Finite Group Databasebeta

← C11×#22193 #14599386

Subgroups — C11×#22193 #14599386

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C11×#2324C212yesmaximal, complemented
3C11×#1926C212yesmaximal, complemented
4C11×#1918C212yesmaximal, complemented
5C11×#1895C212yesmaximal, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1864C212yesmaximal, complemented
8C11×#1807C211yesmaximal, characteristic, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2212yes—
15C2×C11×#117C2211yescharacteristic
16C11×#466C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C11×#390—22no—
24C11×#390C2212yes—
25C11×#389C2212yes—
26C11×#388—22no—
27C11×#386—22no—
28C11×#385—22no—
29C11×#380C2212yes—
30C4×C11×C4⋊C4C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×D4×C11—22no—
37C22×D4×C11C2312yes—
38C23×C4×C11—22no—
39C23×C4×C11C2311yescharacteristic
40C2×C11×D8—41no—
41C2×C11×D8—41no—
42C2×C11×D8C2×C414yes—
43C2×C11×M16—22no—
44C2×C11×M16—41no—
45C2×C11×M16—41no—
46C22×C8×C11—41no—
47C22×C8×C11—41no—
48C22×C8×C11C2×C414yescomplemented
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#121—24no—
53C11×#121C2×C418yescomplemented
54C4×D4×C11—42no—
55C4×D4×C11—42no—
56C11×#117—41no—
57C11×#117—41no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C11×#107C2×C414yescomplemented
73C11×#106—41no—
74C11×#106—41no—
75C11×#102—42no—
76C11×#102—42no—
77C11×#102C2×C418yescomplemented
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#22193C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—22no—
83C24×C11C2×D411yescharacteristic
84C2×D4×C11—28no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—82no—
91C2×D4×C11—82no—
92C2×D4×C11C22×C414yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—44no—
101C22×C4×C11—82no—
102C22×C4×C11—82no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C11×D8—44no—
110C11×M16—44no—
111C2×C8×C11—22no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—44no—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C22×C412yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4C22×C414yes—
129C11×C22⋊C4—28no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—82no—
134C11×C22⋊C4—82no—
135C11×C22⋊C4—82no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—82no—
139C2×#466C2×C1111yescharacteristic
140#2324C2×C1112yescomplemented
141#1926C2×C1112yescomplemented
142#1918C2×C1112yescomplemented
143#1895C2×C1112yescomplemented
144#1879C2×C1112yescomplemented
145#1864C2×C1112yescomplemented
146#1807C2×C1111yescharacteristic, complemented
147#1729C2×C1111yescharacteristic, complemented
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—24no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11C4×D412yes—
160C23×C11C22×D411yescharacteristic
161D4×C11—24no—
162D4×C11—24no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—88no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—88no—
188C2×C4×C11C4×D412yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11H(5,𝔽2)11yescharacteristic
192C2×C4×C11H(5,𝔽2)11yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C8×C11—22no—
196C8×C11—22no—
197C8×C11—42no—
198C22×D8C22×C1111yescharacteristic
199C22×M16C22×C1111yescharacteristic
200C23×C8C22×C1111yescharacteristic
201C2×#121C22×C1112yes—
202C2×C4×D4C22×C1112yes—
203C2×#117C22×C1111yescharacteristic
204#466C4×C1118yescomplemented
205C2×#107C22×C1111yescharacteristic
206C2×#106C22×C1111yescharacteristic
207C2×#106C22×C1111yescharacteristic
208C2×#102C22×C1112yes—
209C2×#102C22×C1112yes—
210C2×#102C22×C1112yes—
211#390—22no—
212#390C22×C1112yes—
213#389C22×C1112yes—
214#388—22no—
215#386—22no—
216#385—22no—
217#380C22×C1112yes—
218C4×C4⋊C4C22×C1112yes—
219#340C22×C1112yes—
220#340C22×C1112yes—
221#340C22×C1112yes—
222#336C22×C1112yes—
223#336C22×C1112yes—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—44no—
230C22×C11—44no—
231C22×C11—44no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11C2×C4×D411yescharacteristic
237C22×C11#53411yescharacteristic
238C22×C11#53711yescharacteristic
239C22×C11#57612yes—
240C22×C11#57712yes—
241C4×C11—22no—
242C4×C11—42no—
243C4×C11—42no—
244C4×C11—44no—
245C4×C11—82no—
246C4×C11—82no—
247C4×C11#51811yescharacteristic
248C4×C11#52011yescharacteristic
