Finite Group Databasebeta

← #14655787

Subgroups — #14655787

Order 2816.

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

normal subgroups only

This group has 582 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#13079734C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3#13067289C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—21no—
12C2×#66922C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622691—21no—
19#10622683—21no—
20#10622646—22no—
21#10622632—22no—
22#10622632—22no—
23#10622620—22no—
24C2×#66874—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622120—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4324—24no—
55C2×#4324—42no—
56C2×#4324—42no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C22×C11⋊C8—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63#66922D412yes—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—22no—
67C11×#102—22no—
68#66896—24no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)D412yes—
71#66874—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10184—111nomaximal, Sylow
80C24×C11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11D812yes—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—82no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—41no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C11×SD16—44no—
112C11×D8—44no—
113C11×M16—41no—
114C11×M16—41no—
115C2×C8×C11—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128#4324—48no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#3226—111no—
139#3036D1111yescharacteristic
140C2×#461—111no—
141#1546—111no—
142#1480—111no—
143#1460—111no—
144#1301—111no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11#12111yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—22no—
155D4×C11—22no—
156D4×C11—42no—
157D4×C11—41no—
158D4×C11—41no—
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—41no—
168C2×C4×C11—82no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—82no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×Dic11—42no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186Dic22—42no—
187Dic22—42no—
188Dic22—81no—
189Dic22—81no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8—81no—
194C2×AGL(1,ℤ/8)—21no—
195C22×SD16—221no—
196#532C2×D1111yescharacteristic
197C2×C4⋊Q8—111no—
198C2×C4×D4C2×D1111yescharacteristic
199#500—221no—
200#486—221no—
201#480—222no—
202#474—222no—
203#463—22no—
204#461—21no—
205#461—222no—
206#461—222no—
207#459—21no—
208#431—111no—
209#431—111no—
210#423C2×D1111yescharacteristic
211C2×C4⋊C8—111no—
212#417—21no—
213C2×#103—221no—
214#332—222no—
215D4⋊C8—222no—
216#323—222no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39211yescharacteristic
228C22×C11#46611yescharacteristic
229C22×C11#46911yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11#44711yescharacteristic
236C4×C11#44711yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#47112yes—
240Dic11—82no—
241C2×#41—21no—
242C22×Q8—221no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245AGL(1,ℤ/8)—42no—
246AGL(1,ℤ/8)—42no—
247C2×SD16—22no—
248C2×SD16—224no—
249C2×SD16—442no—
250C2×SD16—442no—
251C2×D8—22no—
252C2×M16—21no—
253C22×C8—221no—
254C4⋊Q8—112no—
255C4⋊Q8—221no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8C22⋊D1111yescharacteristic
259#127C22⋊D1111yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C22×D1111yescharacteristic
274#107—224no—
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8C22⋊D1112yes—
281#103—22no—
282#103—224no—
283#102—22no—
284#102—224no—
285C22⋊C8—112no—
286C22⋊C8—221no—
287C4×C8—221no—
288C4×C8—221no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11—161no—
293C2×C11#199911yescharacteristic
294C2×C11#200911yescharacteristic
295C2×C11#201911yescharacteristic
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×Q8—222no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4#432312yes—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—82no—
323C22×C4—441no—
324C22×C4D4×D1111yescharacteristic
325C22×C4#434111yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327SD16—44no—
328SD16—448no—
329D8—44no—
330M16—41no—
331M16—41no—
332C2×C8—22no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—441no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42D4×D1111yescharacteristic
351C42D4×D1111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C11#1018411yescharacteristic, complemented, Sylow
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23#6699211yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—442no—
365Q8—442no—
366Q8—881no—
367Q8—881no—
368D4—22no—
369D4—22no—
370D4—42no—
371D4—42no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—442no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4C2×#432311yescharacteristic
391C2×C4#6698511yescharacteristic
392C2×C4#6699011yescharacteristic
393C2×C4#6699011yescharacteristic
394C2×C4#6699111yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6699311yescharacteristic
397C2×C4#6700211yescharacteristic
398C2×C4#6700311yescharacteristic
399C2×C4#6700611yescharacteristic
400C8—42no—
401C8—442no—
402C8—442no—
403C8—881no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—82no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22#1062265111yescharacteristic
415C22#1062265211yescharacteristic
416C22#1062283611yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—81no—
421C4—81no—
422C4—882no—
423C4#1062264911yescharacteristic
424C4#1062265011yescharacteristic
425C4#1062281312yes—
426C4#1062283011yescharacteristic
427C4#1062285111yescharacteristic
428C2—21no—
429C2—21no—
430C2—82no—
431C2—161no—
432C2#1306961211yescharacteristic
433C2#1306967311yescharacteristic
434C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10184
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
2. C2×#10622632C2semidirect
3. #13067289C2semidirect
4. #13067015C2semidirect
5. #13066937C2semidirect
6. #13066511C2semidirect
354. C11#10184semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106226322
#130672892
#130670152
#130669372
#130665112
C11×#30362
#1018411