Finite Group Databasebeta

← #14656293

Subgroups — #14656293

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#462C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4325—21no—
12C2×#66927C2211yescharacteristic
13C11×#462—22no—
14C11×#462—22no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622701—22no—
18#10622701—22no—
19#10622640—22no—
20#10622640—22no—
21C2×#66873—21no—
22C2×#66873—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622185—22no—
27#10622162—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C2×C11×Q16—24no—
35C2×C11×Q16—42no—
36C2×C11×Q16—42no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yes—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—24no—
53C2×#4325—42no—
54C2×#4325—42no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65#66873—24no—
66#66873—28no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#10263—111nomaximal, Sylow
74C23×D11—41no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11D812yes—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—42no—
105C2×D44—82no—
106C11×Q16—48no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4325—48no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—41no—
133C2×#486—111no—
134C2×#462D1111yescharacteristic, complemented
135C2×#460—111no—
136#1984—111no—
137C2×#332—111no—
138C2×#331—111no—
139#1277—111no—
140C23×C11#12111yescharacteristic
141C22×D11—42no—
142C22×D11—82no—
143C22×D11—81no—
144C22×D11—81no—
145C22×D11—82no—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—81no—
153Q8×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11#13512yes—
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13712yes—
175D44—42no—
176D44—42no—
177D44—44no—
178D44—82no—
179D44—82no—
180D44—81no—
181D44—81no—
182D44—81no—
183D44—81no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C11⋊C8—81no—
188C22×Q16—21no—
189C22×SD16—221no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191C2×#127—111no—
192C2×C4×Q8C2×D1111yescharacteristic
193#486—222no—
194#486—222no—
195#462—22no—
196#462—22no—
197#460—222no—
198#460—222no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8—111no—
201C2×C4⋊C8C2×D1111yescharacteristic
202C2×#103—21no—
203C2×#102—222no—
204C2×#102—221no—
205C2×C4×C8—111no—
206#336—222no—
207#332—222no—
208#331—222no—
209C22×C11#39211yescharacteristic
210C22×C11#46412yes—
211C22×C11#46611yescharacteristic
212C22×C11#46911yescharacteristic
213C22×C11#47112yes—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—162no—
218C2×D11—162no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11#44711yescharacteristic
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45212yes—
229C4×C11#49511yescharacteristic
230C4×C11#49711yescharacteristic
231C22×Q8—21no—
232C22×Q8C22⋊D1111yescharacteristic
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×Q16—24no—
237C2×Q16—42no—
238C2×Q16—42no—
239C2×SD16—224no—
240C2×SD16—442no—
241C2×SD16—442no—
242C22×C8—21no—
243C22×C8—112no—
244C22×C8—221no—
245C22×C8—221no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C22⋊D1112yes—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C42—21no—
263C2×C42C22×D1111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—24no—
271#102—224no—
272#102—228no—
273C4×C8—221no—
274C4×C8—221no—
275C2×C11#168212yes—
276C2×C11#170212yes—
277C2×C11#199911yescharacteristic
278C2×C11#201511yescharacteristic
279C2×C11#201911yescharacteristic
280D11—162no—
281C24—441no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8#432312yes—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—882no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4D4×D1111yescharacteristic
311C22×C4#434111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313Q16—48no—
314SD16—448no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—441no—
323C2×C8—441no—
324C2×C8—442no—
325C2×C8—441no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C42—41no—
335C42—41no—
336C42D4×D1111yescharacteristic
337C42D4×D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C11#1026311yescharacteristic, complemented, Sylow
341C23—442no—
342C23—882no—
343C23—882no—
344C23—881no—
345C23—881no—
346C23#6699211yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355D4—444no—
356D4—442no—
357D4—442no—
358D4—882no—
359D4—882no—
360D4—881no—
361D4—881no—
362D4—881no—
363D4—881no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#6697112yes—
374C2×C4#6697212yes—
375C2×C4C2×#432311yescharacteristic
376C2×C4#6698511yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6699011yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699311yescharacteristic
382C2×C4#6700211yescharacteristic
383C2×C4#6700311yescharacteristic
384C2×C4#6700611yescharacteristic
385C8—42no—
386C8—442no—
387C8—442no—
388C8—881no—
389C22—882no—
390C22—882no—
391C22—882no—
392C22—1762no—
393C22—1762no—
394C22#1062265111yescharacteristic
395C22#1062265211yescharacteristic
396C22#1062279812yes—
397C22#1062281612yes—
398C22#1062283611yescharacteristic
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4—81no—
404C4#1062264911yescharacteristic
405C4#1062265011yescharacteristic
406C4#1062280012yes—
407C4#1062280311yescharacteristic
408C4#1062280411yescharacteristic
409C4#1062283011yescharacteristic
410C4#1062285111yescharacteristic
411C2—1762no—
412C2#1306806212yes—
413C2#1306818612yes—
414C2#1306961211yescharacteristic
415C2#1306970711yescharacteristic
416C2#1306972711yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#462C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#462D11
hypocenterC11#10263
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13069553C2semidirect
4. C2×#10622185C2semidirect
6. #13066450C2semidirect
7. C2×C11×#462C2semidirect
134. C2×#462D11semidirect
340. C11#10263semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
#130695532
C2×#106221852
C2×#106221232
#130664502
C2×C11×#4622
#1026311