Finite Group Databasebeta

← #14670684

Subgroups — #14670684

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081719C211yesmaximal, characteristic, complemented
2#13070244C211yesmaximal, characteristic, complemented
3#13070244C211yesmaximal, characteristic, complemented
4#13070237C211yesmaximal, characteristic, complemented
5#13066700C211yesmaximal, characteristic, complemented
6#13066696C211yesmaximal, characteristic, complemented
7C2×C11×#444C211yesmaximal, characteristic
8C2×C11×#135C411yescharacteristic
9C2×C11×#131C2211yescharacteristic
10C2×C11×#131C2211yescharacteristic
11C11×#444—22no—
12C11×#444—22no—
13C2×C11×#108C411yescharacteristic
14C2×C11×#104C411yescharacteristic
15C2×C11×#104C411yescharacteristic
16C2×C11×#97C2211yescharacteristic
17#10622753—22no—
18#10622753—22no—
19C2×#66876—22no—
20C2×#66876C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22C2×#66876C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24#10622199—22no—
25#10622199—22no—
26#10622191—22no—
27C2×C11×#41C2×C411yescharacteristic
28C2×C11×#41C2×C411yescharacteristic
29C11×#135—22no—
30C11×#135—22no—
31C2×C11×Q16C811yescharacteristic
32C2×C11×SD16C811yescharacteristic
33C2×C11×SD16C811yescharacteristic
34C2×C11×D8C811yescharacteristic
35C11×#131—21no—
36C11×#131—21no—
37C11×#131—21no—
38C11×#131—21no—
39C11×#131—21no—
40C11×#131—21no—
41C11×#131D412yes—
42C11×#131D412yes—
43C2×C11×M16—21no—
44C2×C11×M16—21no—
45C2×C11×M16C2×C411yescharacteristic
46C2×C11×M16C2×C411yescharacteristic
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C22×C8×C11C2×C411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C11×#108—22no—
53C11×#104—22no—
54C11×#104—22no—
55C11×#97—21no—
56C11×#97—21no—
57#66876—24no—
58#66876—21no—
59#66876—21no—
60#66876—21no—
61#66876—21no—
62#66876—21no—
63#66876—21no—
64#66876—21no—
65#66876D412yes—
66C2×C11⋊C16—24no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16D412yes—
71#12986—111nomaximal, Sylow
72C11×#41—21no—
73C11×#41—21no—
74C11×#41—21no—
75C11×#41—21no—
76C11×#41—21no—
77C11×#41—21no—
78C11×#41C22⋊C412yes—
79C11×#41M1612yes—
80C2×Q8×C11C2×C811yescharacteristic
81C2×Q8×C11C2×C811yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11C2×C811yescharacteristic
85C2×D4×C11C2×C811yescharacteristic
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C22×C411yescharacteristic
90C11×Q16—22no—
91C11×SD16—22no—
92C11×SD16—22no—
93C11×D8—22no—
94C11×M16—22no—
95C11×M16—22no—
96C11×M16—21no—
97C11×M16—21no—
98C11×M16—21no—
99C11×M16—41no—
100C11×M16—41no—
101C11×M16C22⋊C412yes—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11C2×C811yescharacteristic
111C2×C8×C11C2×C811yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C2×C8×C11#4111yescharacteristic
118C42×C11—21no—
119C42×C11—21no—
120C11⋊C16—22no—
121C11⋊C16—22no—
122C11⋊C16—41no—
123C11⋊C16—41no—
124#3407—111no—
125C2×#444D1111yescharacteristic
126#2117—111no—
127#2117—111no—
128#2115—111no—
129#1377—111no—
130#1375—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11#13111yescharacteristic
134Q8×C11—21no—
135Q8×C11—21no—
136Q8×C11—21no—
137Q8×C11C22⋊C812yes—
138D4×C11—22no—
139D4×C11—22no—
140D4×C11—21no—
141D4×C11—21no—
142D4×C11—21no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11C22⋊C812yes—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C22×C811yescharacteristic
158C2×C4×C11C2×M1611yescharacteristic
159C2×C4×C11#13111yescharacteristic
160C8×C11—22no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—41no—
164C8×C11#12011yescharacteristic
165C8×C11#12111yescharacteristic
166C8×C11#12111yescharacteristic
167C8×C11#12311yescharacteristic
168C2×#135Dic1111yescharacteristic
169C2×#131C2×D1111yescharacteristic
170C2×#131C2×D1111yescharacteristic
171#504—222no—
172#504—222no—
173C2×M32—111no—
174C2×M32—111no—
175C2×M32—111no—
176C2×M32—111no—
177C2×M32—222no—
178#444—22no—
179#444—22no—
180C2×#108Dic1111yescharacteristic
