Finite Group Databasebeta

← #14655789

Subgroups — #14655789

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#13079739C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4324—21no—
10C2×#66985—21no—
11#10623008C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15#10622632—22no—
16#10622632—21no—
17#10622632—22no—
18#10622629—22no—
19#10622628—21no—
20C2×#66874—21no—
21#10622579—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622459—22no—
25#10622349—22no—
26#10622307—21no—
27#10622295—21no—
28C11×#323—22no—
29#10622124—22no—
30#10622097—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×#4339—21no—
34C22×Dic22—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—22no—
43C2×#4324—24no—
44C2×#4324—42no—
45C2×#4324—42no—
46#66985—42no—
47#66985—42no—
48C2×#4323—22no—
49#66983—21no—
50#66983—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×#4318—21no—
54C22×C11⋊C8—21no—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D412yes—
63#66922D411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yes—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#66885—24no—
71#66882—24no—
72#66874—22no—
73#66874—24no—
74#66873—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78C4⋊(C11⋊C8)D412yes—
79#10184—111nomaximal, Sylow
80C24×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11D812yes—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—82no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96#4339—41no—
97#4339—41no—
98#4339—41no—
99#4339—41no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×Dic22—22no—
105C2×Dic22—21no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#4324—44no—
122#4324—48no—
123#4323—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#3226—111no—
139#3036—111no—
140C2×#461—111no—
141#1546—111no—
142#1480—111no—
143#1460D1111yescharacteristic, complemented
144#1301—111no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11#12111yescharacteristic
151C22×D11—41no—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—41no—
155D4×C11—41no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12711yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C22⋊D11—81no—
173C22⋊D11—81no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178D44—42no—
179D44—41no—
180D44—41no—
181D44—42no—
182C4×D11—81no—
183C4×D11—81no—
184Dic22—42no—
185Dic22—41no—
186Dic22—42no—
187Dic22—41no—
188Dic22—81no—
189Dic22—81no—
190C8×C11—42no—
191C8×C11—81no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194C2×AGL(1,ℤ/8)—221no—
195C22×SD16—221no—
196#532—111no—
197C2×C4⋊Q8—111no—
198C2×C4×D4C2×D1111yescharacteristic
199#500—221no—
200#486—221no—
201#480—222no—
202#474—222no—
203#463—222no—
204#461—222no—
205#461—222no—
206#461—221no—
207#459—221no—
208#431C2×D1111yescharacteristic
209#431C2×D1111yescharacteristic
210#423—111no—
211C2×C4⋊C8—111no—
212#417—221no—
213C2×#103—221no—
214#332—222no—
215D4⋊C8—222no—
216#323—22no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#39211yescharacteristic
225C22×C11#46611yescharacteristic
226C22×C11#46911yescharacteristic
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11#44711yescharacteristic
235C4×C11#44711yescharacteristic
236C4×C11#44911yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#47112yes—
239Dic11—82no—
240Dic11—81no—
241C2×#41—221no—
242C22×Q8—221no—
243C22×D4D4411yescharacteristic
244C23×C4—21no—
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—112no—
255C4⋊Q8—111no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259#127—111no—
260#124—221no—
261#121—221no—
262#121—221no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—221no—
268C4×D4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4D4411yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C22×D1111yescharacteristic
274#107—224no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—112no—
278C4⋊C8—112no—
279C4⋊C8—221no—
280C4⋊C8—221no—
281#103—224no—
282#103—222no—
283#102—222no—
284#102—224no—
285C22⋊C8—21no—
286C22⋊C8C22⋊D1112yes—
287C4×C8—21no—
288C4×C8—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11#199911yescharacteristic
293C2×C11#200911yescharacteristic
294C2×C11#201911yescharacteristic
295D11—161no—
296C24—21no—
297#41—441no—
298#41—441no—
299#41—441no—
300#41—441no—
301C2×Q8—221no—
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—221no—
314C2×D4—221no—
315C2×D4—221no—
316C2×D4—441no—
317C2×D4D8812yes—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—82no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4C2×D4411yescharacteristic
325C22×C4#433911yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327SD16—448no—
328SD16—444no—
329D8—444no—
330M16—441no—
331M16—441no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—222no—
341C4⋊C4—221no—
342C4⋊C4—222no—
343C4⋊C4—221no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42D4×D1111yescharacteristic
351C42D4×D1111yescharacteristic
352C42D4×D1111yescharacteristic
353C42D4×D1111yescharacteristic
354C11#1018411yescharacteristic, complemented, Sylow
355C23—22no—
356C23—41no—
357C23—41no—
358C23—81no—
359C23—81no—
360C23—441no—
361C23#6698311yescharacteristic
362Q8—442no—
363Q8—441no—
364Q8—442no—
365Q8—441no—
366Q8—881no—
367Q8—881no—
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372D4—442no—
373D4—441no—
374D4—441no—
375D4—442no—
376D4—881no—
377D4—881no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4#6693511yescharacteristic
391C2×C4#6693511yescharacteristic
392C2×C4#6693711yescharacteristic
393C2×C4#6693711yescharacteristic
394C2×C4C2×D8811yescharacteristic
395C2×C4#6695711yescharacteristic
396C2×C4#6696111yescharacteristic
397C2×C4#6696111yescharacteristic
398C2×C4#6699011yescharacteristic
399C2×C4#6699311yescharacteristic
400C8—42no—
401C8—81no—
402C8—442no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—82no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22#1062257311yescharacteristic
415C22#1062272811yescharacteristic
416C22#1062274811yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—81no—
421C4—881no—
422C4—882no—
423C4#1062234511yescharacteristic
424C4#1062234511yescharacteristic
425C4#1062234711yescharacteristic
426C4#1062234711yescharacteristic
427C4#1062236112yes—
428C2—21no—
429C2—21no—
430C2—82no—
431C2—1761no—
432C2#1306961411yescharacteristic
433C2#1306967511yescharacteristic
434C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#1460D11
hypocenterC11#10184
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #13079739C2semidirect
3. C2×#10622632C2semidirect
4. #13067287C2semidirect
5. #13067016C2semidirect
6. #13066512C2semidirect
7. C11×#1460C2semidirect
143. #1460D11semidirect
354. C11#10184semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130780802
C2×#106226322
#130672872
#130670162
#130665122
C11×#14602
#1018411