Finite Group Databasebeta

← C11×#61379 #14638572

Subgroups — C11×#61379 #14638572

Order 2816.

1674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C212yesmaximal
2C11×#3390C218yesmaximal, complemented
3C11×#3387C218yesmaximal, complemented
4C11×#3163C212yesmaximal
5C11×#3162C211yesmaximal, characteristic
6C11×#3082C214yesmaximal
7C11×#3078C212yesmaximal
8C11×#2961C211yesmaximal, characteristic
9C11×#2950C212yesmaximal
10C2×C11×#441C211yesmaximal, characteristic
11C22×C11×Q16C2211yescharacteristic
12Q82×C11—22no—
13Q82×C11C2214yes—
14C11×#557—22no—
15C11×#557—24no—
16C11×#557C2218yes—
17C11×#557C2214yes—
18C11×#544—24no—
19C11×#544C2214yes—
20C11×#533—24no—
21C11×#533C2212yes—
22C11×#533C2211yescharacteristic
23C11×#519C2214yes—
24C2×C4×Q8×C11C2212yes—
25C11×#501C2214yes—
26C11×#501C2214yes—
27C11×#501C2218yes—
28C11×#499C2214yes—
29C11×#498C2214yes—
30C11×#479C2218yes—
31C11×#479C2218yes—
32C11×#479C2218yes—
33C11×#477C2214yes—
34C11×#477C2218yes—
35C11×#475C2214yes—
36C11×#475C2218yes—
37C11×#446C2218yes—
38C11×#441C2218yes—
39C11×#441C2214yes—
40C11×#441C2214yes—
41C4×C11×Q16C2218yes—
42C11×#428C2214yes—
43C11×#427C2212yes—
44C11×#427C2212yes—
45C2×C11×#106C2211yescharacteristic
46C11×#424C2212yes—
47C11×#423C2211yescharacteristic
48C11×#419C2214yes—
49C2×C11×#103C2212yes—
50C11×#405C2212yes—
51C2×C11×#97C2211yescharacteristic
52C22×Q8×C11C2312yes—
53C2×C11×Q16Q818yescomplemented
54C2×C11×Q16C2314yes—
55C2×C11×M16C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—28no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—28no—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8D412yes—
64C11×C4⋊Q8C2318yes—
65C11×C4⋊Q8C2312yes—
66C11×C4⋊Q8C2312yes—
67C11×#125—28no—
68C11×#125—28no—
69C11×#125—28no—
70C11×#125—24no—
71C11×#125D412yes—
72C11×#125C2318yes—
73C11×#125C2314yes—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8D414yes—
78C4×Q8×C11—24no—
79C4×Q8×C11—24no—
80C4×Q8×C11—24no—
81C4×Q8×C11—28no—
82C4×Q8×C11—24no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11C2314yes—
88C4×Q8×C11C2314yes—
89C4×Q8×C11C2318yes—
90C4×Q8×C11C2318yes—
91C4×Q8×C11C2314yes—
92C11×#117—28no—
93C11×#117C2314yes—
94C11×#117C2312yes—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4C2312yes—
97C2×C42×C11—22no—
98C2×C42×C11C2311yescharacteristic
99C11×#107C2318yes—
100C11×#107C2314yes—
101C11×#107C2314yes—
102C11×#106C2312yes—
103C11×#106C2314yes—
104C11×#106C2318yes—
105C11×#106C2312yes—
106C11×#106C2312yes—
107C11×#106C2312yes—
108C11×C4⋊C8C2314yes—
109C11×C4⋊C8C2318yes—
110C11×#103C2318yes—
111C11×#103C2318yes—
112C11×#103C2318yes—
113C11×#97C2314yes—
114C11×#97C2314yes—
115C4×C8×C11C2314yes—
116#61379C1111yesmaximal, characteristic, direct product factor, Sylow
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—24no—
122C2×Q8×C11C2×D414yes—
123C2×Q8×C11C2×Q818yes—
124C2×Q8×C11C2414yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C11×Q16C2×Q8116yes—
130C11×M16—24no—
131C2×C8×C11—22no—
132C2×C8×C11C2×Q814yes—
