Finite Group Databasebeta

← #14670833

Subgroups — #14670833

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic
2C2×C4×D88C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5#13066707C211yesmaximal, characteristic, complemented
6#13066694C211yesmaximal, characteristic, complemented
7C11×#1970C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C2×C4×D44—21no—
11C2×C11×#107C2211yescharacteristic
12C2×C11×#102—21no—
13C2×C4×C8×C11C2211yescharacteristic
14C11×#390—21no—
15C2×#66890—22no—
16C2×#66890—22no—
17C2×#66890C414yescomplemented
18C2×#66885—21no—
19C2×#66882C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21C22×C11⋊C16C2211yescharacteristic
22C4×D88—22no—
23C4×D88—22no—
24#10622200—22no—
25#10622129—22no—
26C22×D4×C11—21no—
27C22×D44—21no—
28C22×C4×D11—41no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8C2×C412yescomplemented
35C22×C8×C11D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C2×C11×C4⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4—41no—
40C2×C42×C11D411yescharacteristic
41C2×(C2×D11)⋊C4—41no—
42C2×C4⋊Dic11—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88C2×C412yes—
47C2×D88D412yes—
48C2×D88D412yes—
49C4×D44—24no—
50C4×D44—42no—
51C11×#107—21no—
52C11×#107—21no—
53C11×#102—42no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56#66890—28no—
57#66885—24no—
58#66882—21no—
59#66882D412yes—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16C2×C412yescomplemented
66#13012—111nomaximal, Sylow
67C24×C11—41no—
68C23×D11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11D811yescharacteristic
77C22×C4×C11D811yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—41no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C4×D11—44no—
87C2×C4×D11—82no—
88C2×C4×D11—82no—
89C11×D8—22no—
90C11×D8—22no—
91C11×D8—41no—
92C11×D8—41no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11C22×C411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—82no—
105C11×C22⋊C4—82no—
106C42×C11—21no—
107C42×C11—21no—
108(C2×D11)⋊C4—44no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111D88—22no—
112D88—22no—
113D88—22no—
114D88C22⋊C414yescomplemented
115C11⋊C16—22no—
116C11⋊C16—41no—
117C22×D16—111no—
118C2×C4×D8—111no—
119C2×#357—111no—
120C2×#357—111no—
121#1970D1111yescharacteristic, complemented
122#1380—111no—
123#1374—111no—
124C23×C11—42no—
125C23×C11—81no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11C2×D811yescharacteristic
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11—81no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11D1612yescomplemented
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161D44—24no—
162D44—42no—
163D44—42no—
164D44—42no—
165C4×D11—88no—
166C8×C11—41no—
167C8×C11C2×C22⋊C411yescharacteristic
168C8×C11C4×D411yescharacteristic
169C8×C11#12111yescharacteristic
170C8×C11#12311yescharacteristic
171C22×D8—111no—
172C22×D8C2×D1111yescharacteristic
173C2×C4×D4—221no—
174C2×D16—114no—
175C2×D16—222no—
176C2×D16—222no—
177C22×C16—111no—
178C22×C16—111no—
179C4×D8—222no—
180C4×D8—222no—
181C2×#107—111no—
182C2×#107C2×D1111yescharacteristic
183C2×#102—21no—
184C2×#102—221no—
185C2×C4×C8C2×D1111yescharacteristic
186#390—21no—
187#357—222no—
188#357—222no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—161no—
193C22×C11—161no—
194C22×C11—161no—
195C22×C11—161no—
196C22×C11C4×D811yescharacteristic
197C22×C11#44711yescharacteristic
198C22×C11#45911yescharacteristic
199C22×C11C2×D1611yescharacteristic
200C22×C11#50811yescharacteristic
201C22×C11#50911yescharacteristic
202C22×C11#50911yescharacteristic
203C2×D11—44no—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—82no—
210C4×C11—22no—
211C4×C11—41no—
212C4×C11—161no—
213C4×C11#38611yescharacteristic
214C4×C11#44211yescharacteristic
215C4×C11#44911yescharacteristic
216C4×C11#46311yescharacteristic
217Dic11—82no—
218C22×D4—21no—
219C22×D4—221no—
220C23×C4—441no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—112no—
227C2×D8—112no—
228C2×D8—112no—
229C2×D8—221no—
230C2×D8—221no—
231C2×D8—221no—
232C2×D8C4×D1112yescomplemented
