Finite Group Databasebeta

← C11×#60175 #14637368

Subgroups — C11×#60175 #14637368

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic
2C4×C11×2−1+4C212yesmaximal, complemented
3C11×#2952C213yesmaximal, complemented
4C11×#2950C213yesmaximal, complemented
5C11×#2947C216yesmaximal, complemented
6C4×C11×#137C216yesmaximal, complemented
7C11×#2943C213yesmaximal, complemented
8C2×C11×#441C213yesmaximal, complemented
9C11×#2912C211yesmaximal, characteristic, complemented
10C11×#2898C212yesmaximal, complemented
11C11×#2875C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yes—
13C11×#578C4116yescomplemented
14C2×C11×#137C2216yes—
15C2×C11×#135C2213yes—
16C22×C11×Q16C2213yes—
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C11×#520—26no—
20C11×#520C2216yes—
21C11×#520C2212yes—
22C11×#519—22no—
23C11×#519C2216yes—
24C4×C11×#41—26no—
25C4×C11×#41C2216yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×Q8×C11—22no—
28C2×C4×Q8×C11C2216yes—
29C11×#442C2211yescharacteristic
30C11×#442C2213yes—
31C11×#441C2213yes—
32C11×#441C2216yes—
33C11×#441C2216yes—
34C11×#441C2216yes—
35C11×#441C2213yes—
36C11×#440C2216yes—
37C11×#440C2216yes—
38C4×C11×Q16C22112yes—
39C4×C11×SD16C22112yes—
40C11×#428C2216yes—
41C11×#427C2213yes—
42C2×C11×#106C2213yes—
43C11×#419C2216yes—
44C11×#417C2216yes—
45C11×#416C2216yes—
46C2×C11×#103C2216yes—
47C11×#405C2213yes—
48C11×#405C2213yes—
49C4×C11×M16C2213yes—
50C2×C11×#97C2213yes—
51C11×2−1+4—28no—
52C11×2−1+4C2×C4116yescomplemented
53C2×C11×#41—26no—
54C2×C11×#41C2316yes—
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11—22no—
57C22×Q8×C11C2316yes—
58C11×#137C2×C4148yescomplemented
59C11×#135C2×C4124yescomplemented
60C2×C11×Q16C2×C4124yescomplemented
61C2×C11×Q16C2313yes—
62C2×C11×Q16C2316yes—
63C2×C11×SD16C2316yes—
64C2×C11×D8C2311yescharacteristic
65C11×#131—24no—
66C11×#131C2×C418yescomplemented
67C2×C11×M16C2313yes—
68C2×C11×M16C2313yes—
69C22×C8×C11C2313yes—
70C22×C8×C11C2313yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—26no—
73C4×Q8×C11—26no—
74C4×Q8×C11—26no—
75C4×Q8×C11—26no—
76C4×Q8×C11D412yes—
77C4×Q8×C11C2316yes—
78C4×Q8×C11C23112yes—
79C4×Q8×C11C2316yes—
80C4×D4×C11—26no—
81C4×D4×C11—26no—
82C4×D4×C11—26no—
83C4×D4×C11—212no—
84C4×D4×C11D416yes—
85C4×D4×C11C2312yes—
86C4×D4×C11C2316yes—
87C11×#117—26no—
88C11×#117—212no—
89C11×#117—26no—
90C11×#117C2316yes—
91C11×#117C2313yes—
92C2×C11×C4⋊C4—26no—
93C2×C11×C4⋊C4—26no—
94C2×C11×C4⋊C4C2316yes—
95C2×C42×C11—26no—
96C2×C42×C11—26no—
97C2×C42×C11C2313yes—
98C11×#107C2316yes—
99C11×#106C2313yes—
100C11×#106C2316yes—
101C11×#106C2311yescharacteristic
102C11×#103C2316yes—
103C11×#103C23112yes—
104C11×#103C2316yes—
105C11×#102C2312yes—
106C11×#102C2316yes—
