Finite Group Databasebeta

← #14655784

Subgroups — #14655784

Order 2816.

582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078076C211yesmaximal, characteristic
2C2×#10622696C211yesmaximal, characteristic, complemented
3#13067288C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#3226C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#67002—21no—
11C22×#4325—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#500—21no—
14C11×#486—21no—
15C11×#480—22no—
16C11×#474—22no—
17C11×#431C2211yescharacteristic
18#10622845—21no—
19C2×#66899—21no—
20#10622696—22no—
21#10622696—21no—
22#10622696—22no—
23#10622685—21no—
24#10622670—22no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622185—22no—
29D4⋊(C11⋊C8)—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49#67002—42no—
50#67002—42no—
51C2×#4325—24no—
52C2×#4325—22no—
53C2×#4325—42no—
54C2×#4325—42no—
55C2×#4323—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×#4318—21no—
59C22×C11⋊C8—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C11×#107—24no—
65C11×C4⋊C8—21no—
66C11×#102—24no—
67C11×C22⋊C8D412yes—
68C4×C8×C11—21no—
69#66899—24no—
70#66899—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4⋊(C11⋊C8)D412yes—
78C4×C11⋊C8—21no—
79#10184—111nomaximal, Sylow
80C23×D11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×Dic11—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44D812yes—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—82no—
111C2×C8×C11—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4325—48no—
125#4325—44no—
126#4323—44no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#3226D1111yescharacteristic, complemented
139#3036—111no—
140C2×#461—111no—
141#1546—111no—
142#1480—111no—
143#1460—111no—
144#1301—111no—
145C23×C11—41no—
146C23×C11#12111yescharacteristic
147C22×D11—22no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—81no—
151C22×D11—81no—
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—42no—
155Q8×C11—41no—
156Q8×C11—81no—
157Q8×C11—81no—
158D4×C11—42no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—42no—
162D4×C11—81no—
163D4×C11—81no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×Dic11—41no—
183C2×Dic11—81no—
184D44—22no—
185D44—22no—
186D44—41no—
187D44—41no—
188C4×D11—82no—
189C4×D11—82no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8—81no—
194C2×AGL(1,ℤ/8)—221no—
195C22×SD16—221no—
196#532C2×D1111yescharacteristic
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×C4×D4—111no—
199#500—21no—
200#486—21no—
201#480—22no—
202#474—22no—
203#463—222no—
204#461—222no—
205#461—222no—
206#461—221no—
207#459—221no—
208#431—111no—
209#431C2×D1111yescharacteristic
210#423—111no—
211C2×C4⋊C8—111no—
212#417—221no—
213C2×#103—221no—
214#332—222no—
215D4⋊C8—222no—
216#323—222no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39211yescharacteristic
223C22×C11#46611yescharacteristic
224C22×C11#46911yescharacteristic
225C2×D11—42no—
226C2×D11—82no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—82no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11—82no—
235C4×C11#44711yescharacteristic
236C4×C11#44711yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#47112yes—
240Dic11—81no—
241C2×#41—21no—
242C22×Q8—21no—
243C22×D4—111no—
244C23×C4—221no—
245AGL(1,ℤ/8)—442no—
246AGL(1,ℤ/8)—442no—
247C2×SD16—224no—
248C2×SD16—222no—
249C2×SD16—442no—
250C2×SD16—442no—
251C2×D8—222no—
252C2×M16—221no—
253C22×C8—221no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8C22⋊D1112yes—
258C4⋊Q8C22⋊D1111yescharacteristic
259#127C22⋊D1111yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—221no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—221no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—111no—
272C2×C22⋊C4—221no—
273C2×C42C22×D1111yescharacteristic
274#107—24no—
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—112no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8—221no—
281#103—224no—
282#103—222no—
283#102—24no—
284#102—222no—
285C22⋊C8—221no—
286C22⋊C8C22⋊D1112yes—
287C4×C8—21no—
288C4×C8—221no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—161no—
292C2×C11#199911yescharacteristic
293C2×C11#200911yescharacteristic
294C2×C11#201911yescharacteristic
295D11—82no—
296C24—221no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—112no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C2×D4—221no—
317C2×D4—221no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—221no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—882no—
324C22×C4D4×D1111yescharacteristic
325C22×C4#434111yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327SD16—448no—
328SD16—444no—
329D8—444no—
330M16—441no—
331M16—441no—
332C2×C8—22no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—441no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42D4×D1111yescharacteristic
351C42D4×D1111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C11#1018411yescharacteristic, complemented, Sylow
355C23—41no—
356C23—222no—
357C23—441no—
358C23—441no—
359C23—881no—
360C23—881no—
361C23#6699111yescharacteristic
362Q8—42no—
363Q8—41no—
364Q8—42no—
365Q8—41no—
366Q8—81no—
367Q8—81no—
368D4—42no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—81no—
373D4—81no—
374D4—222no—
375D4—222no—
376D4—441no—
377D4—441no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—441no—
387C2×C4—882no—
388C2×C4—882no—
389C2×C4—881no—
390C2×C4D8×D1111yescharacteristic
391C2×C4#6696411yescharacteristic
392C2×C4#6696411yescharacteristic
393C2×C4#6696511yescharacteristic
394C2×C4#6699011yescharacteristic
395C2×C4#6699011yescharacteristic
396C2×C4#6699211yescharacteristic
397C2×C4#6699211yescharacteristic
398C2×C4#6699311yescharacteristic
399C2×C4#6700611yescharacteristic
400C8—42no—
401C8—442no—
402C8—442no—
403C8—881no—
404C22—21no—
405C22—21no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—442no—
410C22—882no—
411C22—882no—
412C22—881no—
413C22—881no—
414C22#1062277011yescharacteristic
415C22#1062277211yescharacteristic
416C22#1062283611yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—81no—
421C4—82no—
422C4—881no—
423C4#1062276911yescharacteristic
424C4#1062276911yescharacteristic
425C4#1062277111yescharacteristic
426C4#1062277111yescharacteristic
427C4#1062281612yes—
428C2—21no—
429C2—21no—
430C2—161no—
431C2—882no—
432C2#1306961111yescharacteristic
433C2#1306967611yescharacteristic
434C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3226C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3226D11
hypocenterC11#10184
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. C2×#10622696C2semidirect
3. #13067288C2semidirect
4. #13067015C2semidirect
5. #13066936C2semidirect
6. #13066512C2semidirect
7. C11×#3226C2semidirect
138. #3226D11semidirect
354. C11#10184semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106226962
#130672882
#130670152
#130669362
#130665122
C11×#32262
#1018411