Finite Group Databasebeta

← #14738610

Subgroups — #14738610

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C212yesmaximal
2#13079130C211yesmaximal, characteristic, complemented
3#13068122C212yesmaximal, complemented
4#13068115C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068015C211yesmaximal, characteristic, complemented
7#13068010C211yesmaximal, characteristic, complemented
8#13068005C211yesmaximal, characteristic, complemented
9#13067375C211yesmaximal, characteristic, complemented
10#13067347C212yesmaximal, 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#10622719—21no—
25#10622719—21no—
26#10622676—22no—
27#10622667—22no—
28#10622665—22no—
29#10622655—22no—
30#10622644C2212yes—
31#10622634C2212yes—
32#10622632C2212yes—
33#10622621C2212yes—
34#10622537C2212yes—
35#10622296—21no—
36#10622296—21no—
37#10622295C2211yescharacteristic
38#10622295C2211yescharacteristic
39#10622293C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
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—
67C2×#4318—22no—
68#66923—22no—
69#66922C2312yes—
70#66922C2312yes—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8C2311yescharacteristic
76C11×C4⋊C8C2311yescharacteristic
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×#97—21no—
81C11×#97—21no—
82C4×C8×C11—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66899—22no—
88#66896—22no—
89#66882—21no—
90#66882—21no—
91#66882—21no—
92#66882—21no—
93#66881—22no—
94#66881—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#19361—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—22no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
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—
148#4318—82no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151#3252—112no—
152#3160—111no—
153#2966D1111yescharacteristic
154#1692—112no—
155#1691—112no—
156#1676—111no—
157#1675—111no—
158#1674—111no—
159#1673—111no—
160#1567—111no—
161#1559—112no—
162C23×C11—21no—
163C23×C11#12111yescharacteristic
164Q8×C11—21no—
165Q8×C11—21no—
166D4×C11—21no—
167D4×C11—21no—
168D4×C11—42no—
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—21no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×Dic11—42no—
186C2×Dic11—42no—
187Dic22—42no—
188Dic22—42no—
189Dic22—82no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—41no—
193C8×C11—41no—
194C8×C11#13712yes—
195C8×C11#13712yes—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#533—112no—
199#529C2×D1111yescharacteristic
200#500—111no—
201#500—111no—
202#499—221no—
203#499—221no—
204#498—112no—
205#479—222no—
206#477—112no—
207#476—112no—
208#470—222no—
209#468—222no—
210#464—222no—
211#462—112no—
212#461—112no—
213#446C2×D1111yescharacteristic
214C8×Q8C2×D1111yescharacteristic
215#436C2×D1111yescharacteristic
216#435—21no—
217C8×D4—21no—
218C8×D4C2×D1111yescharacteristic
219#433—21no—
220#432C2×D1111yescharacteristic
221#427—221no—
222#427—221no—
223#423—112no—
224#405—21no—
225C2×C4×C8C2×D1111yescharacteristic
226#335—111no—
227#335—111no—
228#335—112no—
229#333—112no—
230#333—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11C2×#12111yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11C2×#13711yescharacteristic
248C4×C11C2×#13711yescharacteristic
249C4×C11#57611yescharacteristic
250C4×C11#57811yescharacteristic
251Dic11—82no—
252Dic11—82no—
253C2×Q16—222no—
254C2×SD16—222no—
255C2×M16—21no—
256C2×M16—222no—
257C22×C8—21no—
258C22×C8C22⋊D1111yescharacteristic
259C22×C8C22⋊D1111yescharacteristic
260C4⋊Q8—112no—
261C4⋊Q8—112no—
262#126—21no—
263#125—222no—
264#125D4411yescharacteristic
265#124D4411yescharacteristic
266#123—21no—
267C22⋊Q8—222no—
268C22⋊Q8—222no—
269C22⋊Q8D4411yescharacteristic
270#121D4411yescharacteristic
271C4×Q8—222no—
272C4×Q8—222no—
273C4×Q8C22×D1111yescharacteristic
274C4×D4—21no—
275C4×D4C22×D1111yescharacteristic
276#117—21no—
277#117—222no—
278C2×C42C22×D1111yescharacteristic
279#107—221no—
280#107—221no—
281#107—221no—
282#107—221no—
283#107—222no—
284#106—222no—
285#106—222no—
286#106—222no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—112no—
290C4⋊C8—112no—
291C4⋊C8—222no—
292C4⋊C8C22×D1111yescharacteristic
293C4⋊C8C22×D1111yescharacteristic
294#103—222no—
295#103—222no—
296#103—222no—
297#102—222no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301#97—21no—
302#97—21no—
303C4×C8—21no—
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C4×C8C22×D1111yescharacteristic
308C2×C11—41no—
309C2×C11—81no—
310C2×C11#303911yescharacteristic
311C2×C11#306111yescharacteristic
312C2×C11#306711yescharacteristic
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8C2×D4411yescharacteristic
316C2×D4—21no—
317C2×D4C2×D4411yescharacteristic
318C22×C4—21no—
319C22×C4C2×D4411yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322Q16—882no—
323SD16—882no—
324M16—42no—
325M16—882no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—42no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4C2×D4411yescharacteristic
348C4⋊C4C2×D4411yescharacteristic
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—442no—
355C42—21no—
356C42—442no—
357C42C2×D4411yescharacteristic
358C42#433911yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C23×D1111yescharacteristic
361C11#1936111yescharacteristic, complemented, Sylow
362C23—21no—
363C23#6698311yescharacteristic
364Q8—21no—
365Q8—21no—
366Q8—442no—
367Q8—442no—
368Q8—882no—
369D4—21no—
370D4—21no—
371D4—42no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4#6698311yescharacteristic
385C2×C4#6698311yescharacteristic
386C2×C4#6698311yescharacteristic
387C2×C4C22×D4411yescharacteristic
388C2×C4C2×#433911yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—21no—
391C8—21no—
392C8—41no—
393C8—41no—
394C8—442no—
395C8—442no—
396C8#6700412yes—
397C8#6700412yes—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22C2×#6698311yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—882no—
413C4—882no—
414C4#1062328311yescharacteristic
415C4#1062328411yescharacteristic
416C4C2×#6700411yescharacteristic
417C4C2×#6700411yescharacteristic
418C2—41no—
419C2—81no—
420C2#1307810311yescharacteristic
421C2#1307828611yescharacteristic
422C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19361
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. #13079130C2semidirect
3. #13068122C2semidirect
4. #13068115C2semidirect
5. #13068020C2semidirect
6. #13068015C2semidirect
7. #13068010C2semidirect
8. #13068005C2semidirect
9. #13067375C2semidirect
10. #13067347C2semidirect
361. C11#19361semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130791302
#130681222
#130681152
#130680202
#130680152
#130680102
#130680052
#130673752
#130673472
C11×#29662
#1936111