Finite Group Databasebeta

← #14672106

Subgroups — #14672106

Order 2816.

452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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#13078257C211yesmaximal, characteristic
2#13070291C211yesmaximal, characteristic, complemented
3#13070287C211yesmaximal, characteristic
4#13070267C211yesmaximal, characteristic
5#13068660C211yesmaximal, characteristic, complemented
6#13068419C211yesmaximal, characteristic, complemented
7C11×#2123C211yesmaximal, characteristic, complemented
8C11×#536C2211yescharacteristic
9#10623361C2211yescharacteristic
10C2×#67001C2211yescharacteristic
11C22×#4325C411yescharacteristic, complemented
12C11×#413C2211yescharacteristic
13C11×#410C2211yescharacteristic
14#10622853C2211yescharacteristic
15#10622853C2211yescharacteristic
16#10622838C411yescharacteristic, complemented
17#10622735—21no—
18#10622662—21no—
19#10622662—21no—
20#10622661—21no—
21#10622661—21no—
22#10622614C411yescharacteristic, complemented
23#10622611—21no—
24#10622611C411yescharacteristic, complemented
25C11×#352—22no—
26#10622197—21no—
27#10622179—22no—
28#10622169—21no—
29#10622113—22no—
30#10622112—22no—
31C2×C11×#41C2311yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×D44C2×C411yescharacteristic
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×#124—21no—
37C11×#123—21no—
38C11×#123—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×#117—21no—
42C11×#117C2×C411yescharacteristic
43#67001—41no—
44#67001—41no—
45#67000—21no—
46C2×#4325—21no—
47C2×#4325—21no—
48C2×#4325—41no—
49C2×#4325—41no—
50#66993—21no—
51#66990—21no—
52#66990—21no—
53#66983—21no—
54#66983—21no—
55#66979—21no—
56#66979—21no—
57#66979C2×C411yescharacteristic
58C2×#4318C2×C411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×#4318D411yescharacteristic
61C22×C11⋊C8C2×C411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C11×#101—21no—
65C11×#100D412yes—
66C11×#99—21no—
67C11×#99—21no—
68#66899—21no—
69#66899—21no—
70#66898—21no—
71#66898—21no—
72#66898—21no—
73#66898D412yes—
74#66879—41no—
75C8×Dic11—41no—
76#66873—21no—
77#66873—21no—
78#66872—21no—
79#66872—41no—
80#66871—21no—
81#66871—41no—
82#13229—111nomaximal, Sylow
83C23×D11—21no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11#4111yescharacteristic
91C2×D4×C11C2×D411yescharacteristic
92C2×D4×C11C2×D411yescharacteristic
93C2×D4×C11#4111yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—41no—
103C2×D44—41no—
104C11×M16—22no—
105C11×M16—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—41no—
117C22⋊Dic11—21no—
118C22⋊Dic11—22no—
119C22⋊Dic11—41no—
120#4325—42no—
121#4325—41no—
122#4325—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4×Dic11—21no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131#4318—41no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8C22⋊C411yescharacteristic
141C2×C11⋊C8C22⋊C411yescharacteristic
142C2×C11⋊C8C22⋊C411yescharacteristic
143C2×C11⋊C8C22⋊C411yescharacteristic
144#3057—111no—
145#2129—111no—
146#2128—111no—
147#2123D1111yescharacteristic, complemented
148#2122—111no—
149#1812—111no—
150#1757—111no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12711yescharacteristic
154C22×D11—41no—
155C22×D11—81no—
156C22×D11—161no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—81no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11C2×C22⋊C411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12411yescharacteristic
178C22⋊D11—161no—
179C22⋊D11—161no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—81no—
183D44—41no—
184D44—41no—
185D44—81no—
186C8×C11—42no—
187C11⋊C8—21no—
188C11⋊C8—21no—
189C11⋊C8—21no—
190C11⋊C8#9911yescharacteristic
191C11⋊C8#9911yescharacteristic
192C22×SD16—111no—
193C2×#131—111no—
194#536C2×D1111yescharacteristic
195#535—111no—
196#468—221no—
197#468—221no—