233C22×C8C22⋊D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C4×D4—224no—
236C4×D4—442no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—221no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—441no—
242C2×C42C22⋊D1111yescharacteristic
243D16—228no—
244C2×C16—112no—
245C2×C16—221no—
246C2×C16—221no—
247C2×C16—221no—
248C2×C16—221no—
249C2×C16—221no—
250#107—21no—
251#107—21no—
252#107—112no—
253#107—221no—
254#102—42no—
255#102—224no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11—162no—
259C2×C11#187911yescharacteristic
260C2×C11C4×D1611yescharacteristic
261C2×C11#217711yescharacteristic
262C2×C11#218411yescharacteristic
263C2×C11#218611yescharacteristic
264C2×C11#220611yescharacteristic
265C2×C11#221011yescharacteristic
266D11—84no—
267C24—41no—
268C24—441no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C22×C4—41no—
282C22×C4—444no—
283C22×C4—441no—
284C22×C4—882no—
285C22×C4—882no—
286C22×C4#432311yescharacteristic
287C22×C4#432311yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289D8—22no—
290D8—22no—
291D8—41no—
292D8—41no—
293D8—114no—
294D8—222no—
295D8—222no—
296D8—222no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8C2×C4×D1111yescharacteristic
301C2×C8#433911yescharacteristic
302C2×C8D4×D1111yescharacteristic
303C2×C8D4×D1111yescharacteristic
304C2×C8D4×D1111yescharacteristic
305C2×C8#434111yescharacteristic
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—222no—
309C4⋊C4—441no—
310C22⋊C4—82no—
311C22⋊C4—82no—
312C22⋊C4—444no—
313C42—21no—
314C42—21no—
315C16—222no—
316C16—441no—
317C11#1301211yescharacteristic, complemented, Sylow
318C23—42no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—442no—
326C23—442no—
327C23—442no—
328C23—881no—
329C23—881no—
330C23—881no—
331C23—881no—
332C23C2×#432311yescharacteristic
333D4—42no—
334D4—42no—
335D4—81no—
336D4—81no—
337D4—224no—
338D4—442no—
339D4—442no—
340D4—442no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—442no—
350C2×C4—888no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4#6689012yescomplemented
354C2×C4C4×C22⋊D1111yescharacteristic
355C2×C4#6698511yescharacteristic
356C2×C4#6699011yescharacteristic
357C2×C4#6699111yescharacteristic
358C2×C4#6700211yescharacteristic
359C2×C4#6700311yescharacteristic
360C8—41no—
361C8C22⋊C4×D1111yescharacteristic
362C8(C22⋊D11)⋊C411yescharacteristic
363C8#6693611yescharacteristic
364C8#6693711yescharacteristic
365C22—82no—
366C22—82no—
367C22—82no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22—161no—
372C22—444no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22—882no—
377C22—882no—
378C22—882no—
379C22C4×#432311yescharacteristic
380C22#1062264911yescharacteristic
381C22#1062268511yescharacteristic
382C22C2×#6689011yescharacteristic
383C22#1062276011yescharacteristic
384C22#1062280611yescharacteristic
385C22#1062280711yescharacteristic
386C4—22no—
387C4—41no—
388C4—161no—
389C4—882no—
390C4#1062256911yescharacteristic
391C4#1062262711yescharacteristic
392C4#1062265011yescharacteristic
393C4#1062267011yescharacteristic
394C2—162no—
395C2—884no—
396C2#1306896711yescharacteristic
397C2C4×#6689011yescharacteristic
398C2#1307049011yescharacteristic
399C2#1307052711yescharacteristic
400C2#1307053711yescharacteristic
401C2#1307064811yescharacteristic
402C2#1307066811yescharacteristic
subgroupG/H
centerC23C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1970C2
socleC23×C11C2×D8
prime radicalC22×#66890C2
cosocleC22×C8×C11C23
hypercenter#1970D11
hypocenterC11#13012
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×C4×D88C2semidirect
3. C2×#10622200C2semidirect
4. C2×#10622129C2semidirect
5. #13066707C2semidirect
6. #13066694C2semidirect
7. C11×#1970C2semidirect
17. C2×#66890C4semidirect
34. C2×C11×D8C2×C4semidirect
65. C2×C11⋊C16C2×C4semidirect
114. D88C22⋊C4semidirect
121. #1970D11semidirect
151. C2×C4×C11D16semidirect
232. C2×D8C4×D11semidirect
317. C11#13012semidirect
353. C2×C4#66890semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
C2×C4×D882
C2×#106222002
C2×#106221292
#130667072
#130666942
C11×#19702
#1301211