Finite Group Databasebeta

← #14672107

Subgroups — #14672107

Order 2816.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078255C211yesmaximal, characteristic
2#13070290C211yesmaximal, characteristic, complemented
3#13070287C211yesmaximal, characteristic
4#13070269C211yesmaximal, characteristic, complemented
5#13070265C211yesmaximal, characteristic
6#13068416C211yesmaximal, characteristic, complemented
7C11×#1812C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623361C2211yescharacteristic
10#10623356C2211yescharacteristic
11C22×#4314C411yescharacteristic, complemented
12C11×#427—21no—
13C11×#410C2211yescharacteristic
14C11×#410C2211yescharacteristic
15#10622853C2211yescharacteristic
16#10622850C2211yescharacteristic
17#10622747—21no—
18#10622747—21no—
19#10622744C411yescharacteristic, complemented
20#10622733C411yescharacteristic, complemented
21#10622727—21no—
22#10622727—21no—
23#10622719C411yescharacteristic, complemented
24#10622714—21no—
25C11×H(3,ℤ/4)—21no—
26#10622194—21no—
27#10622112—22no—
28#10622111—22no—
29#10622110—22no—
30#10622109—22no—
31C2×C11×#41C2311yescharacteristic
32C22×D44C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C11×#131—41no—
35C11×#131—41no—
36C2×C11×M16C2×C411yescharacteristic
37C2×C11×M16D411yescharacteristic
38C2×C11×M16D411yescharacteristic
39C22×C8×C11C2×C411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×#117—21no—
43C11×#117—21no—
44#67000—21no—
45#66997—21no—
46#66993—21no—
47#66990—21no—
48#66990—21no—
49#66989—21no—
50#66988—21no—
51#66988—21no—
52#66983—21no—
53#66983—21no—
54#66979—21no—
55#66979C2×C411yescharacteristic
56#66979C2×C411yescharacteristic
57#66977—21no—
58#66977—21no—
59C2×#4318—21no—
60C2×#4314—21no—
61C2×#4314—21no—
62C2×#4314—41no—
63C2×#4314—41no—
64C11×#107—41no—
65C11×#106—41no—
66C11×#99—21no—
67C11×#99—21no—
68C11×#99—21no—
69C11×#99—21no—
70#66900—21no—
71#66898—21no—
72#66898D412yes—
73#66897D412yes—
74#66885—21no—
75#66885—21no—
76#66882—21no—
77#66881—21no—
78#66880—21no—
79#66880—21no—
80#66879—41no—
81C8×Dic11—41no—
82#13229—111nomaximal, Sylow
83C23×D11—21no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11#4111yescharacteristic
87C2×D4×C11C2×D411yescharacteristic
88C2×D4×C11C2×D411yescharacteristic
89C2×D4×C11#4111yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C22×Dic11—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—41no—
99C2×D44—41no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C11×M16—41no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11C22⋊C411yescharacteristic
114C2×C8×C11C22⋊C411yescharacteristic
115C2×C8×C11C22⋊C411yescharacteristic
116C2×C8×C11C22⋊C411yescharacteristic
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C22⋊Dic11—21no—
124C22⋊Dic11—21no—
125C22⋊Dic11—22no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—41no—
138#4318—22no—
139#4318—41no—
140C2×C11⋊C8—41no—
141#4314—42no—
142#4314—41no—
143#4314—41no—
144#3057—111no—
145#2129—111no—
146#2128—111no—
147#2123—111no—
148#2122—111no—
149#1812D1111yescharacteristic, complemented
150#1757—111no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12711yescharacteristic
154C22×D11—41no—
155C22×D11—81no—
156C22×D11—161no—
157Q8×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11C2×C22⋊C411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12411yescharacteristic
173C22⋊D11—161no—
174C22⋊D11—161no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—81no—
180D44—41no—
181D44—41no—
182D44—81no—
183Dic22—41no—
184Dic22—41no—
185Dic22—81no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11#9911yescharacteristic
190C8×C11#9911yescharacteristic
191C11⋊C8—42no—
192C22×SD16—111no—
193C2×#131C2×D1111yescharacteristic
194#536—111no—
195#535—111no—
196#468—221no—
197#468—221no—
198#465—221no—
199#465—221no—
200#427—21no—
201#427—111no—
202#419—111no—
203#418—111no—
204#413—111no—
205#410—111no—
206#410C2×D1111yescharacteristic
207#410C2×D1111yescharacteristic
208#405—221no—
209#354—222no—
210#353—222no—
211#352—222no—
212AΣL(1,𝔽16)—222no—
213#344—221no—
