Finite Group Databasebeta

← #14908167

Subgroups — #14908167

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081752C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic, complemented
3C2×#10622313C211yesmaximal, characteristic, complemented
4#13070698C212yesmaximal, complemented
5#13070693C212yesmaximal, complemented
6#13070686C214yesmaximal, complemented
7#13070366C212yesmaximal, complemented
8C2×C11×#364C211yesmaximal, characteristic, complemented
9C2×#66957—21no—
10C2×#66957C2211yescharacteristic
11C2×#66957C2212yes—
12C2×#66954—21no—
13#10623008—21no—
14C2×C11×M32C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66883C2211yescharacteristic
17C2×#66869—21no—
18#10622522—22no—
19#10622522C2214yes—
20#10622521—22no—
21#10622521C2214yes—
22#10622517—24no—
23#10622313—21no—
24#10622313—21no—
25#10622313C2212yes—
26#10622313C2212yes—
27#10622312C2211yescharacteristic, complemented
28#10622309—21no—
29#10622309C2212yescomplemented
30#10622308C2211yescharacteristic, complemented
31#10622306—21no—
32C11×#364C2212yescomplemented
33C11×#364C2212yescomplemented
34#10622155C2214yescomplemented
35#10622154C2214yescomplemented
36C2×#4339—21no—
37C2×#4339—22no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C2×C42×C11D411yescharacteristic
41#66983—42no—
42C2×#4318—21no—
43C2×Dic44—21no—
44C2×Dic44D411yescharacteristic, complemented
45C2×Dic44C2312yes—
46#66957—21no—
47#66957—21no—
48#66957—22no—
49#66957—22no—
50#66957—22no—
51#66957—22no—
52#66957—41no—
53#66957—41no—
54#66957—41no—
55#66957—41no—
56#66957D412yescomplemented
57#66957C2312yes—
58C2×D88—21no—
59C2×D88D411yescharacteristic, complemented
60C2×D88C2312yes—
61C2×#4314—21no—
62C2×#4314—22no—
63C2×#4314—22no—
64#66954—22no—
65#66954—22no—
66#66954—41no—
67#66954—41no—
68C2×#4313—41no—
69C2×C8×D11—41no—
70#66928—22no—
71#66927—21no—
72C4×D44—42no—
73#66922—21no—
74C11×M32—22no—
75C11×M32C2314yes—
76C2×C11×C16—22no—
77C4×C8×C11D411yescharacteristic
78C4×C8×C11D411yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C4×C8×C11C2311yescharacteristic
81#66883—21no—
82#66883C2312yes—
83#66869—22no—
84#66869—22no—
85Dic88—24no—
86#66864—24no—
87#66864—24no—
88D176—24no—
89#33594—111nomaximal, Sylow
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93C2×C22⋊D11—42no—
94#4339—22no—
95#4339—22no—
96#4339—42no—
97#4339—42no—
98#4339—41no—
99#4339—42no—
100#4339—42no—
101#4339—41no—
102C2×D44—21no—
103C2×D44—22no—
104C2×D44—42no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×C8×C11D811yescharacteristic
110C2×C8×C11D811yescharacteristic
111C2×C8×C11D811yescharacteristic
112C2×C8×C11D811yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11#4111yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C42×C11—21no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124(C2×D11)⋊C4—44no—
125C4⋊Dic11—42no—
126#4318—22no—
127#4318—41no—
128C2×C11⋊C8—41no—
129Dic44—21no—
130Dic44—22no—
131Dic44—22no—
132Dic44—41no—
133Dic44—41no—
134Dic44C2×D412yes—
135D88—21no—
136D88—22no—
137D88—22no—
138D88—41no—
139D88—41no—
140D88C2×D412yes—
141#4314—22no—
142#4314—22no—
143#4314—42no—
144#4314—42no—
145#4314—42no—
146#4314—42no—
147#4313—42no—
