Finite Group Databasebeta

← #14764139

Subgroups — #14764139

Order 2816.

790 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
1C2×#10622333C212yesmaximal
2#13071098C211yesmaximal, characteristic
3#13069338C212yesmaximal, complemented
4#13069336C212yesmaximal, complemented
5#13069333C212yesmaximal, complemented
6#13069331C212yesmaximal, complemented
7#13068600C211yesmaximal, characteristic
8#13068594C212yesmaximal
9C11×#1798C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16C2×C22⋊(C11⋊C8)C2212yes—
17C2×#66879C2212yes—
18C2×Dic11⋊C8C2212yes—
19C2×Dic11⋊C8C2212yes—
20C2×Dic11⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×C8×Dic11C2212yes—
23#10622586C412yes—
24#10622586C412yes—
25#10622559C411yescharacteristic
26#10622559C411yescharacteristic
27#10622559C411yescharacteristic
28#10622559C411yescharacteristic
29C4×Dic11⋊C4C2212yes—
30C4×Dic11⋊C4C2212yes—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622333—28no—
34C11×#336C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622162C2212yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C11×#117—41no—
44C11×#117—41no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11C2×C411yescharacteristic
52C2×C22⋊Dic11C2×C411yescharacteristic
53#66979D414yes—
54#66979Q814yes—
55C2×C4⋊Dic11C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C412yes—
60C2×C4×Dic11—41no—
61C2×C4×Dic11—41no—
62C2×C4×Dic11C2×C412yes—
63C2×C4×Dic11C2312yes—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C11×C4⋊C8—41no—
68C11×C4⋊C8—41no—
69C11×C22⋊C8—24no—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C22⋊(C11⋊C8)—24no—
75#66879—24no—
76Dic11⋊C8—24no—
77Dic11⋊C8—24no—
78Dic11⋊C8—42no—
79Dic11⋊C8—42no—
80C8×Dic11—24no—
81C4⋊(C11⋊C8)—41no—
82C4⋊(C11⋊C8)—41no—
83#21958—111nomaximal, Sylow
84C24×C11C22×C411yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×Q812yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—42no—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—21no—
119C22⋊Dic11C4⋊C414yes—
120C22⋊Dic11C4⋊C414yes—
121C4⋊Dic11C4⋊C418yes—
122Dic11⋊C4—24no—
123Dic11⋊C4—24no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—42no—
129C4×Dic11C2×D414yes—
130C4×Dic11C2×Q814yes—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×#433—112no—
138#2296—111no—
139#1940—112no—
140#1940—112no—
141#1939—112no—
142#1939—112no—
143#1798—111no—
144#1798D1111yescharacteristic
145#1797—112no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11C2×C4⋊C412yes—
151C23×C11C23×C411yescharacteristic
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11C2×C4⋊C412yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×Q811yescharacteristic
169C2×C4×C11H(5,𝔽2)11yescharacteristic
170C2×C4×C11H(5,𝔽2)11yescharacteristic
171C2×C4×C112−1+411yescharacteristic
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—22no—
181C2×Dic11—22no—
182C2×Dic11—44no—
183C2×Dic11—44no—
184C2×Dic11C2×C4⋊C414yes—
185C2×Dic11C2×C4⋊C414yes—
186C2×Dic11#13114yes—
187C8×C11—42no—
188C8×C11—42no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191C2×#117—111no—
192C2×#117C2×D1111yescharacteristic
193C22×C42—111no—
194#433—228no—
195C2×C4⋊C8—112no—
196C2×C4⋊C8—112no—
197C2×C4⋊C8—112no—
198C2×C4⋊C8—112no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8—111no—
201C2×C4⋊C8C2×D1111yescharacteristic
202C2×C4⋊C8C2×D1111yescharacteristic
203C2×C22⋊C8—112no—
204C2×C22⋊C8C2×D1112yes—
205C2×#97—112no—
206C2×C4×C8—112no—
207#389—112no—
208#389—112no—
209#385—111no—
210#385—111no—
211#385—111no—
212#385—111no—
213C4×C4⋊C4—112no—
214C4×C4⋊C4—112no—
215#336—112no—
216#336—112no—
217#336—112no—
218#336C2×D1112yes—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—42no—
224C22×C11C22×C4⋊C411yescharacteristic
