Finite Group Databasebeta

← #14654387

Subgroups — #14654387

Order 2816.

544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079364C211yesmaximal, characteristic
2#13078556C211yesmaximal, characteristic, complemented
3#13068687C211yesmaximal, characteristic, complemented
4#13066977C211yesmaximal, characteristic, complemented
5#13066976C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#3094C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C11×#482—22no—
12C11×#481—21no—
13C11×#480—21no—
14C11×#428—21no—
15C11×#418—21no—
16C11×#407C2211yescharacteristic
17#10622830—21no—
18#10622820C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21#10622651—22no—
22#10622649—21no—
23#10622646—21no—
24#10622616—22no—
25#10622614—21no—
26#10622608—21no—
27#10622581—21no—
28#10622580—21no—
29#10622580—21no—
30#10622163—22no—
31#10622162—22no—
32#10622106—22no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C22×D44D411yescharacteristic
38C2×C11×M16—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#117—21no—
44C11×#117—21no—
45C11×#117—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×#4323—22no—
54#66983—21no—
55#66983—21no—
56#66983—21no—
57#66983—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11D411yescharacteristic
60C2×#4318—21no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8D412yes—
63C11×#107—22no—
64C11×#106—22no—
65C11×#102—22no—
66C11×#102—22no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8D412yes—
69#66896—22no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)D412yes—
76#66873—22no—
77#66873—22no—
78#66873—22no—
79#66872—22no—
80#66871—22no—
81#66871—22no—
82#9977—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11#4111yescharacteristic
85C23×D11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—82no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—82no—
105C22×Dic11—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—42no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123#4323—82no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8—41no—
134#3186—111no—
135#3094—111no—
136#3094D1111yescharacteristic, complemented
137#1818—111no—
138#1471—111no—
139#1471—111no—
140#1293—111no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149C23×C11#12111yescharacteristic
150C23×C11#12111yescharacteristic
151C22×D11—41no—
152C22×D11—42no—
153C22×D11—81no—
154C22×D11—81no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—82no—
158D4×C11—82no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C22⋊D11—82no—
176C22⋊D11—82no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179D44—42no—
180D44—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C11⋊C8—81no—
185C2×#121—111no—
186C2×#121C2×D1111yescharacteristic
187C2×#117C2×D1111yescharacteristic
188#482—22no—
189#482—222no—
190#481—21no—
191#481—221no—
192#480—21no—
193#480—221no—
194#480—221no—
195#480—221no—
196#466—222no—
197#447—221no—
198#447—221no—
199#428—21no—
200#428—221no—
201#418—21no—
202#418—221no—
203#407—111no—
204#407C2×D1111yescharacteristic
205C2×C22⋊C8—111no—
206C2×C22⋊C8—111no—
207#336—222no—
208#323—222no—
209#323—222no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—82no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—162no—
223C22×C11#39211yescharacteristic
224C22×C11#47212yes—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—162no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11#45812yes—
236Dic11—81no—
237C22×D4—21no—
238C22×D4—111no—
239C22×D4—221no—
240C22×D4C22⋊D1111yescharacteristic
241C23×C4C22×D1111yescharacteristic
242C2×D8—222no—
243C2×M16—21no—
244C2×M16—221no—
245C22×C8—112no—
246C22×C8—221no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251#121—221no—
252#121—221no—
253#121—221no—
254#121—221no—
255#117—21no—
256#117—21no—
257#117—21no—
258#117—21no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4C22⋊D1111yescharacteristic
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C4⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—221no—
266C2×C42—21no—
267#107—22no—
268#107—222no—
269#107—222no—
270#106—22no—
271#106—222no—
272#102—22no—
273#102—22no—
274#102—222no—
275#102—222no—
276#102—222no—
277#102—222no—
278C22⋊C8—21no—
279C22⋊C8—112no—
280C22⋊C8—221no—
281C22⋊C8—221no—
282C22⋊C8—221no—
283C22⋊C8—221no—
284C22⋊C8—221no—
285C22⋊C8C22⋊D1112yes—
286C2×C11—22no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—161no—
290C2×C11#201711yescharacteristic
291C2×C11#201811yescharacteristic
292C2×C11#202211yescharacteristic
293D11—161no—
294C24—21no—
295C24—221no—
296C24#434111yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—82no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—442no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—882no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—221no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320D8—882no—
321M16—42no—
322M16—442no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—442no—
327C2×C8—442no—
328C2×C8—441no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C42—41no—
344C42—41no—
345C11#997711yescharacteristic, complemented, Sylow
346C23—22no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—41no—
351C23—81no—
352C23—81no—
353C23—442no—
354C23—441no—
355C23—881no—
356C23—881no—
357C23#6699111yescharacteristic
358C23#6699211yescharacteristic
359C23#6699211yescharacteristic
360D4—42no—
361D4—42no—
362D4—82no—
363D4—82no—
364D4—442no—
365D4—442no—
366D4—882no—
367D4—882no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4#6699011yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699311yescharacteristic
385C2×C4#6700611yescharacteristic
386C8—42no—
387C8—442no—
388C8—442no—
389C8—881no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—82no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—162no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—1762no—
407C22#1062281212yes—
408C22#1062283611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—881no—
416C4#1062266612yes—
417C2—22no—
418C2—41no—
419C2—41no—
420C2—161no—
421C2—1761no—
422C2#1306971911yescharacteristic
423C2#1306972211yescharacteristic
424C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3094C2
socleC22×C11#392
prime radical#13079364C2
hypercenter#3094D11
hypocenterC11#9977
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
2. #13078556C2semidirect
3. #13068687C2semidirect
4. #13066977C2semidirect
5. #13066976C2semidirect
6. #13066492C2semidirect
7. C11×#3094C2semidirect
136. #3094D11semidirect
345. C11#9977semidirect

Maximal subgroups

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

subgroupindex
#130793642
#130785562
#130686872
#130669772
#130669762
#130664922
C11×#30942
#997711