Finite Group Databasebeta

← #14670652

Subgroups — #14670652

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622753C211yesmaximal, characteristic, complemented
2C2×#10622199C211yesmaximal, characteristic, complemented
3C2×#10622199C211yesmaximal, characteristic, complemented
4#13070230C211yesmaximal, characteristic, complemented
5#13066698C211yesmaximal, characteristic, complemented
6#13066694C211yesmaximal, characteristic, complemented
7C2×C11×#443C211yesmaximal, characteristic
8C2×C11×#135C411yescharacteristic
9C2×C11×#131C2211yescharacteristic
10C2×C11×#131C2211yescharacteristic
11C11×#443—22no—
12C11×#443—22no—
13C2×C11×#108C411yescharacteristic
14C2×C11×#104C411yescharacteristic
15C2×C11×#104C411yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622753—22no—
18#10622753—22no—
19C2×#66876—21no—
20C2×#66876C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22C22×C11⋊C16—21no—
23C22×C11⋊C16C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622199—22no—
26#10622199—22no—
27C22⋊(C11⋊C16)—21no—
28C22⋊(C11⋊C16)—21no—
29C2×C11×#41C2×C411yescharacteristic
30C2×C11×#41C2×C411yescharacteristic
31C11×#135—22no—
32C11×#135—22no—
33C2×C11×Q16C811yescharacteristic
34C2×C11×SD16C811yescharacteristic
35C2×C11×SD16C811yescharacteristic
36C2×C11×D8C811yescharacteristic
37C11×#131—21no—
38C11×#131—21no—
39C11×#131—21no—
40C11×#131—21no—
41C11×#131—21no—
42C11×#131—21no—
43C11×#131D412yes—
44C11×#131D412yes—
45C2×C11×M16—21no—
46C2×C11×M16—21no—
47C2×C11×M16C2×C411yescharacteristic
48C2×C11×M16C2×C411yescharacteristic
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C22×C8×C11C2×C411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C11×#108—22no—
55C11×#104—22no—
56C11×#104—22no—
57C4×C8×C11—21no—
58C4×C8×C11—21no—
59#66876—24no—
60#66876—21no—
61#66876—21no—
62#66876—21no—
63#66876D412yes—
64C2×C11⋊C16—24no—
65C2×C11⋊C16—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72C2×C11⋊C16D411yescharacteristic
73C2×C11⋊C16D411yescharacteristic
74#12980—111nomaximal, Sylow
75C11×#41—21no—
76C11×#41—21no—
77C11×#41—21no—
78C11×#41—21no—
79C11×#41—21no—
80C11×#41—21no—
81C11×#41C22⋊C412yes—
82C11×#41M1612yes—
83C2×Q8×C11C2×C811yescharacteristic
84C2×Q8×C11C2×C811yescharacteristic
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11C2×C811yescharacteristic
88C2×D4×C11C2×C811yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C22×C411yescharacteristic
93C11×Q16—22no—
94C11×SD16—22no—
95C11×SD16—22no—
96C11×D8—22no—
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—21no—
100C11×M16—21no—
101C11×M16—21no—
102C11×M16—41no—
103C11×M16—41no—
104C11×M16C22⋊C412yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11C2×C811yescharacteristic
114C2×C8×C11C2×C811yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C42×C11—21no—
122C42×C11—21no—
123C11⋊C16—21no—
124C11⋊C16—22no—
125C11⋊C16—21no—
126C11⋊C16—41no—
127C11⋊C16—41no—
128C2×#504—111no—
129C2×#443D1111yescharacteristic
130C2×#350—111no—
131C2×#350—111no—
132#2113—111no—
133#1376—111no—
134#1374—111no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11#13111yescharacteristic
138Q8×C11—21no—
139Q8×C11—21no—
140Q8×C11—21no—
141Q8×C11C22⋊C812yes—
142D4×C11—22no—
143D4×C11—22no—
144D4×C11—21no—
145D4×C11—21no—
146D4×C11—21no—
147D4×C11—41no—
148D4×C11—41no—
149D4×C11C22⋊C812yes—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11C2×C22⋊C411yescharacteristic
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C22×C811yescharacteristic
163C2×C4×C11C2×M1611yescharacteristic
164C2×C4×C11#13111yescharacteristic
165C8×C11—22no—
166C8×C11—21no—
167C8×C11—21no—
168C8×C11—41no—
169C8×C11#12011yescharacteristic
170C8×C11#12111yescharacteristic
171C8×C11#12111yescharacteristic
172C8×C11#12311yescharacteristic
173C2×#135Dic1111yescharacteristic
174C2×#131C2×D1111yescharacteristic
175C2×#131C2×D1111yescharacteristic
176#504—222no—
177#504—222no—
178C2×M32—111no—
179C2×M32—111no—
180C2×M32—221no—
181C22×C16—111no—
182C22×C16—111no—
183C22×C16—221no—
184#443—22no—
185#443—22no—
186C2×#108Dic1111yescharacteristic
187C2×#104Dic1111yescharacteristic
188C2×#104Dic1111yescharacteristic
189C2×C4×C8C2×D1111yescharacteristic
190#350—222no—
191#350—222no—
192C22⋊C16—221no—
