Finite Group Databasebeta

← #14670685

Subgroups — #14670685

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#13081718C211yesmaximal, characteristic, complemented
2C2×#10622758C211yesmaximal, characteristic
3#13070245C211yesmaximal, characteristic, complemented
4#13070244C211yesmaximal, characteristic, complemented
5#13066699C211yesmaximal, characteristic, complemented
6#13066695C211yesmaximal, characteristic, complemented
7C11×#2115C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9C2×#67003C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×#66901C411yescharacteristic
14#10622758—22no—
15#10622758—22no—
16C2×#66889C411yescharacteristic
17C2×#66886C411yescharacteristic
18C2×#66879C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622520—22no—
22D11×M32—22no—
23#10622514—22no—
24C11×#349—22no—
25#10622199—22no—
26#10622153—22no—
27C2×C11×#41C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131—21no—
32C11×#131—21no—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#67003—22no—
38#67003—22no—
39C2×#4326C811yescharacteristic
40C2×#4325C811yescharacteristic
41C2×#4324C811yescharacteristic
42C2×#4323C811yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C2×#4318C2×C411yescharacteristic
45C22×C11⋊C8C2×C411yescharacteristic
46#66954—21no—
47#66954—21no—
48#66954D412yes—
49#66954D412yes—
50C2×#4313—21no—
51C2×C8×D11—21no—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32D412yes—
56C2×C11×C16—21no—
57C2×C11×C16—21no—
58#66901—22no—
59#66889—22no—
60#66886—22no—
61#66879—21no—
62#66879—21no—
63#66876—21no—
64#66876—21no—
65#66876—21no—
66#66876—21no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16D412yes—
69#66862—24no—
70C16×D11—24no—
71#12986—111nomaximal, Sylow
72C11×#41—21no—
73C11×#41—21no—
74C11×#41—21no—
75C11×#41—21no—
76C2×Q8×C11C2×C811yescharacteristic
77C2×D4×C11—21no—
78C2×D4×C11C2×C811yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11C22×C411yescharacteristic
81C2×C22⋊D11—21no—
82C22×Dic11—21no—
83#4339—21no—
84#4339—21no—
85#4339C22⋊C412yes—
86#4339M1612yes—
87C2×D44C2×C811yescharacteristic
88C2×C4×D11—21no—
89C2×Dic22C2×C811yescharacteristic
90C11×M16—21no—
91C11×M16—21no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—21no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103#4326—22no—
104#4325—22no—
105#4324—22no—
106#4323—22no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109#4318—21no—
110#4318C22⋊C412yes—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8C2×C811yescharacteristic
115C2×C11⋊C8C2×C811yescharacteristic
116#4313—22no—
117#4313—22no—
118C8×D11—22no—
119C8×D11—22no—
120C11×C16—22no—
121C11×C16—41no—
122C11⋊C16—22no—
123C11⋊C16—41no—
124#3407—111no—
125C2×#444—111no—
126#2117—111no—
127#2117—111no—
128#2115D1111yescharacteristic, complemented
129#1377—111no—
130#1375—111no—
131C23×C11—21no—
132C23×C11#13111yescharacteristic
133C22×D11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—41no—
139D4×C11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C22×C811yescharacteristic
147C2×C4×C11C2×M1611yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C22⋊D11—22no—
150C22⋊D11—22no—
151C2×Dic11—21no—
152C2×Dic11—41no—
153C2×Dic11—81no—
154D44—21no—
155D44C22⋊C812yes—
156C4×D11—22no—
157C4×D11—22no—
158Dic22—21no—
159Dic22C22⋊C812yes—
160C8×C11—41no—
161C8×C11#12011yescharacteristic
162C8×C11#12111yescharacteristic
163C8×C11#12111yescharacteristic
164C8×C11#12311yescharacteristic
165C11⋊C8—22no—
166C11⋊C8—21no—
167C11⋊C8—21no—
168C2×#135—111no—
169C2×#131—111no—
170C2×#131C2×D1111yescharacteristic
171#504—222no—
172#504—222no—
173C2×M32—111no—
174C2×M32—111no—
175C2×M32—222no—
176C2×M32C2×D1111yescharacteristic
177C2×M32C2×D1111yescharacteristic
178#444—222no—
179#444—222no—
180C2×#108—111no—
181C2×#104—111no—
182C2×#104—111no—
183C2×#97—111no—
184#350—222no—
