Finite Group Databasebeta

← #14672126

Subgroups — #14672126

Order 2816.

448 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 99 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#13070310C211yesmaximal, characteristic, complemented
3#13070307C211yesmaximal, characteristic
4#13070269C211yesmaximal, characteristic, complemented
5#13070265C211yesmaximal, characteristic
6#13068666C211yesmaximal, characteristic, complemented
7C11×#1757C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623361C2211yescharacteristic
10#10623356C2211yescharacteristic
11C22×#4314C411yescharacteristic, complemented
12C11×#413C2211yescharacteristic
13C11×#410C2211yescharacteristic
14C11×#405—21no—
15#10622850C2211yescharacteristic
16#10622850C2211yescharacteristic
17#10622747—21no—
18#10622747—21no—
19#10622744C411yescharacteristic, complemented
20#10622733C411yescharacteristic, complemented
21#10622727—21no—
22#10622727—21no—
23C2×#66883—21no—
24#10622719C411yescharacteristic, complemented
25C11×#344—21no—
26C11⋊#338—21no—
27#10622116—22no—
28#10622115—22no—
29#10622110—22no—
30#10622109—22no—
31C2×C11×#41C2311yescharacteristic
32C22×D44C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C11×#131—41no—
35C11×#131—41no—
36C2×C11×M16—21no—
37C2×C11×M16C2×C411yescharacteristic
38C2×C11×M16D411yescharacteristic
39C2×C11×M16D411yescharacteristic
40C22×C8×C11C2×C411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
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#66979C2×C411yescharacteristic
55#66979C2×C411yescharacteristic
56#66977—21no—
57#66977—21no—
58C2×#4318—21no—
59C2×#4318—21no—
60C2×#4314—21no—
61C2×#4314—21no—
62C2×#4314—41no—
63C2×#4314—41no—
64C11×#101D412yes—
65C11×#100—21no—
66C11×#99—21no—
67C11×#99D412yes—
68C11×#97—41no—
69C4×C8×C11—41no—
70#66900—21no—
71#66900—21no—
72#66897—21no—
73#66897—21no—
74#66885—21no—
75#66885—21no—
76#66883—41no—
77#66883—41no—
78#66882—21no—
79#66881—21no—
80#66880—21no—
81#66880—21no—
82#13232—111nomaximal, Sylow
83C23×D11—21no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11C2×D411yescharacteristic
87C2×D4×C11C2×D411yescharacteristic
88C2×D4×C11#4111yescharacteristic
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—22no—
105C11×M16—41no—
106C11×M16—41no—
107C11×M16—41no—
108C11×M16—41no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—41no—
116C2×C8×C11C22⋊C411yescharacteristic
117C2×C8×C11C22⋊C411yescharacteristic
118C2×C8×C11C22⋊C411yescharacteristic
119C2×C8×C11C22⋊C411yescharacteristic
120C11×C4⋊C4—41no—
121C11×C22⋊C4—22no—
122C42×C11—41no—
123C22⋊Dic11—21no—
124C22⋊Dic11—21no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135#4318—41no—
136#4318—41no—
137#4318—41no—
138#4318—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141#4314—42no—
142#4314—41no—
143#4314—41no—
144#3057—111no—
145#2135—111no—
146#2134—111no—
147#2123—111no—
148#2122—111no—
149#1813—111no—
150#1757D1111yescharacteristic, complemented
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12411yescharacteristic
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—42no—
168C2×C4×C11C2×C22⋊C411yescharacteristic
169C2×C4×C11C4×D411yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C22⋊D11—161no—
173C22⋊D11—161no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—81no—
178D44—41no—
179D44—41no—
180D44—81no—
181Dic22—41no—
182Dic22—41no—
183Dic22—81no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11—21no—
187C8×C11—42no—
188C8×C11#9911yescharacteristic
189C8×C11#9911yescharacteristic
190C11⋊C8—81no—
191C11⋊C8—81no—
192C22×SD16—111no—
193C2×#131C2×D1111yescharacteristic
194#536—111no—
195#535—111no—
196#468—221no—
197#468—221no—
198#465—221no—
199#465—221no—
200C2×#108—221no—
201#427—111no—
202#419—111no—