225C22×C11#51811yescharacteristic
226C22×C11#51911yescharacteristic
227C22×C11C2×#13112yes—
228C22×C11#56812yes—
229C4×C11—22no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11#53711yescharacteristic
235C4×C11#53711yescharacteristic
236C4×C11#54411yescharacteristic
237C4×C11#54411yescharacteristic
238Dic11—24no—
239Dic11—24no—
240Dic11—24no—
241Dic11—42no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4C22×D1111yescharacteristic
245C22×C8—112no—
246C22×C8—112no—
247C22×C8C22×D1112yes—
248C22×C8C22×D1112yes—
249#117—41no—
250#117—41no—
251#117—114no—
252#117—114no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C4⋊C4C4×D1111yescharacteristic
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4C4×D1111yescharacteristic
263C2×C22⋊C4C4×D1111yescharacteristic
264C2×C42—112no—
265C2×C42—112no—
266C2×C42—112no—
267C2×C42—441no—
268C2×C42—441no—
269C2×C42C22×D1111yescharacteristic
270C2×C42C22×D1111yescharacteristic
271C4⋊C8—41no—
272C4⋊C8—41no—
273C4⋊C8—224no—
274C4⋊C8—224no—
275C4⋊C8—441no—
276C4⋊C8—441no—
277C4⋊C8—442no—
278C4⋊C8—442no—
279C22⋊C8—24no—
280C22⋊C8—224no—
281#97—224no—
282C4×C8—224no—
283#95—112no—
284#95—112no—
285#95—112no—
286#95—112no—
287C2×C11—42no—
288C2×C11#231611yescharacteristic
289C2×C11#290612yes—
290C2×C11#297711yescharacteristic
291C2×C11#297811yescharacteristic
292C2×C11#298512yes—
293C24C2×C4×D1111yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—112no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—224no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4—442no—
306C22×C4C2×C4×D1111yescharacteristic
307C22×C4C2×C4×D1111yescharacteristic
308C22×C4C2×C4×D1111yescharacteristic
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4D4×D1112yes—
312C22×C4Q8×D1112yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—222no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—118no—
329C4⋊C4—224no—
330C4⋊C4—224no—
331C4⋊C4—442no—
332C4⋊C4—442no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—114no—
336C22⋊C4—114no—
337C42—21no—
338C42—21no—
339C42—21no—
340C42—21no—
341C42—114no—
342C42—114no—
343C42—222no—
344C42—222no—
345C42—442no—
346C11#2195811yescharacteristic, complemented, Sylow
347C23—21no—
348C23—22no—
349C23—22no—
350C23—21no—
351C23C4⋊C4×D1112yes—
352C23C22×C4×D1111yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—114no—
368C2×C4—114no—
369C2×C4—114no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—444no—
380C2×C4—444no—
381C2×C4C4⋊C4×D1112yes—
382C2×C4C2×D4×D1111yescharacteristic
383C2×C4#6703711yescharacteristic
384C2×C4#6703711yescharacteristic
385C2×C4C2×Q8×D1111yescharacteristic
386C2×C4#6704311yescharacteristic
387C2×C4#6704311yescharacteristic
388C8—42no—
389C8—42no—
390C8—442no—
391C8—442no—
392C22—22no—
393C22—24no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22#1062301711yescharacteristic
398C22C2×C4⋊C4×D1111yescharacteristic
399C22#1062304711yescharacteristic
400C22D11×#13112yes—
401C22#1062328112yes—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—224no—
408C4—224no—
409C4—224no—
410C4—442no—
411C4#1062312811yescharacteristic
412C4#1062312811yescharacteristic
413C4#1062315411yescharacteristic
414C4#1062315411yescharacteristic
415C2—42no—
416C2#1307123311yescharacteristic
417C2#1307718312yes—
418C2#1307766811yescharacteristic
419C2#1307767411yescharacteristic
420C2#1307770812yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#21958
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
3. #13069338C2semidirect
4. #13069336C2semidirect
5. #13069333C2semidirect
6. #13069331C2semidirect
346. C11#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
#130710982
#130693382
#130693362
#130693332
#130693312
#130686002
#130685942
C11×#17982
#2195811