Finite Group Databasebeta

← #14672128

Subgroups — #14672128

Order 2816.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070311C211yesmaximal, characteristic, complemented
2#13070308C211yesmaximal, characteristic
3#13070270C211yesmaximal, characteristic, complemented
4#13070266C211yesmaximal, characteristic
5#13068666C211yesmaximal, characteristic, complemented
6#13068416C211yesmaximal, characteristic, complemented
7C11×#3057C211yesmaximal, characteristic
8C22×C11×SD16C411yescharacteristic, complemented
9C2×C11×#131C2211yescharacteristic
10C11×#536C2211yescharacteristic
11C11×#535C2211yescharacteristic
12C11×#468—21no—
13C11×#468—21no—
14C11×#465—21no—
15C11×#465—21no—
16C11×#427C411yescharacteristic, complemented
17C11×#419C411yescharacteristic, complemented
18C11×#418C411yescharacteristic, complemented
19#10622853C2211yescharacteristic
20#10622850C2211yescharacteristic
21#10622850C2211yescharacteristic
22#10622850C2211yescharacteristic
23C2×#66883—21no—
24#10622714—21no—
25C11⋊#338—21no—
26#10622194—21no—
27#10622186—22no—
28#10622180—22no—
29#10622177—22no—
30#10622174—22no—
31C2×C11×#41C2311yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×D4×C11C2×C411yescharacteristic
34C2×C11×SD16—21no—
35C2×C11×SD16—21no—
36C2×C11×SD16—41no—
37C2×C11×SD16—41no—
38C11×#131—41no—
39C11×#131—41no—
40C2×C11×M16C2×C411yescharacteristic
41C2×C11×M16D411yescharacteristic
42C2×C11×M16D411yescharacteristic
43C22×C8×C11C2×C411yescharacteristic
44C22×C8×C11D411yescharacteristic
45C22×C8×C11D411yescharacteristic
46C11×C4⋊Q8—21no—
47C11×#127—21no—
48C11×#124—21no—
49C11×#124—21no—
50C11×#123—21no—
51C11×#123—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C11×#121—21no—
55C11×#121—21no—
56C11×#120—21no—
57C11×#120—21no—
58C11×#117C2×C411yescharacteristic
59C11×#117C2×C411yescharacteristic
60#66979—21no—
61C2×#4318—21no—
62C2×#4318—21no—
63C2×#4318—21no—
64C11×#107—21no—
65C11×#106—21no—
66C11×#103—21no—
67C11×#103—21no—
68C11×#102—21no—
69C11×#102—21no—
70#66900—21no—
71#66900—21no—
72#66900D412yes—
73#66898—21no—
74#66898D412yes—
75#66897—21no—
76#66897—21no—
77#66897—21no—
78#66883—41no—
79#66883—41no—
80#66879—41no—
81C8×Dic11—41no—
82#13232—111nomaximal, Sylow
83C24×C11—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×C11C2×D411yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11C2×D411yescharacteristic
98C2×D4×C11#4111yescharacteristic
99C2×D4×C11#4111yescharacteristic
100C22×C4×C11—21no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×SD16—42no—
105C11×SD16—41no—
106C11×SD16—41no—
107C11×M16—41no—
108C11×M16—41no—
109C11×M16—41no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11C22⋊C411yescharacteristic
117C2×C8×C11C22⋊C411yescharacteristic
118C2×C8×C11C22⋊C411yescharacteristic
119C2×C8×C11C22⋊C411yescharacteristic
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—21no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11—21no—
131C42×C11—21no—
132C22⋊Dic11—22no—
133C4⋊Dic11—41no—
134C4×Dic11—41no—
135#4318—22no—
136#4318—41no—
137#4318—41no—
138#4318—41no—
139#4318—41no—
140#4318—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144#3057D1111yescharacteristic
145#2135—111no—
146#2134—111no—
147#2123—111no—
148#2122—111no—
149#1813—111no—
150#1757—111no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—161no—
154C23×C11C4×D411yescharacteristic
155C23×C11#12111yescharacteristic
156C23×C11#12411yescharacteristic
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—81no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—81no—
167D4×C11—161no—
168D4×C11—161no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12711yescharacteristic
183C2×Dic11—42no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11—21no—
187C8×C11#9911yescharacteristic
188C8×C11#9911yescharacteristic
189C11⋊C8—42no—
190C11⋊C8—81no—
191C11⋊C8—81no—
192C22×SD16Dic1111yescharacteristic, complemented
193C2×#131C2×D1111yescharacteristic
194#536C2×D1111yescharacteristic
195#535C2×D1111yescharacteristic
196#468—21no—
197#468—21no—
198#465—21no—
199#465—21no—
