Finite Group Databasebeta

← C11×#22615 #14599808

Subgroups — C11×#22615 #14599808

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#106C211yesmaximal, characteristic
2C11×#2345C211yesmaximal, characteristic
3C11×#2344C211yesmaximal, characteristic
4C11×#1944C212yesmaximal, complemented
5C11×#1920C212yesmaximal, complemented
6C11×#1919C212yesmaximal, complemented
7C11×#1824C211yesmaximal, characteristic
8C11×#1823C211yesmaximal, characteristic
9C11×#1808C211yesmaximal, characteristic
10C11×#1776C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×C11×#107C2212yes—
17C2×C11×#106C418yescomplemented
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2212yes—
24C11×#389C2212yes—
25C11×#389C2212yes—
26C11×#387—22no—
27C11×#387—22no—
28C11×#381—21no—
29C11×#380—21no—
30C11×#380C2211yescharacteristic
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C22⋊C4—21no—
35C4×C11×C22⋊C4C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11—24no—
46C22×C8×C11C2×C414yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#117—44no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C11×#107—24no—
73C11×#106C2×C414yes—
74C11×#106C2×C414yes—
75C11×#106C2×C414yes—
76C11×#106C2×C414yes—
77C11×C22⋊C8—22no—
78C11×#97—24no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95D412yes—
86#22615C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—82no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C8×C11—28no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11C22×C412yes—
113C2×C8×C11C22×C412yes—
114C2×C8×C11#4114yes—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4C22×C412yes—
128C11×C4⋊C4C22×C412yes—
129C11×C4⋊C4C22×C412yes—
130C11×C4⋊C4C22×C412yes—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—42no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—44no—
138C42×C11—82no—
139C22×#106C2×C1111yescharacteristic
140#2345C2×C1111yescharacteristic
141#2344C2×C1111yescharacteristic
142#1944C2×C1112yescomplemented
143#1920C2×C1112yescomplemented
144#1919C2×C1112yescomplemented
145#1824C2×C1111yescharacteristic
146#1823C2×C1111yescharacteristic
147#1808C2×C1111yescharacteristic
148#1776C2×C1112yescomplemented
149#1752C2×C1111yescharacteristic
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C4×D412yes—
153C23×C11AGL(1,ℤ/8)12yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—48no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—84no—
184C2×C4×C11C4×D412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+412yes—
189C8×C11—22no—
190C8×C11—42no—
191C8×C11#11714yescomplemented
192C23×C8C22×C1111yescharacteristic
193C2×#117—21no—
194C22×C4⋊C4C22×C1111yescharacteristic
195C22×C4⋊C4C22×C1111yescharacteristic
196C2×#107C22×C1112yes—
197C2×#106C4×C1118yescomplemented
198C2×#106C22×C1111yescharacteristic
199C2×#106C22×C1111yescharacteristic
200C2×#106C22×C1111yescharacteristic
201C2×#106C22×C1111yescharacteristic
202C2×C22⋊C8C22×C1111yescharacteristic
203C2×#97C22×C1112yes—
204#389C22×C1112yes—
205#389C22×C1112yes—
206#387—22no—
207#387—22no—
208#381—21no—
209#380—21no—
210#380C22×C1111yescharacteristic
211#380C22×C1111yescharacteristic
212C4×C4⋊C4C22×C1112yes—
213C4×C4⋊C4C22×C1112yes—
214C4×C22⋊C4—21no—
215C4×C22⋊C4C22×C1111yescharacteristic
216#340C22×C1112yes—
217#340C22×C1112yes—
218#340C22×C1112yes—
219#340C22×C1112yes—
220#340C22×C1112yes—
221#336C22×C1112yes—
222C22×C11—24no—
223C22×C11—24no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#44014yes—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#54712yes—