107C11×#97C2311yescharacteristic
108C11×#97C2313yes—
109C11×#97C2313yes—
110C11×#97C2313yes—
111C4×C8×C11C2316yes—
112#60175C1111yesmaximal, characteristic, direct product factor, Sylow
113C11×#41—248no—
114C11×#41—212no—
115C11×#41C22×C4124yes—
116C11×#41C22×C414yes—
117C11×#41#4114yes—
118C2×Q8×C11—216no—
119C2×Q8×C11—26no—
120C2×Q8×C11—212no—
121C2×Q8×C11C22×C4124yes—
122C2×Q8×C11C2×D411yescharacteristic
123C2×Q8×C11C2416yes—
124C2×D4×C11—26no—
125C2×D4×C11C2×D413yes—
126C2×D4×C11C2412yes—
127C22×C4×C11—26no—
128C22×C4×C11—26no—
129C22×C4×C11—26no—
130C22×C4×C11—22no—
131C22×C4×C11—26no—
132C22×C4×C11C2×D416yes—
133C22×C4×C11C2413yes—
134C11×Q16C22×C4112yes—
135C11×Q16C22×C4124yes—
136C11×SD16C22×C4124yes—
137C11×D8C22×C414yes—
138C11×M16—26no—
139C11×M16C22×C4112yes—
140C2×C8×C11—26no—
141C2×C8×C11C22×C4112yes—
142C2×C8×C11C2413yes—
143C2×C8×C11C2411yescharacteristic
144C2×C8×C11C2413yes—
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—26no—
147C11×C4⋊C4—212no—
148C11×C4⋊C4—26no—
149C11×C4⋊C4—26no—
150C11×C4⋊C4C2×D416yes—
151C11×C4⋊C4C2416yes—
152C11×C4⋊C4C2412yes—
153C11×C22⋊C4—26no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—26no—
156C11×C22⋊C4C2×D416yes—
157C42×C11—26no—
158C42×C11—26no—
159C42×C11—212no—
160C42×C11—26no—
161C42×C11C2×D416yes—
162C42×C11C2413yes—
163C42×C11C2411yescharacteristic
164C2×#578C2×C1111yescharacteristic
165C4×2−1+4C2×C1112yescomplemented
166#2952C2×C1113yescomplemented
167#2950C2×C1113yescomplemented
168#2947C2×C1116yescomplemented
169C4×#137C2×C1116yescomplemented
170#2943C2×C1113yescomplemented
171C2×#441C2×C1113yescomplemented
172#2912C2×C1111yescharacteristic, complemented
173#2898C2×C1112yescomplemented
174#2875C2×C1111yescharacteristic, complemented
175C23×C11—22no—
176C23×C11C22×D413yes—
177Q8×C11—224no—
178Q8×C11—26no—
179Q8×C11C4×D414yes—
180Q8×C11C23×C4112yes—
181D4×C11—224no—
182D4×C11—22no—
183D4×C11C4×D4112yes—
184D4×C11C23×C414yes—
185C2×C4×C11—224no—
186C2×C4×C11—26no—
187C2×C4×C11—224no—
188C2×C4×C11—22no—
189C2×C4×C11—26no—
190C2×C4×C11—46no—
191C2×C4×C11—44no—
192C2×C4×C11—86no—
193C2×C4×C11—86no—
194C2×C4×C11C23×C416yes—
195C2×C4×C11C22×D412yes—
196C2×C4×C11C22×D416yes—
197C2×C4×C11C22×D413yes—
198C2×C4×C11C2×#4116yes—
199C2×C4×C11C2511yescharacteristic
200C8×C11—21no—
201C8×C11—23no—
202C8×C11C23×C412yes—
203C8×C11C23×C416yes—
204C2×2−1+4C22×C1112yes—
205#578C4×C11116yescomplemented
206C2×#137C22×C1116yes—
207C2×#135C22×C1113yes—
208C22×Q16C22×C1113yes—
209C2×#131C22×C1111yescharacteristic
210C2×#131C22×C1111yescharacteristic
211#520—26no—
212#520C22×C1116yes—
213#520C22×C1112yes—
214#519—22no—
215#519C22×C1116yes—
216C4×#41—26no—
217C4×#41C22×C1116yes—
218C4×#41C22×C1111yescharacteristic
219C2×C4×Q8—22no—
