Finite Group Databasebeta

← #14645359

Subgroups — #14645359

Order 2816.

846 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#10623094C211yesmaximal, characteristic
2#13068716C212yesmaximal, complemented
3#13067131C212yesmaximal, complemented
4#13066954C211yesmaximal, characteristic, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66991—21no—
8C2×#66983C411yescharacteristic, complemented
9C2×#66983C2211yescharacteristic
10C2×#66979C411yescharacteristic, complemented
11C2×#66979C2211yescharacteristic
12#10623094—24no—
13#10623094—24no—
14C2×#66945—21no—
15C2×#66938—21no—
16C2×#66938—21no—
17C2×C4×D44C411yescharacteristic, complemented
18C2×#66922C411yescharacteristic, complemented
19C2×C11×#99—21no—
20C4×C11×C22⋊C4C2212yes—
21#10622820C2212yes—
22C11×#342—21no—
23#10622166—21no—
24#10622163—21no—
25#10622161—24no—
26#10622089—24no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C22×C22⋊D11—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C42×C11—22no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45#66991—28no—
46#66983—22no—
47#66983—22no—
48#66983—22no—
49#66983D414yes—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53#66979—22no—
54#66979—22no—
55#66979—22no—
56#66979D414yes—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11C2×C411yescharacteristic
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C2×#4318—22no—
64#66945—28no—
65#66938—28no—
66#66938—28no—
67C4×D44—22no—
68C4×D44—22no—
69#66922—22no—
70#66922—22no—
71C11×#99—24no—
72C11×#95—22no—
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75#8360—111nomaximal, Sylow
76C24×C11C22⋊C411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—24no—
95C2×C22⋊D11—24no—
96C2×C22⋊D11—82no—
97C2×C22⋊D11—82no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C2×D44—21no—
102C2×D44—42no—
103C2×D44C22⋊C412yes—
104C2×C4×D11—24no—
105C2×C4×D11—42no—
106C2×C4×D11—42no—
107C2×Dic22—24no—
108C2×Dic22—82no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—42no—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—44no—
117C22⋊Dic11—24no—
118C22⋊Dic11—24no—
119(C2×D11)⋊C4—24no—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—24no—
122C4⋊Dic11—24no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11C22⋊C412yes—
127C4⋊Dic11C22⋊C412yes—
128C4⋊Dic11C22⋊C412yes—
129C4×Dic11—24no—
130C4×Dic11—24no—
131#4318—44no—
132C2×C11⋊C8—42no—
133C2×#555—111no—
134#1826—112no—
135C4×#99D1111yescharacteristic, complemented
136#1507—112no—
137#1465—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11#12012yes—
149C22×D11—22no—
150C22×D11—42no—
151C22×D11—42no—
152C22×D11—41no—
153C22×D11—41no—
154D4×C11—44no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—44no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11#10412yes—
171C2×C4×C11C2×C22⋊C411yescharacteristic
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11#12012yes—
174C22⋊D11—84no—
175C22⋊D11—84no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183D44—42no—
184D44—42no—
185C4×D11—48no—
186Dic22—84no—
187C11⋊C8—82no—
188#555—224no—
189#555—224no—
190C2×C4⋊Q8—111no—
191C2×#124—221no—
192C2×#124—221no—
193C2×#121—111no—
194C2×#121—111no—
195C2×#121—221no—
196C2×C4×D4—111no—
197C2×C4×D4C2×D1111yescharacteristic
198C2×#117—111no—
199C2×#117—111no—
200C2×#117—221no—
201C2×#99—21no—
202#407—112no—
203C4×C22⋊C4C2×D1112yes—
204#342—21no—
205#339—224no—
206#327—224no—
207#324—221no—
208#323—221no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#37911yescharacteristic
222C22×C11C2×#10411yescharacteristic
223C22×C11#42111yescharacteristic
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—82no—
228C2×D11—82no—