229C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11#57712yes—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—82no—
240C4×C11—82no—
241C4×C11C2×#11711yescharacteristic
242C4×C11#51911yescharacteristic
243C4×C11#55212yes—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4C23×C1111yescharacteristic
247C22×C8—24no—
248C22×C8C2×C4×C1114yes—
249C22×C8C23×C1112yes—
250C22×C8C23×C1111yescharacteristic
251C22×C8C23×C1111yescharacteristic
252#117—44no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4C2×C4×C1114yes—
260C2×C4⋊C4C2×C4×C1114yes—
261C2×C4⋊C4C23×C1112yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1111yescharacteristic
264C2×C4⋊C4C23×C1111yescharacteristic
265C2×C4⋊C4C23×C1111yescharacteristic
266C2×C4⋊C4C23×C1111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4D4×C1111yescharacteristic
270C2×C22⋊C4D4×C1111yescharacteristic
271C2×C42—22no—
272C2×C42—22no—
273C2×C42C23×C1112yes—
274#107—24no—
275#106C2×C4×C1114yes—
276#106C2×C4×C1114yes—
277#106C2×C4×C1114yes—
278#106C2×C4×C1114yes—
279C22⋊C8—22no—
280#97—24no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95D4×C1112yes—
288C2×C11—24no—
289C2×C11#234411yescharacteristic
290C2×C11C2×#44011yescharacteristic
291C2×C11#294911yescharacteristic
292C2×C11#334412yes—
293C2×C11#334512yes—
294C24C2×D4×C1111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4C22×C4×C1112yes—
309C22×C4C2×D4×C1112yes—
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C11×#4112yes—
313C22×C4C24×C1111yescharacteristic
314C2×C8—22no—
315C2×C8—28no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8C22×C4×C1112yes—
320C2×C8C22×C4×C1112yes—
321C2×C8C11×#4114yes—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—44no—
333C4⋊C4—82no—
334C4⋊C4C22×C4×C1112yes—
335C4⋊C4C22×C4×C1112yes—
336C4⋊C4C22×C4×C1112yes—
337C4⋊C4C22×C4×C1112yes—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C42—22no—
343C42—22no—
344C42—44no—
345C42—82no—
346C11#2261511yescharacteristic, direct product factor, Sylow
347C23—22no—
348C23—22no—
349C23C4×D4×C1112yes—
350C23C11×AGL(1,ℤ/8)12yes—
351C23C11×#13712yes—
352C23C22×D4×C1111yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—48no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—84no—
381C2×C4C4×D4×C1112yes—
382C2×C4C23×C4×C1111yescharacteristic
383C2×C4C2×C11×#4112yes—
384C2×C4C2×C11×#4111yescharacteristic
385C2×C4C11×2−1+412yes—
386C8—22no—
387C8—42no—
388C8C11×#11714yescomplemented
389C22—22no—
390C22—24no—
391C22—24no—
392C22—22no—
393C22C11×#44014yes—
394C22C2×C4×D4×C1111yescharacteristic
395C22C11×#54712yes—
396C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
397C22C2×C11×#13711yescharacteristic
398C22C11×#57712yes—
399C4—22no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—82no—
407C4—82no—
408C4C2×C11×#11711yescharacteristic
409C4C11×#51911yescharacteristic
410C4C11×#55212yes—
411C2—24no—
412C2C11×#234411yescharacteristic
413C2C2×C11×#44011yescharacteristic
414C2C11×#294911yescharacteristic
415C2C11×#334412yes—
416C2C11×#334512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1944C2semidirect
5. C11×#1920C2semidirect
6. C11×#1919C2semidirect
10. C11×#1776C2semidirect
17. C2×C11×#106C4semidirect
86. #22615C11direct (N × H)
142. #1944C2×C11semidirect
143. #1920C2×C11semidirect
144. #1919C2×C11semidirect
148. #1776C2×C11semidirect
191. C8×C11#117semidirect
197. C2×#106C4×C11semidirect
346. C11#22615direct (N × H)
388. C8C11×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1062
C11×#23452
C11×#23442
C11×#19442
C11×#19202
C11×#19192
C11×#18242
C11×#18232
C11×#18082
C11×#17762
C11×#17522
#2261511