Finite Group Databasebeta

← #14656310

Subgroups — #14656310

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×#10622698C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13069411C211yesmaximal, characteristic, complemented
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#474C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C22×#4325—22no—
11C22×#4323—21no—
12C2×#66927C2211yescharacteristic
13C11×#474—22no—
14C11×#474—22no—
15C2×C11×#107—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622698—22no—
20#10622698—22no—
21#10622628—22no—
22#10622628—22no—
23C2×#66873—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622185—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—28no—
50C2×#4325—44no—
51C2×#4325—44no—
52C2×#4323—24no—
53C2×#4323—42no—
54C2×#4323—42no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927D412yes—
62C11×#107—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#102—24no—
66C22⋊(C11⋊C8)—44no—
67#66873—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#10266—111nomaximal, Sylow
75C24×C11—21no—
76C23×D11—41no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11SD1612yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—42no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—42no—
107C2×D44—41no—
108C2×D44—82no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4325—416no—
125#4323—48no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8D814yescomplemented
134C2×#492—111no—
135C2×#474D1111yescharacteristic, complemented
136C2×#459—111no—
137#1954—111no—
138C2×#332—111no—
139C2×#331—111no—
140#1277—111no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11#12111yescharacteristic
147C22×D11—42no—
148C22×D11—82no—
149C22×D11—81no—
150C22×D11—81no—
151C22×D11—82no—
152Q8×C11—44no—
153Q8×C11—81no—
154Q8×C11—81no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—41no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×D812yes—
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11#13711yescharacteristic
179D44—44no—
180D44—42no—
181D44—42no—
182D44—82no—
183D44—82no—
184D44—81no—
185D44—81no—
186D44—81no—
187D44—81no—
188C8×C11—42no—
189C11⋊C8—24no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C22×SD16—222no—
193C22×D8—221no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×#127—111no—
196C2×C4×D4C2×D1111yescharacteristic
197#492—222no—
198#492—222no—
199#474—22no—
200#474—22no—
201#459—222no—
202#459—222no—
203C2×#107—21no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×#102—21no—
208C2×#102—221no—
209C2×C22⋊C8—222no—
210C2×C4×C8—111no—
211#332—222no—
212#331—222no—
213C22×C11—44no—
214C22×C11—42no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#39211yescharacteristic
219C22×C11#45912yes—
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C22×C11#47112yes—
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—82no—
226C2×D11—162no—
227C2×D11—162no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11—82no—
232C4×C11#44712yes—
233C4×C11#44811yescharacteristic
234C4×C11#44911yescharacteristic
235C4×C11#45011yescharacteristic
236C4×C11#45211yescharacteristic
237C4×C11#49311yescharacteristic
238C4×C11#49611yescharacteristic
239C22×Q8—21no—
240C22×D4—221no—
241C22×D4—221no—
242C22×D4—221no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245C2×SD16—228no—
246C2×SD16—444no—
247C2×SD16—444no—
248C2×D8—224no—
249C2×D8—442no—
250C2×D8—442no—
251C22×C8—21no—
252C22×C8—112no—
253C22×C8—221no—
254C22×C8—221no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C22⋊D1112yes—
259#127—112no—
260#127—221no—
261#127—221no—
262#127—221no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C42C22×D1111yescharacteristic
272#107—24no—
273C4⋊C8—21no—
274C4⋊C8—112no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8—221no—
278C4⋊C8C22⋊D1112yes—
279#102—24no—
280#102—224no—
281C22⋊C8—444no—
282C4×C8—221no—
283C4×C8—221no—
284C2×C11—82no—
285C2×C11#166512yes—
286C2×C11#168512yes—
287C2×C11#200011yescharacteristic
288C2×C11#201111yescharacteristic
289C2×C11#201911yescharacteristic
290D11—162no—
291C24—21no—
292C24—441no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—882no—
315C2×D4#432512yescomplemented
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—4416no—
326D8—448no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—114no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—442no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42D4×D1111yescharacteristic
347C42D4×D1111yescharacteristic
348C42C2×C22⋊D1111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C11#1026611yescharacteristic, complemented, Sylow
351C23—22no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23—442no—
357C23—882no—
358C23—882no—
359C23—881no—
360C23—881no—
361C23#6699211yescharacteristic
362Q8—44no—
363Q8—81no—
364Q8—81no—
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369D4—444no—
370D4—442no—
371D4—442no—
372D4—882no—
373D4—882no—
374D4—881no—
375D4—881no—
376D4—881no—
377D4—881no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4D8×D1112yes—
387C2×C4#6696412yes—
388C2×C4#6699011yescharacteristic
389C2×C4#6699011yescharacteristic
390C2×C4#6699111yescharacteristic
391C2×C4#6699211yescharacteristic
392C2×C4#6699311yescharacteristic
393C2×C4C2×#432511yescharacteristic
394C2×C4#6699511yescharacteristic
395C2×C4#6700211yescharacteristic
396C2×C4#6700311yescharacteristic
397C2×C4#6700611yescharacteristic
398C8—42no—
399C8—224no—
400C8—442no—
401C8—881no—
402C22—42no—
403C22—44no—
404C22—82no—
405C22—81no—
406C22—81no—
407C22—882no—
408C22—882no—
409C22—882no—
410C22—1762no—
411C22—1762no—
412C22#1062266111yescharacteristic
413C22#1062266211yescharacteristic
414C22#1062276312yes—
415C22#1062281612yes—
416C22#1062283611yescharacteristic
417C4—21no—
418C4—21no—
419C4—81no—
420C4—82no—
421C4#1062265911yescharacteristic
422C4#1062266011yescharacteristic
423C4#1062276411yescharacteristic
424C4#1062276711yescharacteristic
425C4#1062276912yes—
426C4#1062284011yescharacteristic
427C4#1062285111yescharacteristic
428C2—82no—
429C2—1762no—
430C2#1306795912yes—
431C2#1306808312yes—
432C2#1306961711yescharacteristic
433C2#1306968511yescharacteristic
434C2#1306972711yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#474C2
socleC23×C11#121
prime radicalC2×#10622628C2
hypercenterC2×#474D11
hypocenterC11#10266
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622698C2semidirect
3. #13069411C2semidirect
4. C2×#10622185C2semidirect
5. C2×#10622123C2semidirect
6. #13066450C2semidirect
7. C2×C11×#474C2semidirect
86. C2×D4×C11SD16semidirect
133. C2×C11⋊C8D8semidirect
135. C2×#474D11semidirect
315. C2×D4#4325semidirect
350. C11#10266semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226282
#130694112
C2×#106221852
C2×#106221232
#130664502
C2×C11×#4742
#1026611