Finite Group Databasebeta

← C11×#19085 #14596278

Subgroups — C11×#19085 #14596278

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3553C211yesmaximal, characteristic
2C11×#3181C212yesmaximal, complemented
3C11×#3166C211yesmaximal, characteristic, complemented
4C11×#1664C212yesmaximal, complemented
5C11×#1663C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1660C212yesmaximal, complemented
8C11×#1524C212yesmaximal, complemented
9C2×C11×#330C211yesmaximal, characteristic, complemented
10C11×#564C2211yescharacteristic
11C11×#563C2212yes—
12C11×#562C2211yescharacteristic
13C11×#554—22no—
14C11×#553—22no—
15C11×#552—22no—
16C11×#541—22no—
17C11×#539—22no—
18C11×#539—22no—
19C11×#533C2211yescharacteristic
20C11×#529C2212yes—
21C2×C11×#125C2211yescharacteristic
22C11×#501C2212yes—
23C11×#501C2212yes—
24C11×#501C2212yes—
25C11×#499—22no—
26C11×#497C2212yes—
27C11×#491C2212yes—
28C11×#489C2212yes—
29C11×#467—22no—
30C11×#465—22no—
31C11×#441—22no—
32C11×#440—22no—
33C11×#428—22no—
34C4×C11×M16C2211yescharacteristic
35C2×C11×#97C2212yes—
36C11×#330C2211yescharacteristic
37C11×#330C2212yes—
38C11×#330C2212yes—
39C11×#330C2212yes—
40C11×#330C2211yescharacteristic
41C11×#329C2212yes—
42C11×#329C2212yes—
43C2×C11×Q16—22no—
44C2×C11×SD16—22no—
45C2×C11×M16—21no—
46C22×C8×C11—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2312yes—
49C11×#126—22no—
50C11×#126—22no—
51C11×#126—22no—
52C11×#126—22no—
53C11×#126—22no—
54C11×#125—22no—
55C11×#125—22no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—21no—
61C11×#125D412yes—
62C11×#125C2312yes—
63C11×#125C2311yescharacteristic
64C11×#125C2311yescharacteristic
65C11×#124C2312yes—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8D412yes—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121D412yes—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11D412yes—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11D412yes—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4D412yes—
96C2×C42×C11C2311yescharacteristic
97C11×#107—22no—
98C11×#107—22no—
99C11×#107—22no—
100C11×#106—22no—
101C11×#106—22no—
102C11×#106—22no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#102—22no—
107C11×#97—22no—
108C11×#97C2312yes—
109C11×#97C2312yes—
110C11×#97C2312yes—
111C4×C8×C11—21no—
112#19085C1111yesmaximal, characteristic, direct product factor, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C11×Q16—44no—
126C11×SD16—44no—
127C11×M16—24no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—44no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—41no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—41no—
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D412yes—
170C42×C11C2411yescharacteristic
171#3553C2×C1111yescharacteristic
172#3181C2×C1112yescomplemented
173#3166C2×C1111yescharacteristic, complemented
174#1664C2×C1112yescomplemented
175#1663C2×C1112yescomplemented
176#1661C2×C1112yescomplemented
177#1660C2×C1112yescomplemented
178#1524C2×C1112yescomplemented
179C2×#330C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11#12011yescharacteristic
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—42no—
185Q8×C11—82no—
186D4×C11—42no—
187D4×C11—44no—
188D4×C11—82no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—82no—
198C2×C4×C11—82no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11#12012yes—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D412yes—
205C8×C11—24no—
206C8×C11—24no—
207C8×C11—42no—
208#564C22×C1111yescharacteristic
209#563C22×C1112yes—
210#562C22×C1111yescharacteristic
211#554—22no—
212#553—22no—
213#552—22no—
214#541—22no—
215#539—22no—
216#539—22no—
217#533C22×C1111yescharacteristic
218#529C22×C1112yes—
219C2×#125C22×C1111yescharacteristic
220#501C22×C1112yes—
221#501C22×C1112yes—
222#501C22×C1112yes—
