Finite Group Databasebeta

← C11×#33778 #14610971

Subgroups — C11×#33778 #14610971

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic, complemented
2C11×#3147C211yesmaximal, characteristic, complemented
3C11×#2249C212yesmaximal, complemented
4C11×#2242C212yesmaximal, complemented
5C11×#2209C211yesmaximal, characteristic, complemented
6C11×#2208C211yesmaximal, characteristic, complemented
7C11×#2207C211yesmaximal, characteristic, complemented
8C11×#2206C211yesmaximal, characteristic, complemented
9C11×#2189C212yesmaximal, complemented
10C11×#2186C212yesmaximal, complemented
11C11×#2162C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135C2212yes—
14C11×#532—21no—
15C11×#529—21no—
16C2×C11×Q32C2212yes—
17C2×C11×SD32C2212yes—
18C2×C11×SD32C2212yes—
19C2×C11×D16C2212yes—
20C11×#499C2211yescharacteristic
21C11×#495—21no—
22C11×#495C2212yes—
23C11×#495C2211yescharacteristic
24C11×#494C2211yescharacteristic
25C11×#493C2211yescharacteristic
26C11×#492—21no—
27C11×#488—21no—
28C11×#467C2211yescharacteristic
29C11×#466C2211yescharacteristic
30C11×#465—21no—
31C4×C11×Q16C2211yescharacteristic
32C4×C11×SD16—21no—
33C4×C11×D8C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×C4⋊C16C2211yescharacteristic
36C11×C4⋊C16C2211yescharacteristic
37C11×#358C2212yes—
38C11×#358C2212yes—
39C11×#357C2212yes—
40C11×#357C2212yes—
41C11×C22⋊C16C2212yes—
42C4×C11×C16C2212yes—
43C2×C11×#41—22no—
44C11×#135—42no—
45C11×#135—42no—
46C11×#135—44no—
47C2×C11×Q16—21no—
48C2×C11×Q16C2312yes—
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—21no—
53C2×C11×D8—21no—
54C2×C11×D8C2312yes—
55C2×C11×D8C2311yescharacteristic
56C22×C8×C11D411yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—21no—
59C11×#127—21no—
60C11×#126—41no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—21no—
64C11×#123—41no—
65C11×C22⋊Q8—21no—
66C11×#121—21no—
67C11×#121—41no—
68C11×#121—41no—
69C4×Q8×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C4×D4×C11—41no—
74C11×#117—41no—
75C2×C42×C11D411yescharacteristic
76C11×Q32—42no—
77C11×SD32—42no—
78C11×SD32—42no—
79C11×D16—42no—
80C2×C11×C16C2312yes—
81C2×C11×C16C2312yes—
82C11×#107C2311yescharacteristic
83C11×#107C2311yescharacteristic
84C11×#106—21no—
85C11×#103—21no—
86C11×#103—21no—
87C11×#102—21no—
88C11×#102—21no—
89C4×C8×C11D411yescharacteristic
90C4×C8×C11D411yescharacteristic
91C4×C8×C11C2311yescharacteristic
92C4×C8×C11C2311yescharacteristic
93#33778C1111yesmaximal, characteristic, direct product factor, Sylow
94C11×#41—44no—
95C11×#41—44no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—22no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11D811yescharacteristic
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C11×Q16—21no—
110C11×Q16—22no—
111C11×Q16—21no—
112C11×Q16—22no—
113C11×Q16—42no—
114C11×SD16—44no—
115C11×SD16—42no—
116C11×SD16—44no—
117C11×D8—21no—
118C11×D8—22no—
119C11×D8—21no—
120C11×D8—22no—
121C11×D8—42no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—41no—
144C42×C11—41no—
145C42×C11D811yescharacteristic