220C2×C4×Q8C22×C1116yes—
221#442C22×C1111yescharacteristic
222#442C22×C1113yes—
223#441C22×C1113yes—
224#441C22×C1116yes—
225#441C22×C1116yes—
226#441C22×C1116yes—
227#441C22×C1113yes—
228#440C22×C1116yes—
229#440C22×C1116yes—
230C4×Q16C22×C11112yes—
231C4×SD16C22×C11112yes—
232#428C22×C1116yes—
233#427C22×C1113yes—
234C2×#106C22×C1113yes—
235#419C22×C1116yes—
236#417C22×C1116yes—
237#416C22×C1116yes—
238C2×#103C22×C1116yes—
239#405C22×C1113yes—
240#405C22×C1113yes—
241C4×M16C22×C1113yes—
242C2×#97C22×C1113yes—
243C22×C11—26no—
244C22×C11—24no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11C2×C4×D416yes—
248C22×C11C23×D411yescharacteristic
249C4×C11—22no—
250C4×C11—26no—
251C4×C11—212no—
252C4×C11—42no—
253C4×C11—46no—
254C4×C11C2×C4×D416yes—
255C4×C11C24×C411yescharacteristic
256C4×C11C22×#4111yescharacteristic
2572−1+4—28no—
2582−1+4C2×C4×C11116yescomplemented
259C2×#41—26no—
260C2×#41C23×C1116yes—
261C2×#41C23×C1111yescharacteristic
262C22×Q8—22no—
263C22×Q8C23×C1116yes—
264#137C2×C4×C11148yescomplemented
265#135C2×C4×C11124yescomplemented
266C2×Q16C2×C4×C11124yescomplemented
267C2×Q16C23×C1113yes—
268C2×Q16C23×C1116yes—
269C2×SD16C23×C1116yes—
270C2×D8C23×C1111yescharacteristic
271#131—24no—
272#131C2×C4×C1118yescomplemented
273C2×M16C23×C1113yes—
274C2×M16C23×C1113yes—
275C22×C8C23×C1113yes—
276C22×C8C23×C1113yes—
277C4×Q8—22no—
278C4×Q8—26no—
279C4×Q8—26no—
280C4×Q8—26no—
281C4×Q8—26no—
282C4×Q8D4×C1112yes—
283C4×Q8C23×C1116yes—
284C4×Q8C23×C11112yes—
285C4×Q8C23×C1116yes—
286C4×D4—26no—
287C4×D4—26no—
288C4×D4—26no—
289C4×D4—212no—
290C4×D4D4×C1116yes—
291C4×D4C23×C1112yes—
292C4×D4C23×C1116yes—
293#117—26no—
294#117—212no—
295#117—26no—
296#117C23×C1116yes—
297#117C23×C1113yes—
298C2×C4⋊C4—26no—
299C2×C4⋊C4—26no—
300C2×C4⋊C4C23×C1116yes—
301C2×C42—26no—
302C2×C42—26no—
303C2×C42C23×C1113yes—
304#107C23×C1116yes—
305#106C23×C1113yes—
306#106C23×C1116yes—
307#106C23×C1111yescharacteristic
308#103C23×C1116yes—
309#103C23×C11112yes—
310#103C23×C1116yes—
311#102C23×C1112yes—
312#102C23×C1116yes—
313#97C23×C1111yescharacteristic
314#97C23×C1113yes—
315#97C23×C1113yes—
316#97C23×C1113yes—
317C4×C8C23×C1116yes—
318C2×C11—26no—
319C2×C11—44no—
320C2×C11C22×C4×D411yescharacteristic
321C2×C11#358612yes—
322#41—248no—
323#41—212no—
324#41C22×C4×C11124yes—
325#41C22×C4×C1114yes—
326#41C11×#4114yes—
327C2×Q8—216no—
328C2×Q8—26no—
329C2×Q8—212no—
330C2×Q8C22×C4×C11124yes—
331C2×Q8C2×D4×C1111yescharacteristic
332C2×Q8C24×C1116yes—
333C2×D4—26no—
334C2×D4C2×D4×C1113yes—
335C2×D4C24×C1112yes—
336C22×C4—26no—
337C22×C4—26no—
338C22×C4—26no—
339C22×C4—22no—
340C22×C4—26no—
341C22×C4C2×D4×C1116yes—
342C22×C4C24×C1113yes—
343Q16C22×C4×C11112yes—
344Q16C22×C4×C11124yes—
