Finite Group Databasebeta

← #14656316

Subgroups — #14656316

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622306C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3C2×#10622456C211yesmaximal, characteristic
4#13069410C211yesmaximal, characteristic, complemented
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×#10622123C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×D88—21no—
9C22×#4314—22no—
10C2×#66927C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66885—21no—
17C2×#66885—21no—
18C2×(C2×D11)⋊C8—22no—
19C2×#66882—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622459—22no—
22#10622459—22no—
23#10622456—22no—
24#10622456—22no—
25#10622306—22no—
26#10622306—22no—
27#10622124—22no—
28#10622123—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11D412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C22×C11⋊C8—21no—
44C2×D88—24no—
45C2×D88—42no—
46C2×D88—42no—
47C2×#4314—28no—
48C2×#4314—44no—
49C2×#4314—44no—
50#66927—21no—
51#66927—21no—
52#66927—21no—
53#66927D412yes—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D412yes—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68#66885—24no—
69#66885—24no—
70(C2×D11)⋊C8—44no—
71#66882—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#10266—111nomaximal, Sylow
75C23×D11—21no—
76C23×D11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—42no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—42no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—82no—
100C2×D44SD1612yescomplemented
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—42no—
108C2×Dic22—42no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11D814yescomplemented
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—42no—
132D88—48no—
133#4314—416no—
134C2×#492—111no—
135C2×#474—111no—
136C2×#459—111no—
137#1954—111no—
138C2×#332—111no—
139C2×#331—111no—
140#1277D1111yescharacteristic, complemented
141C23×C11#12111yescharacteristic
142C22×D11—22no—
143C22×D11—41no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—82no—
149C22×D11—81no—
150C22×D11—81no—
151C22×D11—82no—
152C2×C4×C11—22no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×D812yes—
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—82no—
169D44—22no—
170D44—22no—
171D44—44no—
172D44—41no—
173D44—42no—
174D44—41no—
175D44—42no—
176D44—82no—
177D44—82no—
178D44—81no—
179D44—81no—
180D44—81no—
181D44—81no—
182C4×D11—82no—
183C4×D11—81no—
184C4×D11—81no—
185Dic22—44no—
186Dic22—81no—
187Dic22—81no—
188C8×C11—24no—
189C8×C11—42no—
190C8×C11—42no—
191C11⋊C8—81no—
192C22×SD16—222no—
193C22×D8—221no—
194C2×C4⋊Q8—111no—
195C2×#127—111no—
196C2×C4×D4—111no—
197#492—222no—
198#492—222no—
199#474—222no—
200#474—222no—
201#459—222no—
202#459—222no—
203C2×#107—221no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8C2×D1111yescharacteristic
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×#102—221no—
208C2×#102—221no—
209C2×C22⋊C8—222no—
210C2×C4×C8C2×D1111yescharacteristic
211#332—222no—
212#331—222no—
213C22×C11#39211yescharacteristic
214C22×C11#45912yes—
215C22×C11#46511yescharacteristic
216C22×C11#46811yescharacteristic
217C22×C11#47112yes—
218C2×D11—44no—
219C2×D11—42no—
220C2×D11—82no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—82no—
226C2×D11—162no—
227C2×D11—162no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11#44712yes—
231C4×C11#44811yescharacteristic
232C4×C11#44911yescharacteristic
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#49311yescharacteristic
236C4×C11#49611yescharacteristic
237Dic11—82no—
238Dic11—81no—
239C22×Q8—221no—
240C22×D4—111no—
241C22×D4—221no—
242C22×D4—221no—
243C22×D4—221no—
244C23×C4—221no—
245C2×SD16—228no—
246C2×SD16—444no—
247C2×SD16—444no—
248C2×D8—224no—
249C2×D8—442no—