193C22⋊C16—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—22no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11#40811yescharacteristic
203C22×C11C8×D411yescharacteristic
204C22×C11#43511yescharacteristic
205C4×C11—22no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11#38611yescharacteristic
209C4×C11C2×C22⋊C811yescharacteristic
210C4×C11C8×D411yescharacteristic
211C4×C11#43511yescharacteristic
212C2×#41C2×Dic1111yescharacteristic
213C2×#41C2×Dic1111yescharacteristic
214#135—22no—
215#135—22no—
216C2×Q16C11⋊C811yescharacteristic
217C2×SD16C11⋊C811yescharacteristic
218C2×SD16C11⋊C811yescharacteristic
219C2×D8C11⋊C811yescharacteristic
220#131—21no—
221#131—21no—
222#131—21no—
223#131—21no—
224#131—21no—
225#131—21no—
226#131C22⋊D1112yes—
227#131C22⋊D1112yes—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16C2×Dic1111yescharacteristic
231C2×M16C2×Dic1111yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8C2×Dic1111yescharacteristic
235C22×C8C22×D1111yescharacteristic
236C2×C42C2×Dic1111yescharacteristic
237M32—112no—
238M32—224no—
239M32—221no—
240M32—221no—
241M32—221no—
242C2×C16—111no—
243C2×C16—111no—
244C2×C16—224no—
245C2×C16—221no—
246C2×C16—221no—
247C2×C16—221no—
248C2×C16—221no—
249C2×C16—221no—
250C2×C16—221no—
251C2×C16—221no—
252#108—22no—
253#104—22no—
254#104—22no—
255C4×C8—21no—
256C4×C8—21no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—42no—
260C2×C11—81no—
261C2×C11#186911yescharacteristic
262C2×C11#217011yescharacteristic
263C2×C11#217111yescharacteristic
264#41—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268#41—21no—
269#41—21no—
270#41#431812yes—
271#41C22⋊Dic1112yes—
272C2×Q8C2×C11⋊C811yescharacteristic
273C2×Q8C2×C11⋊C811yescharacteristic
274C2×D4—21no—
275C2×D4—21no—
276C2×D4C2×C11⋊C811yescharacteristic
277C2×D4C2×C11⋊C811yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4C22×Dic1111yescharacteristic
282Q16—22no—
283SD16—22no—
284SD16—22no—
285D8—22no—
286M16—21no—
287M16—22no—
288M16—22no—
289M16—21no—
290M16—21no—
291M16—41no—
292M16—41no—
293M16C22⋊Dic1112yes—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—21no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8C2×C11⋊C811yescharacteristic
303C2×C8C2×C11⋊C811yescharacteristic
304C2×C8D4×D1111yescharacteristic
305C2×C8D4×D1111yescharacteristic
306C2×C8#434111yescharacteristic
307C2×C8#434111yescharacteristic
308C2×C8C2×C22⋊D1111yescharacteristic
309C2×C8C2×C22⋊D1111yescharacteristic
310C42—21no—
311C42—21no—
312C16—221no—
313C16—221no—
314C16—222no—
315C16—441no—
316C16—441no—
317C11#1298011yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23#6700111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8C22⋊(C11⋊C8)12yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—41no—
331D4—41no—
332D4C22⋊(C11⋊C8)12yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4C22×C11⋊C811yescharacteristic
343C2×C4C2×#431811yescharacteristic
344C2×C4D4×Dic1111yescharacteristic
345C2×C4D4×Dic1111yescharacteristic
346C2×C4#6700111yescharacteristic
347C2×C4C2×C22⋊Dic1111yescharacteristic
348C8—21no—
349C8—21no—
350C8—22no—
351C8—41no—
352C8#6698811yescharacteristic
353C8#6699011yescharacteristic
354C8#6699211yescharacteristic
355C8#6699211yescharacteristic
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22D4×C11⋊C811yescharacteristic
365C22#1062262411yescharacteristic
366C22#1062284711yescharacteristic
367C4—22no—
368C4—42no—
369C4—41no—
370C4D4×C11⋊C811yescharacteristic
371C4#1062262411yescharacteristic
372C4C2×C22⋊(C11⋊C8)11yescharacteristic
373C4#1062283311yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2#1306890911yescharacteristic
379C2#1307045311yescharacteristic
380C2#1307045811yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C11×#443C2
socleC22×C11C8×D4
prime radicalC2×C11×#135C4
cosocleC22×C8×C11C23
hypercenterC2×#443D11
hypocenterC11#12980
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. C2×#10622753C2semidirect
2. C2×#10622199C2semidirect
3. C2×#10622199C2semidirect
4. #13070230C2semidirect
5. #13066698C2semidirect
6. #13066694C2semidirect
317. C11#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#106227532
C2×#106221992
#130702302
#130666982
#130666942
C2×C11×#4432
#1298011