133C2×C8×C11C2414yes—
134C2×C8×C11C2412yes—
135C2×C8×C11C2412yes—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4C2×D414yes—
149C11×C4⋊C4C2×D418yes—
150C11×C4⋊C4C2×D414yes—
151C11×C4⋊C4C2414yes—
152C11×C4⋊C4C2414yes—
153C11×C4⋊C4C2414yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4C2×D414yes—
156C42×C11—24no—
157C42×C11—24no—
158C42×C11—28no—
159C42×C11—28no—
160C42×C11—24no—
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2414yes—
164C42×C11C2412yes—
165#3502C2×C1112yes—
166#3390C2×C1118yescomplemented
167#3387C2×C1118yescomplemented
168#3163C2×C1112yes—
169#3162C2×C1111yescharacteristic
170#3082C2×C1114yes—
171#3078C2×C1112yes—
172#2961C2×C1111yescharacteristic
173#2950C2×C1112yes—
174C2×#441C2×C1111yescharacteristic
175C23×C11C22×D411yescharacteristic
176Q8×C11—28no—
177Q8×C11—24no—
178Q8×C11—44no—
179Q8×C11—44no—
180Q8×C11—82no—
181Q8×C11—88no—
182Q8×C11C22×Q818yes—
183C2×C4×C11—28no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×D412yes—
192C2×C4×C11C22×D418yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q812yes—
195C2×C4×C112−1+412yes—
196C2×C4×C11C2511yescharacteristic
197C8×C11—22no—
198C8×C11—24no—
199C8×C11C22×Q814yes—
200C22×Q16C22×C1111yescharacteristic
201Q82—22no—
202Q82C22×C1114yes—
203#557—22no—
204#557—24no—
205#557C22×C1118yes—
206#557C22×C1114yes—
207#544—24no—
208#544C22×C1114yes—
209#533—24no—
210#533C22×C1112yes—
211#533C22×C1111yescharacteristic
212#519C22×C1114yes—
213C2×C4×Q8C22×C1112yes—
214#501C22×C1114yes—
215#501C22×C1118yes—
216#501C22×C1114yes—
217#499C22×C1114yes—
218#498C22×C1114yes—
219#479C22×C1118yes—
220#479C22×C1118yes—
221#479C22×C1118yes—
222#477C22×C1114yes—
223#477C22×C1118yes—
224#475C22×C1114yes—
225#475C22×C1118yes—
226#446C22×C1118yes—
227#441C22×C1114yes—
228#441C22×C1118yes—
229#441C22×C1114yes—
230C4×Q16C22×C1118yes—
231#428C22×C1114yes—
232#427C22×C1112yes—
233#427C22×C1112yes—
234C2×#106C22×C1111yescharacteristic
235#424C22×C1112yes—
236#423C22×C1111yescharacteristic
237#419C22×C1114yes—
238C2×#103C22×C1112yes—
239#405C22×C1112yes—
240C2×#97C22×C1111yescharacteristic
241C22×C11—22no—
242C22×C11D4×Q812yes—
243C22×C11C23×D411yescharacteristic
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—28no—
247C4×C11—28no—
248C4×C11—44no—
249C4×C11—44no—
250C4×C11—44no—
251C4×C11D4×Q812yes—
252C4×C11C23×Q811yescharacteristic
253C4×C11C2×2−1+411yescharacteristic
254C22×Q8C23×C1112yes—
255C2×Q16Q8×C1118yescomplemented
256C2×Q16C23×C1114yes—
257C2×M16C23×C1112yes—
258C22×C8C23×C1111yescharacteristic
259C22×C8C23×C1111yescharacteristic
260C4⋊Q8—24no—
261C4⋊Q8—28no—
262C4⋊Q8—24no—
263C4⋊Q8—28no—
264C4⋊Q8—24no—
265C4⋊Q8D4×C1112yes—
266C4⋊Q8C23×C1112yes—
267C4⋊Q8C23×C1112yes—
268C4⋊Q8C23×C1118yes—
269#125—28no—
270#125—28no—
271#125—28no—
272#125—24no—
273#125D4×C1112yes—
274#125C23×C1114yes—
275#125C23×C1118yes—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—28no—
279C22⋊Q8D4×C1114yes—
280C4×Q8—24no—
281C4×Q8—24no—
282C4×Q8—24no—
283C4×Q8—28no—
284C4×Q8—24no—
