Finite Group Databasebeta

← #14737172

Subgroups — #14737172

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C212yesmaximal
2#13079202C211yesmaximal, characteristic, complemented
3#13068170C212yesmaximal, complemented
4#13068163C212yesmaximal, complemented
5#13068010C211yesmaximal, characteristic, complemented
6#13068005C211yesmaximal, characteristic, complemented
7#13067986C211yesmaximal, characteristic, complemented
8#13067981C211yesmaximal, characteristic, complemented
9C2×#10622096C211yesmaximal, characteristic, complemented
10#13067317C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic
12C11×#529C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622729—21no—
25#10622729—21no—
26#10622676—22no—
27#10622667—22no—
28#10622664—22no—
29#10622654—22no—
30#10622644C2212yes—
31#10622633C2212yes—
32#10622632C2212yes—
33#10622620C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622120C2212yes—
43#10622120C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
47C2×C11×M16—21no—
48C22×C8×C11—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×#126—21no—
52C11×#125D411yescharacteristic
53C11×#124D411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8D411yescharacteristic
56C11×#121D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4324—22no—
64#66979—22no—
65#66977—22no—
66#66977—22no—
67C22×C11⋊C8—22no—
68C2×Dic44—21no—
69C2×Dic44—21no—
70#66923—22no—
71#66922C2312yes—
72#66922C2312yes—
73C4×Dic22—22no—
74C4×Dic22—22no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2311yescharacteristic
78C11×C4⋊C8C2311yescharacteristic
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×#97—21no—
83C11×#97—21no—
84C4×C8×C11—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#66899—22no—
90#66896—22no—
91#66882—21no—
92#66882—21no—
93#66880—22no—
94#66880—22no—
95#66874—22no—
96#66874—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19223—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—22no—
111C2×Dic22—22no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—42no—
139#4326—82no—
140#4324—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145Dic11⋊C4—42no—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—82no—
151Dic44—42no—
152Dic44—42no—
153#3248—112no—
154#3170—111no—
155#2966D1111yescharacteristic
156#1700—112no—
157#1699—112no—
158#1674—111no—
159#1673—111no—
160#1670—111no—
161#1669—111no—
162C2×#335—111no—
163#1552—112no—
164C23×C11—21no—
165C23×C11#12111yescharacteristic
166Q8×C11—21no—
167Q8×C11—21no—
168D4×C11—21no—
169D4×C11—21no—
170D4×C11—42no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×Dic11—42no—
188C2×Dic11—42no—
189Dic22—42no—
190Dic22—42no—
191Dic22—42no—
192Dic22—42no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11—41no—
197C8×C11—41no—
198C8×C11#13512yes—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533—112no—
202#529C2×D1111yescharacteristic
203#500—111no—
204#494—111no—
205#487—112no—
206#479—222no—
207#475—112no—
208#474—112no—
209#467—221no—
210#467—221no—
211#467—222no—
212#465—222no—
213#464—222no—
214#462—112no—
215#461—112no—
216#446C2×D1111yescharacteristic
217C8×Q8C2×D1111yescharacteristic
218C4×Q16—221no—
219C4×Q16—221no—
220#436C2×D1111yescharacteristic
221#435—21no—
222C8×D4—21no—
223C8×D4C2×D1111yescharacteristic
224#433—21no—
225#432C2×D1111yescharacteristic
226C2×C4⋊C8—112no—
227#405—21no—
228C2×C4×C8C2×D1111yescharacteristic
229#335—111no—
230#335—111no—
231#335—112no—
232#332—112no—
233#332—112no—
234#332—112no—
235#332—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11#47312yes—
242C22×C11C2×#12111yescharacteristic
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11C2×#13511yescharacteristic
251C4×C11#57511yescharacteristic
252C4×C11#57611yescharacteristic
253C4×C11#57811yescharacteristic
254Dic11—82no—
255Dic11—82no—
256C2×Q16—222no—
257C2×Q16—221no—
258C2×Q16—221no—
259C2×SD16—222no—
260C2×M16—21no—
261C22×C8—21no—
262C22×C8—222no—
263C22×C8C22⋊D1111yescharacteristic
264C22×C8C22⋊D1111yescharacteristic
265C4⋊Q8—112no—
266C4⋊Q8—112no—
267#126—21no—
268#125—222no—
269#125D4411yescharacteristic
270#124D4411yescharacteristic
271#123—21no—
272C22⋊Q8—222no—
273C22⋊Q8—222no—
274C22⋊Q8D4411yescharacteristic
275#121D4411yescharacteristic
276C4×Q8—222no—
277C4×Q8—222no—
278C4×Q8C22×D1111yescharacteristic
279C4×D4—21no—
280C4×D4C22×D1111yescharacteristic
281#117—21no—
282#117—222no—
283C2×C42C22×D1111yescharacteristic
284#107—221no—
285#107—221no—
286#107—222no—
287#106—222no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—222no—
293C4⋊C8C22×D1111yescharacteristic
294C4⋊C8C22×D1111yescharacteristic
295#103—222no—
296#103—222no—
297#103—222no—
298#103—222no—
299#103—222no—
300#102—222no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304#97—21no—
305#97—21no—
306C4×C8—21no—
307C4×C8C22⋊D1111yescharacteristic
308C4×C8C22⋊D1111yescharacteristic
309C4×C8C22×D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C2×C11—22no—
312C2×C11—81no—
313C2×C11#303511yescharacteristic
314C2×C11#306111yescharacteristic
315C2×C11C2×#47311yescharacteristic
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8C2×D4411yescharacteristic
319C2×D4—21no—
320C2×D4C2×D4411yescharacteristic
321C22×C4—21no—
322C22×C4C2×D4411yescharacteristic
323C22×C4#433911yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—442no—
326Q16—442no—
327Q16—882no—
328SD16—882no—
329M16—42no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—41no—
334C2×C8—42no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—882no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—442no—
351C4⋊C4—442no—
352C4⋊C4C2×D4411yescharacteristic
353C4⋊C4C2×D4411yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—442no—
360C42—21no—
361C42—442no—
362C42C2×D4411yescharacteristic
363C42#433911yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1922311yescharacteristic, complemented, Sylow
367C23—21no—
368C23#6698311yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—442no—
372Q8—442no—
373Q8—442no—
374Q8—442no—
375D4—21no—
376D4—21no—
377D4—42no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4#6698311yescharacteristic
391C2×C4#6698311yescharacteristic
392C2×C4#6698311yescharacteristic
393C2×C4C22×D4411yescharacteristic
394C2×C4C2×#433911yescharacteristic
395C2×C4C22×C22⋊D1111yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—41no—
400C8—41no—
401C8—442no—
402C8—442no—
403C8#6700312yes—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22#1062275612yes—
410C22C2×#6698311yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—882no—
419C4—882no—
420C4#1062328311yescharacteristic
421C4#1062328411yescharacteristic
422C4C2×#6700311yescharacteristic
423C4#1062335311yescharacteristic
424C2—22no—
425C2—81no—
426C2#1307807111yescharacteristic
427C2#1307828611yescharacteristic
428C2C2×#1062275611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19223
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13079202C2semidirect
3. #13068170C2semidirect
4. #13068163C2semidirect
5. #13068010C2semidirect
6. #13068005C2semidirect
7. #13067986C2semidirect
8. #13067981C2semidirect
9. C2×#10622096C2semidirect
10. #13067317C2semidirect
366. C11#19223semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130792022
#130681702
#130681632
#130680102
#130680052
#130679862
#130679812
C2×#106220962
#130673172
C11×#29662
#1922311