Finite Group Databasebeta

← #14649258

Subgroups — #14649258

Order 2816.

488 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
1#13077577C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic
3#13067004C211yesmaximal, characteristic
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5#13066465C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995C411yescharacteristic
10C4×#4339C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622838C411yescharacteristic
14#10622643—21no—
15C4×#4326—21no—
16#10622639—21no—
17C4×#4325—21no—
18#10622579C411yescharacteristic
19#10622577C411yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622451—21no—
24#10622444—21no—
25#10622343—22no—
26C4×#4313—21no—
27#10622298—21no—
28C11×#324—22no—
29Q8⋊(C11⋊C8)—21no—
30Q8⋊(C11⋊C8)—21no—
31#10622097—21no—
32#10622094—21no—
33C22×Q8×C11C2×C411yescharacteristic
34C2×#4339C2×C411yescharacteristic
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4326—21no—
44#66995—22no—
45#66995—22no—
46C2×#4325—21no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49#66979C2×C411yescharacteristic
50C2×#4318C2×C411yescharacteristic
51C2×#4318C2×C411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C2×#4313—22no—
55C4×D44D411yescharacteristic
56C4×D44D411yescharacteristic
57#66925—21no—
58C42×D11—21no—
59C4×Dic22D411yescharacteristic
60C4×Dic22D411yescharacteristic
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66899—21no—
68#66899—21no—
69(C2×D11)⋊C8—22no—
70#66879—22no—
71Dic11⋊C8—22no—
72#66874—21no—
73#66873—21no—
74#66872—21no—
75#66871—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78#66867—21no—
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8D411yescharacteristic
82C4×C11⋊C8D411yescharacteristic
83#9098—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11M1612yescomplemented
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—21no—
96#4339—21no—
97#4339—21no—
98#4339—21no—
99#4339—21no—
100C2×D44C22⋊C411yescharacteristic
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×Dic22C22⋊C411yescharacteristic
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—21no—
118#4326—24no—
119#4325—24no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122C4⋊Dic11C22⋊C411yescharacteristic
123C4⋊Dic11C22⋊C411yescharacteristic
124Dic11⋊C4—21no—
125Dic11⋊C4—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129#4318—21no—
130#4318—21no—
131#4318—21no—
132#4318M1612yescomplemented
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—81no—
140#4313—44no—
141#2965—111no—
142C4×#137—111no—
143#1477—111no—
144C2×Q8⋊C8—111no—
145#1461D1111yescharacteristic, complemented
146#1283—111no—
147#1278—111no—
148C23×C11C4×D411yescharacteristic
149C22×D11—21no—
150Q8×C11—22no—
151Q8×C11—22no—
152Q8×C11—41no—
153Q8×C11—41no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×C4×C11C2×M1611yescharacteristic
169C2×C4×C11C2×M1611yescharacteristic
170C2×C4×C11#13111yescharacteristic
171C2×C4×C11#13111yescharacteristic
172C22⋊D11—41no—
173C22⋊D11—41no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177D44—21no—
178D44—21no—
179C4×D11—42no—
180C4×D11—41no—
181C4×D11—41no—
182C4×D11—41no—
183C4×D11—41no—
184Dic22—21no—
185Dic22—21no—
186C8×C11—42no—
187C8×C11—81no—
188C11⋊C8—22no—
189C11⋊C8—22no—
190C11⋊C8—41no—
191C11⋊C8—41no—
192C11⋊C8—81no—
193C2×#137—111no—
194C4×#41—111no—
195C2×C4×Q8C2×D1111yescharacteristic
196#446—221no—
197#441—221no—
198#440—221no—
199C4×Q16—221no—
200C4×SD16—221no—
201#436—221no—
202#435—222no—
203#431—221no—
204#431C2×D1111yescharacteristic
205#431C2×D1111yescharacteristic
206#428—111no—
207C2×C4⋊C8—111no—
208#419—111no—
209#417—111no—
210C4×M16—111no—
211C4×M16—221no—
212C2×C4×C8—111no—
213Q8⋊C8—221no—
214Q8⋊C8—221no—
215Q8⋊C8—221no—
216D4⋊C8—221no—
217#324—22no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11#38611yescharacteristic
221C22×C11#43511yescharacteristic
222C22×C11#43611yescharacteristic
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—42no—
230C4×C11—81no—
