Finite Group Databasebeta

← C2×C11×#2085 #14600847

Subgroups — C2×C11×#2085 #14600847

Order 2816.

998 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
1C22×C11×#107C211yesmaximal, characteristic
2C22×C11×#106C211yesmaximal, characteristic
3C2×C11×#389C211yesmaximal, characteristic
4C2×C11×#382C211yesmaximal, characteristic
5C11×#2085C218yesmaximal, direct product factor
6C2×C11×#340C211yesmaximal, characteristic
7C2×C11×#340C211yesmaximal, characteristic
8C2×C11×#336C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×C11×#107—24no—
18C2×C11×#107C2214yes—
19C2×C11×#106—24no—
20C2×C11×#106C2214yes—
21C11×#389—22no—
22C11×#389C2214yes—
23C11×#382—22no—
24C11×#382C2214yes—
25C2×C11×#95—21no—
26C2×C11×#95—21no—
27C2×C11×#95—21no—
28C11×#340C2214yes—
29C11×#340C2214yes—
30C11×#336C2214yes—
31C23×C4×C11—21no—
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C22×C8×C11—22no—
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11—22no—
42C22×C8×C11Q814yes—
43C22×C8×C11Q814yes—
44C22×C8×C11C2312yes—
45C22×C8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—44no—
59C2×C11×C4⋊C4D414yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11D412yes—
67C2×C42×C11C2312yes—
68C11×#107—28no—
69C11×#106—28no—
70C11×#95—24no—
71C11×#95—24no—
72C11×#95—24no—
73C2×#2085C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—24no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C8×C11—28no—
108C2×C8×C11—28no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C2×Q814yes—
114C2×C8×C11C2×Q814yes—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—48no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4C2×D414yes—
128C42×C11—24no—
129C42×C11—22no—
130C42×C11—22no—
131C22×#107C2×C1111yescharacteristic
132C22×#106C2×C1111yescharacteristic
133C2×#389C2×C1111yescharacteristic
134C2×#382C2×C1111yescharacteristic
135#2085C2×C1118yesdirect product factor
136C2×#340C2×C1111yescharacteristic
137C2×#340C2×C1111yescharacteristic
138C2×#336C2×C1111yescharacteristic
139C23×C11#12112yes—
140C23×C11#12312yes—
141C23×C11C4⋊Q812yes—
142C23×C11#13512yes—
143C23×C11#13512yes—
144C23×C11AGL(1,ℤ/8)12yes—
145C23×C11#13712yes—
146C23×C11C22×D411yescharacteristic
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—48no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—84no—
169C2×C4×C11—84no—
170C2×C4×C11—84no—
171C2×C4×C11#12112yes—
172C2×C4×C11C22⋊Q814yes—
173C2×C4×C11C22⋊Q814yes—
174C2×C4×C11#12312yes—
175C2×C4×C11#12514yes—
176C2×C4×C11#12514yes—
177C2×C4×C11C4⋊Q812yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C8×C11—24no—
185C8×C11—24no—
186C23×C8C22×C1111yescharacteristic
187C23×C8C22×C1111yescharacteristic
188C22×C4⋊C4—21no—
189C22×C4⋊C4C22×C1111yescharacteristic
190C22×C4⋊C4C22×C1111yescharacteristic
191C22×C4⋊C4C22×C1111yescharacteristic
192C22×C4⋊C4C22×C1111yescharacteristic
193C22×C42C22×C1111yescharacteristic
194C2×#107—24no—
195C2×#107C22×C1114yes—
196C2×#106—24no—
197C2×#106C22×C1114yes—
198#389—22no—
199#389C22×C1114yes—
200#382—22no—
201#382C22×C1114yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205#340C22×C1114yes—
206#340C22×C1114yes—
207#336C22×C1114yes—
208C22×C11#39814yes—
209C22×C11#46314yes—
210C22×C11#46414yes—
211C22×C11#48214yes—
212C22×C11#48514yes—
213C22×C11#49914yes—
214C22×C11#50114yes—
215C22×C11C2×#12111yescharacteristic
216C22×C11C2×#12311yescharacteristic
217C22×C11C2×C4⋊Q811yescharacteristic
218C22×C11C2×#13511yescharacteristic
219C22×C11C2×#13511yescharacteristic
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C11C2×#13711yescharacteristic
222C4×C11—42no—
223C4×C11—42no—
224C4×C11—44no—
225C4×C11—82no—
226C4×C11—82no—
227C4×C11—82no—
228C4×C11#39814yes—
229C4×C11C2×C22⋊Q811yescharacteristic