198#465—221no—
199#465—221no—
200#427—111no—
201#427—221no—
202#419—111no—
203#418—111no—
204#413C2×D1111yescharacteristic
205#410—111no—
206#410—111no—
207#410C2×D1111yescharacteristic
208#405—221no—
209#354—222no—
210#353—222no—
211#352—22no—
212AΣL(1,𝔽16)—222no—
213#344—221no—
214H(3,ℤ/4)—221no—
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—81no—
230C4×C11—81no—
231C4×C11—161no—
232C4×C11C2×#9911yescharacteristic
233C4×C11#41011yescharacteristic
234Dic11—81no—
235Dic11—82no—
236Dic11—161no—
237C2×#41C22×D1111yescharacteristic
238C22×Q8C4×D1111yescharacteristic
239C22×D4—111no—
240C2×SD16—221no—
241C2×SD16—221no—
242C2×SD16—441no—
243C2×SD16—441no—
244#131—441no—
245#131—441no—
246C2×M16—21no—
247C2×M16—111no—
248C2×M16—111no—
249C2×M16—111no—
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—111no—
253C4⋊Q8—21no—
254#127—221no—
255#124—21no—
256#124—221no—
257#123—21no—
258#123—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—221no—
262#121—221no—
263#120—221no—
264#120—221no—
265#117—21no—
266#117—111no—
267#117—221no—
268#117—221no—
269#117C4×D1111yescharacteristic
270#107—221no—
271#107—441no—
272#106—221no—
273#106—441no—
274#103—221no—
275#103—221no—
276#102—221no—
277#102—221no—
278#101—21no—
279#100C22⋊D1112yes—
280#99—21no—
281#99—21no—
282#99—112no—
283#99—221no—
284#99—221no—
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—21no—
298C2×Q8—21no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8#434111yescharacteristic
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4#433911yescharacteristic
309C2×D4D4×D1111yescharacteristic
310C2×D4C2×C22⋊D1111yescharacteristic
311C22×C4—21no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315SD16—441no—
316SD16—441no—
317SD16—442no—
318M16—22no—
319M16—41no—
320M16—441no—
321M16—441no—
322M16—441no—
323C2×C8—41no—
324C2×C8—111no—
325C2×C8—111no—
326C2×C8—111no—
327C2×C8—111no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—221no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C22⋊C4—21no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—222no—
346C22⋊C4—221no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—21no—
351C42—41no—
352C42—221no—
353C42—441no—
354C42—441no—
355C11#1322911yescharacteristic, complemented, Sylow
356C23—441no—
357C23—881no—
358C23—1761no—
359C23#6693711yescharacteristic
360C23C4×C22⋊D1111yescharacteristic
361C23#6699311yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—41no—
365Q8—81no—
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—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4C22⋊C4×D1111yescharacteristic
388C2×C4(C22⋊D11)⋊C411yescharacteristic
389C2×C4#6693811yescharacteristic
390C2×C4#6699211yescharacteristic
391C8—42no—
392C8—111no—
393C8—111no—
394C8—221no—
395C8—221no—
396C8—221no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—1762no—
407C22#1062257011yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—161no—
414C4—881no—
415C4—882no—
416C4—1761no—
417C4#1062235311yescharacteristic
418C4D11×#9911yescharacteristic
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—1761no—
424C2#1306945011yescharacteristic
subgroupG/H
centerC2#13069450
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2123C2
socleC2×C11#1964
prime radical#10623361C22
cosocleC2×C11×#41C23
hypercenter#2123D11
hypocenterC11#13229
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
2. #13070291C2semidirect
5. #13068660C2semidirect
6. #13068419C2semidirect
7. C11×#2123C2semidirect
11. C22×#4325C4semidirect
16. #10622838C4semidirect
22. #10622614C4semidirect
24. #10622611C4semidirect
147. #2123D11semidirect
355. C11#13229semidirect

Maximal subgroups

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

subgroupindex
#130782572
#130702912
#130702872
#130702672
#130686602
#130684192
C11×#21232
#1322911