148#4313—42no—
149C8×D11—42no—
150C8×D11—42no—
151C11×C16—24no—
152#3414—112no—
153#3147—111no—
154C2×#443—111no—
155#2214—112no—
156#2213—112no—
157#2212—114no—
158C2×#364D1111yescharacteristic, complemented
159#2148—112no—
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C22×D11—41no—
162C22×D11—42no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—42no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—42no—
173C22⋊D11—42no—
174C22⋊D11—82no—
175C22⋊D11—82no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178D44—22no—
179D44—42no—
180D44—42no—
181D44—41no—
182D44—84no—
183C4×D11—42no—
184C4×D11—42no—
185C4×D11—82no—
186C4×D11—82no—
187Dic22—22no—
188Dic22—41no—
189Dic22—42no—
190Dic22—42no—
191C8×C11#12111yescharacteristic
192C8×C11#12111yescharacteristic
193C8×C11C2×D811yescharacteristic
194C8×C11C2×D811yescharacteristic
195C8×C11C2×D811yescharacteristic
196C8×C11C2×D811yescharacteristic
197C8×C11C22×D411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—42no—
200C2×#135—111no—
201C2×#135—112no—
202C2×#135—221no—
203C2×#131—221no—
204#532—221no—
205#510—114no—
206#510—222no—
207#509—114no—
208#509—222no—
209#508—224no—
210C2×M32C2×D1112yes—
211#495—112no—
212#495—221no—
213#494—111no—
214#493—111no—
215#492—221no—
216#443—112no—
217#443—112no—
218#443—221no—
219#443—221no—
220C2×#108—111no—
221C2×#104—221no—
222C2×C4×C8C2×D1111yescharacteristic
223#364C2×D1112yescomplemented
224#364C2×D1112yescomplemented
225#362—114no—
226#361—114no—
227C22×C11—41no—
228C22×C11#45911yescharacteristic
229C22×C11#45911yescharacteristic
230C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C2×D11—42no—
232C2×D11—82no—
233C2×D11—84no—
234C2×D11—82no—
235C4×C11—22no—
236C4×C11—41no—
237C4×C11#45911yescharacteristic
238C4×C11#45911yescharacteristic
239C4×C11C2×#12111yescharacteristic
240C4×C11C22×D811yescharacteristic
241Dic11—42no—
242Dic11—82no—
243C2×#41—221no—
244C2×#41—222no—
245#135—112no—
246#135—112no—
247#135—221no—
248#135—222no—
249#135—222no—
250#135—221no—
251#135—222no—
252#135—222no—
253#135—441no—
254#135—441no—
255#135—441no—
256#135—441no—
257C2×Q16—111no—
258C2×Q16—112no—
259C2×Q16—221no—
260C2×SD16—222no—
261C2×SD16—222no—
262C2×SD16—221no—
263C2×D8—111no—
264C2×D8—112no—
265C2×D8—221no—
266#131—222no—
267#131—222no—
268#131—441no—
269#131—441no—
270C2×M16—221no—
271C2×M16—441no—
272C22×C8—441no—
273C22×C8D4411yescharacteristic
274C22×C8C22×D1111yescharacteristic
275C4⋊Q8—221no—
276#127—221no—
277#124—222no—
278#121—442no—
279C4×D4—442no—
280C2×C42D4411yescharacteristic
281Q32—224no—
282SD32—224no—
283SD32—224no—
284D16—224no—
285M32—22no—
286M32C22×D1114yes—
287C2×C16—22no—
288#108—112no—
289#108—221no—
290#104—222no—
291#104—222no—
292C4×C8D4411yescharacteristic
293C4×C8D4411yescharacteristic
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11C2×#45911yescharacteristic
300D11—82no—
301D11—162no—
302#41—222no—
303#41—222no—
304#41—441no—
305#41—441no—
306#41—442no—
307#41—442no—
308#41—442no—
309#41—442no—
310C2×Q8—221no—
311C2×Q8—222no—
312C2×D4—221no—
313C2×D4—222no—
314C2×D4—442no—
315C2×D4—441no—
316C2×D4—442no—
317C22×C4—21no—
318C22×C4—441no—
319C22×C4—442no—
