Finite Group Databasebeta

← #14656168

Subgroups — #14656168

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079737C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12#10623008C2211yescharacteristic
13C11×#398—22no—
14C11×#391—21no—
15C11×#389—22no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20#10622644—21no—
21#10622641—22no—
22#10622640—21no—
23#10622580—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×#4339—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—42no—
39C11×C4⋊Q8—42no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D412yes—
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—22no—
54#66995—42no—
55#66995—42no—
56C2×#4325—22no—
57#66983—21no—
58#66983—21no—
59C2×#4318—21no—
60#66928—21no—
61#66927D411yescharacteristic
62C4×D44—21no—
63C4×D44—21no—
64#66922D411yescharacteristic
65C11×#95—24no—
66C11×#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66874—22no—
70#66873—22no—
71#66873—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10243—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11D812yes—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100#4339—41no—
101#4339—41no—
102#4339—41no—
103#4339—41no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—48no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127#4326—44no—
128#4325—44no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133#4318—41no—
134#4318—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3226—111no—
139#3037—111no—
140#2546D1111yescharacteristic, complemented
141#1546—111no—
142#1502—111no—
143#1479—111no—
144#1303—111no—
145C23×C11#12011yescharacteristic
146C22×D11—41no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—81no—
152Q8×C11—81no—
153Q8×C11—81no—
154Q8×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C22⋊D11—81no—
179C22⋊D11—81no—
180C2×Dic11—41no—
181D44—41no—
182D44—41no—
183D44—42no—
184D44—81no—
185C4×D11—81no—
186C4×D11—81no—
187Dic22—41no—
188Dic22—41no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×#137—221no—
193#532—111no—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8C2×D1111yescharacteristic
196C2×C4×Q8C2×D1111yescharacteristic
197#500—221no—
198#486—221no—
199#480—222no—
200#474—222no—
201#464—222no—
202#462—221no—
203#460—221no—
204#431—111no—
205#431—111no—
206#423—111no—
207#417—221no—
208#398—22no—
209#391—21no—
210#389—22no—
211C4×C4⋊C4C2×D1111yescharacteristic
212#332—222no—
213#327—222no—
214Q8⋊C8—222no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11#39211yescharacteristic
218C22×C11#44711yescharacteristic
219C22×C11#44911yescharacteristic
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—44no—
227C4×C11—42no—
228C4×C11—82no—
229C4×C11—81no—
230C4×C11#44711yescharacteristic
231C4×C11#44911yescharacteristic
232C4×C11#45612yes—
233C4×C11#46611yescharacteristic
234C4×C11#46911yescharacteristic
235Dic11—81no—
236C2×#41—221no—
237C22×Q8—21no—
238C22×Q8C22⋊D1111yescharacteristic
239#137—442no—
240#137—442no—
241C2×Q16—222no—
242C2×SD16—222no—
243C2×M16—221no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—42no—
249C4⋊Q8—42no—
250C4⋊Q8—111no—
251#127—111no—
252#124—221no—
253#121—221no—
254#121—221no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×D4—221no—
260C4×D4—221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C4⋊C4C22⋊D1112yes—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42C22×D1111yescharacteristic
270#107—224no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—221no—
274C4⋊C8—221no—
275#103—222no—
276#102—222no—
277#102—224no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C4×C8—221no—
281C4×C8—221no—
282#95—24no—
283#95C22⋊D1112yes—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11#199911yescharacteristic
287C2×C11#200511yescharacteristic
288C2×C11#200911yescharacteristic
289D11—161no—
290#41—441no—
291#41—441no—
292#41—441no—
293#41—441no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—221no—
306C2×Q8#432312yes—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—441no—
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319Q16—444no—
320SD16—444no—
321M16—441no—
322M16—441no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—441no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—48no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C42—41no—
341C42—41no—
342C42—41no—
343C42—41no—
344C42D4×D1111yescharacteristic
345C42D4×D1111yescharacteristic
346C42D4×D1111yescharacteristic
347C42#434111yescharacteristic
348C11#1024311yescharacteristic, complemented, Sylow
349C23—441no—
350C23#6700611yescharacteristic
351Q8—22no—
352Q8—22no—
353Q8—41no—
354Q8—41no—
355Q8—81no—
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—441no—
360Q8—441no—
361D4—441no—
362D4—441no—
363D4—442no—
364D4—881no—
365D4—881no—
366D4—881no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4C2×#432311yescharacteristic
384C2×C4#6698511yescharacteristic
385C2×C4#6699011yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699111yescharacteristic
388C2×C4#6699211yescharacteristic
389C2×C4#6699211yescharacteristic
390C2×C4#6699311yescharacteristic
391C2×C4#6700211yescharacteristic
392C2×C4#6700311yescharacteristic
393C8—442no—
394C8—442no—
395C8—881no—
396C22—21no—
397C22—21no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22#1062283011yescharacteristic
402C22#1062283611yescharacteristic
403C22#1062285111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—44no—
408C4—42no—
409C4—82no—
410C4—81no—
411C4—881no—
412C4#1062264911yescharacteristic
413C4#1062265011yescharacteristic
414C4#1062265111yescharacteristic
415C4#1062265211yescharacteristic
416C4#1062270812yes—
417C2—21no—
418C2—21no—
419C2—1761no—
420C2#1306961211yescharacteristic
421C2#1306965211yescharacteristic
422C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2546C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2546D11
hypocenterC11#10243
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
3. #13067288C2semidirect
5. #13067011C2semidirect
6. #13066519C2semidirect
7. C11×#2546C2semidirect
140. #2546D11semidirect
348. C11#10243semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780882
#130672882
#130671102
#130670112
#130665192
C11×#25462
#1024311