146C42×C11D811yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C11×C16—22no—
150C11×C16—22no—
151#3168C2×C1111yescharacteristic, complemented
152#3147C2×C1111yescharacteristic, complemented
153#2249C2×C1112yescomplemented
154#2242C2×C1112yescomplemented
155#2209C2×C1111yescharacteristic, complemented
156#2208C2×C1111yescharacteristic, complemented
157#2207C2×C1111yescharacteristic, complemented
158#2206C2×C1111yescharacteristic, complemented
159#2189C2×C1112yescomplemented
160#2186C2×C1112yescomplemented
161#2162C2×C1111yescharacteristic, complemented
162C23×C11—41no—
163C23×C11—42no—
164C23×C11C2×D811yescharacteristic
165Q8×C11—42no—
166Q8×C11—41no—
167Q8×C11—42no—
168Q8×C11—41no—
169D4×C11—42no—
170D4×C11—41no—
171D4×C11—42no—
172D4×C11—41no—
173D4×C11—82no—
174D4×C11—82no—
175D4×C11—84no—
176D4×C11—82no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—84no—
186C2×C4×C11—82no—
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C8×C11—21no—
194C8×C11—21no—
195C8×C11AGL(1,ℤ/8)12yes—
196C8×C11H(5,𝔽2)11yescharacteristic
197C8×C11H(5,𝔽2)11yescharacteristic
198C2×#135—21no—
199C2×#135C22×C1112yes—
200#532—21no—
201#529—21no—
202C2×Q32C22×C1112yes—
203C2×SD32C22×C1112yes—
204C2×SD32C22×C1112yes—
205C2×D16C22×C1112yes—
206#499C22×C1111yescharacteristic
207#495—21no—
208#495C22×C1112yes—
209#495C22×C1111yescharacteristic
210#494C22×C1111yescharacteristic
211#493C22×C1111yescharacteristic
212#492—21no—
213#488—21no—
214#467C22×C1111yescharacteristic
215#466C22×C1111yescharacteristic
216#465—21no—
217C4×Q16C22×C1111yescharacteristic
218C4×SD16—21no—
219C4×D8C22×C1111yescharacteristic
220C2×C4×C8C22×C1111yescharacteristic
221C4⋊C16C22×C1111yescharacteristic
222C4⋊C16C22×C1111yescharacteristic
223#358C22×C1112yes—
224#358C22×C1112yes—
225#357C22×C1112yes—
226#357C22×C1112yes—
227C22⋊C16C22×C1112yes—
228C4×C16C22×C1112yes—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—81no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—81no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11C22×D811yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—82no—
246C4×C11—81no—
247C4×C11#50812yes—
248C4×C11#53511yescharacteristic
249C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C2×#41—22no—
251#135—42no—
252#135—42no—
253#135—44no—
254C2×Q16—21no—
255C2×Q16C23×C1112yes—
256C2×Q16C23×C1111yescharacteristic
257C2×SD16—22no—
258C2×SD16—22no—
259C2×SD16—21no—
260C2×D8—21no—
261C2×D8C23×C1112yes—
262C2×D8C23×C1111yescharacteristic
263C22×C8D4×C1111yescharacteristic
264C22×C8C23×C1111yescharacteristic
265C4⋊Q8—21no—
266#127—21no—
267#126—41no—
268#125—21no—
269#124—21no—
270#124—22no—
271#123—41no—
272C22⋊Q8—21no—
273#121—21no—
274#121—41no—
275#121—41no—
276C4×Q8—21no—
277C4×D4—21no—
278C4×D4—41no—
279C4×D4—41no—
280C4×D4—41no—
281#117—41no—
282C2×C42D4×C1111yescharacteristic
283Q32—42no—
284SD32—42no—
285SD32—42no—
286D16—42no—
287C2×C16C23×C1112yes—
288C2×C16C23×C1112yes—
289#107C23×C1111yescharacteristic
290#107C23×C1111yescharacteristic
291#106—21no—
292#103—21no—
293#103—21no—
294#102—21no—
295#102—21no—
296C4×C8D4×C1111yescharacteristic