214H(3,ℤ/4)—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11#39011yescharacteristic
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—162no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—161no—
230C4×C11—161no—
231C4×C11C2×#9911yescharacteristic
232C4×C11#41011yescharacteristic
233Dic11—81no—
234Dic11—81no—
235Dic11—82no—
236Dic11—81no—
237C2×#41C22×D1111yescharacteristic
238C22×Q8—111no—
239C22×D4—111no—
240C2×SD16—221no—
241C2×SD16—221no—
242C2×SD16—441no—
243C2×SD16—441no—
244#131—41no—
245#131—41no—
246C2×M16—221no—
247C2×M16C4×D1111yescharacteristic
248C2×M16D4411yescharacteristic
249C2×M16C22⋊D1111yescharacteristic
250C22×C8C4×D1111yescharacteristic
251C22×C8D4411yescharacteristic
252C22×C8C22⋊D1111yescharacteristic
253C4⋊Q8—221no—
254#127—221no—
255#124—221no—
256#124—221no—
257#123—221no—
258#123—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261#121—221no—
262#121—221no—
263#120—221no—
264#120—221no—
265#117—21no—
266#117—21no—
267#117—111no—
268#117—111no—
269#117—221no—
270#107—41no—
271#107—221no—
272#106—41no—
273#106—221no—
274#103—221no—
275#103—221no—
276#102—221no—
277#102—221no—
278#101—221no—
279#100—112no—
280#99—21no—
281#99—21no—
282#99—21no—
283#99—21no—
284#99—112no—
285#99—221no—
286#97—441no—
287C4×C8—441no—
288C2×C11—21no—
289C2×C11—41no—
290C2×C11—41no—
291C2×C11—41no—
292C2×C11#196411yescharacteristic
293D11—161no—
294C24—221no—
295#41—41no—
296#41—41no—
297C2×Q8—221no—
298C2×Q8—221no—
299C2×Q8—441no—
300C2×Q8—441no—
301C2×Q8#434311yescharacteristic
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4D4×D1111yescharacteristic
309C2×D4D4×D1111yescharacteristic
310C2×D4#434311yescharacteristic
311C22×C4—221no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4C2×D4411yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315SD16—442no—
316SD16—441no—
317SD16—441no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—222no—
322M16—441no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—441no—
330C2×C8(C2×D11)⋊C411yescharacteristic
331C2×C8(C2×D11)⋊C411yescharacteristic
332C2×C8(C2×D11)⋊C411yescharacteristic
333C2×C8(C2×D11)⋊C411yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C22⋊C4—222no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—41no—
351C42—41no—
352C42—221no—
353C42—221no—
354C42—441no—
355C11#1322911yescharacteristic, complemented, Sylow
356C23—441no—
357C23—881no—
358C23—1761no—
359C23#6694611yescharacteristic
360C23#6694811yescharacteristic
361C23#6699311yescharacteristic
362Q8—41no—
363Q8—441no—
364Q8—441no—
365Q8—881no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—441no—
370D4—441no—
371D4—881no—
372D4—1761no—
373D4—1761no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4#6694611yescharacteristic
388C2×C4#6694811yescharacteristic
389C2×C4C2×(C2×D11)⋊C411yescharacteristic
390C2×C4#6700011yescharacteristic
391C8—21no—
392C8—21no—
393C8—21no—
394C8—442no—
395C8#6687011yescharacteristic
396C8#6687011yescharacteristic
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—1762no—
407C22#1062260111yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—161no—
412C4—161no—
413C4—881no—
414C4—881no—
415C4—882no—
416C4—881no—
417C4C2×#6687011yescharacteristic
418C4#1062261911yescharacteristic
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—1761no—
424C2#1306945111yescharacteristic
subgroupG/H
centerC2#13069451
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1812C2
socleC2×C11#1964
prime radical#10623361C22
cosocleC2×C11×#41C23
hypercenter#1812D11
hypocenterC11#13229
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1812

Complements

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

NH ≅ G/Ntype
2. #13070290C2semidirect
4. #13070269C2semidirect
6. #13068416C2semidirect
7. C11×#1812C2semidirect
11. C22×#4314C4semidirect
19. #10622744C4semidirect
20. #10622733C4semidirect
23. #10622719C4semidirect
149. #1812D11semidirect
355. C11#13229semidirect

Maximal subgroups

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

subgroupindex
#130782552
#130702902
#130702872
#130702692
#130702652
#130684162
C11×#18122
#1322911