Finite Group Databasebeta

← C2×C11×#2133 #14610559

Subgroups — C2×C11×#2133 #14610559

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C22×C11×#101C212yesmaximal, complemented
3C11×#2133C218yesmaximal, direct product factor
4C2×C11×#356C212yesmaximal, complemented
5C2×C11×#355C212yesmaximal, complemented
6C22×C11×#41C411yescharacteristic
7C23×Q8×C11C2211yescharacteristic
8C22×C11×M16—22no—
9C11×#536—24no—
10C11×#536C414yes—
11C11×#536C2214yes—
12C2×C11×C4⋊Q8C411yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#124C411yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×#117C411yescharacteristic
19C2×C11×#101—24no—
20C2×C11×#101—22no—
21C2×C11×#101C2214yes—
22C2×C11×#101C2218yescomplemented
23C11×#356C2218yescomplemented
24C11×#355C2218yescomplemented
25C2×C11×#41—22no—
26C2×C11×#41—42no—
27C2×C11×#41—42no—
28C2×C11×#41C2×C414yes—
29C22×Q8×C11—42no—
30C22×Q8×C11—42no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×Q8×C11C2×C412yes—
34C22×Q8×C11D412yes—
35C22×Q8×C11D414yes—
36C22×Q8×C11C2311yescharacteristic
37C22×Q8×C11C2312yes—
38C22×D4×C11—21no—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11D412yes—
43C2×C11×M16—24no—
44C2×C11×M16—28no—
45C2×C11×M16—44no—
46C2×C11×M16—42no—
47C22×C8×C11—42no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
51C11×C4⋊Q8C2×C412yes—
52C11×C4⋊Q8C2312yes—
53C11×#124—22no—
54C11×#124—22no—
55C11×#124C2×C414yes—
56C11×#124C2×C412yes—
57C11×#124C2312yes—
58C11×#123—28no—
59C11×#123—28no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—28no—
62C11×#117—22no—
63C11×#117C2×C414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11C2×C411yescharacteristic
71C2×C42×C11C2×C411yescharacteristic
72C11×#101—24no—
73C11×#101—28no—
74C11×#101C2318yes—
75C2×#2133C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C24×C11C22⋊C411yescharacteristic
78C11×#41—48no—
79C11×#41—48no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—44no—
83C2×Q8×C11—41no—
84C2×Q8×C11—44no—
85C2×Q8×C11—42no—
86C2×Q8×C11—44no—
87C2×Q8×C11—42no—
88C2×Q8×C11—44no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C2×Q8×C11C22⋊C414yes—
94C2×Q8×C11C22⋊C412yes—
95C2×Q8×C11C22×C412yes—
96C2×Q8×C11C22×C412yes—
97C2×Q8×C11C22×C411yescharacteristic
98C2×Q8×C11C2×D414yes—
99C2×Q8×C11C2×D412yes—
100C2×Q8×C11C2411yescharacteristic
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—24no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C22⋊C412yes—
120C22×C4×C11C22⋊C411yescharacteristic
121C22×C4×C11C22⋊C412yes—
122C22×C4×C11C22⋊C414yes—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D414yes—
127C11×M16—28no—
128C11×M16—44no—
129C11×M16—48no—
130C2×C8×C11—48no—
131C2×C8×C11—44no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11C22×C412yes—
143C42×C11C22×C412yes—
144C2×#536C2×C1111yescharacteristic
145C22×#101C2×C1112yescomplemented
146#2133C2×C1118yesdirect product factor
147C2×#356C2×C1112yescomplemented
148C2×#355C2×C1112yescomplemented
149C23×C11—22no—
150C23×C11—42no—
151C23×C11—44no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11#9912yes—
155C23×C11#9912yes—
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11C2×C22⋊C412yes—
158Q8×C11—44no—
159Q8×C11—42no—
160Q8×C11—42no—
161Q8×C11—41no—
162Q8×C11—44no—
163Q8×C11—42no—
164Q8×C11—41no—
165Q8×C11—42no—
166Q8×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—48no—
170C2×C4×C11—24no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—21no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—48no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11C2×C22⋊C414yes—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D412yes—
198C8×C11—48no—
199C22×#41C4×C1111yescharacteristic
200C23×Q8C22×C1111yescharacteristic
201C22×M16—22no—
202#536—24no—
203#536C4×C1114yes—
204#536C22×C1114yes—
205C2×C4⋊Q8C4×C1111yescharacteristic
206C2×C4⋊Q8C22×C1111yescharacteristic
207C2×#124C4×C1111yescharacteristic
208C2×#124C22×C1111yescharacteristic
209C2×#123—22no—
210C2×C22⋊Q8—22no—
211C2×#117C4×C1111yescharacteristic
212C2×#101—24no—
213C2×#101—22no—
214C2×#101C22×C1114yes—
215C2×#101C22×C1118yescomplemented
216#356C22×C1118yescomplemented
217#355C22×C1118yescomplemented
218C22×C11—22no—
219C22×C11—24no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—82no—
226C22×C11C2×#9911yescharacteristic
227C22×C11C2×#9914yes—
228C22×C11C2×#9911yescharacteristic
229C22×C11C22×C22⋊C411yescharacteristic