297C4×C8D4×C1111yescharacteristic
298C4×C8C23×C1111yescharacteristic
299C4×C8C23×C1111yescharacteristic
300C2×C11—41no—
301C2×C11—161no—
302C2×C11—162no—
303C2×C11#320511yescharacteristic
304C2×C11C2×#50811yescharacteristic
305C2×C11#341411yescharacteristic
306#41—44no—
307#41—44no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×D4—21no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4C11×D811yescharacteristic
319C22×C4C11×D811yescharacteristic
320C22×C4C2×D4×C1111yescharacteristic
321Q16—21no—
322Q16—22no—
323Q16—21no—
324Q16—22no—
325Q16—42no—
326SD16—44no—
327SD16—44no—
328SD16—42no—
329D8—21no—
330D8—22no—
331D8—21no—
332D8—22no—
333D8—42no—
334C2×C8—22no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8C2×D4×C1111yescharacteristic
338C2×C8C2×D4×C1111yescharacteristic
339C2×C8C2×D4×C1111yescharacteristic
340C2×C8C24×C1111yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C42—41no—
357C42C11×D811yescharacteristic
358C42C11×D811yescharacteristic
359C42C2×D4×C1111yescharacteristic
360C42C2×D4×C1111yescharacteristic
361C16—22no—
362C16—22no—
363C11#3377811yescharacteristic, direct product factor, Sylow
364C23—41no—
365C23—42no—
366C23C2×C11×D811yescharacteristic
367Q8—42no—
368Q8—41no—
369Q8—42no—
370Q8—41no—
371D4—42no—
372D4—41no—
373D4—42no—
374D4—41no—
375D4—82no—
376D4—82no—
377D4—84no—
378D4—82no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—84no—
388C2×C4—82no—
389C2×C4C2×C11×D811yescharacteristic
390C2×C4C2×C11×D811yescharacteristic
391C2×C4C2×C11×D811yescharacteristic
392C2×C4C2×C11×D811yescharacteristic
393C2×C4C2×C11×D811yescharacteristic
394C2×C4C22×D4×C1111yescharacteristic
395C8—21no—
396C8—21no—
397C8C11×AGL(1,ℤ/8)12yes—
398C8C11×H(5,𝔽2)11yescharacteristic
399C8C11×H(5,𝔽2)11yescharacteristic
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—82no—
405C22—82no—
406C22—81no—
407C22—82no—
408C22—81no—
409C22C22×C11×D811yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—81no—
415C4—81no—
416C4—82no—
417C4—81no—
418C4C11×#50812yes—
419C4C11×#53511yescharacteristic
420C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
421C2—41no—
422C2—161no—
423C2—162no—
424C2C11×#320511yescharacteristic
425C2C2×C11×#50811yescharacteristic
426C2C11×#341411yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3168C2semidirect
2. C11×#3147C2semidirect
3. C11×#2249C2semidirect
4. C11×#2242C2semidirect
5. C11×#2209C2semidirect
6. C11×#2208C2semidirect
7. C11×#2207C2semidirect
8. C11×#2206C2semidirect
9. C11×#2189C2semidirect
10. C11×#2186C2semidirect
11. C11×#2162C2semidirect
93. #33778C11direct (N × H)
151. #3168C2×C11semidirect
152. #3147C2×C11semidirect
153. #2249C2×C11semidirect
154. #2242C2×C11semidirect
155. #2209C2×C11semidirect
156. #2208C2×C11semidirect
157. #2207C2×C11semidirect
158. #2206C2×C11semidirect
159. #2189C2×C11semidirect
160. #2186C2×C11semidirect
161. #2162C2×C11semidirect
363. C11#33778direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31682
C11×#31472
C11×#22492
C11×#22422
C11×#22092
C11×#22082
C11×#22072
C11×#22062
C11×#21892
C11×#21862
C11×#21622
#3377811