Finite Group Databasebeta

← #14798903

Subgroups — #14798903

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622805C211yesmaximal, characteristic
2#13070084C212yesmaximal, complemented
3#13069894C212yesmaximal
4#13069532C211yesmaximal, characteristic, complemented
5#13069406C211yesmaximal, characteristic, complemented
6#13069110C212yesmaximal
7#13068739C211yesmaximal, characteristic, complemented
8#13068730C212yesmaximal, complemented
9#13068667C211yesmaximal, characteristic
10#13068417C211yesmaximal, characteristic
11C11×#2950C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C11×#519C2212yes—
14C2×#66995C2212yes—
15C2×#66954C2211yescharacteristic
16C11×#441—22no—
17C4×C11×Q16—22no—
18C11×#427C2211yescharacteristic
19C11×#419C2212yes—
20C11×#405C2211yescharacteristic
21C2×#66900C2212yes—
22C2×#66900C2212yes—
23#10622838C2212yes—
24#10622805—22no—
25#10622805—22no—
26#10622745C2211yescharacteristic
27#10622737C2212yes—
28C2×#66883C2211yescharacteristic
29C2×#66883C2211yescharacteristic
30#10622714C2211yescharacteristic
31#10622619C2211yescharacteristic
32#10622618C2212yes—
33#10622197C2211yescharacteristic
34#10622171C2212yes—
35#10622171C2212yes—
36#10622171C2212yes—
37#10622171C2211yescharacteristic
38#10622169C2212yes—
39C22×Q8×C11C2312yes—
40C2×#4339C2311yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16D412yes—
46C2×C11×Q16D412yes—
47C2×C11×M16C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—24no—
50C4×Q8×C11—42no—
51C11×#117—24no—
52C11×#117C2312yes—
53C11×#117C2311yescharacteristic
54C2×#4326—22no—
55#66995—24no—
56#66995—42no—
57C2×#4325—22no—
58#66979C2311yescharacteristic
59C2×#4318C2312yes—
60C2×#4318C2312yes—
61C2×#4318C2311yescharacteristic
62C2×#4318C2311yescharacteristic
63#66954—21no—
64#66954—21no—
65#66954—21no—
66#66954—21no—
67C2×#4313—21no—
68C2×C8×D11—21no—
69C11×#107—21no—
70C11×#106—21no—
71C11×#103—24no—
72C11×#97—21no—
73C4×C8×C11—21no—
74#66900—24no—
75#66900—42no—
76#66899—42no—
77#66888—21no—
78#66887—21no—
79#66886—42no—
80#66883—21no—
81#66883—21no—
82#66883—21no—
83#66883—21no—
84#66879—21no—
85C8×Dic11—21no—
86#66870—22no—
87#66869—42no—
88#24989—111nomaximal, Sylow
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11C2×D414yes—
95C22×C4×C11—22no—
96C22×C4×C11C2411yescharacteristic
97C2×C22⋊D11—21no—
98#4339—21no—
99#4339—21no—
100#4339—21no—
101#4339—21no—
102C2×D44#4111yescharacteristic
103C2×C4×D11—21no—
104C2×Dic22#4111yescharacteristic
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×M16—21no—
110C11×M16—21no—
111C2×C8×C11—21no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11#4111yescharacteristic
115C2×C8×C11#4111yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C2×C8×C11#4111yescharacteristic
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—44no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4#4112yes—
123C42×C11—21no—
124C42×C11—22no—
125C42×C11—44no—
126C22⋊Dic11—21no—
127#4326—44no—
128#4325—44no—
129C4⋊Dic11—21no—
130C4×Dic11—21no—
131#4318—22no—
132#4318—21no—
133#4318—22no—
134#4318—21no—
135#4318—21no—
136#4318—22no—
137#4318—22no—
138#4318—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143#4313—41no—
144#4313—41no—
145C8×D11—41no—
146C8×D11—41no—
147C2×#473—111no—
148#2950D1111yescharacteristic, complemented
149#2082—112no—
150#2049—112no—
151#1979—111no—
152#1953—111no—
153#1905—112no—
154#1833—111no—
155#1830—112no—
156#1814—111no—
157#1757—111no—
158C23×C11C2×#4111yescharacteristic
159C22×D11—21no—
160Q8×C11—24no—
161Q8×C11—24no—
162Q8×C11—42no—
163Q8×C11—42no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11H(5,𝔽2)11yescharacteristic
174C2×C4×C11H(5,𝔽2)11yescharacteristic
175C22⋊D11—41no—
176C22⋊D11—41no—
177C2×Dic11—21no—
178C2×Dic11—41no—
179D44—21no—
180D44—21no—
181C4×D11—41no—
182C4×D11—41no—
183Dic22—21no—
184Dic22—21no—
185C8×C11—41no—
186C8×C11#12311yescharacteristic
187C8×C11#12311yescharacteristic
188C8×C11#12311yescharacteristic
189C8×C11#12311yescharacteristic
190C11⋊C8—41no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8—41no—
194C2×#137—112no—
195C22×Q16C2×D1111yescharacteristic
196C2×#131—111no—
197#519C2×D1112yes—
198#473—222no—
199#473—222no—
200#441—22no—
201C4×Q16—22no—
202#430—112no—
203C2×#108—111no—
204C2×#108—111no—
205#427C2×D1111yescharacteristic
206#421—112no—
207#419—112no—
