Finite Group Databasebeta

← C2×C11×#2088 #14600857

Subgroups — C2×C11×#2088 #14600857

Order 2816.

1054 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×#106C211yesmaximal, characteristic
2C22×C11×C4⋊C8C211yesmaximal, characteristic
3C2×C11×#389C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic
5C11×#2088C218yesmaximal, direct product factor
6C2×C11×#340C211yesmaximal, characteristic
7C2×C11×#340C211yesmaximal, characteristic
8C2×C11×#340C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×C11×#106—24no—
19C2×C11×#106C2214yes—
20C2×C11×C4⋊C8—24no—
21C2×C11×C4⋊C8C2214yes—
22C11×#389—22no—
23C11×#389—22no—
24C11×#389C2214yes—
25C11×#389C2214yes—
26C2×C11×#95—21no—
27C2×C11×#95—21no—
28C11×#340C2214yes—
29C11×#340C2214yes—
30C11×#340C2214yes—
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×C11—22no—
43C22×C8×C11D414yes—
44C22×C8×C11C2312yes—
45C22×C8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
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—24no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—44no—
59C2×C11×C4⋊C4—44no—
60C2×C11×C4⋊C4Q814yes—
61C2×C11×C4⋊C4Q814yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C11×#106—28no—
71C11×C4⋊C8—28no—
72C11×#95—24no—
73C11×#95—24no—
74C2×#2088C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
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×C11SD1614yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11C2411yescharacteristic
108C2×C8×C11—28no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—44no—
115C2×C8×C11C2×D414yes—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—48no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—48no—
128C11×C4⋊C4C2×Q814yes—
129C11×C4⋊C4C2×Q814yes—
130C42×C11—24no—
131C42×C11—22no—
132C42×C11—22no—
133C22×#106C2×C1111yescharacteristic
134C22×C4⋊C8C2×C1111yescharacteristic
135C2×#389C2×C1111yescharacteristic
136C2×#389C2×C1111yescharacteristic
137#2088C2×C1118yesdirect product factor
138C2×#340C2×C1111yescharacteristic
139C2×#340C2×C1111yescharacteristic
140C2×#340C2×C1111yescharacteristic
141C23×C11#12112yes—
142C23×C11C22⋊Q812yes—
143C23×C11C22⋊Q812yes—
144C23×C11C2×SD1612yes—
145C23×C11#13512yes—
146C23×C11AGL(1,ℤ/8)12yes—
147C23×C11#13712yes—
148C23×C11C22×D411yescharacteristic
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—28no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—48no—
163C2×C4×C11—48no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—84no—
171C2×C4×C11—84no—
172C2×C4×C11#12112yes—
173C2×C4×C11C22⋊Q812yes—
174C2×C4×C11C22⋊Q812yes—
175C2×C4×C11#12314yes—
176C2×C4×C11#12514yes—
177C2×C4×C11#12514yes—
178C2×C4×C11C4⋊Q814yes—
179C2×C4×C11C2×SD1614yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C8×C11—24no—
187C8×C11—42no—
188C23×C8C22×C1111yescharacteristic
189C23×C8C22×C1111yescharacteristic
190C22×C4⋊C4—21no—
191C22×C4⋊C4—21no—
192C22×C4⋊C4C22×C1111yescharacteristic
193C22×C4⋊C4C22×C1111yescharacteristic
194C22×C4⋊C4C22×C1111yescharacteristic
195C22×C4⋊C4C22×C1111yescharacteristic
196C22×C42C22×C1111yescharacteristic
197C2×#106—24no—
198C2×#106C22×C1114yes—
199C2×C4⋊C8—24no—
200C2×C4⋊C8C22×C1114yes—
201#389—22no—
202#389—22no—
203#389C22×C1114yes—
204#389C22×C1114yes—
205C2×#95—21no—
206C2×#95—21no—
207#340C22×C1114yes—
208#340C22×C1114yes—
209#340C22×C1114yes—
210C22×C11#39814yes—
211C22×C11#46514yes—
212C22×C11#46814yes—
213C22×C11#47514yes—
214C22×C11#47614yes—
215C22×C11#47814yes—
216C22×C11#47914yes—
217C22×C11C2×#12111yescharacteristic
218C22×C11C2×C22⋊Q811yescharacteristic
219C22×C11C2×C22⋊Q811yescharacteristic
220C22×C11C22×SD1611yescharacteristic
221C22×C11C2×#13511yescharacteristic
222C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C22×C11C2×#13711yescharacteristic
224C4×C11—24no—
225C4×C11—44no—
226C4×C11—42no—
227C4×C11—44no—
228C4×C11—82no—
229C4×C11—82no—
230C4×C11#39814yes—
231C4×C11C2×#12311yescharacteristic
232C4×C11C2×#12511yescharacteristic