231C4×C11#40711yescharacteristic
232C4×C11#40811yescharacteristic
233C4×C11#43511yescharacteristic
234C4×C11#43611yescharacteristic
235C4×C11#47111yescharacteristic
236C4×C11#47311yescharacteristic
237Dic11—41no—
238Dic11—41no—
239Dic11—41no—
240C2×#41—111no—
241C22×Q8C4×D1111yescharacteristic
242#137—222no—
243#137—222no—
244C2×Q16—221no—
245C2×SD16—221no—
246C2×M16—111no—
247C2×M16—111no—
248C2×M16—222no—
249C22×C8—221no—
250C22×C8—221no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—111no—
256C4×Q8—111no—
257C4×D4—111no—
258C4×D4—111no—
259C4×D4—221no—
260C4×D4—221no—
261#117—111no—
262#117—221no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C4×D1111yescharacteristic
265C2×C42—21no—
266C2×C42—221no—
267C2×C42C22×D1111yescharacteristic
268#107—221no—
269#106—221no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—222no—
273C4⋊C8—221no—
274C4⋊C8—221no—
275#103—221no—
276#103—221no—
277#103—221no—
278#102—221no—
279C22⋊C8—21no—
280C22⋊C8—222no—
281C22⋊C8C22⋊D1112yes—
282#97—222no—
283#97—221no—
284C4×C8—21no—
285C4×C8—21no—
286C4×C8—111no—
287C4×C8—111no—
288C4×C8—221no—
289C4×C8—221no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11#187011yescharacteristic
293C2×C11#190611yescharacteristic
294C2×C11#190811yescharacteristic
295D11—81no—
296#41—221no—
297#41—221no—
298#41—221no—
299#41—221no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—111no—
306C2×Q8#431312yescomplemented
307C2×D4—111no—
308C2×D4—221no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4#433911yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—224no—
318SD16—224no—
319M16—112no—
320M16—221no—
321M16—221no—
322M16—221no—
323M16—444no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—442no—
331C2×C8—441no—
332C2×C8—881no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—111no—
338C4⋊C4—111no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C42—41no—
345C42—41no—
346C42—221no—
347C42—221no—
348C42—221no—
349C42D4×D1111yescharacteristic
350C42D4×D1111yescharacteristic
351C42D4×D1111yescharacteristic
352C42#434111yescharacteristic
353C11#909811yescharacteristic, complemented, Sylow
354C23—221no—
355C23C4×C22⋊D1111yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—221no—
361Q8—221no—
362D4—221no—
363D4—221no—
364D4—441no—
365D4—441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4C22⋊C4×D1111yescharacteristic
383C2×C4(C22⋊D11)⋊C411yescharacteristic
384C2×C4#6693611yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4C2×#431311yescharacteristic
387C2×C4#6695411yescharacteristic
388C2×C4M16×D1111yescharacteristic
389C2×C4#6696011yescharacteristic
390C2×C4#6699011yescharacteristic
391C2×C4#6699111yescharacteristic
392C8—42no—
393C8—81no—
394C8—222no—
395C8—222no—
396C8—441no—
397C8—441no—
398C8—881no—
399C22—21no—
400C22—21no—
401C22—441no—
402C22—441no—
403C22—441no—
404C22#1062256911yescharacteristic
405C22#1062272411yescharacteristic
406C22#1062274111yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—441no—
413C4—441no—
414C4—441no—
415C4#1062233911yescharacteristic
416C4#1062234011yescharacteristic
417C4#1062234211yescharacteristic
418C4#1062234311yescharacteristic
419C4#1062236711yescharacteristic
420C4#1062236811yescharacteristic
421C2—21no—
422C2—21no—
423C2—881no—
424C2#1306891011yescharacteristic
425C2#1306911411yescharacteristic
426C2#1306912811yescharacteristic
subgroupG/H
centerC2×C4#66937
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#386
prime radicalC2×#4339C2×C4
cosocleC2×C42×C11C23
hypercenter#1461D11
hypocenterC11#9098
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C11⋊C8)C2semidirect
5. #13066465C2semidirect
6. #13066452C2semidirect
7. C11×#1461C2semidirect
89. C2×Q8×C11M16semidirect
132. #4318M16semidirect
145. #1461D11semidirect
306. C2×Q8#4313semidirect
353. C11#9098semidirect

Maximal subgroups

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

subgroupindex
#130775772
C4×#669952
#130670042
C2×Q8⋊(C11⋊C8)2
#130664652
#130664522
C11×#14612
#909811