Finite Group Databasebeta

← #25007428

Subgroups — #25007428

Order 11008.

400 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 87 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#19134587C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132625C212yesmaximal, complemented
4#19132601C212yesmaximal, complemented
5C43×#2638C211yesmaximal, characteristic
6#14582923—21no—
7C2×#13063242—21no—
8#14582863—21no—
9#14582668C2212yes—
10#14582625C2212yes—
11#14582623—21no—
12C2×C22⋊Q8×C43C411yescharacteristic
13C2×C4×D4×C43C2211yescharacteristic
14C43×#398C2211yescharacteristic
15C43×#397—21no—
16C43×#397C411yescharacteristic
17C43×#395C2211yescharacteristic
18C43×#394—21no—
19C43×#393C411yescharacteristic
20C43×#387—21no—
21C43×#385—21no—
22C43×#381C411yescharacteristic
23C2×#10621877—22no—
24C2×#10621877—41no—
25C4⋊(C43⋊C8)—41no—
26C4⋊(C43⋊C8)—41no—
27#13063242—42no—
28C22⋊(C43⋊C8)—22no—
29C22⋊(C43⋊C8)—41no—
30C22×Q8×C43C2×C411yescharacteristic
31C22×D4×C43D411yescharacteristic
32C23×C4×C43C2×C411yescharacteristic
33C23×C4×C43D411yescharacteristic
34C22⋊Q8×C43—41no—
35C22⋊Q8×C43—41no—
36C4×D4×C43—41no—
37C4×D4×C43—41no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43C2×C411yescharacteristic
56#95×C43C2×C411yescharacteristic
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×Q8×C43—41no—
60C2×Q8×C43—81no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—81no—
74C22×C4×C43—81no—
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—81no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—42no—
91C22⋊C4×C43—81no—
92C22⋊C4×C43—81no—
93C42×C43—21no—
94C42×C43—21no—
95#10621877—42no—
96#10621877—42no—
97#10621877—82no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—42no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111Q8×C43—82no—
112D4×C43—42no—
113D4×C43—42no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43#9911yescharacteristic
140C2×C4×C43#9911yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C43⋊C8—82no—
144C43⋊C8—82no—
145#11834—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—42no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43C2×#9911yescharacteristic
159C22×C43#41711yescharacteristic
160C22×C43#42111yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—81no—
169C4×C43—81no—
170C4×C43—81no—
171C4×C43—81no—
172#2638D4311yescharacteristic
173#1800—431no—
174#1465—431no—
175#1354—432no—
176#1346—432no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—81no—
180C2×C43—81no—
181C2×C43#151311yescharacteristic
182C2×C43#212111yescharacteristic
183C2×C43#213511yescharacteristic
184C2×C22⋊Q8Dic4311yescharacteristic
185C2×C4×D4C2×D4311yescharacteristic
186#423—861no—
187C2×#100—861no—
188#407—861no—
189#398C2×D4311yescharacteristic
190#397—21no—
191#397Dic4311yescharacteristic
192#395C2×D4311yescharacteristic
193#394—21no—
194#393Dic4311yescharacteristic
195#387—21no—
196#385—21no—
197#381Dic4311yescharacteristic
198#343—432no—
199#324—432no—
200#323—861no—
201C43#1183411yescharacteristic, complemented, Sylow
202C22×Q8C2×Dic4311yescharacteristic
203C22×D4C22⋊D4311yescharacteristic
204C23×C4C2×Dic4311yescharacteristic
205C23×C4C22⋊D4311yescharacteristic
206C2×M16—862no—
207C2×M16—1721no—
208C22⋊Q8—41no—
209C22⋊Q8—41no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic4311yescharacteristic
216C2×C4⋊C4C22×D4311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4C2×Dic4311yescharacteristic
222C2×C22⋊C4C22⋊D4311yescharacteristic
223C2×C42C22⋊D4311yescharacteristic
224C4⋊C8—1721no—
225C4⋊C8—1721no—
226#100—1722no—
227C22⋊C8—862no—
228C22⋊C8—1721no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95C2×Dic4311yescharacteristic
235#95C2×Dic4311yescharacteristic
236C24C22⋊Dic4311yescharacteristic
237C24C22⋊Dic4311yescharacteristic
238C2×Q8—41no—
239C2×Q8—81no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4C22⋊Dic4311yescharacteristic
255C22×C4C22⋊Dic4311yescharacteristic
256C22×C4C22×Dic4311yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259M16—3442no—
260M16—1722no—
261M16—1722no—
262C2×C8—1722no—
263C2×C8—1722no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C42—21no—
278C42—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊Dic4311yescharacteristic
290Q8—82no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4#1306324011yescharacteristic
319C2×C4#1306324011yescharacteristic
320C2×C4#1306335011yescharacteristic
321C2×C4#1306335511yescharacteristic
322C8—3442no—
323C8—3442no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#1306324011yescharacteristic
337C22#1458290011yescharacteristic
338C22#1458291611yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1913313811yescharacteristic
355C2#1913624111yescharacteristic
356C2#1913629011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2638C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#2638D43
hypocenterC43#11834
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #19132625C2semidirect
4. #19132601C2semidirect
201. C43#11834semidirect

Maximal subgroups

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

subgroupindex
#191345872
#191329332
#191326252
#191326012
C43×#26382
#1183443