Finite Group Databasebeta

← #14647875

Subgroups — #14647875

Order 2816.

464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077664C211yesmaximal, characteristic
2#13068821C211yesmaximal, characteristic, complemented
3#13068799C211yesmaximal, characteristic, complemented
4#13067107C211yesmaximal, characteristic
5#13066502C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#1871C211yesmaximal, characteristic
8C22×C11×M16C2211yescharacteristic
9C11×#525C2211yescharacteristic
10C2×C11×#104—21no—
11C4×C11×C22⋊C4C2211yescharacteristic
12#10622847—21no—
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66886—21no—
18C2×Dic11⋊C8—21no—
19#10622625—21no—
20#10622624—21no—
21#10622624—21no—
22D4×C11⋊C8—21no—
23#10622613—21no—
24C11×#339—21no—
25#10622196—21no—
26#10622188—21no—
27#10622176C411yescharacteristic, complemented
28#10622176C411yescharacteristic, complemented
29#10622175C411yescharacteristic, complemented
30#10622175C411yescharacteristic, complemented
31C2×C11×#41D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16—42no—
36C22×C8×C11—21no—
37C11×#123—21no—
38C11×C22⋊Q8C2×C411yescharacteristic
39C11×C22⋊Q8Q811yescharacteristic
40C11×#121C2×C411yescharacteristic
41C11×#121Q811yescharacteristic
42C11×#120—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C11×#117D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—21no—
48C2×C22⋊Dic11—21no—
49C2×C4×Dic11—21no—
50C2×#4318—21no—
51C2×#4318D411yescharacteristic
52C2×#4318D411yescharacteristic
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55C22×C11⋊C8D411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57C11×#104—42no—
58C11×#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)C2×C411yescharacteristic
69C22⋊(C11⋊C8)C2×C411yescharacteristic
70#66886—42no—
71Dic11⋊C8—42no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76#8874—111nomaximal, Sylow
77C24×C11#4111yescharacteristic
78C11×#41—41no—
79C11×#41—41no—
80C2×Q8×C11C4⋊C411yescharacteristic
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11C4⋊C411yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×Q811yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4C4⋊C411yescharacteristic
107C11×C4⋊C4C4⋊C411yescharacteristic
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—21no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—41no—
117C42×C11—41no—
118C22⋊Dic11—42no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121#4318—41no—
122#4318—41no—
123#4318—81no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—81no—
135#2976—111no—
136#1871D1111yescharacteristic
137#1855—111no—
138#1851—111no—
139#1501—111no—
140#1297—111no—
141#1282—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11C4×D411yescharacteristic
148C23×C11C22⋊Q811yescharacteristic
149C23×C11#12311yescharacteristic
150Q8×C11—41no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11C2×C4⋊C411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11C22⋊Q811yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C8×C11—42no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186C11⋊C8—41no—
187C11⋊C8—41no—
188C11⋊C8—41no—
189C11⋊C8—41no—
190C22×M16C2×D1111yescharacteristic
191#525C2×D1111yescharacteristic
192#436—221no—
193#435—221no—
194#435—221no—
195C8×D4—221no—
196#433—221no—
197C2×#108—221no—
198C2×C4⋊C8—221no—
199C2×#104—21no—
200#408—221no—
201#407—111no—
202C2×C22⋊C8—111no—
203C2×C22⋊C8—111no—
204C4×C22⋊C4—111no—
205C4×C22⋊C4C2×D1111yescharacteristic
206#341—221no—
207#339—21no—
208#336—221no—
209#328—111no—
210#328—111no—
211#327—111no—
212#327—111no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#38511yescharacteristic
227C22×C11#44311yescharacteristic
228C22×C11#44411yescharacteristic
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—82no—
236C4×C11B(4,𝔽2)11yescharacteristic
237C4×C11#45811yescharacteristic
238Dic11—42no—
239Dic11—81no—
240C2×#41C22⋊D1111yescharacteristic
241C23×C4C22×D1111yescharacteristic
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—42no—
245C2×M16—111no—
246C2×M16—111no—
247C2×M16—221no—
248C22×C8—21no—
249C22×C8—111no—
250C22×C8—111no—
251C22×C8—221no—
252C22×C8—221no—
253#123—21no—
254C22⋊Q8Dic2211yescharacteristic
255C22⋊Q8C4×D1111yescharacteristic
256#121Dic2211yescharacteristic
257#121C4×D1111yescharacteristic
258#120—21no—
259C4×D4—21no—
260C4×D4—21no—
261#117C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—221no—
264C2×C42—21no—
265C2×C42—221no—
266#108—442no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—442no—
270#104—42no—
271C22⋊C8—111no—
272C22⋊C8—111no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280#97—221no—
281C4×C8—221no—
282#95—21no—
283#95—111no—
284#95—111no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—81no—
290C2×C11#186111yescharacteristic
291C2×C11#186611yescharacteristic
292C2×C11#186711yescharacteristic
293C24#434111yescharacteristic
294#41—41no—
295#41—41no—
296C2×Q8Dic11⋊C411yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4Dic11⋊C411yescharacteristic
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4C2×Dic2211yescharacteristic
308C22×C4C2×C4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4#434111yescharacteristic
312C22×C4C2×C22⋊D1111yescharacteristic
313M16—22no—
314M16—22no—
315M16—41no—
316M16—41no—
317M16—441no—
318M16—441no—
319M16—881no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—221no—
324C2×C8—221no—
325C2×C8—221no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—441no—
330C2×C8—441no—
331C2×C8—441no—
332C2×C8—441no—
333C2×C8—881no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4Dic11⋊C411yescharacteristic
337C4⋊C4Dic11⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—22no—
344C22⋊C4—41no—
345C22⋊C4—442no—
346C42—21no—
347C42—41no—
348C42—41no—
349C42—441no—
350C42—441no—
351C11#887411yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23#6693111yescharacteristic
358C23(C22⋊D11)⋊C411yescharacteristic
359C23#6698811yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—222no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4#6693111yescharacteristic
390C2×C4(C22⋊D11)⋊C411yescharacteristic
391C2×C4C2×Dic11⋊C411yescharacteristic
392C2×C4#6699011yescharacteristic
393C8—42no—
394C8—441no—
395C8—441no—
396C8—441no—
397C8—441no—
398C8—441no—
399C8—441no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1062243611yescharacteristic
414C22#1062243711yescharacteristic
415C22#1062255911yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—82no—
423C4—442no—
424C4—881no—
425C4#1062264511yescharacteristic
426C4#1062266611yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—81no—
432C2#1306885411yescharacteristic
433C2#1306888911yescharacteristic
434C2#1306889611yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1871C2
socleC22×C11#385
prime radicalC11×#525C22
cosocleC23×C4×C11C23
hypercenter#1871D11
hypocenterC11#8874
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #13068821C2semidirect
3. #13068799C2semidirect
5. #13066502C2semidirect
6. #13066464C2semidirect
27. #10622176C4semidirect
28. #10622176C4semidirect
29. #10622175C4semidirect
30. #10622175C4semidirect
351. C11#8874semidirect

Maximal subgroups

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

subgroupindex
#130776642
#130688212
#130687992
#130671072
#130665022
#130664642
C11×#18712
#887411