Finite Group Databasebeta

← #14670683

Subgroups — #14670683

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×#10622330C211yesmaximal, characteristic
3#13070245C211yesmaximal, characteristic, complemented
4#13070243C211yesmaximal, characteristic, complemented
5#13070236C211yesmaximal, characteristic, complemented
6#13066700C211yesmaximal, characteristic, complemented
7C11×#1375C211yesmaximal, characteristic, complemented
8C2×#66957C411yescharacteristic
9C2×#66954C2211yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14C2×#66883C411yescharacteristic
15C2×#66876C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17C2×#66869C411yescharacteristic
18C2×#66869C411yescharacteristic
19#10622520—22no—
20D11×M32—22no—
21#10622514—22no—
22#10622330—22no—
23#10622330—22no—
24#10622153—22no—
25#10622152—22no—
26#10622146—22no—
27C2×#4339C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×#4318C2×C411yescharacteristic
33C2×#4318C2×C411yescharacteristic
34C2×Dic44C811yescharacteristic
35#66957—22no—
36#66957—22no—
37C2×D88C811yescharacteristic
38C2×#4314C811yescharacteristic
39C2×#4314C811yescharacteristic
40#66954—21no—
41#66954—21no—
42#66954—21no—
43#66954—21no—
44#66954—21no—
45#66954—21no—
46#66954D412yes—
47#66954D412yes—
48C2×#4313—21no—
49C2×#4313—21no—
50C2×C8×D11—21no—
51C2×C8×D11—21no—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32—21no—
56C2×C11×C16—21no—
57C2×C11×C16D412yes—
58C11×#97—21no—
59C11×#97—21no—
60#66883—22no—
61#66876—21no—
62#66876—21no—
63#66876—21no—
64#66876D412yes—
65C2×C11⋊C16—21no—
66C2×C11⋊C16—21no—
67#66869—22no—
68#66869—22no—
69#66862—24no—
70C16×D11—24no—
71#12986—111nomaximal, Sylow
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76#4339—21no—
77#4339—21no—
78#4339—21no—
79#4339—21no—
80#4339—21no—
81#4339—21no—
82#4339C22⋊C412yes—
83#4339M1612yes—
84C2×D44C2×C811yescharacteristic
85C2×D44C2×C811yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×Dic22C2×C811yescharacteristic
89C2×Dic22C2×C811yescharacteristic
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11C2×C811yescharacteristic
93C2×C8×C11C2×C811yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C42×C11—21no—
101C42×C11—21no—
102#4318—21no—
103#4318—21no—
104#4318—21no—
105#4318C22⋊C412yes—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108Dic44—22no—
109D88—22no—
110#4314—22no—
111#4314—22no—
112#4313—22no—
113#4313—22no—
114#4313—41no—
115#4313—41no—
116C8×D11—22no—
117C8×D11—22no—
118C8×D11—41no—
119C8×D11—41no—
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#2115—111no—
129#1377—111no—
130#1375D1111yescharacteristic, complemented
131C23×C11#13111yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C22×C811yescharacteristic
140C2×C4×C11C2×M1611yescharacteristic
141C2×C4×C11#13111yescharacteristic
142C22⋊D11—22no—
143C22⋊D11—22no—
144C22⋊D11—41no—
145C22⋊D11—41no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44C22⋊C812yes—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—41no—
155C4×D11—41no—
156Dic22—21no—
157Dic22—21no—
158Dic22—21no—
159Dic22C22⋊C812yes—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11#12011yescharacteristic
163C8×C11#12111yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C11⋊C8—22no—
167C11⋊C8—41no—
168C2×#135—111no—
169C2×#131—111no—
170C2×#131—111no—
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×#97C2×D1111yescharacteristic
184#350—222no—
185#350—222no—
186#349—222no—
187C22×C11—41no—
188C22×C11#40811yescharacteristic
189C22×C11C8×D411yescharacteristic
190C22×C11#43511yescharacteristic
191C2×D11—22no—
192C2×D11—41no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—81no—
196C4×C11#38611yescharacteristic
197C4×C11C2×C22⋊C811yescharacteristic