229C4×C11—21no—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—84no—
235C4×C11#41012yes—
236Dic11—42no—
237Dic11—42no—
238Dic11—42no—
239C22×Q8—221no—
240C22×D4—111no—
241C22×D4—221no—
242C22×D4—221no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—221no—
245C23×C4C4×D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C2×M16—222no—
248C4⋊Q8—222no—
249C4⋊Q8—222no—
250#124—228no—
251#124—228no—
252#121—114no—
253#121—222no—
254#121—222no—
255#121—228no—
256#121—222no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—222no—
260C4×D4—222no—
261#117—114no—
262#117—228no—
263#117—222no—
264#117—222no—
265#117—222no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4D4411yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4D4411yescharacteristic
278C2×C22⋊C4C22⋊D1111yescharacteristic
279C2×C42—22no—
280C2×C42—221no—
281C2×C42—221no—
282C2×C42C4×D1111yescharacteristic
283#99—24no—
284C22⋊C8—222no—
285C22⋊C8—222no—
286#95—22no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—42no—
290C2×C11—81no—
291C2×C11#178211yescharacteristic
292C2×C11#178911yescharacteristic
293C2×C11#179511yescharacteristic
294D11—82no—
295C24—221no—
296C24(C2×D11)⋊C411yescharacteristic
297C24C2×C22⋊D1111yescharacteristic
298C2×Q8—224no—
299C2×Q8—882no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—112no—
304C2×D4—224no—
305C2×D4—224no—
306C2×D4—221no—
307C2×D4—442no—
308C2×D4—882no—
309C2×D4—882no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—224no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4(C2×D11)⋊C411yescharacteristic
322C22×C4(C2×D11)⋊C411yescharacteristic
323C22×C4(C2×D11)⋊C411yescharacteristic
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4C2×D4411yescharacteristic
326C22×C4D4×D1112yes—
327C22×C4D4×D1112yes—
328M16—444no—
329C2×C8—442no—
330C4⋊C4—22no—
331C4⋊C4—112no—
332C4⋊C4—112no—
333C4⋊C4—112no—
334C4⋊C4—224no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—24no—
341C22⋊C4—42no—
342C22⋊C4—224no—
343C22⋊C4—224no—
344C22⋊C4—224no—
345C22⋊C4—224no—
346C22⋊C4—224no—
347C42—21no—
348C42—21no—
349C42—44no—
350C42—224no—
351C42—224no—
352C11#836011yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—222no—
363C23—442no—
364C23—442no—
365C23—441no—
366C23—441no—
367C23C2×(C2×D11)⋊C411yescharacteristic
368C23#6699012yes—
369Q8—884no—
370D4—44no—
371D4—442no—
372D4—442no—
373D4—884no—
374D4—884no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—448no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4#6686912yes—
399C2×C4C22⋊C4×D1111yescharacteristic
400C2×C4C22⋊C4×D1111yescharacteristic
401C2×C4#6693512yes—
402C8—882no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—442no—
416C22—442no—
417C22—442no—
418C22—882no—
419C22—882no—
420C22C2×#6686911yescharacteristic
421C22#1062256811yescharacteristic
422C22#1062261811yescharacteristic
423C4—22no—
424C4—22no—
425C4—21no—
426C4—41no—
427C4—41no—
428C4—84no—
429C4—442no—
430C4—442no—
431C4—442no—
432C4#1062235312yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—882no—
438C2#1306853211yescharacteristic
439C2#1306856111yescharacteristic
440C2#1306858411yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#99C2
socleC22×C11#379
prime radicalC2×#10623094C2
cosocleC23×C4×C11C23
hypercenterC4×#99D11
hypocenterC11#8360
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13068716C2semidirect
3. #13067131C2semidirect
4. #13066954C2semidirect
5. C4×C11×#99C2semidirect
8. C2×#66983C4semidirect
10. C2×#66979C4semidirect
17. C2×C4×D44C4semidirect
18. C2×#66922C4semidirect
135. C4×#99D11semidirect
352. C11#8360semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
#130687162
#130671312
#130669542
C4×C11×#992
#836011