Finite Group Databasebeta

← #14672102

Subgroups — #14672102

Order 2816.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073592C211yesmaximal, characteristic
2C2×#10622116C212yesmaximal, complemented
3C2×#10622115C212yesmaximal
4C4×#66900C211yesmaximal, characteristic, complemented
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C2211yescharacteristic
8C2×#66997C2211yescharacteristic
9C2×#66928C411yescharacteristic
10C11×#423—21no—
11C2×C11×#101C2212yes—
12C2×#66900C2212yes—
13#10622607—21no—
14#10622607—21no—
15#10622601C411yescharacteristic
16#10622587C411yescharacteristic
17#10622553—21no—
18#10622553—21no—
19C4×C4⋊Dic11C411yescharacteristic
20C4×#4318—21no—
21C11×#343—21no—
22#10622168—21no—
23#10622116—24no—
24#10622115—24no—
25C22×Q8×C11C2311yescharacteristic
26C22×D44C2×C411yescharacteristic
27C22×Dic22C2×C411yescharacteristic
28C2×C11×M16—22no—
29C4×Q8×C11—41no—
30C4×Q8×C11—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37#67000—22no—
38#67000—22no—
39#66997—22no—
40#66997—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11C2×C411yescharacteristic
52C2×#4318—22no—
53#66928—41no—
54#66928—41no—
55C11×C4⋊C8—41no—
56C11×C4⋊C8—41no—
57C11×#101—22no—
58C11×#101—22no—
59#66900—22no—
60#66900D414yes—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64#66867—41no—
65C4×C11⋊C8—41no—
66#13228—111nomaximal, Sylow
67C23×D11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11C2×D412yes—
71C2×Q8×C11#4112yes—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×Dic22—22no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C11×M16—42no—
89C11×M16—42no—
90C2×C8×C11—42no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—21no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—22no—
113C4×Dic11—22no—
114#4318—24no—
115#4318—42no—
116C2×C11⋊C8—42no—
117#2545—111no—
118C2×#356—112no—
119C2×#355—112no—
120#1801D1111yescharacteristic, complemented
121C4×#101—111no—
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130Q8×C11—42no—
131Q8×C11—42no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#9911yescharacteristic
147C2×C4×C11C4×D412yes—
148C2×C4×C11#12112yes—
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—82no—
161Dic22—82no—
162C8×C11—82no—
163C11⋊C8—44no—
164C2×C4⋊Q8—111no—
165C2×#124—111no—
166C2×#124—111no—
167C2×C4×Q8C2×D1111yescharacteristic
168#423—21no—
169C2×#101—112no—
170C2×#101C2×D1112yes—
171C4×M16—221no—
172#396—221no—
173#396—221no—
174#391—111no—
175#390—111no—
176#388—221no—
177#388—221no—
178C4×C4⋊C4—111no—
179#356—224no—
180#355—224no—
181#343—21no—
182#343—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#39011yescharacteristic
186C22×C11C2×#9911yescharacteristic
187C22×C11#41011yescharacteristic
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—42no—
205Dic11—81no—
206Dic11—81no—
207C22×Q8—111no—
208C22×Q8C22×D1111yescharacteristic
209C22×D4—111no—
210C2×M16—22no—
211C2×M16—222no—
212C4⋊Q8—222no—
213C4⋊Q8—222no—
214#124—222no—
215#124—222no—
216#124—441no—
217#124—441no—
218C4×Q8—41no—
219C4×Q8—41no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4C4×D1111yescharacteristic
224C2×C4⋊C4D4411yescharacteristic
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42C4×D1111yescharacteristic
235C2×C42D4411yescharacteristic
236C2×C42C22⋊D1111yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#101—22no—
240#101—22no—
241#101—114no—
242#101—222no—
243#97—441no—
244C4×C8—441no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#196411yescharacteristic
251C2×C11#213211yescharacteristic
252C2×C11#213311yescharacteristic
253D11—161no—
254C24—221no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—222no—
258C2×Q8—441no—
259C2×Q8—441no—
260C2×Q8D4×D1112yes—
261C2×Q8#434312yes—
262C2×D4—222no—
263C2×D4—441no—
264C2×D4—441no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×D4411yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275M16—42no—
276M16—42no—
277M16—224no—
278M16—442no—
279C2×C8—42no—
280C2×C8—442no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—441no—
292C22⋊C4—441no—
293C22⋊C4—442no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—222no—
303C42—222no—
304C11#1322811yescharacteristic, complemented, Sylow
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23C2×(C2×D11)⋊C411yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—882no—
316D4—882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—222no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4#6687011yescharacteristic
340C2×C4#6687011yescharacteristic
341C2×C4#6694612yes—
342C2×C4#6694812yes—
343C2×C4#6699311yescharacteristic
344C2×C4#6700011yescharacteristic
345C8—82no—
346C8—444no—
347C22—21no—
348C22—21no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22C2×#6687011yescharacteristic
357C22#1062260111yescharacteristic
358C22#1062261911yescharacteristic
359C4—21no—
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—442no—
369C4—881no—
370C4—881no—
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306945111yescharacteristic
375C2#1307029911yescharacteristic
376C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC22×Q8×C11C23
hypercenter#1801D11
hypocenterC11#13228
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C2×#10622116C2semidirect
4. C4×#66900C2semidirect
5. C11×#1801C2semidirect
120. #1801D11semidirect
304. C11#13228semidirect

Maximal subgroups

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

subgroupindex
#130735922
C2×#106221162
C2×#106221152
C4×#669002
C11×#18012
#1322811