Finite Group Databasebeta

← #14853491

Subgroups — #14853491

Order 2816.

706 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
1#13077001C211yesmaximal, characteristic, complemented
2C4×#66989C211yesmaximal, characteristic
3#13070187C212yesmaximal, complemented
4#13069856C212yesmaximal
5#13069310C212yesmaximal
6#13069304C212yesmaximal, complemented
7#13068632C211yesmaximal, characteristic, complemented
8#13068628C211yesmaximal, characteristic, complemented
9#13068626C211yesmaximal, characteristic
10#13068471C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102C2212yes—
17C11×#382C2211yescharacteristic
18#10622834C2211yescharacteristic
19C2×#66896C2212yes—
20C4×C22⋊Dic11—22no—
21C2×#66880C2212yes—
22C2×#66879C2212yes—
23#10622598C2212yes—
24#10622590C2211yescharacteristic
25#10622587C2211yescharacteristic
26#10622586C2212yes—
27C2×#66874C2212yes—
28#10622558—22no—
29#10622549C2211yescharacteristic
30C42×Dic11C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622268—22no—
33#10622267—22no—
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—21no—
41C22×Dic22C2311yescharacteristic
42C22×C8×C11C2312yes—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51#66989—22no—
52#66989—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2311yescharacteristic
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—22no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11D412yes—
60C2×C4×Dic11D412yes—
61C2×C4×Dic11C2311yescharacteristic
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C4×Dic22—22no—
65C4×Dic22—22no—
66C11×C4⋊C8—22no—
67C11×#102—42no—
68C11×#95—21no—
69C11×#95—21no—
70#66896—24no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77#66880—24no—
78#66879—42no—
79#66874—42no—
80C4⋊(C11⋊C8)—22no—
81#29128—111nomaximal, Sylow
82C24×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11#4112yes—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11—42no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11C2×D412yes—
100C22×Dic11C2×D412yes—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22#4112yes—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C22⋊C4—42no—
115C42×C11#4112yes—
116C42×C11#4112yes—
117C22⋊Dic11—28no—
118C22⋊Dic11—44no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—44no—
124Dic11⋊C4—44no—
125Dic11⋊C4—42no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C4×Dic11—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136#2864—111no—
137C4×#124—111no—
138#2101—112no—
139#2042—112no—
140#1936—112no—
141#1935—112no—
142#1805—111no—
143#1805—111no—
144#1804—111no—
145#1804D1111yescharacteristic
146#1767—111no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11C22×D411yescharacteristic
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—84no—
165C2×C4×C11#12412yes—
166C2×C4×C11#12412yes—
167C2×C4×C11C2×#4111yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11H(5,𝔽2)11yescharacteristic
172C2×C4×C112−1+411yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187Dic22—22no—
188Dic22—22no—
189Dic22—41no—
190Dic22—41no—
191C8×C11—42no—
192C11⋊C8—42no—
193C2×#124—111no—
194C2×C4×Q8—111no—
195C2×C4×D4C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198C2×#103—112no—
199C2×#103—112no—
200C2×#102—112no—
201C2×#102C2×D1112yes—
202C2×#97—112no—
203#391—111no—
204#390—111no—
205#389—112no—
206#389—112no—
207#388—222no—
208#387—222no—
209#387—222no—
210#382—111no—
211#382—111no—
212#382C2×D1111yescharacteristic
213C4×C22⋊C4—222no—
214C43—111no—
215#340—112no—
216#340—112no—
217#340—112no—
218#340C2×D1112yes—
219#336—112no—
220C22×C11—42no—
221C22×C11—44no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—82no—