185#350—222no—
186#349—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—81no—
190C22×C11#40811yescharacteristic
191C22×C11C8×D411yescharacteristic
192C22×C11#43511yescharacteristic
193C2×D11—22no—
194C2×D11—81no—
195C4×C11—41no—
196C4×C11#38611yescharacteristic
197C4×C11C2×C22⋊C811yescharacteristic
198C4×C11C8×D411yescharacteristic
199C4×C11#43511yescharacteristic
200Dic11—22no—
201Dic11—81no—
202C2×#41—111no—
203C2×#41C4×D1111yescharacteristic
204#135—222no—
205#135—222no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×D8—111no—
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—112no—
215#131—112no—
216#131—221no—
217#131—221no—
218C2×M16—21no—
219C2×M16—111no—
220C2×M16—221no—
221C2×M16C4×D1111yescharacteristic
222C22×C8—21no—
223C22×C8—111no—
224C22×C8—221no—
225C22×C8C22×D1111yescharacteristic
226C2×C42—111no—
227M32—21no—
228M32—21no—
229M32—21no—
230M32—224no—
231M32—221no—
232M32—221no—
233M32—221no—
234M32—221no—
235M32C22⋊D1112yes—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—112no—
239C2×C16—224no—
240C2×C16—221no—
241#108—222no—
242#104—222no—
243#104—222no—
244#97—221no—
245#97—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—81no—
250C2×C11#186911yescharacteristic
251D11—42no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—112no—
257#41—112no—
258#41—221no—
259#41—221no—
260C2×Q8—111no—
261C2×Q8C8×D1111yescharacteristic
262C2×D4—21no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4C8×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C2×C4×D1111yescharacteristic
270Q16—222no—
271SD16—222no—
272SD16—222no—
273D8—222no—
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—112no—
279M16—221no—
280M16—222no—
281M16—222no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8#433911yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8#434111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C42—221no—
299C42—221no—
300C16—22no—
301C16—41no—
302C16—222no—
303C16—441no—
304C11#1298611yescharacteristic, complemented, Sylow
305C23—21no—
306C23—221no—
307C23#6695411yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—112no—
311Q8—221no—
312D4—21no—
313D4—21no—
314D4—41no—
315D4—41no—
316D4—112no—
317D4—222no—
318D4—222no—
319D4—221no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—221no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—881no—
328C2×C4C22⋊C4×D1111yescharacteristic
329C2×C4(C22⋊D11)⋊C411yescharacteristic
330C2×C4C2×C8×D1111yescharacteristic
331C2×C4M16×D1111yescharacteristic
332C2×C4#6696011yescharacteristic
333C2×C4C4×C22⋊D1111yescharacteristic
334C8—41no—
335C8—222no—
336C8—221no—
337C8—221no—
338C8#6693611yescharacteristic
339C8#6693711yescharacteristic
340C8#6699011yescharacteristic
341C8#6699111yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—222no—
346C22—881no—
347C22#1062234011yescharacteristic
348C22#1062234111yescharacteristic
349C22C8×C22⋊D1111yescharacteristic
350C4—41no—
351C4—222no—
352C4—881no—
353C4D11×C22⋊C811yescharacteristic
354C4(C22⋊D11)⋊C811yescharacteristic
355C4#1062256911yescharacteristic
356C4#1062274011yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—442no—
362C2#1306890511yescharacteristic
subgroupG/H
centerC4#10622569
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2115C2
socleC2×C11#1869
prime radicalC2×#67003C4
cosocleC22×C8×C11C23
hypercenter#2115D11
hypocenterC11#12986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2115

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. #13070245C2semidirect
4. #13070244C2semidirect
5. #13066699C2semidirect
6. #13066695C2semidirect
7. C11×#2115C2semidirect
128. #2115D11semidirect
304. C11#12986semidirect

Maximal subgroups

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

subgroupindex
#130817182
C2×#106227582
#130702452
#130702442
#130666992
#130666952
C11×#21152
#1298611