Finite Group Databasebeta

← C11×#10978 #14588171

Subgroups — C11×#10978 #14588171

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×C11×#419C212yesmaximal
3C22×C11×#101C211yesmaximal, characteristic
4C11×#2310C211yesmaximal, characteristic
5C2×C11×#339C212yesmaximal
6C23×Q8×C11C2211yescharacteristic
7C23×Q8×C11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C2×C11×C4⋊Q8—24no—
10C2×C11×C4⋊Q8—22no—
11C2×C11×C4⋊Q8—24no—
12C2×C11×C4⋊Q8C414yescomplemented
13C2×C11×#117C2212yes—
14C22×C11×C4⋊C4—22no—
15C22×C42×C11C2211yescharacteristic
16C11×#419—24no—
17C11×#419—24no—
18C2×C11×#103—24no—
19C2×C11×#101—22no—
20C2×C11×#101—24no—
21C11×#391—24no—
22C11×#381—22no—
23C11×#339—24no—
24C22×Q8×C11—22no—
25C22×Q8×C11—21no—
26C22×Q8×C11—22no—
27C22×Q8×C11—22no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—22no—
33C22×Q8×C11—22no—
34C22×Q8×C11—22no—
35C22×Q8×C11—22no—
36C22×Q8×C11C2×C412yes—
37C22×Q8×C11C2×C412yes—
38C22×Q8×C11D414yes—
39C22×Q8×C11D412yes—
40C23×C4×C11—21no—
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×M16—22no—
45C2×C11×M16—22no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16D414yes—
50C22×C8×C11—22no—
51C11×C4⋊Q8—216no—
52C11×C4⋊Q8—28no—
53C11×C4⋊Q8—28no—
54C11×#117—22no—
55C11×#117—22no—
56C11×#117—22no—
57C11×#117—22no—
58C2×C11×C4⋊C4—216no—
59C2×C11×C4⋊C4—28no—
60C2×C11×C4⋊C4D414yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63C2×C42×C11—21no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C412yes—
66C2×C42×C11D414yes—
67C11×#103—216no—
68C11×#101—28no—
69C11×#95—28no—
70#10978C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—24no—
76C2×Q8×C11—24no—
77C2×Q8×C11—22no—
78C2×Q8×C11—24no—
79C2×Q8×C11—24no—
80C2×Q8×C11—24no—
81C2×Q8×C11—22no—
82C2×Q8×C11—24no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—24no—
86C2×Q8×C11—24no—
87C2×Q8×C11—24no—
88C2×Q8×C11—41no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—41no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C22⋊C414yes—
104C22×C4×C11—28no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—41no—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C11×M16—24no—
127C11×M16—24no—
128C11×M16—42no—
129C11×M16—42no—
130C2×C8×C11—24no—
131C2×C8×C11—42no—
132C2×C8×C11—42no—
133C11×C4⋊C4—232no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—42no—
138C42×C11—22no—
139C42×C11—24no—
140C42×C11—42no—
141C42×C11—42no—
142C42×C11C22⋊C414yes—
143C22×C4⋊Q8C2×C1111yescharacteristic
144C2×#419C2×C1112yes—
145C22×#101C2×C1111yescharacteristic
146#2310C2×C1111yescharacteristic
147C2×#339C2×C1112yes—
148C23×C11—24no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11#12012yes—
151C23×C11#12011yescharacteristic
152C23×C11#12112yes—
153C23×C11#12311yescharacteristic
154Q8×C11—28no—
155Q8×C11—44no—
156Q8×C11—44no—
157Q8×C11—44no—
158Q8×C11—44no—
159Q8×C11—44no—
160Q8×C11—44no—
161Q8×C11—44no—
162C2×C4×C11—28no—
163C2×C4×C11—216no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—48no—
177C2×C4×C11C2×C22⋊C411yescharacteristic
178C2×C4×C11C2×C22⋊C411yescharacteristic
179C2×C4×C11C4×D412yes—
180C2×C4×C11C4×D412yes—
181C2×C4×C11#12012yes—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12012yes—
184C2×C4×C11#12112yes—
185C2×C4×C11#12112yes—
186C2×C4×C11#12112yes—
187C2×C4×C11#12112yes—
188C2×C4×C11#12112yes—
189C2×C4×C11#12312yes—
190C2×C4×C11#12311yescharacteristic
191C2×C4×C11#12412yes—
192C2×C4×C11#12712yes—
193C8×C11—44no—
194C23×Q8C22×C1111yescharacteristic
195C23×Q8C22×C1111yescharacteristic
196C22×M16C22×C1112yes—
197C2×C4⋊Q8—24no—
198C2×C4⋊Q8—22no—
199C2×C4⋊Q8—24no—
200C2×C4⋊Q8C4×C1114yescomplemented
201C2×#117C22×C1112yes—
202C22×C4⋊C4—22no—
203C22×C42C22×C1111yescharacteristic
204#419—24no—
205#419—24no—
206C2×#103—24no—
207C2×#101—22no—
208C2×#101—24no—
209#391—24no—
