Finite Group Databasebeta

← #14909729

Subgroups — #14909729

Order 2816.

598 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#13079186C211yesmaximal, characteristic, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13070877C212yesmaximal, complemented
4#13070848C212yesmaximal, complemented
5#13070667C211yesmaximal, characteristic, complemented
6#13070662C211yesmaximal, characteristic, complemented
7#13070657C211yesmaximal, characteristic, complemented
8#13070652C211yesmaximal, characteristic, complemented
9#13070558C212yesmaximal, complemented
10#13070541C212yesmaximal, complemented
11C11×#2162C211yesmaximal, characteristic, complemented
12C2×#66957—21no—
13C2×#66957C2212yes—
14#10623010—21no—
15#10623008—21no—
16C2×C4×C8×C11C2211yescharacteristic
17#10622729C2211yescharacteristic
18#10622728C2211yescharacteristic
19#10622727—21no—
20C2×Dic88C2212yes—
21C2×#66864C2212yes—
22C2×#66864C2212yes—
23C2×D176C2212yes—
24#10622312C2211yescharacteristic
25C4×Dic44C2211yescharacteristic
26#10622310—21no—
27#10622309—21no—
28#10622309C2212yes—
29#10622309C2211yescharacteristic
30#10622308C2211yescharacteristic
31#10622306—21no—
32C4×D88C2211yescharacteristic
33C4×#4314—21no—
34#10622296C2211yescharacteristic
35C11×C4⋊C16C2211yescharacteristic
36C11×C4⋊C16C2211yescharacteristic
37C11×C22⋊C16C2212yes—
38C4×C11×C16C2212yes—
39#10622147C2212yes—
40#10622147C2212yes—
41#10622141C2212yes—
42#10622141C2212yes—
43C2×#4339—22no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C42×C11D411yescharacteristic
47#66983—21no—
48#66983—41no—
49#66983—41no—
50#66982—41no—
51C4×C22⋊D11—41no—
52#66977—21no—
53C2×Dic44—21no—
54C2×Dic44C2311yescharacteristic
55C2×Dic44C2312yes—
56#66957—42no—
57#66957—42no—
58#66957—44no—
59C2×D88—21no—
60C2×D88C2311yescharacteristic
61C2×D88C2312yes—
62C2×#4314—21no—
63C2×#4314—22no—
64C2×#4314—22no—
65#66929—41no—
66#66928—22no—
67#66928—21no—
68#66927—21no—
69C4×D44—21no—
70C4×D44—41no—
71C4×D44—41no—
72#66925—41no—
73#66923—21no—
74#66922—21no—
75C4×Dic22—21no—
76C2×C11×C16C2312yes—
77C2×C11×C16C2312yes—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66885—21no—
83#66885—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87#66880—21no—
88#66880—21no—
89Dic88—42no—
90#66864—42no—
91#66864—42no—
92D176—42no—
93#33778—111nomaximal, Sylow
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98C2×C22⋊D11—42no—
99#4339—44no—
100#4339—44no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C42×C11D811yescharacteristic
117C42×C11D811yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—41no—
136Dic44—21no—
137Dic44—22no—
138Dic44—21no—
139Dic44—22no—
140Dic44—42no—
141D88—21no—
142D88—22no—
143D88—21no—
144D88—22no—
145D88—42no—
146#4314—44no—
147#4314—42no—
148#4314—44no—
149C11×C16—22no—
150C11×C16—22no—
151#3168—111no—
152#3147—111no—
153#2249—112no—
154#2242—112no—
155#2209—111no—
156#2208—111no—
157#2207—111no—
158#2206—111no—
159#2189—112no—
160#2186—112no—
161#2162D1111yescharacteristic, complemented
162C23×C11C2×D811yescharacteristic
163C22×D11—41no—
164C22×D11—42no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C22⋊D11—84no—
176C22⋊D11—82no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181D44—42no—
182D44—41no—
183D44—42no—
184D44—41no—
185D44—82no—
186D44—82no—
187C4×D11—84no—
188C4×D11—82no—
189Dic22—42no—
190Dic22—41no—
191Dic22—42no—
192Dic22—41no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11AGL(1,ℤ/8)12yes—
196C8×C11H(5,𝔽2)11yescharacteristic
197C8×C11H(5,𝔽2)11yescharacteristic
198C2×#135—112no—
199C2×#135—221no—
200#532—221no—
201#529—221no—
202C2×Q32—112no—
203C2×SD32—112no—
204C2×SD32—112no—
205C2×D16—112no—
206#499—111no—
207#495—112no—
208#495—111no—
209#495—221no—
210#494—111no—
211#493—111no—
212#492—221no—
213#488—221no—
214#467—111no—
215#466—111no—
216#465—221no—
217C4×Q16—111no—
218C4×SD16—221no—
219C4×D8—111no—
220C2×C4×C8C2×D1111yescharacteristic
221C4⋊C16C2×D1111yescharacteristic
222C4⋊C16C2×D1111yescharacteristic
223#358—112no—
224#358—112no—
225#357—112no—
226#357—112no—
227C22⋊C16C2×D1112yes—