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—24no—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—22no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11—42no—
239C2×#41—22no—
240C2×#41—42no—
241C2×#41—42no—
242C2×#41C2×C4×C1114yes—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8C2×C4×C1111yescharacteristic
246C22×Q8C2×C4×C1111yescharacteristic
247C22×Q8C2×C4×C1112yes—
248C22×Q8D4×C1112yes—
249C22×Q8D4×C1114yes—
250C22×Q8C23×C1111yescharacteristic
251C22×Q8C23×C1112yes—
252C22×D4—21no—
253C22×D4C2×C4×C1111yescharacteristic
254C23×C4—21no—
255C23×C4C2×C4×C1111yescharacteristic
256C23×C4D4×C1112yes—
257C2×M16—24no—
258C2×M16—28no—
259C2×M16—42no—
260C2×M16—44no—
261C22×C8—42no—
262C4⋊Q8—22no—
263C4⋊Q8—22no—
264C4⋊Q8C2×C4×C1114yes—
265C4⋊Q8C2×C4×C1112yes—
266C4⋊Q8C23×C1112yes—
267#124—22no—
268#124—22no—
269#124C2×C4×C1114yes—
270#124C2×C4×C1112yes—
271#124C23×C1112yes—
272#123—28no—
273#123—28no—
274C22⋊Q8—28no—
275C22⋊Q8—28no—
276#117—22no—
277#117C2×C4×C1114yes—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C42C2×C4×C1111yescharacteristic
285C2×C42C2×C4×C1111yescharacteristic
286#101—24no—
287#101—28no—
288#101C23×C1118yes—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—24no—
292C2×C11—82no—
293C2×C11#213312yesdirect product factor
294C2×C11C22×#9911yescharacteristic
295C24—21no—
296C24C11×C22⋊C411yescharacteristic
297#41—48no—
298#41—48no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—44no—
303C2×Q8—42no—
304C2×Q8—44no—
305C2×Q8—42no—
306C2×Q8—44no—
307C2×Q8—41no—
308C2×Q8—44no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8C11×C22⋊C414yes—
313C2×Q8C11×C22⋊C412yes—
314C2×Q8C22×C4×C1112yes—
315C2×Q8C22×C4×C1112yes—
316C2×Q8C22×C4×C1111yescharacteristic
317C2×Q8C2×D4×C1114yes—
318C2×Q8C2×D4×C1112yes—
319C2×Q8C24×C1111yescharacteristic
320C2×D4—24no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4C22×C4×C1112yes—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4C11×C22⋊C412yes—
339C22×C4C11×C22⋊C411yescharacteristic
340C22×C4C11×C22⋊C412yes—
341C22×C4C11×C22⋊C414yes—
342C22×C4C22×C4×C1111yescharacteristic
343C22×C4C22×C4×C1112yes—
344C22×C4C2×D4×C1112yes—
345C22×C4C2×D4×C1114yes—
346M16—28no—
347M16—44no—
348M16—48no—
349C2×C8—44no—
350C2×C8—48no—
351C4⋊C4—24no—
352C4⋊C4—28no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—28no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C42—21no—
360C42—21no—
361C42C22×C4×C1112yes—
362C42C22×C4×C1112yes—
363C11C2×#213311yescharacteristic, direct product factor, Sylow
364C23—22no—
365C23—42no—
366C23—44no—
367C23—41no—
368C23—41no—
369C23C11×#9912yes—
370C23C11×#9912yes—
371C23C2×C11×C22⋊C411yescharacteristic
372C23C2×C11×C22⋊C412yes—
373Q8—44no—
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—44no—
378Q8—42no—
379Q8—41no—
380Q8—42no—
381Q8—42no—
382D4—42no—
383D4—42no—
384D4—48no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—48no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4C2×C11×C22⋊C411yescharacteristic
408C2×C4C2×C11×C22⋊C414yes—
409C2×C4C2×C11×C22⋊C412yes—
410C2×C4C2×C11×C22⋊C412yes—
411C2×C4C23×C4×C1111yescharacteristic
412C2×C4C22×D4×C1112yes—
413C8—48no—
414C22—22no—
415C22—24no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22C2×C11×#9911yescharacteristic
423C22C2×C11×#9914yes—
424C22C2×C11×#9911yescharacteristic
425C22C22×C11×C22⋊C411yescharacteristic
426C4—22no—
427C4—22no—
428C4—21no—
429C4—24no—
430C4—22no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—42no—
435C2—21no—
436C2—21no—
437C2—24no—
438C2—82no—
439C2C11×#213312yesdirect product factor
440C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
prime radicalC22×C11×#41C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C23×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#101C2semidirect
3. C11×#2133C2direct (N × H)
4. C2×C11×#356C2semidirect
5. C2×C11×#355C2semidirect
22. C2×C11×#101C22semidirect
23. C11×#356C22semidirect
24. C11×#355C22semidirect
75. C2×#2133C11direct (N × H)
145. C22×#101C2×C11semidirect
146. #2133C2×C11direct (N × H)
147. C2×#356C2×C11semidirect
148. C2×#355C2×C11semidirect
215. C2×#101C22×C11semidirect
216. #356C22×C11semidirect
217. #355C22×C11semidirect
293. C2×C11#2133direct (N × H)
363. C11C2×#2133direct (N × H)
439. C2C11×#2133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C22×C11×#1012
C11×#21332
C2×C11×#3562
C2×C11×#3552
C2×#213311