345SD16C22×C4×C11124yes—
346D8C22×C4×C1114yes—
347M16—26no—
348M16C22×C4×C11112yes—
349C2×C8—26no—
350C2×C8C22×C4×C11112yes—
351C2×C8C24×C1113yes—
352C2×C8C24×C1111yescharacteristic
353C2×C8C24×C1113yes—
354C2×C8C24×C1111yescharacteristic
355C4⋊C4—26no—
356C4⋊C4—212no—
357C4⋊C4—26no—
358C4⋊C4—26no—
359C4⋊C4C2×D4×C1116yes—
360C4⋊C4C24×C1116yes—
361C4⋊C4C24×C1112yes—
362C22⋊C4—26no—
363C22⋊C4—22no—
364C22⋊C4—26no—
365C22⋊C4C2×D4×C1116yes—
366C42—26no—
367C42—26no—
368C42—212no—
369C42—26no—
370C42C2×D4×C1116yes—
371C42C24×C1113yes—
372C42C24×C1111yescharacteristic
373C11#6017511yescharacteristic, direct product factor, Sylow
374C23—22no—
375C23C22×D4×C1113yes—
376Q8—224no—
377Q8—26no—
378Q8C4×D4×C1114yes—
379Q8C23×C4×C11112yes—
380D4—224no—
381D4—22no—
382D4C4×D4×C11112yes—
383D4C23×C4×C1114yes—
384C2×C4—224no—
385C2×C4—26no—
386C2×C4—224no—
387C2×C4—22no—
388C2×C4—26no—
389C2×C4—46no—
390C2×C4—44no—
391C2×C4—86no—
392C2×C4—86no—
393C2×C4C23×C4×C1116yes—
394C2×C4C22×D4×C1112yes—
395C2×C4C22×D4×C1116yes—
396C2×C4C22×D4×C1113yes—
397C2×C4C2×C11×#4116yes—
398C2×C4C25×C1111yescharacteristic
399C8—21no—
400C8—23no—
401C8C23×C4×C1112yes—
402C8C23×C4×C1116yes—
403C22—26no—
404C22—24no—
405C22—42no—
406C22—42no—
407C22C2×C4×D4×C1116yes—
408C22C23×D4×C1111yescharacteristic
409C4—212no—
410C4—22no—
411C4—26no—
412C4—42no—
413C4—46no—
414C4C2×C4×D4×C1116yes—
415C4C24×C4×C1111yescharacteristic
416C4C22×C11×#4111yescharacteristic
417C2—26no—
418C2—44no—
419C2C22×C4×D4×C1111yescharacteristic
420C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#578C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×2−1+4C2semidirect
3. C11×#2952C2semidirect
4. C11×#2950C2semidirect
5. C11×#2947C2semidirect
6. C4×C11×#137C2semidirect
7. C11×#2943C2semidirect
8. C2×C11×#441C2semidirect
9. C11×#2912C2semidirect
10. C11×#2898C2semidirect
11. C11×#2875C2semidirect
13. C11×#578C4semidirect
52. C11×2−1+4C2×C4semidirect
58. C11×#137C2×C4semidirect
59. C11×#135C2×C4semidirect
60. C2×C11×Q16C2×C4semidirect
66. C11×#131C2×C4semidirect
112. #60175C11direct (N × H)
165. C4×2−1+4C2×C11semidirect
166. #2952C2×C11semidirect
167. #2950C2×C11semidirect
168. #2947C2×C11semidirect
169. C4×#137C2×C11semidirect
170. #2943C2×C11semidirect
171. C2×#441C2×C11semidirect
172. #2912C2×C11semidirect
173. #2898C2×C11semidirect
174. #2875C2×C11semidirect
205. #578C4×C11semidirect
258. 2−1+4C2×C4×C11semidirect
264. #137C2×C4×C11semidirect
265. #135C2×C4×C11semidirect
266. C2×Q16C2×C4×C11semidirect
272. #131C2×C4×C11semidirect
373. C11#60175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C4×C11×2−1+42
C11×#29522
C11×#29502
C11×#29472
C4×C11×#1372
C11×#29432
C2×C11×#4412
C11×#29122
C11×#28982
C11×#28752
#6017511