Finite Group Databasebeta

← C2×C11×#2189 #14610708

Subgroups — C2×C11×#2189 #14610708

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic
2C22×C11×Q32C211yesmaximal, characteristic, complemented
3C22×C11×SD32C211yesmaximal, characteristic, complemented
4C2×C11×#467C211yesmaximal, characteristic, complemented
5C11×#2189C218yesmaximal, direct product factor
6C2×C11×#358C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C2×C11×#135—24no—
11C2×C11×#135—24no—
12C2×C11×#135—22no—
13C2×C11×#135C2214yes—
14C22×C11×Q16C2211yescharacteristic
15C22×C11×Q16C2211yescharacteristic
16C22×C11×SD16—21no—
17C22×C11×D8C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8—21no—
20C2×C11×Q32—24no—
21C2×C11×Q32C2214yescomplemented
22C2×C11×SD32—24no—
23C2×C11×SD32C2214yescomplemented
24C22×C11×C16C2211yescharacteristic
25C22×C11×C16C2211yescharacteristic
26C11×#467—22no—
27C11×#467C2214yescomplemented
28C2×C11×#107C2211yescharacteristic
29C2×C11×#103—21no—
30C11×#358C2214yescomplemented
31C11×#357C2214yescomplemented
32C11×C22⋊C16C2214yescomplemented
33C2×C11×#41—28no—
34C2×C11×#41—24no—
35C2×C11×#41—44no—
36C2×C11×#41—42no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—41no—
41C23×C4×C11—41no—
42C23×C4×C11D411yescharacteristic
43C11×#135—216no—
44C11×#135—28no—
45C11×#135—28no—
46C2×C11×Q16—22no—
47C2×C11×Q16—21no—
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16—21no—
51C2×C11×Q16D414yes—
52C2×C11×Q16C2312yes—
53C2×C11×Q16C2312yes—
54C2×C11×SD16—28no—
55C2×C11×SD16—24no—
56C2×C11×D8—22no—
57C2×C11×D8—21no—
58C2×C11×D8D414yes—
59C2×C11×D8C2312yes—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11D411yescharacteristic
63C22×C8×C11D412yes—
64C22×C8×C11C2312yes—
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—42no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—41no—
70C2×C11×C22⋊C4—41no—
71C11×Q32—28no—
72C11×SD32—28no—
73C2×C11×C16—22no—
74C2×C11×C16—22no—
75C2×C11×C16C2312yes—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2312yes—
79C11×#103—24no—
80C2×#2189C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—41no—
82C24×C11D811yescharacteristic
83C11×#41—216no—
84C11×#41—48no—
85C11×#41—416no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—48no—
97C2×D4×C11—44no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—48no—
103C22×C4×C11—41no—
104C22×C4×C11—44no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11D812yes—
108C22×C4×C11D811yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C11×Q16—24no—
112C11×Q16—22no—
113C11×Q16—22no—
114C11×Q16—22no—
115C11×Q16—42no—
116C11×Q16C2×D414yes—
117C11×SD16—216no—
118C11×D8—24no—
119C11×D8—22no—
120C11×D8C2×D414yes—
121C2×C8×C11—24no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—22no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—44no—
133C11×C22⋊C4—44no—
134C11×C16—22no—
135C11×C16—22no—
136C22×#135C2×C1111yescharacteristic
137C22×Q32C2×C1111yescharacteristic, complemented
138C22×SD32C2×C1111yescharacteristic, complemented
139C2×#467C2×C1111yescharacteristic, complemented
140#2189C2×C1118yesdirect product factor
141C2×#358C2×C1111yescharacteristic, complemented
142C2×#357C2×C1111yescharacteristic, complemented
143C2×C22⋊C16C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11C2×D812yes—
152C23×C11C2×D811yescharacteristic
153Q8×C11—24no—
154Q8×C11—42no—
155Q8×C11—44no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—82no—
159D4×C11—24no—
160D4×C11—416no—
161D4×C11—42no—
162D4×C11—44no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—416no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11#12012yes—
175C2×C4×C11C2×D812yes—
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11C22×D411yescharacteristic
179C8×C11—22no—
180C8×C11#12012yes—
181C8×C11C22×D411yescharacteristic
182C8×C11C22×D411yescharacteristic
183C22×#41—21no—
184C2×#135—24no—
185C2×#135—24no—
186C2×#135—22no—
187C2×#135C22×C1114yes—
188C22×Q16C22×C1111yescharacteristic
189C22×Q16C22×C1111yescharacteristic
190C22×SD16—21no—
191C22×D8C22×C1111yescharacteristic
192C23×C8C22×C1111yescharacteristic
193C2×C22⋊Q8—21no—
194C2×Q32—24no—
195C2×Q32C22×C1114yescomplemented
196C2×SD32—24no—
197C2×SD32C22×C1114yescomplemented
198C22×C16C22×C1111yescharacteristic
199C22×C16C22×C1111yescharacteristic
200#467—22no—
201#467C22×C1114yescomplemented
202C2×#107C22×C1111yescharacteristic
203C2×#103—21no—
204#358C22×C1114yescomplemented
205#357C22×C1114yescomplemented
206C22⋊C16C22×C1114yescomplemented
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—44no—
211C22×C11—44no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—88no—
215C22×C11#44712yes—
216C22×C11#50812yes—
217C22×C11#51012yes—