225C22×C11#52511yescharacteristic
226C22×C11C2×#12411yescharacteristic
227C22×C11#53711yescharacteristic
228C22×C11#57512yes—
229C22×C11#57512yes—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—81no—
233C4×C11—82no—
234C4×C11#55211yescharacteristic
235C4×C11#55211yescharacteristic
236C4×C11#55311yescharacteristic
237C4×C11#55311yescharacteristic
238Dic11—42no—
239Dic11—42no—
240Dic11—42no—
241Dic11—82no—
242Dic11—81no—
243C22×Q8—111no—
244C22×D4C22×D1111yescharacteristic
245C23×C4—21no—
246C22×C8—112no—
247C22×C8C22×D1112yes—
248#124—222no—
249#124—222no—
250C4×Q8—222no—
251C4×Q8—222no—
252C4×D4—22no—
253C4×D4—22no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4C22×D1111yescharacteristic
260C2×C4⋊C4C22×D1112yes—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—222no—
264C2×C42—111no—
265C2×C42—111no—
266C2×C42—112no—
267C2×C42—112no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—22no—
271C4⋊C8—222no—
272#103—224no—
273#103—442no—
274#102—42no—
275#102—224no—
276#97—442no—
277#95—21no—
278#95—21no—
279#95—222no—
280#95—222no—
281#95—222no—
282#95—222no—
283#95—221no—
284#95—221no—
285C2×C11—82no—
286C2×C11#256211yescharacteristic
287C2×C11#311112yes—
288C2×C11#313511yescharacteristic
289C2×C11#314011yescharacteristic
290C2×C11#325612yes—
291C24—21no—
292C2×Q8—112no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—221no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4#434312yes—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—44no—
307C22×C4—42no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—221no—
311C22×C4—222no—
312C22×C4—221no—
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—444no—
331C4⋊C4—444no—
332C4⋊C4—442no—
333C22⋊C4—42no—
334C22⋊C4—228no—
335C22⋊C4—444no—
336C42—221no—
337C42—221no—
338C42—221no—
339C42—221no—
340C42—442no—
341C42—442no—
342C42—442no—
343C42#433912yes—
344C42#434112yes—
345C11#2912811yescharacteristic, complemented, Sylow
346C23—22no—
347C23—41no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23C2×D4×D1111yescharacteristic
352Q8—222no—
353Q8—222no—
354Q8—441no—
355Q8—441no—
356D4—22no—
357D4—22no—
358D4—41no—
359D4—41no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—84no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6693812yes—
383C2×C4#6693812yes—
384C2×C4C2×#433911yescharacteristic
385C2×C4C2×#434111yescharacteristic
386C2×C4#6703711yescharacteristic
387C2×C4C2×#434311yescharacteristic
388C2×C4#41×D1111yescharacteristic
389C2×C4#6704311yescharacteristic
390C8—42no—
391C8—442no—
392C22—42no—
393C22—44no—
394C22—81no—
395C22—82no—
396C22—81no—
397C22C2×#6693811yescharacteristic
398C22#1062313911yescharacteristic
399C22#1062315811yescharacteristic
400C22#1062329912yes—
401C22#1062330412yes—
402C4—22no—
403C4—22no—
404C4—82no—
405C4—81no—
406C4—442no—
407C4—442no—
408C4—442no—
409C4—881no—
410C4—882no—
411C4#1062304511yescharacteristic
412C4#1062306011yescharacteristic
413C4#1062314511yescharacteristic
414C4#1062317311yescharacteristic
415C2—82no—
416C2#1307378111yescharacteristic
417C2#1307873012yes—
418C2#1307895911yescharacteristic
419C2#1307900011yescharacteristic
420C2#1308001412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1804D11
hypocenterC11#29128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #13077001C2semidirect
3. #13070187C2semidirect
6. #13069304C2semidirect
7. #13068632C2semidirect
8. #13068628C2semidirect
10. #13068471C2semidirect
345. C11#29128semidirect

Maximal subgroups

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

subgroupindex
#130770012
C4×#669892
#130701872
#130698562
#130693102
#130693042
#130686322
#130686282
#130686262
#130684712
C11×#18042
#2912811