320C22×C4C2×D4411yescharacteristic
321Q16—112no—
322Q16—221no—
323Q16—222no—
324Q16—222no—
325Q16—441no—
326Q16—441no—
327SD16—222no—
328SD16—222no—
329SD16—442no—
330SD16—442no—
331SD16—442no—
332SD16—442no—
333D8—112no—
334D8—221no—
335D8—222no—
336D8—222no—
337D8—441no—
338D8—441no—
339M16—222no—
340M16—441no—
341M16—442no—
342M16—442no—
343C2×C8—441no—
344C2×C8—442no—
345C2×C8—442no—
346C2×C8D8811yescharacteristic
347C2×C8D8811yescharacteristic
348C2×C8D8811yescharacteristic
349C2×C8D8811yescharacteristic
350C2×C8C2×D4411yescharacteristic
351C2×C8C2×D4411yescharacteristic
352C2×C8C2×D4411yescharacteristic
353C2×C8D4×D1111yescharacteristic
354C2×C8D4×D1111yescharacteristic
355C2×C8#434311yescharacteristic
356C2×C8#434311yescharacteristic
357C2×C8C23×D1111yescharacteristic
358C4⋊C4—442no—
359C22⋊C4—444no—
360C42—21no—
361C42C2×D4411yescharacteristic
362C42C2×D4411yescharacteristic
363C16—24no—
364C11#3359411yescharacteristic, complemented, Sylow
365C23—441no—
366C23—442no—
367C23#6696111yescharacteristic
368Q8—222no—
369Q8—441no—
370Q8—442no—
371Q8—442no—
372D4—222no—
373D4—442no—
374D4—442no—
375D4—442no—
376D4—442no—
377D4—441no—
378D4—884no—
379D4—882no—
380D4—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—882no—
389C2×C4—882no—
390C2×C4#6694811yescharacteristic
391C2×C4#6694811yescharacteristic
392C2×C4C2×D8811yescharacteristic
393C2×C4C2×D8811yescharacteristic
394C2×C4#6696111yescharacteristic
395C2×C4C22×D4411yescharacteristic
396C8—442no—
397C8#6694811yescharacteristic
398C8#6694811yescharacteristic
399C8C2×D8811yescharacteristic
400C8C2×D8811yescharacteristic
401C8C2×D8811yescharacteristic
402C8C2×D8811yescharacteristic
403C8C2×D4×D1111yescharacteristic
404C8C2×#434311yescharacteristic
405C22—41no—
406C22—442no—
407C22—882no—
408C22—884no—
409C22—882no—
410C22#1062245611yescharacteristic
411C22#1062245611yescharacteristic
412C22C2×#6696111yescharacteristic
413C4—22no—
414C4—41no—
415C4—442no—
416C4—882no—
417C4#1062245611yescharacteristic
418C4#1062245611yescharacteristic
419C4C2×#6694811yescharacteristic
420C4C22×D8811yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—882no—
425C2—1762no—
426C2C2×#1062245611yescharacteristic
subgroupG/H
centerC4#10622456
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#364C2
socleC2×C11C2×#459
hypercenterC2×#364D11
hypocenterC11#33594
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
1. #13081752C2semidirect
2. #13079044C2semidirect
3. C2×#10622313C2semidirect
4. #13070698C2semidirect
5. #13070693C2semidirect
6. #13070686C2semidirect
7. #13070366C2semidirect
8. C2×C11×#364C2semidirect
27. #10622312C22semidirect
29. #10622309C22semidirect
30. #10622308C22semidirect
32. C11×#364C22semidirect
33. C11×#364C22semidirect
34. #10622155C22semidirect
35. #10622154C22semidirect
44. C2×Dic44D4semidirect
56. #66957D4semidirect
59. C2×D88D4semidirect
158. C2×#364D11semidirect
223. #364C2×D11semidirect
224. #364C2×D11semidirect
364. C11#33594semidirect

Maximal subgroups

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

subgroupindex
#130817522
#130790442
C2×#106223132
#130706982
#130706932
#130706862
#130703662
C2×C11×#3642
#3359411