198C4×C11C8×D411yescharacteristic
199C4×C11#43511yescharacteristic
200Dic11—22no—
201Dic11—41no—
202C2×#41—111no—
203C2×#41—111no—
204#135—222no—
205#135—222no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×D8—111no—
210#131—112no—
211#131—112no—
212#131—221no—
213#131—221no—
214#131—221no—
215#131—221no—
216#131—221no—
217#131—221no—
218C2×M16—111no—
219C2×M16—111no—
220C2×M16—221no—
221C2×M16—221no—
222C22×C8—221no—
223C22×C8—221no—
224C22×C8C4×D1111yescharacteristic
225C22×C8C22×D1111yescharacteristic
226C2×C42C4×D1111yescharacteristic
227M32—21no—
228M32—21no—
229M32—21no—
230M32—21no—
231M32—112no—
232M32—224no—
233M32—221no—
234M32—221no—
235M32—221no—
236C2×C16—21no—
237C2×C16—224no—
238C2×C16—221no—
239C2×C16—221no—
240C2×C16D4412yes—
241#108—222no—
242#104—222no—
243#104—222no—
244#97—21no—
245#97—21no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#186911yescharacteristic
250D11—42no—
251D11—81no—
252#41—112no—
253#41—112no—
254#41—221no—
255#41—221no—
256#41—221no—
257#41—221no—
258#41—221no—
259#41—221no—
260C2×Q8—111no—
261C2×Q8—111no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C22×C4—21no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C2×C4×D1111yescharacteristic
270Q16—222no—
271SD16—222no—
272SD16—222no—
273D8—222no—
274M16—112no—
275M16—221no—
276M16—222no—
277M16—222no—
278M16—221no—
279M16—221no—
280M16—441no—
281M16—441no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—221no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—221no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8C8×D1111yescharacteristic
291C2×C8C8×D1111yescharacteristic
292C2×C8C2×D4411yescharacteristic
293C2×C8#433911yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8D4×D1111yescharacteristic
297C2×C8#434311yescharacteristic
298C42—21no—
299C42—21no—
300C16—22no—
301C16—41no—
302C16—222no—
303C16—441no—
304C11#1298611yescharacteristic, complemented, Sylow
305C23—221no—
306C23—221no—
307C23#6696011yescharacteristic
308Q8—112no—
309Q8—221no—
310Q8—221no—
311Q8—221no—
312D4—112no—
313D4—222no—
314D4—222no—
315D4—221no—
316D4—221no—
317D4—221no—
318D4—441no—
319D4—441no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—221no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—221no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4C4×D4411yescharacteristic
329C2×C4C22⋊C4×D1111yescharacteristic
330C2×C4#6694611yescharacteristic
331C2×C4C2×C8×D1111yescharacteristic
332C2×C4#6695411yescharacteristic
333C2×C4M16×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—222no—
337C8—441no—
338C8#6693511yescharacteristic
339C8#6693711yescharacteristic
340C8#6694711yescharacteristic
341C8#6694811yescharacteristic
342C22—41no—
343C22—222no—
344C22—441no—
345C22—881no—
346C22—881no—
347C22#1062231911yescharacteristic
348C22#1062234011yescharacteristic
349C22#1062244711yescharacteristic
350C4—81no—
351C4—222no—
352C4—441no—
353C4#1062227811yescharacteristic
354C4C8×D4411yescharacteristic
355C4D11×C22⋊C811yescharacteristic
356C4#1062244911yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—442no—
361C2—881no—
362C2#1306890711yescharacteristic
subgroupG/H
centerC4#10622278
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1375C2
socleC2×C11#1869
prime radicalC2×#66957C4
cosocleC22×C8×C11C23
hypercenter#1375D11
hypocenterC11#12986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1375

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. #13070245C2semidirect
4. #13070243C2semidirect
5. #13070236C2semidirect
6. #13066700C2semidirect
7. C11×#1375C2semidirect
130. #1375D11semidirect
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×#106223302
#130702452
#130702432
#130702362
#130667002
C11×#13752
#1298611