Finite Group Databasebeta

← C2×C11×#1702 #14596346

Subgroups — C2×C11×#1702 #14596346

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C2×C11×#446C211yesmaximal, characteristic, complemented
5C11×#1702C218yesmaximal, direct product factor
6C2×C11×#334C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×#331C211yesmaximal, characteristic
9C22×C11×Q16—21no—
10C22×C11×SD16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C11×#486—22no—
15C11×#486C2214yes—
16C11×#462—22no—
17C11×#462C2214yescomplemented
18C11×#460—22no—
19C11×#460C2214yes—
20C11×#446—22no—
21C11×#446C2214yescomplemented
22C2×C11×C4⋊C8—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27C2×C11×#102—21no—
28C2×C11×#102—21no—
29C2×C11×#102—21no—
30C2×C11×#97—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#334C2214yescomplemented
33C11×#332C2214yescomplemented
34C11×#331C2214yes—
35C22×Q8×C11—21no—
36C22×Q8×C11D411yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C2×C11×Q16—24no—
41C2×C11×Q16—44no—
42C2×C11×SD16—24no—
43C2×C11×SD16—44no—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8C2312yes—
53C11×#127—21no—
54C11×#127—21no—
55C11×#127—21no—
56C11×#127C2312yes—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11D412yes—
60C4×Q8×C11C2312yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C11×C4⋊C8—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×#103—24no—
75C11×#102—24no—
76C11×#102—24no—
77C11×#102—24no—
78C11×#97—24no—
79C4×C8×C11D412yes—
80C4×C8×C11C2312yes—
81C2×#1702C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11C2×D412yes—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—82no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C11×Q16—48no—
109C11×SD16—48no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C2×C8×C11—42no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×D412yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4C2×D412yes—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C2×#486C2×C1111yescharacteristic
135C2×#462C2×C1111yescharacteristic, complemented
136C2×#460C2×C1111yescharacteristic
137C2×#446C2×C1111yescharacteristic, complemented
138#1702C2×C1118yesdirect product factor
139C2×#334C2×C1111yescharacteristic, complemented
140C2×#332C2×C1111yescharacteristic, complemented
141C2×#331C2×C1111yescharacteristic
142C23×C11—42no—
143C23×C11—82no—
144C23×C11—82no—
145C23×C11—82no—
146C23×C11#12111yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—82no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—82no—
160D4×C11—82no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—82no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#13512yes—
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11#13712yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C8×C11—22no—
179C8×C11—22no—
180C8×C11—42no—
181C8×C11—42no—
182C8×C11—42no—
183C22×Q16—21no—
184C22×SD16—21no—
185C2×C4⋊Q8C22×C1111yescharacteristic
186C2×#127C22×C1111yescharacteristic
187C2×C4×Q8C22×C1111yescharacteristic
188#486—22no—
189#486C22×C1114yes—
190#462—22no—
191#462C22×C1114yescomplemented
192#460—22no—
193#460C22×C1114yes—
194#446—22no—
195#446C22×C1114yescomplemented
196C2×C4⋊C8—21no—
197C2×C4⋊C8C22×C1111yescharacteristic
198C2×C4⋊C8C22×C1111yescharacteristic
199C2×C4⋊C8C22×C1111yescharacteristic
200C2×#103—21no—
201C2×#102—21no—
202C2×#102—21no—
203C2×#102—21no—
204C2×#97—21no—
205C2×C4×C8C22×C1111yescharacteristic
206#334C22×C1114yescomplemented
207#332C22×C1114yescomplemented
208#331C22×C1114yes—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—164no—
213C22×C11#46412yes—
214C22×C11#46912yes—
215C22×C11#47112yes—
216C22×C11C2×#12111yescharacteristic
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—42no—
221C4×C11—82no—
222C4×C11#46412yes—
223C4×C11#46912yes—
224C4×C11C2×#13511yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11C2×#13711yescharacteristic
228C22×Q8—21no—
229C22×Q8D4×C1111yescharacteristic
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C2×Q16—24no—
234C2×Q16—44no—
235C2×SD16—24no—
236C2×SD16—44no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8D4×C1111yescharacteristic
241C22×C8D4×C1111yescharacteristic
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C23×C1112yes—
246#127—21no—
247#127—21no—
248#127—21no—
249#127C23×C1112yes—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D4×C1112yes—
253C4×Q8C23×C1112yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C1111yescharacteristic
258C2×C42—21no—
259C2×C42C23×C1111yescharacteristic
260C4⋊C8—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8C23×C1112yes—
265C4⋊C8C23×C1112yes—
266C4⋊C8C23×C1112yes—
267#103—24no—
268#102—24no—
269#102—24no—
270#102—24no—
271#97—24no—
272C4×C8D4×C1112yes—
273C4×C8C23×C1112yes—
274C2×C11—162no—
275C2×C11#170214yesdirect product factor
276C2×C11C2×#46411yescharacteristic
277C2×C11C2×#46911yescharacteristic
278C2×C11C2×#47111yescharacteristic
279C24—41no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8C2×D4×C1112yes—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—82no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C11×#4111yescharacteristic
305Q16—48no—
306SD16—48no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8C2×D4×C1112yes—
316C2×C8C2×D4×C1112yes—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C2×D4×C1112yes—
325C42—22no—
326C42—22no—
327C42C2×D4×C1111yescharacteristic
328C42C2×D4×C1111yescharacteristic
329C42C11×#4111yescharacteristic
330C42C24×C1111yescharacteristic
331C11C2×#170211yescharacteristic, direct product factor, Sylow
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23C11×#12111yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—82no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—82no—
349D4—82no—
350D4—82no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4C11×#12111yescharacteristic
359C2×C4C11×#12111yescharacteristic
360C2×C4C11×#12111yescharacteristic
361C2×C4C11×#13512yes—
362C2×C4C11×AGL(1,ℤ/8)12yes—
363C2×C4C11×AGL(1,ℤ/8)12yes—
364C2×C4C11×#13712yes—
365C2×C4C22×D4×C1111yescharacteristic
366C2×C4C22×D4×C1111yescharacteristic
367C2×C4C2×C11×#4111yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—42no—
372C8—42no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22C11×#46412yes—
378C22C11×#46912yes—
379C22C11×#47112yes—
380C22C2×C11×#12111yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4C11×#46412yes—
387C4C11×#46912yes—
388C4C2×C11×#13511yescharacteristic
389C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
390C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
391C4C2×C11×#13711yescharacteristic
392C2—162no—
393C2C11×#170214yesdirect product factor
394C2C2×C11×#46411yescharacteristic
395C2C2×C11×#46911yescharacteristic
396C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
4. C2×C11×#446C2semidirect
5. C11×#1702C2direct (N × H)
6. C2×C11×#334C2semidirect
7. C2×C11×#332C2semidirect
17. C11×#462C22semidirect
21. C11×#446C22semidirect
32. C11×#334C22semidirect
33. C11×#332C22semidirect
81. C2×#1702C11direct (N × H)
135. C2×#462C2×C11semidirect
137. C2×#446C2×C11semidirect
138. #1702C2×C11direct (N × H)
139. C2×#334C2×C11semidirect
140. C2×#332C2×C11semidirect
191. #462C22×C11semidirect
195. #446C22×C11semidirect
206. #334C22×C11semidirect
207. #332C22×C11semidirect
275. C2×C11#1702direct (N × H)
331. C11C2×#1702direct (N × H)
393. C2C11×#1702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4622
C2×C11×#4602
C2×C11×#4462
C11×#17022
C2×C11×#3342
C2×C11×#3322
C2×C11×#3312
C2×#170211