203#418—111no—
204#413—111no—
205#413—111no—
206#413C2×D1111yescharacteristic
207#410C2×D1111yescharacteristic
208#405—21no—
209#356—222no—
210#355—222no—
211#352—222no—
212AΣL(1,𝔽16)—222no—
213#344—21no—
214#338—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—82no—
230C4×C11C2×#9911yescharacteristic
231C4×C11#41011yescharacteristic
232Dic11—81no—
233Dic11—81no—
234Dic11—81no—
235C2×#41C22×D1111yescharacteristic
236C22×Q8—111no—
237C22×D4—111no—
238C2×SD16—221no—
239C2×SD16—221no—
240C2×SD16—441no—
241C2×SD16—441no—
242#131—41no—
243#131—41no—
244C2×M16—21no—
245C2×M16—221no—
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—111no—
267#117—111no—
268#108—441no—
269#108—441no—
270#107—221no—
271#106—221no—
272#103—221no—
273#103—221no—
274#102—221no—
275#102—221no—
276#101—221no—
277#101—221no—
278#101D4412yes—
279#100—21no—
280#100—221no—
281#100—221no—
282#99—21no—
283#99D4412yes—
284#97—41no—
285C4×C8—41no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11#196411yescharacteristic
291D11—161no—
292C24—221no—
293#41—41no—
294#41—41no—
295C2×Q8—221no—
296C2×Q8—221no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×Q8C2×D4411yescharacteristic
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4C2×D4411yescharacteristic
307C2×D4#433911yescharacteristic
308C2×D4#433911yescharacteristic
309C22×C4—221no—
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4C2×D4411yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313SD16—442no—
314SD16—441no—
315SD16—441no—
316M16—22no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—441no—
322M16—441no—
323M16—441no—
324M16—441no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—441no—
333C2×C8—441no—
334C2×C8(C2×D11)⋊C411yescharacteristic
335C2×C8(C2×D11)⋊C411yescharacteristic
336C2×C8(C2×D11)⋊C411yescharacteristic
337C2×C8(C2×D11)⋊C411yescharacteristic
338C4⋊C4—41no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C22⋊C4—22no—
344C22⋊C4—221no—
345C22⋊C4—221no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—41no—
351C42—221no—
352C42—221no—
353C11#1323211yescharacteristic, complemented, Sylow
354C23—441no—
355C23—881no—
356C23—1761no—
357C23C4×D4411yescharacteristic
358C23#6692811yescharacteristic
359C23#6698311yescharacteristic
360Q8—41no—
361Q8—441no—
362Q8—441no—
363Q8—881no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—441no—
368D4—441no—
369D4—881no—
370D4—1761no—
371D4—1761no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—881no—
383C2×C4C4×D4411yescharacteristic
384C2×C4#6692711yescharacteristic
385C2×C4C2×(C2×D11)⋊C411yescharacteristic
386C2×C4#6698311yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—42no—
391C8—881no—
392C8—881no—
393C8#6687011yescharacteristic
394C8#6687011yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22—1762no—
405C22#1062255211yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—82no—
410C4—881no—
411C4—881no—
412C4—881no—
413C4C2×#6687011yescharacteristic
414C4#1062261911yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—1761no—
420C2#1306945211yescharacteristic
subgroupG/H
centerC2#13069452
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1757C2
socleC2×C11#1964
prime radical#10623361C22
cosocleC2×C11×#41C23
hypercenter#1757D11
hypocenterC11#13232
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
2. #13070310C2semidirect
4. #13070269C2semidirect
6. #13068666C2semidirect
7. C11×#1757C2semidirect
11. C22×#4314C4semidirect
19. #10622744C4semidirect
20. #10622733C4semidirect
24. #10622719C4semidirect
150. #1757D11semidirect
353. C11#13232semidirect

Maximal subgroups

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

subgroupindex
#130782552
#130703102
#130703072
#130702692
#130702652
#130686662
C11×#17572
#1323211