Finite Group Databasebeta

← #14909525

Subgroups — #14909525

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622500C211yesmaximal, characteristic
2D11×#467C211yesmaximal, characteristic
3#13070820C212yesmaximal, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070708C212yesmaximal, complemented
6#13070706C212yesmaximal, complemented
7#13070552C211yesmaximal, characteristic, complemented
8#13070551C212yesmaximal, complemented
9#13070549C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic
11C11×#2236C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13C22×Dic44C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15D11×C22⋊Q8—21no—
16C2×#66950—21no—
17C11×#467C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622801C2211yescharacteristic
20C2×#66893C2212yescomplemented
21#10622729C2211yescharacteristic
22#10622664—21no—
23C2×#66874—21no—
24C2×Dic88C2212yescomplemented
25C2×C16×D11C2212yes—
26#10622500—21no—
27#10622500—21no—
28#10622500C2212yes—
29#10622500C2211yescharacteristic
30#10622500C2212yes—
31D11×#107C2211yescharacteristic
32#10622426—21no—
33D11×#103—21no—
34C11×#366C2212yescomplemented
35C11×#358C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38(C2×D11)⋊C16C2212yes—
39#10622141C2212yescomplemented
40#10622130C2212yescomplemented
41#10622130C2212yescomplemented
42#10622127C2212yescomplemented
43C2×Q8×D11—21no—
44C22×C4×D11D411yescharacteristic
45C22×Dic22—21no—
46C2×C11×Q16C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C22⋊Q8—21no—
49C2×C11×C4⋊C4—21no—
50#66999—21no—
51C2×#4326—21no—
52C2×(C2×D11)⋊C4—41no—
53C2×C4⋊Dic11—41no—
54#66977—21no—
55C22×C11⋊C8D411yescharacteristic
56Q16×D11—42no—
57C2×Dic44—21no—
58C2×Dic44—42no—
59C2×Dic44C2311yescharacteristic
60C2×Dic44C2312yes—
61C2×C8×D11—42no—
62C2×C8×D11D411yescharacteristic
63C2×C8×D11D411yescharacteristic
64C2×C8×D11C2311yescharacteristic
65C2×C8×D11C2311yescharacteristic
66#66950—22no—
67#66950—22no—
68#66950—21no—
69#66950—41no—
70#66950—41no—
71#66949—41no—
72C4⋊C4×D11—21no—
73C4⋊C4×D11—41no—
74C22⋊C4×D11—41no—
75#66931—41no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#103—21no—
81#66899—21no—
82#66893—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C2×C11⋊C16C2312yes—
86#66874—22no—
87#66874—22no—
88#66874—21no—
89#66871—21no—
90Dic88—42no—
91C16×D11—42no—
92#33755—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C2×Q8×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—41no—
98C22×Dic11D811yescharacteristic
99Q8×D11—42no—
100Q8×D11—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11D811yescharacteristic
106C2×C4×D11D811yescharacteristic
107C2×C4×D11C2×D411yescharacteristic
108C2×C4×D11C2×D411yescharacteristic
109C2×Dic22—22no—
110C2×Dic22—21no—
111C2×Dic22—42no—
112C2×Dic22—42no—
113C2×Dic22—41no—
114C2×Dic22—41no—
115C11×Q16—22no—
116C2×C8×C11—22no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2411yescharacteristic
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—41no—
125#4326—42no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132C4⋊Dic11—42no—
133C4⋊Dic11—42no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140Dic44—22no—
141Dic44—22no—
142Dic44—22no—
143Dic44—42no—
144C8×D11—22no—
145C8×D11—22no—
146C8×D11—41no—
147C8×D11—41no—
148C11×C16—22no—
149C11⋊C16—22no—
150C2×#467—111no—
151C2×#467—111no—
152#2236—111no—
153#2236—112no—
154#2236D1111yescharacteristic, complemented
155#2216—112no—
156#2216—112no—
157#2188—111no—
158#2188—112no—
159#2188—111no—
160C2×C22⋊C16—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—41no—
163C22×D11—41no—
164C22×D11Q3214yescomplemented
165C22×D11C2×D811yescharacteristic
166C22×D11C2×D811yescharacteristic
167Q8×C11—41no—
168Q8×C11—41no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—82no—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—82no—
182C2×Dic11C2×D811yescharacteristic
183C2×Dic11C2×D811yescharacteristic
184C4×D11—21no—
185C4×D11—21no—
186C4×D11—21no—
187C4×D11—21no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11—82no—
191C4×D11—82no—
192Dic22—42no—
193Dic22—41no—
194Dic22—42no—
195Dic22—41no—
196Dic22—82no—
197Dic22—82no—
198C8×C11—21no—
199C8×C11H(5,𝔽2)12yes—
200C11⋊C8—21no—
201C11⋊C8—21no—
202C22×Q16—111no—
203C22×Q16—111no—
204C23×C8—111no—
205C2×C22⋊Q8—221no—
206C2×C22⋊Q8—221no—
207C2×Q32—112no—
208C2×Q32—112no—
209C22×C16—112no—
210#467—111no—
211#467—111no—
212#467—112no—
