Finite Group Databasebeta

← #14655795

Subgroups — #14655795

Order 2816.

550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079734C211yesmaximal, characteristic
2#13078084C211yesmaximal, characteristic
3C2×#10622462C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13066939C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C11×#1480C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—21no—
10C22×Dic44—21no—
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15#10622845—21no—
16C2×#66880—21no—
17#10622703—21no—
18#10622691—21no—
19#10622688—21no—
20#10622683—21no—
21#10622667—22no—
22#10622646—22no—
23#10622620—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26#10622462—22no—
27#10622462—22no—
28C11×D4⋊C8—22no—
29#10622124—22no—
30#10622107—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#67004—42no—
44#67004—42no—
45C2×#4326—22no—
46C2×#4324—22no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53C2×Dic44—24no—
54C2×Dic44—42no—
55C2×Dic44—42no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69#66899—22no—
70#66896—22no—
71#66896—24no—
72C22⋊(C11⋊C8)D412yes—
73#66880—24no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78C4×C11⋊C8—21no—
79#10185—111nomaximal, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—41no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—22no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22D812yes—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4326—44no—
121#4324—44no—
122C4⋊Dic11—22no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136Dic44—48no—
137#3226—111no—
138#3037—111no—
139C2×#462—111no—
140#1546—111no—
141#1480D1111yescharacteristic
142#1461—111no—
143#1301—111no—
144C23×C11—41no—
145C23×C11#12111yescharacteristic
146Q8×C11—41no—
147Q8×C11—41no—
148D4×C11—42no—
149D4×C11—41no—
150D4×C11—41no—
151D4×C11—42no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177Dic22—22no—
178Dic22—22no—
179Dic22—41no—
180Dic22—41no—
181Dic22—42no—
182Dic22—42no—
183Dic22—81no—
184Dic22—81no—
185C8×C11—42no—
186C8×C11—81no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×#137—221no—
190C22×Q16—221no—
191#532C2×D1111yescharacteristic
192C2×C4⋊Q8—111no—
193C2×C4×Q8—111no—
194#500—221no—
195#486—221no—
196#480—222no—
197#474—222no—
198#464—222no—
199#462—222no—
200#462—221no—
201#462—222no—
202#460—221no—
203#431—111no—
204#431C2×D1111yescharacteristic
205#423—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207#417—221no—
208C2×#103—221no—
209#332—222no—
210D4⋊C8—22no—
211#324—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#39211yescharacteristic
218C22×C11#46611yescharacteristic
219C22×C11#46911yescharacteristic
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—81no—
224C4×C11#44711yescharacteristic
225C4×C11#44711yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#47312yes—
229Dic11—42no—
230Dic11—82no—
231Dic11—81no—
232C2×#41—21no—
233C22×Q8—111no—
234C22×Q8—221no—
235#137—442no—
236#137—442no—
237C2×Q16—224no—
238C2×Q16—222no—
239C2×Q16—442no—
240C2×Q16—442no—
241C2×SD16—222no—
242C2×M16—221no—
243C22×C8—21no—
244C4⋊Q8—112no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8D4411yescharacteristic
249#127D4411yescharacteristic
250#124—21no—
251#121—21no—
252#121—21no—
253C4×Q8—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×Q8—221no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C42—221no—
264C2×C42C22×D1111yescharacteristic
265#107—224no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8C22⋊D1112yes—
272#103—224no—
273#103—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—112no—
278C4×C8—21no—
279C4×C8—221no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—161no—
283C2×C11#199911yescharacteristic
284C2×C11#200911yescharacteristic
285C2×C11#202011yescharacteristic
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—112no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—221no—
296C2×Q8—221no—
297C2×Q8—222no—
298C2×Q8—441no—
299C2×Q8—441no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C22×C4—41no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—441no—
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314Q16—448no—
315Q16—444no—
316SD16—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—221no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—441no—
338C42—441no—
339C42C2×D4411yescharacteristic
340C42D4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C11#1018511yescharacteristic, complemented, Sylow
344C23—41no—
345C23#6693711yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—222no—
349Q8—222no—
350Q8—441no—
351Q8—441no—
352Q8—442no—
353Q8—442no—
354Q8—881no—
355Q8—881no—
356D4—42no—
357D4—42no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—81no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—222no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4#6693511yescharacteristic
376C2×C4#6693511yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4D8×D1111yescharacteristic
379C2×C4#6696411yescharacteristic
380C2×C4#6696711yescharacteristic
381C2×C4#6696911yescharacteristic
382C2×C4#6698311yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699311yescharacteristic
385C8—42no—
386C8—81no—
387C8—442no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22#1062238811yescharacteristic
395C22#1062239511yescharacteristic
396C22#1062257311yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—442no—
402C4—882no—
403C4—881no—
404C4#1062238611yescharacteristic
405C4#1062239411yescharacteristic
406C4#1062275612yes—
407C4#1062276911yescharacteristic
408C4#1062278511yescharacteristic
409C2—21no—
410C2—21no—
411C2—161no—
412C2#1306961311yescharacteristic
413C2#1306967711yescharacteristic
414C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1480C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1480D11
hypocenterC11#10185
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
3. C2×#10622462C2semidirect
4. #13067287C2semidirect
5. #13066939C2semidirect
6. #13066513C2semidirect
343. C11#10185semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130780842
C2×#106224622
#130672872
#130669392
#130665132
C11×#14802
#1018511