Finite Group Databasebeta

← C11×#13339 #14590532

Subgroups — C11×#13339 #14590532

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#510C211yesmaximal, characteristic
2C22×C11×Q32C211yesmaximal, characteristic, complemented
3C11×#3156C211yesmaximal, characteristic
4C2×C11×#362C211yesmaximal, characteristic, complemented
5C2×C11×#359C211yesmaximal, characteristic
6C11×#1979C211yesmaximal, characteristic, complemented
7C11×#1379C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11C22×C11×Q16C2211yescharacteristic
12C11×#536—21no—
13C11×#510—22no—
14C11×#510—22no—
15C2×C11×Q32—22no—
16C2×C11×Q32—22no—
17C2×C11×Q32—21no—
18C2×C11×Q32—22no—
19C2×C11×SD32—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C11×#497—22no—
23C11×#495—21no—
24C11×#494—21no—
25C2×C11×#108C2211yescharacteristic
26C11×#419—21no—
27C2×C11×#101—21no—
28C11×#405C2211yescharacteristic
29C11×#362—22no—
30C11×#359—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C11×#137—42no—
35C11×#137—42no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135—21no—
39C11×#135—21no—
40C2×C11×Q16—22no—
41C2×C11×Q16—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—21no—
51C2×C11×Q16D411yescharacteristic
52C2×C11×Q16D412yes—
53C2×C11×Q16D412yes—
54C2×C11×SD16—22no—
55C2×C11×SD16—21no—
56C2×C11×D8D411yescharacteristic
57C2×C11×M16—21no—
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×#124—22no—
62C11×#123—42no—
63C11×C22⋊Q8—42no—
64C11×#117D411yescharacteristic
65C11×Q32—28no—
66C11×Q32—24no—
67C11×SD32—24no—
68C11×M32—21no—
69C11×M32D412yes—
70C2×C11×C16—21no—
71C2×C11×C16—21no—
72C2×C11×C16—21no—
73C2×C11×C16D412yes—
74C11×#108—21no—
75C11×#108—21no—
76C11×#103—42no—
77C11×#101—42no—
78C11×#97—21no—
79C4×C8×C11—21no—
80#13339C1111yesmaximal, characteristic, direct product factor, Sylow
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—21no—
108C11×Q16—22no—
109C11×Q16—21no—
110C11×Q16—44no—
111C11×Q16—41no—
112C11×Q16—41no—
113C11×Q16—41no—
114C11×Q16—41no—
115C11×SD16—44no—
116C11×SD16—41no—
117C11×SD16—41no—
118C11×D8—21no—
119C11×D8—21no—
120C11×M16—21no—
121C11×M16—41no—
122C11×M16—41no—
123C11×M16D812yes—
124C2×C8×C11—21no—
125C2×C8×C11—41no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11#4111yescharacteristic
132C11×C4⋊C4—44no—
133C11×C4⋊C4D812yes—
134C11×C22⋊C4—21no—
135C11×C22⋊C4—44no—
136C42×C11—21no—
137C11×C16—22no—
138C11×C16—22no—
139C2×#510C2×C1111yescharacteristic
140C22×Q32C2×C1111yescharacteristic, complemented
141#3156C2×C1111yescharacteristic
142C2×#362C2×C1111yescharacteristic, complemented
143C2×#359C2×C1111yescharacteristic
144#1979C2×C1111yescharacteristic, complemented
145#1379C2×C1111yescharacteristic, complemented
146C23×C11—41no—
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148Q8×C11—41no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—41no—
153Q8×C11—42no—
154Q8×C11—81no—
155Q8×C11—81no—
156Q8×C11—81no—
157Q8×C11—81no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—81no—
161D4×C11—81no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C8×C11—22no—
179C8×C11—81no—
180C8×C11#12011yescharacteristic
181C8×C11#12011yescharacteristic
182C8×C11#12111yescharacteristic
183C8×C11#12111yescharacteristic
184C2×#137—21no—
185C2×#135C22×C1111yescharacteristic
186C22×Q16C22×C1111yescharacteristic
187C22×Q16C22×C1111yescharacteristic
188#536—21no—
189#510—22no—
190#510—22no—
191C2×Q32—22no—
192C2×Q32—22no—
193C2×Q32—21no—
194C2×Q32—22no—
195C2×SD32—21no—
196C2×M32C22×C1111yescharacteristic
197C22×C16C22×C1111yescharacteristic
198#497—22no—
199#495—21no—
200#494—21no—
201C2×#108C22×C1111yescharacteristic
202#419—21no—
203C2×#101—21no—
204#405C22×C1111yescharacteristic