228C4×C16C2×D1112yes—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11C22×D811yescharacteristic
233C2×D11—81no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—82no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11#50812yes—
244C4×C11#53511yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246Dic11—81no—
247Dic11—81no—
248Dic11—82no—
249Dic11—81no—
250C2×#41—222no—
251#135—442no—
252#135—442no—
253#135—444no—
254C2×Q16—112no—
255C2×Q16—111no—
256C2×Q16—221no—
257C2×SD16—222no—
258C2×SD16—222no—
259C2×SD16—221no—
260C2×D8—112no—
261C2×D8—111no—
262C2×D8—221no—
263C22×C8D4411yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4⋊Q8—221no—
266#127—221no—
267#126—441no—
268#125—221no—
269#124—221no—
270#124—222no—
271#123—441no—
272C22⋊Q8—221no—
273#121—221no—
274#121—441no—
275#121—441no—
276C4×Q8—221no—
277C4×D4—221no—
278C4×D4—441no—
279C4×D4—441no—
280C4×D4—441no—
281#117—441no—
282C2×C42D4411yescharacteristic
283Q32—442no—
284SD32—442no—
285SD32—442no—
286D16—442no—
287C2×C16C22×D1112yes—
288C2×C16C22×D1112yes—
289#107—111no—
290#107—111no—
291#106—221no—
292#103—221no—
293#103—221no—
294#102—221no—
295#102—221no—
296C4×C8D4411yescharacteristic
297C4×C8D4411yescharacteristic
298C4×C8C22×D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C2×C11—41no—
301C2×C11#320511yescharacteristic
302C2×C11C2×#50811yescharacteristic
303C2×C11#341411yescharacteristic
304D11—161no—
305D11—162no—
306#41—444no—
307#41—444no—
308C2×Q8—221no—
309C2×Q8—222no—
310C2×D4—221no—
311C2×D4—222no—
312C2×D4—441no—
313C2×D4—442no—
314C2×D4—441no—
315C2×D4—441no—
316C22×C4—441no—
317C22×C4—442no—
318C22×C4D8811yescharacteristic
319C22×C4D8811yescharacteristic
320C22×C4C2×D4411yescharacteristic
321Q16—221no—
322Q16—222no—
323Q16—221no—
324Q16—222no—
325Q16—442no—
326SD16—444no—
327SD16—444no—
328SD16—442no—
329D8—221no—
330D8—222no—
331D8—221no—
332D8—222no—
333D8—442no—
334C2×C8—22no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8C2×D4411yescharacteristic
338C2×C8C2×D4411yescharacteristic
339C2×C8C2×D4411yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—442no—
354C22⋊C4—442no—
355C22⋊C4—441no—
356C42—441no—
357C42D8811yescharacteristic
358C42D8811yescharacteristic
359C42C2×D4411yescharacteristic
360C42C2×D4411yescharacteristic
361C16—22no—
362C16—22no—
363C11#3377811yescharacteristic, complemented, Sylow
364C23—441no—
365C23—442no—
366C23C2×D8811yescharacteristic
367Q8—442no—
368Q8—441no—
369Q8—442no—
370Q8—441no—
371D4—442no—
372D4—441no—
373D4—442no—
374D4—441no—
375D4—882no—
376D4—884no—
377D4—882no—
378D4—882no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—884no—
388C2×C4—882no—
389C2×C4C2×D8811yescharacteristic
390C2×C4C2×D8811yescharacteristic
391C2×C4C2×D8811yescharacteristic
392C2×C4C2×D8811yescharacteristic
393C2×C4C2×D8811yescharacteristic
394C2×C4C22×D4411yescharacteristic
395C8—21no—
396C8—21no—
397C8#6696112yes—
398C8#6704211yescharacteristic
399C8#6704211yescharacteristic
400C22—21no—
401C22—21no—
402C22—21no—
403C22—881no—
404C22—882no—
405C22—882no—
406C22—881no—
407C22—882no—
408C22—881no—
409C22C22×D8811yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—881no—
415C4—881no—
416C4—882no—
417C4—881no—
418C4#1062251712yes—
419C4#1062305611yescharacteristic
420C4C2×#6696111yescharacteristic
421C2—41no—
422C2—1761no—
423C2—1762no—
424C2#1307953611yescharacteristic
425C2C2×#1062251711yescharacteristic
426C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2162C2
socleC22×C11C22×D8
hypercenter#2162D11
hypocenterC11#33778
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13079044C2semidirect
3. #13070877C2semidirect
4. #13070848C2semidirect
5. #13070667C2semidirect
6. #13070662C2semidirect
7. #13070657C2semidirect
8. #13070652C2semidirect
9. #13070558C2semidirect
10. #13070541C2semidirect
11. C11×#2162C2semidirect
161. #2162D11semidirect
363. C11#33778semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130790442
#130708772
#130708482
#130706672
#130706622
#130706572
#130706522
#130705582
#130705412
C11×#21622
#3377811