223#499—22no—
224#497C22×C1112yes—
225#491C22×C1112yes—
226#489C22×C1112yes—
227#467—22no—
228#465—22no—
229#441—22no—
230#440—22no—
231#428—22no—
232C4×M16C22×C1111yescharacteristic
233C2×#97C22×C1112yes—
234#330C22×C1111yescharacteristic
235#330C22×C1112yes—
236#330C22×C1112yes—
237#330C22×C1112yes—
238#330C22×C1111yescharacteristic
239#329C22×C1112yes—
240#329C22×C1112yes—
241C22×C11—22no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11#45612yes—
246C22×C11C2×#12011yescharacteristic
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C2×Q16—22no—
258C2×SD16—22no—
259C2×M16—21no—
260C22×C8—22no—
261C4⋊Q8—22no—
262C4⋊Q8C23×C1112yes—
263#126—22no—
264#126—22no—
265#126—22no—
266#126—22no—
267#126—22no—
268#125—22no—
269#125—22no—
270#125—22no—
271#125—22no—
272#125—22no—
273#125—22no—
274#125—21no—
275#125D4×C1112yes—
276#125C23×C1111yescharacteristic
277#125C23×C1111yescharacteristic
278#125C23×C1112yes—
279#124C23×C1112yes—
280#123—22no—
281#123—22no—
282#123—22no—
283#123—22no—
284#123—22no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8D4×C1112yes—
293#121—22no—
294#121—22no—
295#121D4×C1112yes—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8D4×C1112yes—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4D4×C1112yes—
304#117—22no—
305#117—22no—
306#117—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4D4×C1112yes—
310C2×C42C23×C1111yescharacteristic
311#107—22no—
312#107—22no—
313#107—22no—
314#106—22no—
315#106—22no—
316#106—22no—
317#103—22no—
318#103—22no—
319#103—22no—
320#102—22no—
321#97—22no—
322#97C23×C1112yes—
323#97C23×C1112yes—
324#97C23×C1112yes—
325C4×C8—21no—
326C2×C11—22no—
327C2×C11—82no—
328C2×C11C2×#45611yescharacteristic
329C2×C11#301812yes—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8C2×D4×C1112yes—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4C2×D4×C1112yes—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C2×D4×C1112yes—
342Q16—44no—
343SD16—44no—
344M16—24no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—44no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4C2×D4×C1112yes—
368C4⋊C4C2×D4×C1112yes—
369C4⋊C4C2×D4×C1112yes—
370C4⋊C4C2×D4×C1112yes—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C42—22no—
382C42—22no—
383C42—22no—
384C42—41no—
385C42C2×D4×C1111yescharacteristic
386C42C2×D4×C1112yes—
387C42C24×C1111yescharacteristic
388C11#1908511yescharacteristic, direct product factor, Sylow
389C23—22no—
390C23C11×#12011yescharacteristic
391Q8—42no—
392Q8—42no—
393Q8—42no—
394Q8—82no—
395D4—42no—
396D4—44no—
397D4—82no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4C11×#12012yes—
411C2×C4C11×#12011yescharacteristic
412C2×C4C22×D4×C1111yescharacteristic
413C2×C4C22×D4×C1112yes—
414C8—24no—
415C8—24no—
416C8—42no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22C11×#45612yes—
422C22C2×C11×#12011yescharacteristic
423C4—21no—
424C4—21no—
425C4—22no—
426C4—22no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—82no—
433C2—22no—
434C2—82no—
435C2C2×C11×#45611yescharacteristic
436C2C11×#301812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3553C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3181C2semidirect
3. C11×#3166C2semidirect
4. C11×#1664C2semidirect
5. C11×#1663C2semidirect
6. C11×#1661C2semidirect
7. C11×#1660C2semidirect
8. C11×#1524C2semidirect
9. C2×C11×#330C2semidirect
112. #19085C11direct (N × H)
172. #3181C2×C11semidirect
173. #3166C2×C11semidirect
174. #1664C2×C11semidirect
175. #1663C2×C11semidirect
176. #1661C2×C11semidirect
177. #1660C2×C11semidirect
178. #1524C2×C11semidirect
179. C2×#330C2×C11semidirect
388. C11#19085direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35532
C11×#31812
C11×#31662
C11×#16642
C11×#16632
C11×#16612
C11×#16602
C11×#15242
C2×C11×#3302
#1908511