285C4×Q8—22no—
286C4×Q8—22no—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×Q8C23×C1114yes—
290C4×Q8C23×C1114yes—
291C4×Q8C23×C1118yes—
292C4×Q8C23×C1118yes—
293C4×Q8C23×C1114yes—
294#117—28no—
295#117C23×C1114yes—
296#117C23×C1112yes—
297C2×C4⋊C4—22no—
298C2×C4⋊C4C23×C1112yes—
299C2×C42—22no—
300C2×C42C23×C1111yescharacteristic
301#107C23×C1114yes—
302#107C23×C1114yes—
303#107C23×C1118yes—
304#106C23×C1114yes—
305#106C23×C1112yes—
306#106C23×C1112yes—
307#106C23×C1112yes—
308#106C23×C1112yes—
309#106C23×C1118yes—
310C4⋊C8C23×C1114yes—
311C4⋊C8C23×C1118yes—
312#103C23×C1118yes—
313#103C23×C1118yes—
314#103C23×C1118yes—
315#97C23×C1114yes—
316#97C23×C1114yes—
317C4×C8C23×C1114yes—
318C2×C11—22no—
319C2×C11C2×D4×Q811yescharacteristic
320C2×C11#358612yes—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—28no—
325C2×Q8—24no—
326C2×Q8C2×D4×C1114yes—
327C2×Q8C2×Q8×C1118yes—
328C2×Q8C24×C1114yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4C2×D4×C1112yes—
332C22×C4C24×C1111yescharacteristic
333Q16C2×Q8×C11116yes—
334M16—24no—
335C2×C8—22no—
336C2×C8C2×Q8×C1114yes—
337C2×C8C24×C1114yes—
338C2×C8C24×C1112yes—
339C2×C8C24×C1112yes—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—22no—
343C4⋊C4—28no—
344C4⋊C4—28no—
345C4⋊C4—24no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—28no—
349C4⋊C4—28no—
350C4⋊C4—24no—
351C4⋊C4—28no—
352C4⋊C4C2×D4×C1114yes—
353C4⋊C4C2×D4×C1118yes—
354C4⋊C4C2×D4×C1114yes—
355C4⋊C4C24×C1114yes—
356C4⋊C4C24×C1114yes—
357C4⋊C4C24×C1114yes—
358C22⋊C4—24no—
359C22⋊C4C2×D4×C1114yes—
360C42—24no—
361C42—24no—
362C42—28no—
363C42—28no—
364C42—24no—
365C42C2×D4×C1111yescharacteristic
366C42C2×D4×C1111yescharacteristic
367C42C24×C1114yes—
368C42C24×C1112yes—
369C11#6137911yescharacteristic, direct product factor, Sylow
370C23C22×D4×C1111yescharacteristic
371Q8—28no—
372Q8—24no—
373Q8—44no—
374Q8—44no—
375Q8—82no—
376Q8—88no—
377Q8C22×Q8×C1118yes—
378C2×C4—28no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4C22×D4×C1112yes—
386C2×C4C22×D4×C1112yes—
387C2×C4C22×D4×C1118yes—
388C2×C4C22×D4×C1111yescharacteristic
389C2×C4C22×Q8×C1112yes—
390C2×C4C11×2−1+412yes—
391C2×C4C25×C1111yescharacteristic
392C8—22no—
393C8—24no—
394C8C22×Q8×C1114yes—
395C22—22no—
396C22D4×Q8×C1112yes—
397C22C23×D4×C1111yescharacteristic
398C4—28no—
399C4—22no—
400C4—22no—
401C4—28no—
402C4—44no—
403C4—44no—
404C4—44no—
405C4D4×Q8×C1112yes—
406C4C23×Q8×C1111yescharacteristic
407C4C2×C11×2−1+411yescharacteristic
408C2—22no—
409C2C2×D4×Q8×C1111yescharacteristic
410C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC23×C11C22×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3390C2semidirect
3. C11×#3387C2semidirect
53. C2×C11×Q16Q8semidirect
116. #61379C11direct (N × H)
166. #3390C2×C11semidirect
167. #3387C2×C11semidirect
255. C2×Q16Q8×C11semidirect
369. C11#61379direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#33902
C11×#33872
C11×#31632
C11×#31622
C11×#30822
C11×#30782
C11×#29612
C11×#29502
C2×C11×#4412
#6137911