181C2×#104Dic1111yescharacteristic
182C2×#104Dic1111yescharacteristic
183C2×#97C2×D1111yescharacteristic
184#350—222no—
185#350—222no—
186#349—222no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#40811yescharacteristic
193C22×C11C8×D411yescharacteristic
194C22×C11#43511yescharacteristic
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11#38611yescharacteristic
199C4×C11C2×C22⋊C811yescharacteristic
200C4×C11C8×D411yescharacteristic
201C4×C11#43511yescharacteristic
202C2×#41C2×Dic1111yescharacteristic
203C2×#41C2×Dic1111yescharacteristic
204#135—22no—
205#135—22no—
206C2×Q16C11⋊C811yescharacteristic
207C2×SD16C11⋊C811yescharacteristic
208C2×SD16C11⋊C811yescharacteristic
209C2×D8C11⋊C811yescharacteristic
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216#131C22⋊D1112yes—
217#131C22⋊D1112yes—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16C2×Dic1111yescharacteristic
221C2×M16C2×Dic1111yescharacteristic
222C22×C8—21no—
223C22×C8—21no—
224C22×C8C2×Dic1111yescharacteristic
225C22×C8C22×D1111yescharacteristic
226C2×C42C2×Dic1111yescharacteristic
227M32—112no—
228M32—224no—
229M32—221no—
230M32—221no—
231M32—221no—
232M32—221no—
233M32—221no—
234M32—221no—
235M32—221no—
236C2×C16—112no—
237C2×C16—224no—
238C2×C16—221no—
239C2×C16—221no—
240C2×C16—221no—
241#108—22no—
242#104—22no—
243#104—22no—
244#97—21no—
245#97—21no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—42no—
250C2×C11—81no—
251C2×C11#186911yescharacteristic
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41#431812yes—
259#41C22⋊Dic1112yes—
260C2×Q8C2×C11⋊C811yescharacteristic
261C2×Q8C2×C11⋊C811yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C2×C11⋊C811yescharacteristic
265C2×D4C2×C11⋊C811yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22×Dic1111yescharacteristic
270Q16—22no—
271SD16—22no—
272SD16—22no—
273D8—22no—
274M16—21no—
275M16—22no—
276M16—22no—
277M16—21no—
278M16—21no—
279M16—41no—
280M16—41no—
281M16C22⋊Dic1112yes—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8C2×C11⋊C811yescharacteristic
291C2×C8C2×C11⋊C811yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8#434111yescharacteristic
295C2×C8#434111yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C42—21no—
299C42—21no—
300C16—222no—
301C16—222no—
302C16—441no—
303C16—441no—
304C11#1298611yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23#6700111yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8C22⋊(C11⋊C8)12yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319D4C22⋊(C11⋊C8)12yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4C22×C11⋊C811yescharacteristic
329C2×C4C2×#431811yescharacteristic
330C2×C4D4×Dic1111yescharacteristic
331C2×C4D4×Dic1111yescharacteristic
332C2×C4#6700111yescharacteristic
333C2×C4C2×C22⋊Dic1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—22no—
337C8—41no—
338C8#6698811yescharacteristic
339C8#6699011yescharacteristic
340C8#6699211yescharacteristic
341C8#6699211yescharacteristic
342C22—22no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22D4×C11⋊C811yescharacteristic
348C22#1062262411yescharacteristic
349C22#1062284711yescharacteristic
350C4—22no—
351C4—41no—
352C4—81no—
353C4D4×C11⋊C811yescharacteristic
354C4#1062262411yescharacteristic
355C4C2×C22⋊(C11⋊C8)11yescharacteristic
356C4#1062283311yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—81no—
362C2#1306890911yescharacteristic
subgroupG/H
centerC4#10622833
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C11×#444C2
socleC2×C11#1869
prime radicalC2×C11×#135C4
cosocleC22×C8×C11C23
hypercenterC2×#444D11
hypocenterC11#12986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. #13081719C2semidirect
2. #13070244C2semidirect
3. #13070244C2semidirect
4. #13070237C2semidirect
5. #13066700C2semidirect
6. #13066696C2semidirect
304. C11#12986semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130702442
#130702372
#130667002
#130666962
C2×C11×#4442
#1298611