Finite Group Databasebeta

← #25015241

Subgroups — #25015241

Order 11008.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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#19138912C211yesmaximal, characteristic
2#19134583C211yesmaximal, characteristic
3#19132714C214yesmaximal
4C4×#100×C43C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic, complemented
6C2×#13063240C2212yes—
7#14582838—21no—
8#14582835—21no—
9#14582797—21no—
10#14582779C2212yes—
11#14582771C412yescomplemented
12#14582759—21no—
13#14582759—21no—
14#14582759C411yescharacteristic, complemented
15#14582666—21no—
16C2×C4×D4×C43C2211yescharacteristic
17C2×#100×C43C2212yes—
18C4×M16×C43—21no—
19C43×#343—21no—
20C23×Dic43C2×C412yes—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43—41no—
26C2×C4⋊Dic43—41no—
27C2×Dic43⋊C4—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43C2×C412yes—
31#13063240—24no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—41no—
36C22×D4×C43C2311yescharacteristic
37C23×C4×C43C2×C411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C2×M16×C43—22no—
40C4×D4×C43—41no—
41C4×D4×C43—41no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46#100×C43—22no—
47#100×C43Q814yes—
48#97×C43—41no—
49C4×C8×C43—41no—
50C24×C43C22×C411yescharacteristic
51C24×C43C2×D411yescharacteristic
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43C2×Q812yes—
55C2×D4×C43#4112yes—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—42no—
70C22×Dic43—42no—
71C22×Dic43—82no—
72M16×C43—24no—
73M16×C43—42no—
74C2×C8×C43—42no—
75C4⋊C4×C43—41no—
76C22⋊C4×C43—41no—
77C22⋊C4×C43—41no—
78C42×C43—21no—
79C42×C43—21no—
80C22⋊Dic43—42no—
81C22⋊Dic43—42no—
82C22⋊Dic43—42no—
83C22⋊Dic43—82no—
84C4⋊Dic43—42no—
85C4⋊Dic43—42no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—82no—
89Dic43⋊C4—82no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—41no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43C2×C22⋊C411yescharacteristic
99C23×C43C4×Q812yes—
100C23×C43#12411yescharacteristic
101C23×C43C4⋊Q811yescharacteristic
102D4×C43—42no—
103D4×C43—42no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—81no—
117C2×C4×C43#9911yescharacteristic
118C2×C4×C43#9911yescharacteristic
119C2×C4×C43C22⋊Q812yes—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—84no—
127C2×Dic43—82no—
128C2×Dic43—82no—
129C2×Dic43—82no—
130C8×C43—44no—
131#13292—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—22no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—42no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—42no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—81no—
146C22×C43#39111yescharacteristic
147C22×C43C2×#9911yescharacteristic
148C22×C43#41011yescharacteristic
149C4×C43—21no—
150C4×C43—22no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43#35212yes—
155Dic43—82no—
156Dic43—82no—
157Dic43—162no—
158#2487—431no—
159#1799—431no—
160C4×#100D4311yescharacteristic
161#1390—434no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—41no—
165C2×C43—42no—
166C2×C43—41no—
167C2×C43#199611yescharacteristic
168C2×C43C2×#35211yescharacteristic
169C2×C43#212211yescharacteristic
170C2×C4×D4C2×D4311yescharacteristic
171C22×C4⋊C4—431no—
172C2×#100C2×D4312yes—
173C2×#99—432no—
174C4×M16—21no—
175#400—861no—
176#399—861no—
177#389—861no—
178#386—432no—
179#385—432no—
180#380—431no—
181#380—861no—
182#380—861no—
183#343—21no—
184#342—861no—
185C43#1329211yescharacteristic, complemented, Sylow
186C22×D4C22×D4311yescharacteristic
187C23×C4—432no—
188C23×C4C4×D4311yescharacteristic
189C23×C4D17211yescharacteristic
190C2×M16—22no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4—862no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—1721no—
198C2×C4⋊C4—1721no—
199C2×C4⋊C4—1721no—
200C2×C4⋊C4C22⋊D4311yescharacteristic
201C2×C22⋊C4—432no—
202C2×C22⋊C4—862no—
203C2×C22⋊C4—862no—
204C2×C22⋊C4C4×D4311yescharacteristic
205C2×C22⋊C4D17211yescharacteristic
206C2×C42C22⋊D4311yescharacteristic
207#100—22no—
208#100Dic8614yes—
209#99—864no—
210#97—41no—
211C4×C8—41no—
212#95—861no—
213#95—862no—
214#95—862no—
215#95—1721no—
216C24C2×C4×D4311yescharacteristic
217C24C2×D17211yescharacteristic
218C2×D4—41no—
219C2×D4—41no—
220C2×D4C2×Dic8612yes—
221C2×D4#1062189812yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—862no—
229C22×C4—862no—
230C22×C4—3442no—
231C22×C4—1722no—
232C22×C4—1722no—
233C22×C4(C2×D43)⋊C411yescharacteristic
234C22×C4(C2×D43)⋊C411yescharacteristic
235C22×C4(C2×D43)⋊C411yescharacteristic
236C22×C4(C2×D43)⋊C411yescharacteristic
237C22×C4C2×C22⋊D4311yescharacteristic
238M16—24no—
239M16—42no—
240C2×C8—42no—
241C4⋊C4—41no—
242C4⋊C4—3442no—
243C4⋊C4—3442no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C4⋊C4—1721no—
247C4⋊C4—1721no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—3442no—
251C22⋊C4—1722no—
252C22⋊C4—1722no—
253C22⋊C4—1722no—
254C42—21no—
255C42—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C2×(C2×D43)⋊C411yescharacteristic
265C23C4×Dic8612yes—
266C23#1306331311yescharacteristic
267C23#1306332511yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—3444no—
284C2×C4—3442no—
285C2×C4—3442no—
286C2×C4—3442no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4—1722no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4#1306323911yescharacteristic
294C2×C4#1306323911yescharacteristic
295C2×C4#1306330412yes—
296C8—44no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22#1458280511yescharacteristic
312C22C2×#1306323911yescharacteristic
313C22#1458287211yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—3442no—
320C4—3442no—
321C4—6882no—
322C4#1458269012yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#1913558011yescharacteristic
329C2C2×#1458269011yescharacteristic
330C2#1913624611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC4×#100×C43C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC4×#100D43
hypocenterC43#13292
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
5. C22×C4⋊Dic43C4semidirect
11. #14582771C4semidirect
14. #14582759C4semidirect
185. C43#13292semidirect

Maximal subgroups

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

subgroupindex
#191389122
#191345832
#191327142
C4×#100×C432
#1329243