Finite Group Databasebeta

← #14658287

Subgroups — #14658287

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#13069543C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic
3#13069335C211yesmaximal, characteristic, complemented
4C2×#10622118C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×C11×#107—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66873—21no—
14C2×#66873—21no—
15C2×#66873—21no—
16C2×#66873—21no—
17C2×C4⋊(C11⋊C8)—21no—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#340—21no—
22#10622162—21no—
23#10622123—22no—
24#10622118—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C22×C11⋊C8—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40#66927—21no—
41#66927—21no—
42#66927—21no—
43#66927Q812yes—
44C11×#107—42no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×#95—21no—
48#66873—42no—
49#66873—42no—
50#66873—42no—
51#66873—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—42no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#10587—111nomaximal, Sylow
60C23×D11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
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—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4SD1612yes—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×Q811yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8D812yes—
113#1982—111no—
114#1957—111no—
115#1947D1111yescharacteristic, complemented
116#1939—111no—
117C2×#334—111no—
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—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11C22⋊Q811yescharacteristic
144C2×C4×C11#12611yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11#13711yescharacteristic
153D44—42no—
154D44—42no—
155D44—42no—
156D44—42no—
157D44—82no—
158D44—82no—
159D44—81no—
160D44—81no—
161D44—81no—
162D44—81no—
163C8×C11—42no—
164C11⋊C8—22no—
165C11⋊C8—41no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168C2×#127—111no—
169C2×#107—21no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8—221no—
173C2×C4⋊C8C2×D1111yescharacteristic
174C2×#102—221no—
175C2×#102—221no—
176C2×#102—221no—
177C2×#102—221no—
178C2×C4×C8—111no—
179#384C2×D1111yescharacteristic
180C4×C4⋊C4C2×D1111yescharacteristic
181#340—21no—
182#336—221no—
183#334—222no—
184#331—222no—
185C22×C11#39611yescharacteristic
186C22×C11#45911yescharacteristic
187C22×C11#46411yescharacteristic
188C22×C11#46511yescharacteristic
189C22×C11#46911yescharacteristic
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—42no—
202C4×C11—81no—
203C4×C11—161no—
204C4×C11#46011yescharacteristic
205C4×C11#46311yescharacteristic
206C4×C11#46611yescharacteristic
207C4×C11#46811yescharacteristic
208C4×C11#47411yescharacteristic
209C4×C11#47611yescharacteristic
210C4×C11#47811yescharacteristic
211C4×C11#47811yescharacteristic
212C22×D4—221no—
213C22×D4—221no—
214C22×D4—221no—
215C22×C8—21no—
216C22×C8—111no—
217C22×C8—111no—
218C22×C8—221no—
219C22×C8—221no—
220#127—112no—
221#127—221no—
222#127—221no—
223#127—221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C42—21no—
230C2×C42C22×D1111yescharacteristic
231#107—42no—
232C4⋊C8—21no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—442no—
238C4⋊C8D4412yes—
239#102—442no—
240#102—442no—
241#102—442no—
242#102—442no—
243C4×C8—221no—
244C4×C8—221no—
245#95—21no—
246C2×C11#166511yescharacteristic
247C2×C11#167811yescharacteristic
248C2×C11#168711yescharacteristic
249C2×C11#170211yescharacteristic
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—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4D4×D1111yescharacteristic
275C22×C4#434111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—112no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—221no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C4⋊C4#432512yes—
301C42—41no—
302C42—41no—
303C42C2×D4411yescharacteristic
304C42#433911yescharacteristic
305C42Q8×D1111yescharacteristic
306C42#434311yescharacteristic
307C11#1058711yescharacteristic, complemented, Sylow
308C23—442no—
309C23—881no—
310C23—881no—
311C23—881no—
312C23—881no—
313C23—881no—
314C23—881no—
315C23#6699211yescharacteristic
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—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#6694811yescharacteristic
338C2×C4#6694911yescharacteristic
339C2×C4#6695011yescharacteristic
340C2×C4#6695111yescharacteristic
341C2×C4D8×D1111yescharacteristic
342C2×C4#6696411yescharacteristic
343C2×C4#6697111yescharacteristic
344C2×C4#6697211yescharacteristic
345C2×C4#6698311yescharacteristic
346C2×C4#6698511yescharacteristic
347C2×C4C2×#432511yescharacteristic
348C2×C4#6699911yescharacteristic
349C2×C4#6700211yescharacteristic
350C2×C4#6700311yescharacteristic
351C8—42no—
352C8—222no—
353C8—441no—
354C8—881no—
355C8—881no—
356C22—882no—
357C22—882no—
358C22—882no—
359C22—1761no—
360C22—1761no—
361C22—1761no—
362C22—1761no—
363C22#1062260711yescharacteristic
364C22#1062265211yescharacteristic
365C22#1062266111yescharacteristic
366C22#1062276311yescharacteristic
367C22#1062279811yescharacteristic
368C22#1062281211yescharacteristic
369C22#1062281611yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1062249611yescharacteristic
376C4#1062249911yescharacteristic
377C4#1062250311yescharacteristic
378C4#1062250411yescharacteristic
379C4#1062262911yescharacteristic
380C4#1062264011yescharacteristic
381C4#1062267911yescharacteristic
382C4#1062269711yescharacteristic
383C2—1762no—
384C2#1306795911yescharacteristic
385C2#1306803411yescharacteristic
386C2#1306809311yescharacteristic
387C2#1306818611yescharacteristic
388C2#1306997311yescharacteristic
389C2#1306998711yescharacteristic
390C2#1306999911yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenter#1947D11
hypocenterC11#10587
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #13069335C2semidirect
4. C2×#10622118C2semidirect
6. #13066499C2semidirect
7. C11×#1947C2semidirect
115. #1947D11semidirect
307. C11#10587semidirect

Maximal subgroups

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

subgroupindex
#130695432
#130694212
#130693352
C2×#106221182
C2×#106221232
#130664992
C11×#19472
#1058711