Finite Group Databasebeta

← #14649656

Subgroups — #14649656

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078099C211yesmaximal, characteristic
2#13077284C211yesmaximal, characteristic
3C2×#10622185C211yesmaximal, characteristic, complemented
4#13067004C211yesmaximal, characteristic
5#13066512C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66995—21no—
10C4×#4339C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622838—21no—
14#10622742—21no—
15#10622735—21no—
16#10622703—21no—
17#10622703C412yes—
18#10622696—21no—
19#10622696C412yes—
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622453—22no—
24#10622448—21no—
25#10622446—21no—
26C11×#332—22no—
27#10622185—21no—
28#10622185—21no—
29#10622097—21no—
30#10622094—21no—
31C22×Q8×C11—21no—
32C2×#4339D411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8C2×C412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—22no—
42#66995—42no—
43#66995—42no—
44C2×#4325—22no—
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47#66979D411yescharacteristic
48C2×#4318—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C4×D44C2×C411yescharacteristic
52C4×D44D411yescharacteristic
53#66925—21no—
54C42×D11—21no—
55C4×Dic22C2×C411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62#66899—22no—
63#66899—22no—
64(C2×D11)⋊C8—22no—
65(C2×D11)⋊C8—22no—
66#66879—22no—
67C8×Dic11—22no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)C2×C412yes—
73C4⋊(C11⋊C8)D411yescharacteristic
74C4⋊(C11⋊C8)D411yescharacteristic
75#9172—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—21no—
87#4339—21no—
88#4339—21no—
89#4339—21no—
90#4339—21no—
91C2×D44C22⋊C411yescharacteristic
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×Dic22C22⋊C411yescharacteristic
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C22×C411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C22⋊Dic11—21no—
109#4326—44no—
110#4325—44no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113C4⋊Dic11C22⋊C411yescharacteristic
114C4⋊Dic11C22⋊C411yescharacteristic
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120#4318—41no—
121#4318—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—81no—
129#3039—111no—
130#2925—111no—
131#1546D1111yescharacteristic, complemented
132C2×#332—111no—
133#1477—111no—
134#1301—111no—
135#1292—111no—
136C23×C11#12311yescharacteristic
137C22×D11—21no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—81no—
141Q8×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C22⋊D11—41no—
159C22⋊D11—41no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163D44—21no—
164D44—21no—
165C4×D11—41no—
166C4×D11—41no—
167C4×D11—41no—
168C4×D11—41no—
169C4×D11—81no—
170Dic22—21no—
171Dic22—21no—
172C8×C11—42no—
173C8×C11—81no—
174C11⋊C8—42no—
175C11⋊C8—41no—
176C11⋊C8—41no—
177C11⋊C8—81no—
178C2×#137—221no—
179C2×C4⋊Q8C2×D1111yescharacteristic
180C4×#41—111no—
181#462—112no—
182#462—221no—
183#461—112no—
184#461—221no—
185#433—222no—
186#432—221no—
187#431—221no—
188#431C2×D1111yescharacteristic
189#423—111no—
190#423C2×D1111yescharacteristic
191C2×C4⋊C8—111no—
192C2×C4⋊C8—111no—
193#419—221no—
194#408—221no—
195#405—221no—
196#332—22no—
197#332—221no—
198#332—221no—
199Q8⋊C8—221no—
200D4⋊C8—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11#38611yescharacteristic
204C22×C11#48211yescharacteristic
205C22×C11#48211yescharacteristic
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11#41611yescharacteristic
214C4×C11#41811yescharacteristic
215C4×C11#44911yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#47111yescharacteristic
218C4×C11#47311yescharacteristic
219Dic11—41no—
220Dic11—41no—
221Dic11—41no—
222C2×#41—111no—
223C22×Q8—21no—
224#137—442no—
225#137—442no—
226C2×Q16—222no—
227C2×SD16—222no—
228C2×M16—21no—
229C2×M16—221no—
230C22×C8—221no—
231C22×C8—221no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C4×D1112yes—
236C4×Q8—111no—
237C4×Q8—111no—
238C4×D4—111no—
239C4×D4—111no—
240C4×D4—221no—
241C4×D4—221no—
242#117—111no—
243#117—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C42—221no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—112no—
251C4⋊C8—111no—
252C4⋊C8—111no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256C4⋊C8—221no—
257C4⋊C8C22⋊D1112yes—
258#103—222no—
259#103—222no—
260C22⋊C8—21no—
261C22⋊C8—222no—
262C22⋊C8—222no—
263#97—222no—
264C4×C8—21no—
265C4×C8—222no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11#187511yescharacteristic
269C2×C11#190211yescharacteristic
270C2×C11#190811yescharacteristic
271D11—81no—
272#41—221no—
273#41—221no—
274#41—221no—
275#41—221no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—111no—
283C2×D4—111no—
284C2×D4—221no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4#433911yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292Q16—444no—
293SD16—444no—
294M16—41no—
295M16—41no—
296M16—441no—
297M16—441no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—222no—
301C2×C8—221no—
302C2×C8—221no—
303C2×C8—441no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—881no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—111no—
312C4⋊C4—111no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C42—221no—
319C42—221no—
320C42—221no—
321C42C2×C4×D1111yescharacteristic
322C42D4×D1111yescharacteristic
323C42D4×D1111yescharacteristic
324C42C2×C22⋊D1111yescharacteristic
325C11#917211yescharacteristic, complemented, Sylow
326C23—221no—
327C23#6693611yescharacteristic
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—81no—
332Q8—221no—
333Q8—221no—
334D4—221no—
335D4—221no—
336D4—441no—
337D4—441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—881no—
352C2×C4C22⋊C4×D1111yescharacteristic
353C2×C4(C22⋊D11)⋊C411yescharacteristic
354C2×C4#6693711yescharacteristic
355C2×C4#6696411yescharacteristic
356C2×C4#6696511yescharacteristic
357C2×C4#6696711yescharacteristic
358C2×C4#6696911yescharacteristic
359C2×C4C4×C22⋊D1111yescharacteristic
360C2×C4#6699011yescharacteristic
361C2×C4#6699111yescharacteristic
362C8—42no—
363C8—81no—
364C8—441no—
365C8—441no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22#1062239211yescharacteristic
374C22#1062239711yescharacteristic
375C22#1062256911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4#1062236711yescharacteristic
384C4#1062236811yescharacteristic
385C4#1062238311yescharacteristic
386C4#1062238511yescharacteristic
387C4#1062277111yescharacteristic
388C4#1062278511yescharacteristic
389C2—21no—
390C2—21no—
391C2—881no—
392C2#1306893511yescharacteristic
393C2#1306908611yescharacteristic
394C2#1306912811yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9172
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#10622185C2semidirect
5. #13066512C2semidirect
6. #13066490C2semidirect
7. C11×#1546C2semidirect
131. #1546D11semidirect
325. C11#9172semidirect

Maximal subgroups

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

subgroupindex
#130780992
#130772842
C2×#106221852
#130670042
#130665122
#130664902
C11×#15462
#917211