218C22×C11C22×D811yescharacteristic
219C4×C11—22no—
220C4×C11—44no—
221C4×C11—82no—
222C4×C11—82no—
223C4×C11#44712yes—
224C4×C11C2×#12011yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226C2×#41—28no—
227C2×#41—24no—
228C2×#41—44no—
229C2×#41—42no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×D4—21no—
233C22×D4—41no—
234C23×C4—41no—
235C23×C4D4×C1111yescharacteristic
236#135—216no—
237#135—28no—
238#135—28no—
239C2×Q16—21no—
240C2×Q16—22no—
241C2×Q16—22no—
242C2×Q16—22no—
243C2×Q16—21no—
244C2×Q16D4×C1114yes—
245C2×Q16C23×C1112yes—
246C2×Q16C23×C1112yes—
247C2×SD16—28no—
248C2×SD16—24no—
249C2×D8—21no—
250C2×D8—22no—
251C2×D8D4×C1114yes—
252C2×D8C23×C1112yes—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8D4×C1111yescharacteristic
256C22×C8D4×C1112yes—
257C22×C8C23×C1112yes—
258C22×C8C23×C1111yescharacteristic
259C22⋊Q8—24no—
260C22⋊Q8—42no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—41no—
263C2×C22⋊C4—41no—
264Q32—28no—
265SD32—28no—
266C2×C16—22no—
267C2×C16—22no—
268C2×C16C23×C1112yes—
269C2×C16C23×C1112yes—
270#107—21no—
271#107C23×C1112yes—
272#103—24no—
273C2×C11—42no—
274C2×C11—84no—
275C2×C11#218914yesdirect product factor
276C2×C11C2×#44711yescharacteristic
277C2×C11C2×#50811yescharacteristic
278C2×C11C2×#51011yescharacteristic
279C24—41no—
280C24C11×D811yescharacteristic
281#41—216no—
282#41—48no—
283#41—416no—
284C2×Q8—24no—
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—42no—
290C2×Q8—42no—
291C2×Q8—42no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—48no—
295C2×D4—44no—
296C2×D4—41no—
297C2×D4—42no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—48no—
301C22×C4—41no—
302C22×C4—44no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C11×D811yescharacteristic
306C22×C4C11×D812yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1111yescharacteristic
309Q16—24no—
310Q16—22no—
311Q16—22no—
312Q16—22no—
313Q16—42no—
314Q16C2×D4×C1114yes—
315SD16—216no—
316D8—24no—
317D8—22no—
318D8C2×D4×C1114yes—
319C2×C8—22no—
320C2×C8—24no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8C2×D4×C1112yes—
324C2×C8C2×D4×C1111yescharacteristic
325C2×C8C2×D4×C1112yes—
326C2×C8C2×D4×C1112yes—
327C2×C8C24×C1111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—44no—
331C22⋊C4—44no—
332C16—22no—
333C16—22no—
334C11C2×#218911yescharacteristic, direct product factor, Sylow
335C23—22no—
336C23—22no—
337C23—22no—
338C23—42no—
339C23—44no—
340C23—82no—
341C23—82no—
342C23C2×C11×D812yes—
343C23C2×C11×D811yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347Q8—42no—
348Q8—42no—
349Q8—82no—
350D4—24no—
351D4—416no—
352D4—42no—
353D4—44no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—416no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4C11×#12012yes—
366C2×C4C2×C11×D812yes—
367C2×C4C2×C11×D811yescharacteristic
368C2×C4C11×AGL(1,ℤ/8)12yes—
369C2×C4C22×D4×C1111yescharacteristic
370C8—22no—
371C8C11×#12012yes—
372C8C22×D4×C1111yescharacteristic
373C8C22×D4×C1111yescharacteristic
374C22—22no—
375C22—22no—
376C22—22no—
377C22—44no—
378C22—44no—
379C22—82no—
380C22—82no—
381C22—88no—
382C22C11×#44712yes—
383C22C11×#50812yes—
384C22C11×#51012yes—
385C22C22×C11×D811yescharacteristic
386C4—22no—
387C4—44no—
388C4—82no—
389C4—82no—
390C4C11×#44712yes—
391C4C2×C11×#12011yescharacteristic
392C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
393C2—42no—
394C2—84no—
395C2C11×#218914yesdirect product factor
396C2C2×C11×#44711yescharacteristic
397C2C2×C11×#50811yescharacteristic
398C2C2×C11×#51011yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC22×C11×#135C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×Q32C2semidirect
3. C22×C11×SD32C2semidirect
4. C2×C11×#467C2semidirect
5. C11×#2189C2direct (N × H)
6. C2×C11×#358C2semidirect
7. C2×C11×#357C2semidirect
8. C2×C11×C22⋊C16C2semidirect
21. C2×C11×Q32C22semidirect
23. C2×C11×SD32C22semidirect
27. C11×#467C22semidirect
30. C11×#358C22semidirect
31. C11×#357C22semidirect
32. C11×C22⋊C16C22semidirect
80. C2×#2189C11direct (N × H)
137. C22×Q32C2×C11semidirect
138. C22×SD32C2×C11semidirect
139. C2×#467C2×C11semidirect
140. #2189C2×C11direct (N × H)
141. C2×#358C2×C11semidirect
142. C2×#357C2×C11semidirect
143. C2×C22⋊C16C2×C11semidirect
195. C2×Q32C22×C11semidirect
197. C2×SD32C22×C11semidirect
201. #467C22×C11semidirect
204. #358C22×C11semidirect
205. #357C22×C11semidirect
206. C22⋊C16C22×C11semidirect
275. C2×C11#2189direct (N × H)
334. C11C2×#2189direct (N × H)
395. C2C11×#2189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C22×C11×Q322
C22×C11×SD322
C2×C11×#4672
C11×#21892
C2×C11×#3582
C2×C11×#3572
C2×C11×C22⋊C162
C2×#218911