210#381—22no—
211#339—24no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—24no—
215C22×C11—24no—
216C22×C11#37911yescharacteristic
217C22×C11#38611yescharacteristic
218C22×C11#38611yescharacteristic
219C22×C11#39212yes—
220C22×C11#39412yes—
221C22×C11#45614yes—
222C4×C11—28no—
223C4×C11—44no—
224C4×C11—44no—
225C4×C11—84no—
226C4×C11#38612yes—
227C4×C11#39012yes—
228C4×C11#39212yes—
229C4×C11#39412yes—
230C22×Q8—21no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8C2×C4×C1112yes—
243C22×Q8C2×C4×C1112yes—
244C22×Q8D4×C1114yes—
245C22×Q8D4×C1112yes—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4D4×C1112yes—
249C23×C4C23×C1111yescharacteristic
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16D4×C1114yes—
256C22×C8—22no—
257C4⋊Q8—216no—
258C4⋊Q8—28no—
259C4⋊Q8—28no—
260#117—22no—
261#117—22no—
262#117—22no—
263#117—22no—
264C2×C4⋊C4—216no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4D4×C1114yes—
267C2×C22⋊C4—22no—
268C2×C42—22no—
269C2×C42—21no—
270C2×C42—22no—
271C2×C42C2×C4×C1112yes—
272C2×C42D4×C1114yes—
273#103—216no—
274#101—28no—
275#95—28no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—22no—
279C2×C11#143811yescharacteristic
280C2×C11#188612yes—
281C2×C11#200514yes—
282C24C2×D4×C1111yescharacteristic
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8—22no—
289C2×Q8—24no—
290C2×Q8—24no—
291C2×Q8—24no—
292C2×Q8—22no—
293C2×Q8—24no—
294C2×Q8—24no—
295C2×Q8—24no—
296C2×Q8—24no—
297C2×Q8—24no—
298C2×Q8—24no—
299C2×Q8—41no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—42no—
306C2×Q8—42no—
307C2×Q8—42no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8C11×C22⋊C414yes—
315C22×C4—28no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—41no—
328C22×C4C11×C22⋊C414yes—
329C22×C4C22×C4×C1111yescharacteristic
330C22×C4C2×D4×C1112yes—
331C22×C4C2×D4×C1112yes—
332C22×C4C2×D4×C1112yes—
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C11×#4112yes—
336C22×C4C11×#4112yes—
337M16—24no—
338M16—24no—
339M16—42no—
340M16—42no—
341C2×C8—24no—
342C2×C8—42no—
343C2×C8—42no—
344C4⋊C4—232no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C42—22no—
350C42—24no—
351C42—42no—
352C42—42no—
353C42C11×C22⋊C414yes—
354C11#1097811yescharacteristic, direct product factor, Sylow
355C23—24no—
356C23C2×C11×C22⋊C411yescharacteristic
357C23C11×#12012yes—
358C23C11×#12011yescharacteristic
359C23C11×#12112yes—
360C23C11×#12311yescharacteristic
361Q8—28no—
362Q8—44no—
363Q8—44no—
364Q8—44no—
365Q8—44no—
366Q8—44no—
367Q8—44no—
368Q8—44no—
369C2×C4—28no—
370C2×C4—216no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—48no—
384C2×C4C2×C11×C22⋊C411yescharacteristic
385C2×C4C2×C11×C22⋊C411yescharacteristic
386C2×C4C4×D4×C1112yes—
387C2×C4C4×D4×C1112yes—
388C2×C4C11×#12012yes—
389C2×C4C11×#12011yescharacteristic
390C2×C4C11×#12012yes—
391C2×C4C11×#12112yes—
392C2×C4C11×#12112yes—
393C2×C4C11×#12112yes—
394C2×C4C11×#12112yes—
395C2×C4C11×#12112yes—
396C2×C4C11×#12312yes—
397C2×C4C11×#12311yescharacteristic
398C2×C4C11×#12412yes—
399C2×C4C11×#12712yes—
400C8—44no—
401C22—22no—
402C22—22no—
403C22—24no—
404C22—24no—
405C22C11×#37911yescharacteristic
406C22C11×#38611yescharacteristic
407C22C11×#38611yescharacteristic
408C22C11×#39212yes—
409C22C11×#39412yes—
410C22C11×#45614yes—
411C4—28no—
412C4—44no—
413C4—44no—
414C4—84no—
415C4C11×#38612yes—
416C4C11×#39012yes—
417C4C11×#39212yes—
418C4C11×#39412yes—
419C2—21no—
420C2—21no—
421C2—22no—
422C2C11×#143811yescharacteristic
423C2C11×#188612yes—
424C2C11×#200514yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
12. C2×C11×C4⋊Q8C4semidirect
70. #10978C11direct (N × H)
200. C2×C4⋊Q8C4×C11semidirect
354. C11#10978direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4192
C22×C11×#1012
C11×#23102
C2×C11×#3392
#1097811