205#362—22no—
206#359—22no—
207C22×C11—22no—
208C22×C11—82no—
209C22×C11—81no—
210C22×C11#44711yescharacteristic
211C22×C11#45911yescharacteristic
212C22×C11#49611yescharacteristic
213C4×C11—42no—
214C4×C11—81no—
215C4×C11—82no—
216C4×C11—82no—
217C4×C11#39211yescharacteristic
218C4×C11#44711yescharacteristic
219C4×C11#45911yescharacteristic
220C4×C11#49311yescharacteristic
221C2×#41—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224#137—42no—
225#137—42no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135—21no—
230C2×Q16—22no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16D4×C1112yes—
242C2×Q16D4×C1112yes—
243C2×Q16D4×C1111yescharacteristic
244C2×SD16—22no—
245C2×SD16—21no—
246C2×D8D4×C1111yescharacteristic
247C2×M16—21no—
248C2×M16D4×C1111yescharacteristic
249C22×C8C23×C1111yescharacteristic
250C4⋊Q8—22no—
251#124—22no—
252#123—42no—
253C22⋊Q8—42no—
254#117D4×C1111yescharacteristic
255Q32—28no—
256Q32—24no—
257SD32—24no—
258M32—21no—
259M32D4×C1112yes—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—21no—
263C2×C16D4×C1112yes—
264#108—21no—
265#108—21no—
266#103—42no—
267#101—42no—
268#97—21no—
269C4×C8—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#201111yescharacteristic
274C2×C11#219512yes—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—22no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—21no—
293C2×D4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C1111yescharacteristic
298Q16—22no—
299Q16—22no—
300Q16—22no—
301Q16—21no—
302Q16—22no—
303Q16—21no—
304Q16—44no—
305Q16—41no—
306Q16—41no—
307Q16—41no—
308Q16—41no—
309SD16—44no—
310SD16—41no—
311SD16—41no—
312D8—21no—
313D8—21no—
314M16—21no—
315M16—41no—
316M16—41no—
317M16C11×D812yes—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8C2×D4×C1111yescharacteristic
321C2×C8C2×D4×C1111yescharacteristic
322C2×C8C2×D4×C1111yescharacteristic
323C2×C8C2×D4×C1111yescharacteristic
324C2×C8C2×D4×C1111yescharacteristic
325C2×C8C11×#4111yescharacteristic
326C4⋊C4—44no—
327C4⋊C4C11×D812yes—
328C22⋊C4—21no—
329C22⋊C4—44no—
330C42—21no—
331C16—22no—
332C16—22no—
333C11#1333911yescharacteristic, direct product factor, Sylow
334C23—41no—
335C23C11×AGL(1,ℤ/8)11yescharacteristic
336Q8—41no—
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—41no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345Q8—81no—
346D4—41no—
347D4—41no—
348D4—81no—
349D4—81no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C11×#12011yescharacteristic
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12711yescharacteristic
363C2×C4C2×C11×D811yescharacteristic
364C2×C4C2×C11×D811yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C8—22no—
367C8—81no—
368C8C11×#12011yescharacteristic
369C8C11×#12011yescharacteristic
370C8C11×#12111yescharacteristic
371C8C11×#12111yescharacteristic
372C22—22no—
373C22—82no—
374C22—81no—
375C22C11×#44711yescharacteristic
376C22C11×#45911yescharacteristic
377C22C11×#49611yescharacteristic
378C4—42no—
379C4—81no—
380C4—82no—
381C4—82no—
382C4C11×#39211yescharacteristic
383C4C11×#44711yescharacteristic
384C4C11×#45911yescharacteristic
385C4C11×#49311yescharacteristic
386C2—21no—
387C2—21no—
388C2—161no—
389C2C11×#201111yescharacteristic
390C2C11×#219512yes—
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×Q32C2semidirect
4. C2×C11×#362C2semidirect
6. C11×#1979C2semidirect
7. C11×#1379C2semidirect
80. #13339C11direct (N × H)
140. C22×Q32C2×C11semidirect
142. C2×#362C2×C11semidirect
144. #1979C2×C11semidirect
145. #1379C2×C11semidirect
333. C11#13339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5102
C22×C11×Q322
C11×#31562
C2×C11×#3622
C2×C11×#3592
C11×#19792
C11×#13792
#1333911