230C4×C11C2×C22⋊Q811yescharacteristic
231C4×C11C2×#12511yescharacteristic
232C4×C11C2×#12511yescharacteristic
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4D4×C1111yescharacteristic
238C23×C4D4×C1111yescharacteristic
239C23×C4C23×C1111yescharacteristic
240C22×C8—22no—
241C22×C8—22no—
242C22×C8—22no—
243C22×C8—22no—
244C22×C8Q8×C1114yes—
245C22×C8Q8×C1114yes—
246C22×C8C23×C1112yes—
247C22×C8C23×C1112yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4D4×C1114yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1112yes—
264C2×C4⋊C4C23×C1112yes—
265C2×C4⋊C4C23×C1112yes—
266C2×C42—22no—
267C2×C42—22no—
268C2×C42D4×C1112yes—
269C2×C42C23×C1112yes—
270#107—28no—
271#106—28no—
272#95—24no—
273#95—24no—
274#95—24no—
275C2×C11#208518yesdirect product factor
276C2×C11C2×#39811yescharacteristic
277C2×C11C2×#46311yescharacteristic
278C2×C11C2×#46411yescharacteristic
279C2×C11C2×#48211yescharacteristic
280C2×C11C2×#48511yescharacteristic
281C2×C11C2×#49911yescharacteristic
282C2×C11C2×#50111yescharacteristic
283C24C2×D4×C1111yescharacteristic
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×D4×C1112yes—
310C22×C4C2×Q8×C1112yes—
311C22×C4C2×Q8×C1112yes—
312C22×C4C11×#4112yes—
313C22×C4C11×#4112yes—
314C22×C4C11×#4112yes—
315C22×C4C24×C1111yescharacteristic
316C2×C8—28no—
317C2×C8—28no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8C2×Q8×C1114yes—
323C2×C8C2×Q8×C1114yes—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—48no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4C2×D4×C1114yes—
337C42—24no—
338C42—22no—
339C42—22no—
340C11C2×#208511yescharacteristic, direct product factor, Sylow
341C23C11×#12112yes—
342C23C11×#12312yes—
343C23C11×C4⋊Q812yes—
344C23C11×#13512yes—
345C23C11×#13512yes—
346C23C11×AGL(1,ℤ/8)12yes—
347C23C11×#13712yes—
348C23C22×D4×C1111yescharacteristic
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—48no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—84no—
371C2×C4—84no—
372C2×C4—84no—
373C2×C4C11×#12112yes—
374C2×C4C11×C22⋊Q814yes—
375C2×C4C11×C22⋊Q814yes—
376C2×C4C11×#12312yes—
377C2×C4C11×#12514yes—
378C2×C4C11×#12514yes—
379C2×C4C11×C4⋊Q812yes—
380C2×C4C22×D4×C1111yescharacteristic
381C2×C4C22×Q8×C1111yescharacteristic
382C2×C4C22×Q8×C1111yescharacteristic
383C2×C4C2×C11×#4111yescharacteristic
384C2×C4C2×C11×#4111yescharacteristic
385C2×C4C2×C11×#4111yescharacteristic
386C8—24no—
387C8—24no—
388C22C11×#39814yes—
389C22C11×#46314yes—
390C22C11×#46414yes—
391C22C11×#48214yes—
392C22C11×#48514yes—
393C22C11×#49914yes—
394C22C11×#50114yes—
395C22C2×C11×#12111yescharacteristic
396C22C2×C11×#12311yescharacteristic
397C22C2×C11×C4⋊Q811yescharacteristic
398C22C2×C11×#13511yescharacteristic
399C22C2×C11×#13511yescharacteristic
400C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
401C22C2×C11×#13711yescharacteristic
402C4—44no—
403C4—42no—
404C4—42no—
405C4—82no—
406C4—82no—
407C4—82no—
408C4C11×#39814yes—
409C4C2×C11×C22⋊Q811yescharacteristic
410C4C2×C11×C22⋊Q811yescharacteristic
411C4C2×C11×#12511yescharacteristic
412C4C2×C11×#12511yescharacteristic
413C2C11×#208518yesdirect product factor
414C2C2×C11×#39811yescharacteristic
415C2C2×C11×#46311yescharacteristic
416C2C2×C11×#46411yescharacteristic
417C2C2×C11×#48211yescharacteristic
418C2C2×C11×#48511yescharacteristic
419C2C2×C11×#49911yescharacteristic
420C2C2×C11×#50111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2085C2direct (N × H)
73. C2×#2085C11direct (N × H)
135. #2085C2×C11direct (N × H)
275. C2×C11#2085direct (N × H)
340. C11C2×#2085direct (N × H)
413. C2C11×#2085direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C22×C11×#1062
C2×C11×#3892
C2×C11×#3822
C11×#20852
C2×C11×#3402
C2×C11×#3362
C2×#208511