Finite Group Databasebeta

← #14670610

Subgroups — #14670610

Order 2816.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#13071704C211yesmaximal, characteristic
2C2×#10622116C211yesmaximal, characteristic
3#13069009C211yesmaximal, characteristic
4#13068831C211yesmaximal, characteristic
5#13066743C211yesmaximal, characteristic
6#13066742C211yesmaximal, characteristic
7C11×#1857C211yesmaximal, characteristic
8C11×#519C2211yescharacteristic
9C2×#66997C2211yescharacteristic
10C11×#428—21no—
11C2×C11×#101C2211yescharacteristic
12C11×#391C2211yescharacteristic
13#10622843C2211yescharacteristic
14C2×#66900C2211yescharacteristic
15C2×#66900C2211yescharacteristic
16#10622617—21no—
17#10622608—21no—
18#10622585—21no—
19C4×Dic11⋊C4—21no—
20#10622262—21no—
21#10622262—21no—
22#10622260—21no—
23#10622259—21no—
24C11×#339—21no—
25#10622170—21no—
26#10622170—21no—
27#10622116C414yescomplemented
28C22×Q8×C11C2311yescharacteristic
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C4×Q8×C11—41no—
32C4×Q8×C11—41no—
33C11×#117—21no—
34C11×#117—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38#66997—21no—
39#66997—21no—
40#66997C2×C412yes—
41#66997Q812yes—
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×#4318—21no—
54C2×#4318—21no—
55C11×#107—41no—
56C11×#106—41no—
57C11×#101—21no—
58C11×#101C2×C412yes—
59C11×#95—21no—
60C11×#95—21no—
61#66900—21no—
62#66900—21no—
63#66900—21no—
64#66900C2×C412yes—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69#66874—41no—
70#66874—41no—
71#66872—41no—
72#66871—41no—
73#12973—111nomaximal, Sylow
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11C22×C411yescharacteristic
77C2×Q8×C11C2×Q811yescharacteristic
78C2×Q8×C11#4111yescharacteristic
79C2×Q8×C11#4111yescharacteristic
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×Dic22—21no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22C4⋊C412yes—
93C11×M16—22no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—24no—
110Dic11⋊C4—22no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—42no—
115Dic11⋊C4—81no—
116C4×Dic11—21no—
117C4×Dic11—41no—
118C4×Dic11—42no—
119C4×Dic11—42no—
120C4×Dic11—81no—
121C4×Dic11C4⋊C412yes—
122#4318—22no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128#2369—111no—
129C2×#356—111no—
130#1886—111no—
131#1857—111no—
132#1857D1111yescharacteristic
133#1394—111no—
134#1394—111no—
135C23×C11#12011yescharacteristic
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—41no—
139Q8×C11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11C2×C4⋊C411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C22⋊Q811yescharacteristic
158C2×C4×C11C22⋊Q811yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172Dic22—42no—
173Dic22—81no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×C4⋊Q8—111no—
178#519C2×D1111yescharacteristic
179#428—21no—
180#428—221no—
181#419—221no—
182C2×#101—111no—
183C2×#101—111no—
184C2×#101C2×D1111yescharacteristic
185#391—111no—
186#391—221no—
187#391C2×D1111yescharacteristic
188#389—221no—
189#389—221no—
190C4×C4⋊C4—221no—
191C4×C4⋊C4—221no—
192C4×C4⋊C4—221no—
193#356—114no—
194#339—21no—
195#339—221no—
196#339—221no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11#38511yescharacteristic
200C22×C11B(4,𝔽2)11yescharacteristic
201C22×C11#45811yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—24no—
213Dic11—42no—
214Dic11—42no—
215Dic11—81no—
216C22×Q8—111no—
217C22×Q8C22×D1111yescharacteristic
218C2×M16—21no—
219C2×M16—221no—
220C2×M16—221no—
221C4⋊Q8—112no—
222C4⋊Q8—112no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4×Q8—41no—
226C4×Q8—41no—
227#117—21no—
228#117—21no—
229#117—21no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4C22⋊D1111yescharacteristic
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—221no—
240C2×C42—221no—
241C2×C42—221no—
242C2×C42C22⋊D1111yescharacteristic
243#107—41no—
244#107—441no—
245#106—41no—
246#106—441no—
247#103—441no—
248#103—441no—
249#101—21no—
250#101—112no—
251#101—221no—
252#101—221no—
253#101—221no—
254#101C4×D1112yes—
255#95—21no—
256#95—21no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#186711yescharacteristic
264C2×C11#220411yescharacteristic
265C2×C11#220511yescharacteristic
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—112no—
269C2×Q8—221no—
270C2×Q8—441no—
271C2×Q8—441no—
272C2×Q8C2×C4×D1111yescharacteristic
273C2×Q8#433911yescharacteristic
274C2×Q8Q8×D1111yescharacteristic
275C2×Q8#434311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285M16—22no—
286M16—41no—
287M16—222no—
288M16—441no—
289M16—441no—
290M16—441no—
291C2×C8—41no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—224no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—441no—
307C4⋊C4—442no—
308C4⋊C4—881no—
309C22⋊C4—41no—
310C42—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—112no—
315C42—221no—
316C42—441no—
317C42—442no—
318C42—442no—
319C42—881no—
320C11#1297311yescharacteristic, complemented, Sylow
321C23#6699011yescharacteristic
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326Q8—442no—
327Q8—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4C4⋊C4×D1111yescharacteristic
355C2×C4#6694611yescharacteristic
356C2×C4#6694711yescharacteristic
357C2×C4#6694911yescharacteristic
358C2×C4C4×C22⋊D1111yescharacteristic
359C2×C4#6699911yescharacteristic
360C8—42no—
361C8—442no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22#1062260211yescharacteristic
366C22#1062264511yescharacteristic
367C22#1062266611yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—224no—
379C4—442no—
380C4—442no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2#1306889511yescharacteristic
385C2#1307064011yescharacteristic
386C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutatorC2×Q8×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1857C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
cosocleC22×Q8×C11C23
hypercenter#1857D11
hypocenterC11#12973
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
27. #10622116C4semidirect
320. C11#12973semidirect

Maximal subgroups

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

subgroupindex
#130717042
C2×#106221162
#130690092
#130688312
#130667432
#130667422
C11×#18572
#1297311