208#419C2×D1112yes—
209#413—111no—
210C2×#101—112no—
211C2×#101—112no—
212#410—111no—
213#405—111no—
214#405C2×D1111yescharacteristic
215#344—111no—
216#344—112no—
217#344—112no—
218#344—111no—
219#344—112no—
220H(3,ℤ/4)—112no—
221C22×C11—41no—
222C22×C11#52911yescharacteristic
223C22×C11#54611yescharacteristic
224C22×C11#55511yescharacteristic
225C2×D11—41no—
226C2×D11—81no—
227C4×C11—42no—
228C4×C11—44no—
229C4×C11—82no—
230C4×C11C2×#12311yescharacteristic
231C4×C11#54011yescharacteristic
232C4×C11#54611yescharacteristic
233C4×C11#55311yescharacteristic
234Dic11—41no—
235Dic11—81no—
236C2×#41—111no—
237C22×Q8C22×D1112yes—
238#137—224no—
239#137—442no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—222no—
245C2×Q16C22⋊D1112yes—
246C2×Q16C22⋊D1112yes—
247C2×SD16—222no—
248#131—221no—
249#131—221no—
250#131—221no—
251#131—221no—
252C2×M16—111no—
253C2×M16—112no—
254C2×M16—111no—
255C2×M16—112no—
256C2×M16—221no—
257C2×M16C22×D1111yescharacteristic
258C22×C8—221no—
259C22×C8C22×D1111yescharacteristic
260C4×Q8—24no—
261C4×Q8—42no—
262#117—24no—
263#117—111no—
264#117C22×D1112yes—
265#117C22×D1111yescharacteristic
266#108—221no—
267#108—221no—
268#108—221no—
269#108—221no—
270#108—442no—
271#107—21no—
272#106—21no—
273#104—442no—
274#103—24no—
275#103—442no—
276#101—221no—
277#101—224no—
278#101—442no—
279#100—221no—
280#99—222no—
281#97—21no—
282#97—221no—
283C4×C8—21no—
284C4×C8—221no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11#242011yescharacteristic
289D11—81no—
290#41—221no—
291#41—221no—
292#41—221no—
293#41—221no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—111no—
300C2×Q8C2×C22⋊D1114yes—
301C2×D4—111no—
302C2×D4—221no—
303C22×C4—22no—
304C22×C4—221no—
305C22×C4C23×D1111yescharacteristic
306Q16—22no—
307Q16—22no—
308Q16—22no—
309Q16—22no—
310Q16—444no—
311SD16—444no—
312M16—21no—
313M16—21no—
314M16—222no—
315M16—221no—
316M16—221no—
317M16—222no—
318M16—221no—
319M16—222no—
320M16—221no—
321M16—222no—
322M16—441no—
323M16—441no—
324C2×C8—21no—
325C2×C8—221no—
326C2×C8—221no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—441no—
330C2×C8—441no—
331C2×C8#433911yescharacteristic
332C2×C8#433911yescharacteristic
333C2×C8#433911yescharacteristic
334C2×C8#433911yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—44no—
340C4⋊C4—221no—
341C22⋊C4—22no—
342C22⋊C4—221no—
343C22⋊C4#434112yes—
344C42—21no—
345C42—22no—
346C42—44no—
347C42—221no—
348C11#2498911yescharacteristic, complemented, Sylow
349C23—221no—
350C23C2×#434111yescharacteristic
351Q8—24no—
352Q8—24no—
353Q8—42no—
354Q8—42no—
355Q8—221no—
356Q8—221no—
357D4—221no—
358D4—221no—
359D4—441no—
360D4—441no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—221no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4C2×#433911yescharacteristic
371C2×C4C2×#433911yescharacteristic
372C2×C4#6703711yescharacteristic
373C2×C4#41×D1111yescharacteristic
374C2×C4#6704211yescharacteristic
375C2×C4C22×C22⋊D1111yescharacteristic
376C8—41no—
377C8—441no—
378C8—441no—
379C8—442no—
380C8—442no—
381C8#6698211yescharacteristic
382C8#6698211yescharacteristic
383C8#6698211yescharacteristic
384C8#6698211yescharacteristic
385C22—41no—
386C22—441no—
387C22—881no—
388C22#1062308811yescharacteristic
389C22#1062309411yescharacteristic
390C22#1062333711yescharacteristic
391C4—42no—
392C4—44no—
393C4—82no—
394C4—441no—
395C4—881no—
396C4#1062308911yescharacteristic
397C4#1062309311yescharacteristic
398C4C2×#6698211yescharacteristic
399C4#1062336011yescharacteristic
400C2—21no—
401C2—21no—
402C2—21no—
403C2—881no—
404C2#1307210211yescharacteristic
subgroupG/H
centerC2#13072102
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2950C2
socleC2×C11#2420
prime radicalC2×#4339C23
hypercenter#2950D11
hypocenterC11#24989
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2950

Complements

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

NH ≅ G/Ntype
2. #13070084C2semidirect
4. #13069532C2semidirect
5. #13069406C2semidirect
7. #13068739C2semidirect
8. #13068730C2semidirect
11. C11×#2950C2semidirect
148. #2950D11semidirect
348. C11#24989semidirect

Maximal subgroups

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

subgroupindex
C2×#106228052
#130700842
#130698942
#130695322
#130694062
#130691102
#130687392
#130687302
#130686672
#130684172
C11×#29502
#2498911