250C2×D8—442no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—221no—
254C22×C8D4412yes—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259#127—112no—
260#127—221no—
261#127—221no—
262#127—221no—
263C4×D4—221no—
264C4×D4—221no—
265C4×D4—221no—
266C4×D4—221no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C42C22×D1111yescharacteristic
272#107—224no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8D4412yes—
278C4⋊C8D4412yes—
279#102—224no—
280#102—224no—
281C22⋊C8—444no—
282C4×C8—21no—
283C4×C8—21no—
284C2×C11#166512yes—
285C2×C11#168512yes—
286C2×C11#200011yescharacteristic
287C2×C11#201111yescharacteristic
288C2×C11#201911yescharacteristic
289D11—82no—
290D11—162no—
291C24—221no—
292C24—441no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—112no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—222no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—442no—
310C2×D4—442no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—882no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4C2×D4411yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4#434311yescharacteristic
325SD16—4416no—
326D8—448no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—441no—
336C2×C8—442no—
337C2×C8D8814yescomplemented
338C4⋊C4—221no—
339C4⋊C4—222no—
340C4⋊C4—221no—
341C4⋊C4—222no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42C2×D4411yescharacteristic
347C42C2×D4411yescharacteristic
348C42D4×D1111yescharacteristic
349C42D4×D1111yescharacteristic
350C11#1026611yescharacteristic, complemented, Sylow
351C23—222no—
352C23—441no—
353C23—442no—
354C23—441no—
355C23—442no—
356C23—442no—
357C23—881no—
358C23—881no—
359C23—882no—
360C23—882no—
361C23#6694811yescharacteristic
362Q8—444no—
363Q8—881no—
364Q8—881no—
365D4—222no—
366D4—222no—
367D4—444no—
368D4—442no—
369D4—441no—
370D4—441no—
371D4—442no—
372D4—882no—
373D4—882no—
374D4—881no—
375D4—881no—
376D4—881no—
377D4—881no—
378C2×C4—22no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—882no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4—882no—
386C2×C4#6692711yescharacteristic
387C2×C4#6693511yescharacteristic
388C2×C4#6693511yescharacteristic
389C2×C4#6693511yescharacteristic
390C2×C4#6694811yescharacteristic
391C2×C4#6694811yescharacteristic
392C2×C4C2×D8812yes—
393C2×C4#6696112yes—
394C2×C4#6696411yescharacteristic
395C2×C4SD16×D1111yescharacteristic
396C2×C4#6696911yescharacteristic
397C2×C4#6697111yescharacteristic
398C8—24no—
399C8—42no—
400C8—42no—
401C8—881no—
402C22—442no—
403C22—444no—
404C22—882no—
405C22—881no—
406C22—881no—
407C22—882no—
408C22—882no—
409C22—882no—
410C22—1762no—
411C22—1762no—
412C22#1062228411yescharacteristic
413C22#1062245612yes—
414C22#1062247711yescharacteristic
415C22#1062249911yescharacteristic
416C22#1062251112yes—
417C4—21no—
418C4—21no—
419C4—881no—
420C4—882no—
421C4#1062230811yescharacteristic
422C4#1062232511yescharacteristic
423C4#1062234512yes—
424C4#1062238911yescharacteristic
425C4#1062239411yescharacteristic
426C4#1062241911yescharacteristic
427C4#1062242311yescharacteristic
428C2—882no—
429C2—1762no—
430C2#1306795812yes—
431C2#1306808212yes—
432C2#1306962211yescharacteristic
433C2#1306968911yescharacteristic
434C2#1306973311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC2×#10622456C2
hypercenter#1277D11
hypocenterC11#10266
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#10622306C2semidirect
2. C2×#10622459C2semidirect
4. #13069410C2semidirect
5. C2×#10622124C2semidirect
6. C2×#10622123C2semidirect
7. C11×#1277C2semidirect
100. C2×D44SD16semidirect
117. C2×C8×C11D8semidirect
140. #1277D11semidirect
337. C2×C8D88semidirect
350. C11#10266semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
C2×#106224592
C2×#106224562
#130694102
C2×#106221242
C2×#106221232
C11×#12772
#1026611