213#467—111no—
214#467—112no—
215#467—221no—
216#467—221no—
217#467—221no—
218#467—221no—
219#467C2×D1111yescharacteristic
220C2×#107—111no—
221C2×#107C2×D1111yescharacteristic
222C2×#103—221no—
223C2×#103—221no—
224#366—112no—
225#366C2×D1112yescomplemented
226#358—112no—
227#358—112no—
228#358—112no—
229#358C2×D1112yescomplemented
230C22⋊C16—111no—
231C22⋊C16—112no—
232C22⋊C16C2×D1111yescharacteristic
233C22×C11—21no—
234C22×C11—21no—
235C22×C11C2×Q3212yes—
236C22×C11C22×D811yescharacteristic
237C2×D11—21no—
238C2×D11—21no—
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—44no—
242C2×D11C2×Q3212yes—
243C2×D11C2×Q3212yes—
244C4×C11—21no—
245C4×C11—82no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11#53411yescharacteristic
249C4×C11#57511yescharacteristic
250Dic11—21no—
251Dic11—21no—
252Dic11—81no—
253Dic11—81no—
254Dic11—82no—
255C22×Q8—221no—
256C22×Q8—221no—
257C23×C4—111no—
258C2×Q16—111no—
259C2×Q16—112no—
260C2×Q16—221no—
261C2×Q16—221no—
262C2×Q16—442no—
263C2×Q16—442no—
264C2×Q16C22×D1111yescharacteristic
265C22×C8—111no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—442no—
271C22×C8C22×D1111yescharacteristic
272C22⋊Q8—21no—
273C22⋊Q8—221no—
274C22⋊Q8—222no—
275C22⋊Q8—222no—
276C22⋊Q8—221no—
277C22⋊Q8—221no—
278C22⋊Q8—441no—
279C22⋊Q8—441no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—441no—
285C2×C4⋊C4—441no—
286C2×C22⋊C4—441no—
287C2×C22⋊C4—441no—
288Q32—442no—
289Q32—442no—
290C2×C16—112no—
291C2×C16—442no—
292C2×C16C22×D1112yes—
293#107—21no—
294#107—111no—
295#107—221no—
296#107C22×D1111yescharacteristic
297#107C22×D1112yes—
298#103—21no—
299#103—221no—
300#103—222no—
301#103—222no—
302#103—221no—
303#103—221no—
304C2×C11—22no—
305C2×C11#318611yescharacteristic
306C2×C11C22×Q3211yescharacteristic
307C2×C11#341411yescharacteristic
308D11—22no—
309D11—22no—
310C24—111no—
311C2×Q8—21no—
312C2×Q8—222no—
313C2×Q8—221no—
314C2×Q8—442no—
315C2×Q8—442no—
316C2×Q8—441no—
317C2×Q8—442no—
318C2×Q8—442no—
319C2×Q8—441no—
320C22×C4—41no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4D4×D1111yescharacteristic
332Q16—22no—
333Q16—222no—
334Q16—222no—
335Q16—222no—
336Q16—442no—
337Q16—442no—
338C2×C8—22no—
339C2×C8—111no—
340C2×C8—111no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—441no—
344C2×C8—441no—
345C2×C8—441no—
346C2×C8D4×D1111yescharacteristic
347C2×C8C23×D1111yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—221no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—441no—
359C22⋊C4—41no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—441no—
365C16—22no—
366C16—222no—
367C11#3375511yescharacteristic, complemented, Sylow
368C23—111no—
369C23—111no—
370C23—114no—
371C23—441no—
372C23—441no—
373C23D8×D1111yescharacteristic
374Q8—41no—
375Q8—41no—
376Q8—442no—
377Q8—441no—
378Q8—442no—
379Q8—441no—
380Q8—882no—
381Q8—882no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4D8×D1111yescharacteristic
404C2×C4C2×D4×D1111yescharacteristic
405C8—21no—
406C8—221no—
407C8—221no—
408C8#6704212yes—
409C22—21no—
410C22—21no—
411C22—112no—
412C22—112no—
413C22—221no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—444no—
418C22D11×Q3212yes—
419C22C2×D8×D1111yescharacteristic
420C4—21no—
421C4—81no—
422C4—82no—
423C4—81no—
424C4—221no—
425C4—221no—
426C4—881no—
427C4—882no—
428C4—881no—
429C4#1062318411yescharacteristic
430C4#1062330811yescharacteristic
431C2—22no—
432C2—222no—
433C2—222no—
434C2#1307936611yescharacteristic
435C2C2×D11×Q3211yescharacteristic
436C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2236D11
hypocenterC11#33755
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #13070820C2semidirect
4. #13070818C2semidirect
5. #13070708C2semidirect
6. #13070706C2semidirect
7. #13070552C2semidirect
8. #13070551C2semidirect
9. #13070549C2semidirect
11. C11×#2236C2semidirect
20. C2×#66893C22semidirect
24. C2×Dic88C22semidirect
34. C11×#366C22semidirect
35. C11×#358C22semidirect
39. #10622141C22semidirect
40. #10622130C22semidirect
41. #10622130C22semidirect
42. #10622127C22semidirect
154. #2236D11semidirect
164. C22×D11Q32semidirect
225. #366C2×D11semidirect
229. #358C2×D11semidirect
367. C11#33755semidirect

Maximal subgroups

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

subgroupindex
C2×#106225002
D11×#4672
#130708202
#130708182
#130707082
#130707062
#130705522
#130705512
#130705492
D11×C22⋊C162
C11×#22362
#3375511