Finite Group Databasebeta

← C11×#22196 #14599389

Subgroups — C11×#22196 #14599389

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C11×#2324C212yesmaximal, complemented
3C11×#1925C212yesmaximal, complemented
4C11×#1921C212yesmaximal, complemented
5C11×#1895C212yesmaximal, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1862C212yesmaximal, complemented
8C11×#1808C211yesmaximal, 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×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
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⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C11×#107—41no—
73C11×#107—41no—
74C11×#107C2×C414yescomplemented
75C11×#102—42no—
76C11×#102—42no—
77C11×#102C2×C418yescomplemented
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#22196C1111yesmaximal, 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—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—82no—
129C11×C4⋊C4C22×C414yes—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—42no—
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#1925C2×C1112yescomplemented
142#1921C2×C1112yescomplemented
143#1895C2×C1112yescomplemented
144#1879C2×C1112yescomplemented
145#1862C2×C1112yescomplemented
146#1808C2×C1111yescharacteristic, complemented
147#1729C2×C1111yescharacteristic, complemented
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—24no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11C4×D412yes—
162C23×C11C22×D411yescharacteristic
163D4×C11—24no—
164D4×C11—24no—
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—88no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
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—42no—
188C2×C4×C11—42no—
189C2×C4×C11—88no—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C8×C11—22no—
198C8×C11—22no—
199C8×C11—42no—
200C22×D8C22×C1111yescharacteristic
201C22×M16C22×C1111yescharacteristic
202C23×C8C22×C1111yescharacteristic
203C2×#121C22×C1112yes—
204C2×C4×D4C22×C1112yes—
205C2×#117C22×C1111yescharacteristic
206#466C4×C1118yescomplemented
207C2×#107C22×C1111yescharacteristic
208C2×#107C22×C1111yescharacteristic
209C2×#107C22×C1111yescharacteristic
210C2×#102C22×C1112yes—
211C2×#102C22×C1112yes—
212C2×#102C22×C1112yes—
213#390—22no—
214#390C22×C1112yes—
215#389C22×C1112yes—
216#388—22no—
217#386—22no—
218#385—22no—
219#380C22×C1112yes—
220C4×C4⋊C4C22×C1112yes—
221#340C22×C1112yes—
222#340C22×C1112yes—
223#340C22×C1112yes—
224#336C22×C1112yes—
225#336C22×C1112yes—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#53411yescharacteristic
242C22×C11#53711yescharacteristic
243C22×C11#57611yescharacteristic
244C22×C11#57611yescharacteristic
245C22×C11#57611yescharacteristic
246C22×C11#57811yescharacteristic
247C4×C11—22no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—44no—
251C4×C11—82no—
252C4×C11—82no—
253C4×C11#51811yescharacteristic
254C4×C11#52011yescharacteristic
255C4×C11#53811yescharacteristic
256C4×C11#53911yescharacteristic
257C22×D4—22no—
258C22×D4C23×C1112yes—
259C23×C4—22no—
260C23×C4C23×C1111yescharacteristic
261C2×D8—41no—
262C2×D8—41no—
263C2×D8C2×C4×C1114yes—
264C2×M16—22no—
265C2×M16—41no—
266C2×M16—41no—
267C22×C8—41no—
268C22×C8—41no—
269C22×C8C2×C4×C1114yescomplemented
270C22×C8C23×C1112yes—
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1111yescharacteristic
273#121—24no—
274#121C2×C4×C1118yescomplemented
275C4×D4—42no—
276C4×D4—42no—
277#117—41no—
278#117—41no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4D4×C1111yescharacteristic
281C2×C4⋊C4D4×C1111yescharacteristic
