, characteristic, complemented
4#13069334C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#335C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66885—21no—
13C2×#66885—21no—
14C2×#66885—21no—
15C2×#66885—21no—
16C2×#66881—21no—
17C2×Dic11⋊C8—21no—
18#10622548C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#335—22no—
22#10622189—21no—
23#10622188—21no—
24#10622123—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4×Dic11—21no—
39C22×C11⋊C8—21no—
40#66927—21no—
41#66927—21no—
42#66927—21no—
43#66927Q812yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8D412yes—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50C11⋊#95—21no—
51#66885—42no—
52#66885—42no—
53#66885—42no—
54#66885—42no—
55#66881—42no—
56Dic11⋊C8—42no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59#10599—111nomaximal, Sylow
60C23×D11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—41no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—81no—
82C2×D44—81no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—22no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11SD1612yes—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×Q811yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—81no—
107C4⋊Dic11D812yes—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#1982—111no—
114#1957—111no—
115#1948—111no—
116#1939—111no—
117C2×#335D1111yescharacteristic, complemented
118C2×#331—111no—
119#1296—111no—
120C23×C11#12111yescharacteristic
121C22×D11—42no—
122C22×D11—81no—
123C22×D11—81no—
124C22×D11—81no—
125C22×D11—81no—
126C22×D11—81no—
127C22×D11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12611yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153D44—42no—
154D44—42no—
155D44—42no—
156D44—42no—
157D44—82no—
158D44—82no—
159D44—81no—
160D44—81no—
161D44—81no—
162D44—81no—
163C8×C11—22no—
164C8×C11—42no—
165C8×C11—41no—
166C8×C11—81no—
167C11⋊C8—81no—
168C2×#127—111no—
169C2×#106—221no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—221no—
172C2×C4⋊C8C2×D1111yescharacteristic
173C2×C4⋊C8C2×D1111yescharacteristic
174C2×#102—221no—
175C2×#102—221no—
176C2×#102—221no—
177C2×#102—221no—
178C2×C4×C8C2×D1111yescharacteristic
179#384—111no—
180C4×C4⋊C4—111no—
181#340—221no—
182#336—221no—
183#335—22no—
184#331—222no—
185C22×C11#39611yescharacteristic
186C22×C11#46011yescharacteristic
187C22×C11#46311yescharacteristic
188C22×C11#46611yescharacteristic
189C22×C11#46811yescharacteristic
190C22×C11#47111yescharacteristic
191C22×C11#47211yescharacteristic
192C2×D11—82no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—161no—
196C2×D11—161no—
197C2×D11—161no—
198C2×D11—161no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11#45911yescharacteristic
202C4×C11#46411yescharacteristic
203C4×C11#46511yescharacteristic
204C4×C11#46911yescharacteristic
205C4×C11#47411yescharacteristic
206C4×C11#47611yescharacteristic
207C4×C11#47811yescharacteristic
208C4×C11#47811yescharacteristic
209Dic11—42no—
210Dic11—81no—
211Dic11—161no—
212C22×D4—221no—
213C22×D4—221no—
214C22×D4—221no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—221no—
218C22×C8D4411yescharacteristic
219C22×C8D4411yescharacteristic
220#127—112no—
221#127—221no—
222#127—221no—
223#127—221no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231#106—442no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—442no—
238C4⋊C8C22⋊D1112yes—
239#102—442no—
240#102—442no—
241#102—442no—
242#102—442no—
243C4×C8—21no—
244C4×C8—21no—
245#95—221no—
246C2×C11#166811yescharacteristic
247C2×C11#168111yescharacteristic
248C2×C11#168611yescharacteristic
249C2×C11#169711yescharacteristic
250C2×C11#206311yescharacteristic
251C2×C11#206511yescharacteristic
252C2×C11#206711yescharacteristic
253D11—162no—
254C24—441no—
255C2×D4—222no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—881no—
270C2×D4—881no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—441no—
274C22×C4C2×D4411yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4#434311yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8#431412yes—
292C4⋊C4—112no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—881no—
301C42—441no—
302C42—441no—
303C42#433911yescharacteristic
304C42#434111yescharacteristic
305C42Q8×D1111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C11#1059911yescharacteristic, complemented, Sylow
308C23—442no—
309C23—881no—
310C23—881no—
311C23—881no—
312C23—881no—
313C23—881no—
314C23—881no—
315C23#6694811yescharacteristic
316D4—442no—
317D4—442no—
318D4—442no—
319D4—442no—
320D4—882no—
321D4—882no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—222no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4#6694911yescharacteristic
338C2×C4#6695011yescharacteristic
339C2×C4#6695111yescharacteristic
340C2×C4C2×#431411yescharacteristic
341C2×C4#6695711yescharacteristic
342C2×C4#6696111yescharacteristic
343C2×C4#6696111yescharacteristic
344C2×C4D8×D1111yescharacteristic
345C2×C4#6696411yescharacteristic
346C2×C4#6697111yescharacteristic
347C2×C4#6697211yescharacteristic
348C2×C4#6698311yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699911yescharacteristic
351C8—22no—
352C8—41no—
353C8—42no—
354C8—81no—
355C8—881no—
356C22—882no—
357C22—882no—
358C22—882no—
359C22—1761no—
360C22—1761no—
361C22—1761no—
362C22—1761no—
363C22#1062245711yescharacteristic
364C22#1062246111yescharacteristic
365C22#1062249611yescharacteristic
366C22#1062249911yescharacteristic
367C22#1062251011yescharacteristic
368C22#1062251111yescharacteristic
369C22#1062260711yescharacteristic
370C4—21no—
371C4—21no—
372C4—442no—
373C4—881no—
374C4—1761no—
375C4#1062245511yescharacteristic
376C4#1062246011yescharacteristic
377C4#1062250311yescharacteristic
378C4#1062250411yescharacteristic
379C4#1062272711yescharacteristic
380C4#1062274811yescharacteristic
381C4#1062276311yescharacteristic
382C4#1062279811yescharacteristic
383C2—1762no—
384C2#1306797711yescharacteristic
385C2#1306805411yescharacteristic
386C2#1306808911yescharacteristic
387C2#1306815011yescharacteristic
388C2#1306997111yescharacteristic
389C2#1306998911yescharacteristic
390C2#1306999911yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#335C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#335D11
hypocenterC11#10599
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. #13069380C2semidirect
4. #13069334C2semidirect
6. #13066500C2semidirect
7. C2×C11×#335C2semidirect
117. C2×#335D11semidirect
307. C11#10599semidirect

Maximal subgroups

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

subgroupindex
#130695422
#130694222
#130693802
#130693342
C2×#106221232
#130665002
C2×C11×#3352
#1059911