233C4×C11C2×#12511yescharacteristic
234C4×C11C2×C4⋊Q811yescharacteristic
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4D4×C1111yescharacteristic
240C23×C4D4×C1111yescharacteristic
241C23×C4C23×C1111yescharacteristic
242C22×C8—22no—
243C22×C8—22no—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—22no—
247C22×C8D4×C1114yes—
248C22×C8C23×C1112yes—
249C22×C8C23×C1112yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4Q8×C1114yes—
265C2×C4⋊C4Q8×C1114yes—
266C2×C4⋊C4C23×C1112yes—
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1112yes—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42D4×C1112yes—
273C2×C42C23×C1112yes—
274#106—28no—
275C4⋊C8—28no—
276#95—24no—
277#95—24no—
278C2×C11#208818yesdirect product factor
279C2×C11C2×#39811yescharacteristic
280C2×C11C2×#46511yescharacteristic
281C2×C11C2×#46811yescharacteristic
282C2×C11C2×#47611yescharacteristic
283C2×C11C2×#47811yescharacteristic
284C2×C11C2×#47511yescharacteristic
285C2×C11C2×#47911yescharacteristic
286C24C2×D4×C1111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
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×C4—42no—
307C22×C4—42no—
308C22×C4C11×SD1614yes—
309C22×C4C2×D4×C1112yes—
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1112yes—
313C22×C4C2×Q8×C1112yes—
314C22×C4C2×Q8×C1112yes—
315C22×C4C11×#4112yes—
316C22×C4C11×#4112yes—
317C22×C4C11×#4112yes—
318C22×C4C24×C1111yescharacteristic
319C2×C8—28no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—44no—
326C2×C8C2×D4×C1114yes—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—48no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—48no—
339C4⋊C4C2×Q8×C1114yes—
340C4⋊C4C2×Q8×C1114yes—
341C42—24no—
342C42—22no—
343C42—22no—
344C11C2×#208811yescharacteristic, direct product factor, Sylow
345C23C11×#12112yes—
346C23C11×C22⋊Q812yes—
347C23C11×C22⋊Q812yes—
348C23C2×C11×SD1612yes—
349C23C11×#13512yes—
350C23C11×AGL(1,ℤ/8)12yes—
351C23C11×#13712yes—
352C23C22×D4×C1111yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—28no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—48no—
367C2×C4—48no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—84no—
375C2×C4—84no—
376C2×C4C11×#12112yes—
377C2×C4C11×C22⋊Q812yes—
378C2×C4C11×C22⋊Q812yes—
379C2×C4C11×#12314yes—
380C2×C4C11×#12514yes—
381C2×C4C11×#12514yes—
382C2×C4C11×C4⋊Q814yes—
383C2×C4C2×C11×SD1614yes—
384C2×C4C22×D4×C1111yescharacteristic
385C2×C4C22×Q8×C1111yescharacteristic
386C2×C4C22×Q8×C1111yescharacteristic
387C2×C4C2×C11×#4111yescharacteristic
388C2×C4C2×C11×#4111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C8—24no—
391C8—42no—
392C22C11×#39814yes—
393C22C11×#46514yes—
394C22C11×#46814yes—
395C22C11×#47514yes—
396C22C11×#47614yes—
397C22C11×#47814yes—
398C22C11×#47914yes—
399C22C2×C11×#12111yescharacteristic
400C22C2×C11×C22⋊Q811yescharacteristic
401C22C2×C11×C22⋊Q811yescharacteristic
402C22C22×C11×SD1611yescharacteristic
403C22C2×C11×#13511yescharacteristic
404C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
405C22C2×C11×#13711yescharacteristic
406C4—24no—
407C4—42no—
408C4—44no—
409C4—44no—
410C4—82no—
411C4—82no—
412C4C11×#39814yes—
413C4C2×C11×#12311yescharacteristic
414C4C2×C11×#12511yescharacteristic
415C4C2×C11×#12511yescharacteristic
416C4C2×C11×C4⋊Q811yescharacteristic
417C2C11×#208818yesdirect product factor
418C2C2×C11×#39811yescharacteristic
419C2C2×C11×#46511yescharacteristic
420C2C2×C11×#46811yescharacteristic
421C2C2×C11×#47611yescharacteristic
422C2C2×C11×#47811yescharacteristic
423C2C2×C11×#47511yescharacteristic
424C2C2×C11×#47911yescharacteristic
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×#2088C2direct (N × H)
74. C2×#2088C11direct (N × H)
137. #2088C2×C11direct (N × H)
278. C2×C11#2088direct (N × H)
344. C11C2×#2088direct (N × H)
417. C2C11×#2088direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1062
C22×C11×C4⋊C82
C2×C11×#3892
C11×#20882
C2×C11×#3402
C2×#208811