249C4×C11#53811yescharacteristic
250C4×C11#53911yescharacteristic
251C22×D4—22no—
252C22×D4C23×C1112yes—
253C23×C4—22no—
254C23×C4C23×C1111yescharacteristic
255C2×D8—41no—
256C2×D8—41no—
257C2×D8C2×C4×C1114yes—
258C2×M16—22no—
259C2×M16—41no—
260C2×M16—41no—
261C22×C8—41no—
262C22×C8—41no—
263C22×C8C2×C4×C1114yescomplemented
264C22×C8C23×C1112yes—
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1111yescharacteristic
267#121—24no—
268#121C2×C4×C1118yescomplemented
269C4×D4—42no—
270C4×D4—42no—
271#117—41no—
272#117—41no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4D4×C1112yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C4⋊C4C23×C1112yes—
277C2×C4⋊C4C23×C1112yes—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4D4×C1111yescharacteristic
284C2×C22⋊C4D4×C1111yescharacteristic
285C2×C42—22no—
286C2×C42C23×C1112yes—
287#107C2×C4×C1114yescomplemented
288#106—41no—
289#106—41no—
290#102—42no—
291#102—42no—
292#102C2×C4×C1118yescomplemented
293#95—22no—
294#95—22no—
295#95—22no—
296C2×C11—42no—
297C2×C11—84no—
298C2×C11#232511yescharacteristic
299C2×C11#294811yescharacteristic
300C2×C11#295211yescharacteristic
301C2×C11#319812yes—
302C2×C11#325712yes—
303C24—22no—
304C24C2×D4×C1111yescharacteristic
305C2×D4—28no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—82no—
312C2×D4—82no—
313C2×D4C22×C4×C1114yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—44no—
322C22×C4—82no—
323C22×C4—82no—
324C22×C4C22×C4×C1112yes—
325C22×C4C2×D4×C1112yes—
326C22×C4C2×D4×C1112yes—
327C22×C4C2×D4×C1111yescharacteristic
328C22×C4C11×#4112yes—
329C22×C4C24×C1111yescharacteristic
330D8—44no—
331M16—44no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—44no—
340C2×C8C22×C4×C1112yes—
341C2×C8C22×C4×C1112yes—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—82no—
349C4⋊C4C22×C4×C1114yes—
350C22⋊C4—28no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—44no—
354C22⋊C4—82no—
355C22⋊C4—82no—
356C22⋊C4—82no—
357C42—22no—
358C42—22no—
359C42—82no—
360C11#2219311yescharacteristic, direct product factor, Sylow
361C23—21no—
362C23—21no—
363C23—22no—
364C23—22no—
365C23—24no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23C4×D4×C1112yes—
373C23C22×D4×C1111yescharacteristic
374D4—24no—
375D4—24no—
376D4—42no—
377D4—42no—
378D4—88no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—88no—
401C2×C4C4×D4×C1112yes—
402C2×C4C23×C4×C1111yescharacteristic
403C2×C4C2×C11×#4111yescharacteristic
404C2×C4C11×H(5,𝔽2)11yescharacteristic
405C2×C4C11×H(5,𝔽2)11yescharacteristic
406C2×C4C11×H(5,𝔽2)11yescharacteristic
407C2×C4C11×2−1+411yescharacteristic
408C8—22no—
409C8—22no—
410C8—42no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C2×C4×D4×C1111yescharacteristic
424C22C11×#53411yescharacteristic
425C22C11×#53711yescharacteristic
426C22C11×#57612yes—
427C22C11×#57712yes—
428C4—22no—
429C4—42no—
430C4—42no—
431C4—44no—
432C4—82no—
433C4—82no—
434C4C11×#51811yescharacteristic
435C4C11×#52011yescharacteristic
436C4C11×#53811yescharacteristic
437C4C11×#53911yescharacteristic
438C2—42no—
439C2—84no—
440C2C11×#232511yescharacteristic
441C2C11×#294811yescharacteristic
442C2C11×#295211yescharacteristic
443C2C11×#319812yes—
444C2C11×#325712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#466C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2324C2semidirect
3. C11×#1926C2semidirect
4. C11×#1918C2semidirect
5. C11×#1895C2semidirect
6. C11×#1879C2semidirect
7. C11×#1864C2semidirect
8. C11×#1807C2semidirect
9. C11×#1729C2semidirect
16. C11×#466C4semidirect
48. C22×C8×C11C2×C4semidirect
53. C11×#121C2×C4semidirect
72. C11×#107C2×C4semidirect
77. C11×#102C2×C4semidirect
81. #22193C11direct (N × H)
140. #2324C2×C11semidirect
141. #1926C2×C11semidirect
142. #1918C2×C11semidirect
143. #1895C2×C11semidirect
144. #1879C2×C11semidirect
145. #1864C2×C11semidirect
146. #1807C2×C11semidirect
147. #1729C2×C11semidirect
204. #466C4×C11semidirect
263. C22×C8C2×C4×C11semidirect
268. #121C2×C4×C11semidirect
287. #107C2×C4×C11semidirect
292. #102C2×C4×C11semidirect
360. C11#22193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C11×#23242
C11×#19262
C11×#19182
C11×#18952
C11×#18792
C11×#18642
C11×#18072
C11×#17292
#2219311