200C2×#108—221no—
201#427Dic1111yescharacteristic, complemented
202#419Dic1111yescharacteristic, complemented
203#418Dic1111yescharacteristic, complemented
204#413—111no—
205#413—111no—
206#413—111no—
207#410—111no—
208#405—221no—
209#356—222no—
210#355—222no—
211#352—222no—
212AΣL(1,𝔽16)—222no—
213#344—221no—
214#338—221no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—162no—
225C22×C11#39011yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11C2×#9911yescharacteristic
233C4×C11#41011yescharacteristic
234Dic11—82no—
235C2×#41C22×D1111yescharacteristic
236C22×Q8C2×Dic1111yescharacteristic
237C22×D4C2×Dic1111yescharacteristic
238C2×SD16—21no—
239C2×SD16—21no—
240C2×SD16—41no—
241C2×SD16—41no—
242#131—41no—
243#131—41no—
244C2×M16—221no—
245C2×M16—221no—
246C2×M16—221no—
247C2×M16C2×Dic1111yescharacteristic
248C2×M16C22⋊D1111yescharacteristic
249C2×M16C22⋊D1111yescharacteristic
250C22×C8C2×Dic1111yescharacteristic
251C22×C8C22⋊D1111yescharacteristic
252C22×C8C22⋊D1111yescharacteristic
253C4⋊Q8—21no—
254#127—21no—
255#124—21no—
256#124—21no—
257#123—21no—
258#123—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—21no—
262#121—21no—
263#120—21no—
264#120—21no—
265#117—221no—
266#117C2×Dic1111yescharacteristic
267#117C2×Dic1111yescharacteristic
268#108—441no—
269#108—441no—
270#107—21no—
271#106—21no—
272#103—21no—
273#103—21no—
274#102—21no—
275#102—21no—
276#101—112no—
277#101—221no—
278#101—221no—
279#100—221no—
280#100—221no—
281#100—221no—
282#99—112no—
283#99—221no—
284#97—441no—
285C4×C8—441no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11—161no—
291C2×C11#196411yescharacteristic
292C24—21no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8D4×D1111yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4D4×D1111yescharacteristic
307C2×D4#434111yescharacteristic
308C2×D4#434111yescharacteristic
309C22×C4—21no—
310C22×C4C22×Dic1111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313SD16—42no—
314SD16—41no—
315SD16—41no—
316M16—41no—
317M16—41no—
318M16—41no—
319M16—222no—
320M16—441no—
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—441no—
332C2×C8—441no—
333C2×C8—441no—
334C2×C8C22⋊Dic1111yescharacteristic
335C2×C8C22⋊Dic1111yescharacteristic
336C2×C8C22⋊Dic1111yescharacteristic
337C2×C8C22⋊Dic1111yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—441no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—222no—
350C42—21no—
351C42—21no—
352C42—441no—
353C11#1323211yescharacteristic, complemented, Sylow
354C23—41no—
355C23—81no—
356C23—161no—
357C23D4×Dic1111yescharacteristic
358C23#6698911yescharacteristic
359C23#6699111yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—442no—
383C2×C4D4×Dic1111yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4#6699311yescharacteristic
386C2×C4C2×C22⋊Dic1111yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—442no—
391C8—881no—
392C8—881no—
393C8#6689811yescharacteristic
394C8#6689811yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22#1062283411yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—882no—
413C4C2×#6689811yescharacteristic
414C4#1062285311yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2#1306945311yescharacteristic
subgroupG/H
centerC2#13069453
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#3057C2
socleC2×C11#1964
prime radicalC11×#535C22
cosocleC2×C11×#41C23
hypercenter#3057D11
hypocenterC11#13232
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #3057

Complements

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

NH ≅ G/Ntype
1. #13070311C2semidirect
3. #13070270C2semidirect
5. #13068666C2semidirect
6. #13068416C2semidirect
8. C22×C11×SD16C4semidirect
16. C11×#427C4semidirect
17. C11×#419C4semidirect
18. C11×#418C4semidirect
192. C22×SD16Dic11semidirect
201. #427Dic11semidirect
202. #419Dic11semidirect
203. #418Dic11semidirect
353. C11#13232semidirect

Maximal subgroups

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

subgroupindex
#130703112
#130703082
#130702702
#130702662
#130686662
#130684162
C11×#30572
#1323211