Finite Group Databasebeta

← #24992583

Subgroups — #24992583

Order 11008.

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

normal subgroups only

This group has 478 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#19143680C211yesmaximal, characteristic, complemented
2#19140455C211yesmaximal, characteristic
3#19133192C212yesmaximal
4#19132460C212yesmaximal, complemented
5C4×#101×C43C211yesmaximal, characteristic, complemented
6C2×#13063313C2211yescharacteristic
7#14583030—24no—
8#14582956—21no—
9#14582956C2212yes—
10#14582952—21no—
11#14582834—21no—
12#14582819C411yescharacteristic
13#14582819C411yescharacteristic
14#14582816C411yescharacteristic
15#14582816C411yescharacteristic
16#14582810—21no—
17#14582790—21no—
18#14582790—21no—
19#14582767C2211yescharacteristic
20#14582638—24no—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×#101×C43—21no—
23C4×M16×C43C2212yes—
24C43×#343—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27#13063313—22no—
28#13063313—22no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)—22no—
39C4⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—22no—
41#13063236—22no—
42#13063236D414yes—
43C4×C43⋊C8—22no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95C2×C411yescharacteristic
49C43⋊#95C2×C411yescharacteristic
50C22×Q8×C43D411yescharacteristic
51C2×M16×C43—22no—
52C4×Q8×C43—22no—
53C4×Q8×C43—22no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#101×C43—24no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C23×D43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×D172—22no—
78C2×D172—81no—
79C2×Dic86—22no—
80C2×Dic86—81no—
81M16×C43—24no—
82M16×C43—42no—
83C2×C8×C43—42no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—22no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43C2×D412yes—
92C42×C43#4112yes—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—81no—
99(C2×D43)⋊C4—81no—
100Dic43⋊C4—81no—
101Dic43⋊C4—81no—
102C2×C43⋊C8—24no—
103C23×C43C2×C22⋊C411yescharacteristic
104C22×D43—41no—
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111Q8×C43—44no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43#10412yes—
126C2×C4×C43C4×D412yes—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12112yes—
129C2×C4×C43#12311yescharacteristic
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139D172—82no—
140Dic86—82no—
141C8×C43—44no—
142C43⋊C8—44no—
143#9188—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#38611yescharacteristic
147C22×C43C2×#10411yescharacteristic
148C22×C43#42111yescharacteristic
149C2×D43—81no—
150C2×D43—81no—
151C2×D43—81no—
152C2×D43—81no—
153C2×D43—81no—
154C2×D43—81no—
155C2×D43—81no—
156C4×C43—22no—
157C4×C43—22no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—22no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167#2983—431no—
168#2632—431no—
169C4×#101D4311yescharacteristic, complemented
170#1527—432no—
171#1288—432no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43#187111yescharacteristic
175C2×C43#191211yescharacteristic
176C2×C43#191411yescharacteristic
177D43—161no—
178C2×#124—431no—
179C2×C4×Q8C2×D4311yescharacteristic
180#446—864no—
181#432—432no—
182#432—861no—
183#431—861no—
184C2×#101—21no—
185C4×M16C2×D4312yes—
186#399—861no—
187#395—431no—
188#395—431no—
189#394—431no—
190#394—431no—
191#393—861no—
192#388—861no—
193#388—861no—
194#383—431no—
195#343—21no—
196#329—864no—
197C43#918811yescharacteristic, complemented, Sylow
198C22×Q8—431no—
199C22×Q8C22⋊D4311yescharacteristic
200C22×D4—431no—
201C2×M16—22no—
202#124—862no—
203#124—862no—
204C4×Q8—22no—
205C4×Q8—22no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4C4×D4311yescharacteristic
209C2×C4⋊C4C4×D4311yescharacteristic
210C2×C4⋊C4C22⋊D4311yescharacteristic
211C2×C22⋊C4—861no—
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C42D17211yescharacteristic
218C2×C42D17211yescharacteristic
219C2×C42C22×D4311yescharacteristic
220C4⋊C8—862no—
221C4⋊C8—862no—
222C4⋊C8—862no—
223#101—24no—
224C22⋊C8—862no—
225#97—22no—
226#97—434no—
227#97—862no—
228C4×C8—22no—
229C4×C8—862no—
230#95—431no—
231#95—431no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236C24—861no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—862no—
241C2×Q8—3441no—
242C2×D4—862no—
243C2×D4—3441no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4C2×D17211yescharacteristic
253C22×C4C2×C22⋊D4311yescharacteristic
254M16—24no—
255M16—42no—
256C2×C8—42no—
257C2×C8—864no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—3441no—
262C4⋊C4—3441no—
263C22⋊C4—3441no—
264C22⋊C4—3441no—
265C22⋊C4—1722no—
266C22⋊C4—1722no—
267C22⋊C4—1721no—
268C22⋊C4—1722no—
269C22⋊C4—1721no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42D4×D4312yes—
275C42#1062190012yes—
276C23—1721no—
277C23—1721no—
278C23—1721no—
279C23—1721no—
280C23—1721no—
281C23—1721no—
282C23—1721no—
283C23C2×(C2×D43)⋊C411yescharacteristic
284Q8—44no—
285Q8—3442no—
286D4—3442no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4#1306325312yes—
310C2×C4(C22⋊D43)⋊C412yes—
311C2×C4#1306329511yescharacteristic
312C2×C4#1306329712yes—
313C2×C4#1306330911yescharacteristic
314C8—44no—
315C8—1724no—
316C22—21no—
317C22—21no—
318C22—3441no—
319C22—3441no—
320C22—3441no—
321C22—3441no—
322C22—3441no—
323C22—3441no—
324C22—3441no—
325C22#1458277611yescharacteristic
326C22C2×#1306325311yescharacteristic
327C22#1458291711yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—3441no—
337C4—3441no—
338C4—3441no—
339C2—21no—
340C2—21no—
341C2—6881no—
342C2#1913489511yescharacteristic
343C2#1913513011yescharacteristic
344C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#101×C43C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#101D43
hypocenterC43#9188
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #19143680C2semidirect
4. #19132460C2semidirect
5. C4×#101×C43C2semidirect
169. C4×#101D43semidirect
197. C43#9188semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191404552
#191331922
#191324602
C4×#101×C432
#918843