Finite Group Databasebeta

← #14648968

Subgroups — #14648968

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077334C211yesmaximal, characteristic, complemented
2#13069415C211yesmaximal, characteristic, complemented
3#13067265C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic, complemented
5#13066512C211yesmaximal, characteristic, complemented
6#13066460C211yesmaximal, characteristic, complemented
7C11×#3100C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#67001—21no—
11C11×#480C412yes—
12C11×#474—21no—
13C11×#459—21no—
14C11×#447C412yes—
15C4×C11×D8—22no—
16C11×#431C2211yescharacteristic
17#10622847—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622624—22no—
21#10622624—22no—
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×#66867C2211yescharacteristic
26#10622185—21no—
27#10622182—21no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11—21no—
32C2×C11×D8—22no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121C2×C412yes—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11D412yes—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47#67001—42no—
48#67001—42no—
49C2×#4318—22no—
50C2×#4318—21no—
51C22×C11⋊C8—22no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8D411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55C11×#107—22no—
56C11×C4⋊C8—21no—
57C11×#102—22no—
58C11×#102—22no—
59C11×C22⋊C8C2×C412yes—
60C4×C8×C11—21no—
61C22⋊(C11⋊C8)—24no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—42no—
64C22⋊(C11⋊C8)—42no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70#66867—21no—
71#66867—21no—
72C4×C11⋊C8—21no—
73#9049—111nomaximal, Sylow
74C24×C11—21no—
75C11×#41—41no—
76C11×#41—41no—
77C11×#41—41no—
78C11×#41—41no—
79C2×Q8×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11C22⋊C412yes—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C11×D8—44no—
99C2×C8×C11—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4C22⋊C412yes—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4318—44no—
113#4318—41no—
114#4318—41no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—44no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8D812yescomplemented
127#3100D1111yescharacteristic
128#2932—111no—
129#1955—111no—
130#1540—111no—
131#1486—111no—
132#1301—111no—
133#1281—111no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C4×D411yescharacteristic
143Q8×C11—41no—
144Q8×C11—41no—
145D4×C11—22no—
146D4×C11—22no—
147D4×C11—42no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—42no—
151D4×C11—42no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C8×C11—42no—
178C11⋊C8—22no—
179C11⋊C8—42no—
180C11⋊C8—41no—
181C11⋊C8—81no—
182C11⋊C8—81no—
183C2×#131—221no—
184#532C2×D1111yescharacteristic
185C2×C4×D4C2×D1111yescharacteristic
186#480Dic1112yes—
187#474—21no—
188#459—21no—
189#447Dic1112yes—
190C4×D8—22no—
191#435—222no—
192#435—222no—
193#431—111no—
194#431C2×D1111yescharacteristic
195#423—111no—
196C2×C4⋊C8—111no—
197#408—221no—
198C2×C22⋊C8—221no—
199C2×C22⋊C8—221no—
200C2×#97—111no—
201#332—221no—
202#331—221no—
203D4⋊C8—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#38611yescharacteristic
217C22×C11C4×D811yescharacteristic
218C22×C11#44211yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#45911yescharacteristic
228C4×C11#46311yescharacteristic
229C2×#41—21no—
230C22×D4C2×Dic1111yescharacteristic
231C23×C4—21no—
232C2×D8—22no—
233#131—442no—
234#131—442no—
235C2×M16—222no—
236C2×M16—221no—
237C22×C8—111no—
238C22×C8—111no—
239C22×C8—222no—
240C22×C8—221no—
241C4⋊Q8C22⋊D1111yescharacteristic
242#127C22⋊D1111yescharacteristic
243#124—21no—
244#121—21no—
245#121C2×Dic1112yes—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C22⋊D1112yes—
252C2×C4⋊C4C2×Dic1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D1111yescharacteristic
255#107—22no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#102—22no—
263#102—22no—
264C22⋊C8—224no—
265C22⋊C8—221no—
266C22⋊C8—442no—
267C22⋊C8—442no—
268C22⋊C8C2×Dic1112yes—
269#97—221no—
270#97—221no—
271C4×C8—21no—
272C4×C8—221no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—82no—
276C2×C11—82no—
277C2×C11#187911yescharacteristic
278C2×C11#188111yescharacteristic
279C2×C11#189111yescharacteristic
280C24—21no—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285C2×Q8—21no—
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4C22⋊Dic1112yes—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4D4×D1111yescharacteristic
302C22×C4#434111yescharacteristic
303C22×C4C22×Dic1111yescharacteristic
304D8—44no—
305M16—444no—
306M16—441no—
307M16—441no—
308C2×C8—22no—
309C2×C8—112no—
310C2×C8—221no—
311C2×C8—221no—
312C2×C8—221no—
313C2×C8—221no—
314C2×C8—221no—
315C2×C8—222no—
316C2×C8—444no—
317C2×C8—441no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—441no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4C22⋊Dic1112yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42D4×D1111yescharacteristic
330C42#434111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C11#904911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—22no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23D4×Dic1111yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—22no—
346D4—22no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—81no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4D8×D1111yescharacteristic
368C2×C4#6696411yescharacteristic
369C2×C4#6696411yescharacteristic
370C2×C4#6696511yescharacteristic
371C2×C4D4×Dic1111yescharacteristic
372C2×C4#6698811yescharacteristic
373C2×C4#6699011yescharacteristic
374C2×C4#6699211yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4C2×C22⋊Dic1111yescharacteristic
377C8—42no—
378C8—222no—
379C8—442no—
380C8—441no—
381C8—881no—
382C8—881no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22D8×Dic1111yescharacteristic
396C22#1062276511yescharacteristic
397C22#1062283311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4#1062276311yescharacteristic
405C4#1062276611yescharacteristic
406C4#1062276911yescharacteristic
407C4#1062277111yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—82no—
412C2#1306896611yescharacteristic
413C2#1306898011yescharacteristic
414C2#1306903511yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11#386
cosocleC2×C42×C11C23
hypercenter#3100D11
hypocenterC11#9049
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13077334C2semidirect
2. #13069415C2semidirect
3. #13067265C2semidirect
4. #13067041C2semidirect
5. #13066512C2semidirect
6. #13066460C2semidirect
126. C2×C11⋊C8D8semidirect
333. C11#9049semidirect

Maximal subgroups

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

subgroupindex
#130773342
#130694152
#130672652
#130670412
#130665122
#130664602
C11×#31002
#904911