Finite Group Databasebeta

← #14657579

Subgroups — #14657579

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622461C211yesmaximal, characteristic
2#13069552C211yesmaximal, characteristic, complemented
3#13069422C211yesmaximal, characteristic
4#13068622C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#335C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×#66927C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885—21no—
15C2×#66885—21no—
16C2×#66885—21no—
17C2×#66880—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622461—22no—
21#10622461—22no—
22C11×#335—22no—
23#10622189—21no—
24#10622188—21no—
25#10622188—21no—
26#10622123—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C22×C11⋊C8—21no—
43C2×#4314—24no—
44C2×#4314—42no—
45C2×#4314—42no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927D412yes—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60#66885—24no—
61#66885—42no—
62#66885—42no—
63#66880—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#10474—111nomaximal, Sylow
67C23×D11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—41no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—81no—
89C2×D44—81no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22D812yes—
96C2×C8×C11—22no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11SD1612yescomplemented
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—81no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—41no—
122C4×Dic11—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126#4314—48no—
127C2×#460—111no—
128#1984—111no—
129#1957—111no—
130#1803—111no—
131C2×#335D1111yescharacteristic, complemented
132C2×#331—111no—
133#1296—111no—
134C23×C11#12111yescharacteristic
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—81no—
140C22×D11—81no—
141C22×D11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167D44—42no—
168D44—42no—
169D44—42no—
170D44—42no—
171D44—82no—
172D44—82no—
173D44—81no—
174D44—81no—
175D44—81no—
176D44—81no—
177Dic22—22no—
178Dic22—22no—
179Dic22—41no—
180Dic22—41no—
181C8×C11—22no—
182C8×C11—42no—
183C8×C11—41no—
184C8×C11—81no—
185C11⋊C8—81no—
186C22×SD16—221no—
187C2×#127—111no—
188C2×C4×Q8—111no—
189#460—222no—
190#460—222no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×#103—221no—
195C2×#102—221no—
196C2×#102—221no—
197C2×#102—221no—
198C2×C4×C8C2×D1111yescharacteristic
199#384—111no—
200#340—221no—
201#336—221no—
202#336—221no—
203#335—22no—
204#331—222no—
205C22×C11#39411yescharacteristic
206C22×C11#46011yescharacteristic
207C22×C11#46411yescharacteristic
208C22×C11#46611yescharacteristic
209C22×C11#46811yescharacteristic
210C22×C11#47111yescharacteristic
211C22×C11#47211yescharacteristic
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—161no—
216C2×D11—161no—
217C2×D11—161no—
218C2×D11—161no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11#44711yescharacteristic
222C4×C11#45211yescharacteristic
223C4×C11#46111yescharacteristic
224C4×C11#46311yescharacteristic
225C4×C11#46511yescharacteristic
226C4×C11#46811yescharacteristic
227C4×C11#48011yescharacteristic
228C4×C11#48211yescharacteristic
229Dic11—42no—
230Dic11—81no—
231Dic11—161no—
232C22×Q8—111no—
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—224no—
237C2×SD16—442no—
238C2×SD16—442no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—221no—
242C22×C8D4411yescharacteristic
243C22×C8D4411yescharacteristic
244#127—112no—
245#127—221no—
246#127—221no—
247#127—221no—
248C4×Q8—221no—
249C4×Q8—221no—
250C4×Q8—221no—
251C4×Q8—221no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C42—221no—
258C2×C42C22×D1111yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8C22⋊D1112yes—
265#103—442no—
266#102—224no—
267#102—442no—
268#102—442no—
269C4×C8—21no—
270C4×C8—21no—
271C2×C11#166811yescharacteristic
272C2×C11#168211yescharacteristic
273C2×C11#168611yescharacteristic
274C2×C11#169811yescharacteristic
275C2×C11#203311yescharacteristic
276C2×C11#205111yescharacteristic
277C2×C11#205511yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—112no—
281C2×Q8—221no—
282C2×Q8—221no—
283C2×Q8—221no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—881no—
301C2×D4—881no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—441no—
305C22×C4C2×D4411yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4#434311yescharacteristic
308SD16—448no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8#431412yescomplemented
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—881no—
333C42—441no—
334C42—441no—
335C42#433911yescharacteristic
336C42D4×D1111yescharacteristic
337C42#434311yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#1047411yescharacteristic, complemented, Sylow
340C23—442no—
341C23—881no—
342C23—881no—
343C23—881no—
344C23—881no—
345C23—881no—
346C23—881no—
347C23#6694811yescharacteristic
348Q8—222no—
349Q8—222no—
350Q8—441no—
351Q8—441no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—882no—
357D4—882no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—222no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6694711yescharacteristic
374C2×C4#6694711yescharacteristic
375C2×C4#6694811yescharacteristic
376C2×C4C2×#431411yescharacteristic
377C2×C4#6695711yescharacteristic
378C2×C4#6696111yescharacteristic
379C2×C4#6696211yescharacteristic
380C2×C4D8×D1111yescharacteristic
381C2×C4#6696411yescharacteristic
382C2×C4#6697111yescharacteristic
383C2×C4#6697211yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6699011yescharacteristic
386C2×C4#6700011yescharacteristic
387C8—22no—
388C8—41no—
389C8—42no—
390C8—81no—
391C8—881no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1761no—
396C22—1761no—
397C22—1761no—
398C22—1761no—
399C22#1062245811yescharacteristic
400C22#1062246111yescharacteristic
401C22#1062249611yescharacteristic
402C22#1062249911yescharacteristic
403C22#1062251011yescharacteristic
404C22#1062251111yescharacteristic
405C22#1062260411yescharacteristic
406C4—21no—
407C4—21no—
408C4—442no—
409C4—881no—
410C4—1761no—
411C4#1062245411yescharacteristic
412C4#1062245711yescharacteristic
413C4#1062249511yescharacteristic
414C4#1062249811yescharacteristic
415C4#1062272711yescharacteristic
416C4#1062274711yescharacteristic
417C4#1062276911yescharacteristic
418C4#1062280011yescharacteristic
419C2—1762no—
420C2#1306797711yescharacteristic
421C2#1306806111yescharacteristic
422C2#1306808911yescharacteristic
423C2#1306815711yescharacteristic
424C2#1306980011yescharacteristic
425C2#1306991011yescharacteristic
426C2#1306993411yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#335C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#335D11
hypocenterC11#10474
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #13069552C2semidirect
4. #13068622C2semidirect
6. #13066500C2semidirect
7. C2×C11×#335C2semidirect
107. C2×C8×C11SD16semidirect
131. C2×#335D11semidirect
323. C2×C8#4314semidirect
339. C11#10474semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
#130695522
#130694222
#130686222
C2×#106221232
#130665002
C2×C11×#3352
#1047411