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4D4×C1112yes—
291C2×C42—22no—
292C2×C42C23×C1112yes—
293#107—41no—
294#107—41no—
295#107C2×C4×C1114yescomplemented
296#102—42no—
297#102—42no—
298#102C2×C4×C1118yescomplemented
299#95—22no—
300#95—22no—
301#95—22no—
302C2×C11—42no—
303C2×C11—84no—
304C2×C11#232511yescharacteristic
305C2×C11#294811yescharacteristic
306C2×C11#295111yescharacteristic
307C2×C11#319911yescharacteristic
308C2×C11#320311yescharacteristic
309C2×C11#325911yescharacteristic
310C2×C11#326211yescharacteristic
311C24—22no—
312C24C2×D4×C1111yescharacteristic
313C2×D4—28no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—82no—
320C2×D4—82no—
321C2×D4C22×C4×C1114yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—44no—
330C22×C4—82no—
331C22×C4—82no—
332C22×C4C22×C4×C1112yes—
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1112yes—
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C11×#4112yes—
337C22×C4C24×C1111yescharacteristic
338D8—44no—
339M16—44no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—44no—
348C2×C8C22×C4×C1112yes—
349C2×C8C22×C4×C1112yes—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—82no—
358C4⋊C4C22×C4×C1114yes—
359C22⋊C4—28no—
360C22⋊C4—42no—
361C22⋊C4—44no—
362C22⋊C4—82no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C42—22no—
366C42—22no—
367C42—82no—
368C11#2219611yescharacteristic, direct product factor, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—24no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23C4×D4×C1112yes—
383C23C22×D4×C1111yescharacteristic
384D4—24no—
385D4—24no—
386D4—42no—
387D4—42no—
388D4—88no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—88no—
411C2×C4C4×D4×C1112yes—
412C2×C4C23×C4×C1111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C2×C4C11×H(5,𝔽2)11yescharacteristic
415C2×C4C11×H(5,𝔽2)11yescharacteristic
416C2×C4C11×H(5,𝔽2)11yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—82no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22C2×C4×D4×C1111yescharacteristic
436C22C11×#53411yescharacteristic
437C22C11×#53711yescharacteristic
438C22C11×#57611yescharacteristic
439C22C11×#57611yescharacteristic
440C22C11×#57611yescharacteristic
441C22C11×#57811yescharacteristic
442C4—22no—
443C4—42no—
444C4—42no—
445C4—44no—
446C4—82no—
447C4—82no—
448C4C11×#51811yescharacteristic
449C4C11×#52011yescharacteristic
450C4C11×#53811yescharacteristic
451C4C11×#53911yescharacteristic
452C2—42no—
453C2—84no—
454C2C11×#232511yescharacteristic
455C2C11×#294811yescharacteristic
456C2C11×#295111yescharacteristic
457C2C11×#319911yescharacteristic
458C2C11×#320311yescharacteristic
459C2C11×#325911yescharacteristic
460C2C11×#326211yescharacteristic
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×#1925C2semidirect
4. C11×#1921C2semidirect
5. C11×#1895C2semidirect
6. C11×#1879C2semidirect
7. C11×#1862C2semidirect
8. C11×#1808C2semidirect
9. C11×#1729C2semidirect
16. C11×#466C4semidirect
48. C22×C8×C11C2×C4semidirect
53. C11×#121C2×C4semidirect
74. C11×#107C2×C4semidirect
77. C11×#102C2×C4semidirect
81. #22196C11direct (N × H)
140. #2324C2×C11semidirect
141. #1925C2×C11semidirect
142. #1921C2×C11semidirect
143. #1895C2×C11semidirect
144. #1879C2×C11semidirect
145. #1862C2×C11semidirect
146. #1808C2×C11semidirect
147. #1729C2×C11semidirect
206. #466C4×C11semidirect
269. C22×C8C2×C4×C11semidirect
274. #121C2×C4×C11semidirect
295. #107C2×C4×C11semidirect
298. #102C2×C4×C11semidirect
368. C11#22196direct (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×#19252
C11×#19212
C11×#18952
C11×#18792
C11×#18622
C11×#18082
C11×#17292
#2219611