Finite Group Databasebeta

← #25006781

Subgroups — #25006781

Order 11008.

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

normal subgroups only

This group has 568 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#19140345C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic, complemented
3#19132591C214yesmaximal, complemented
4C43×#1740C211yesmaximal, characteristic, complemented
5C2×#13063322C411yescharacteristic, complemented
6C2×#13063299—21no—
7#14582952—21no—
8#14582816—21no—
9#14582816C412yescomplemented
10#14582808—21no—
11#14582808C2212yes—
12#14582801—21no—
13#14582765C411yescharacteristic, complemented
14#14582625—21no—
15#14582623C2212yes—
16C2×#117×C43—21no—
17C2×#117×C43C2211yescharacteristic
18C43×#342—21no—
19C43×#342C2212yes—
20C22×D172—21no—
21C22×D172—21no—
22C22×D172C2×C412yes—
23C22×C22⋊D43—22no—
24#13063322—41no—
25#13063322—41no—
26#13063299—42no—
27#13063299—42no—
28C2×C4⋊Dic43—21no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C4⋊(C43⋊C8)—41no—
33C22⋊(C43⋊C8)—22no—
34C4×C43⋊C8—41no—
35C43⋊#95—21no—
36C43⋊#95C2×C412yes—
37C23×C4×C43D411yescharacteristic
38#117×C43—24no—
39#117×C43—41no—
40#117×C43—41no—
41#117×C43—42no—
42C2×C4⋊C4×C43—41no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C22⋊C4×C43C2311yescharacteristic
48C2×C42×C43—41no—
49C2×C42×C43C2×C411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C24×C43C2×D411yescharacteristic
52C23×D43—22no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—22no—
56C22×C4×C43—42no—
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43D812yes—
62C22×C4×C43SD1612yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C2×C22⋊D43—42no—
66C2×C22⋊D43—42no—
67C2×C22⋊D43—82no—
68C2×C22⋊D43—82no—
69C22×Dic43—22no—
70C2×D172—42no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172—42no—
74C2×D172—42no—
75C2×D172—42no—
76C2×D172—82no—
77C2×D172—82no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—44no—
81C22⋊C4×C43—24no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—42no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—44no—
90(C2×D43)⋊C4—44no—
91(C2×D43)⋊C4—82no—
92(C2×D43)⋊C4—82no—
93C4⋊Dic43—42no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43C2×C22⋊C411yescharacteristic
100C23×C43C2×D811yescharacteristic
101C23×C43C2×SD1611yescharacteristic
102C22×D43—42no—
103C22×D43—42no—
104C22×D43—42no—
105C22×D43—42no—
106C22×D43—42no—
107C22×D43—42no—
108C22×D43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—44no—
124C2×C4×C43—82no—
125C2×C4×C43—82no—
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#10212yes—
129C2×C4×C43#10212yes—
130C2×C4×C43#10412yes—
131C22⋊D43—84no—
132C22⋊D43—84no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136D172—84no—
137D172—84no—
138D172—82no—
139D172—82no—
140C43⋊C8—82no—
141#11693—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—81no—
151C22×C43C2×#9911yescharacteristic
152C22×C43C2×#10211yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C2×D43—82no—
155C2×D43—82no—
156C2×D43—82no—
157C2×D43—82no—
158C2×D43—82no—
159C2×D43—82no—
160C2×D43—82no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—84no—
167C4×C43#32712yes—
168C4×C43#32712yes—
169Dic43—82no—
170#2619—431no—
171#1740D4311yescharacteristic, complemented
172#1458—431no—
173#1343—434no—
174C2×C43—21no—
175C2×C43—21no—
176C2×C43—41no—
177C2×C43—41no—
178C2×C43C2×#32711yescharacteristic
179C2×C43#212211yescharacteristic
180C2×C43#212811yescharacteristic
181D43—162no—
182C2×#127—431no—
183C2×#121—861no—
184C2×#117—21no—
185C2×#117C2×D4311yescharacteristic
186#431—861no—
187#394—432no—
188#394—861no—
189#392—432no—
190#392—861no—
191#390—861no—
192#382—431no—
193#342—21no—
194#342C2×D4312yes—
195#324—861no—
196#323—432no—
197C43#1169311yescharacteristic, complemented, Sylow
198C22×D4—432no—
199C22×D4—862no—
200C22×D4—861no—
201C22×D4—861no—
202C23×C4C22⋊D4311yescharacteristic
203#127—1721no—
204#127—1721no—
205#121—1722no—
206#121—1722no—
207#117—24no—
208#117—41no—
209#117—41no—
210#117—42no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C4×D4311yescharacteristic
214C2×C4⋊C4D17211yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—862no—
217C2×C22⋊C4—862no—
218C2×C22⋊C4—862no—
219C2×C22⋊C4C22⋊D4311yescharacteristic
220C2×C22⋊C4C22×D4311yescharacteristic
221C2×C42—41no—
222C2×C42C4×D4311yescharacteristic
223C2×C42D17211yescharacteristic
224C4⋊C8—1721no—
225C22⋊C8—862no—
226C4×C8—1721no—
227#95—432no—
228#95—861no—
229C24—862no—
230C24C2×C22⋊D4311yescharacteristic
231C2×D4—3442no—
232C2×D4—3442no—
233C2×D4—3442no—
234C2×D4—3442no—
235C2×D4—1722no—
236C2×D4—1722no—
237C2×D4—1722no—
238C2×D4—1722no—
239C2×D4—1721no—
240C2×D4—1721no—
241C2×D4—1722no—
242C2×D4—1722no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—42no—
247C22×C4—862no—
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4#1062188212yes—
253C22×C4#1062188412yes—
254C22×C4C2×C4×D4311yescharacteristic
255C22×C4C2×D17211yescharacteristic
256C2×C8—1722no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—44no—
260C4⋊C4—1722no—
261C22⋊C4—24no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—3442no—
266C22⋊C4—3442no—
267C22⋊C4—1724no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—44no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—1722no—
278C23—1722no—
279C23—1722no—
280C23—1722no—
281C23—1722no—
282C23—1722no—
283C23—1722no—
284C23C2×(C2×D43)⋊C411yescharacteristic
285C23C2×#1062188211yescharacteristic
286C23C2×#1062188411yescharacteristic
287D4—3444no—
288D4—3444no—
289D4—3444no—
290D4—3444no—
291D4—3442no—
292D4—3442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—1722no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4#1306323911yescharacteristic
314C2×C4#1306323911yescharacteristic
315C2×C4#1306324512yes—
316C2×C4#1306324512yes—
317C2×C4#1306325312yes—
318C8—3442no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—3442no—
329C22—3442no—
330C22—3442no—
331C22—3442no—
332C22—3442no—
333C22—3442no—
334C22—3442no—
335C22C2×#1306323911yescharacteristic
336C22C2×#1306324511yescharacteristic
337C22C2×#1306325311yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—84no—
344C4—3442no—
345C4#1458263212yes—
346C4#1458263212yes—
347C2—21no—
348C2—21no—
349C2—41no—
350C2—41no—
351C2—6882no—
352C2C2×#1458263211yescharacteristic
353C2#1913624411yescharacteristic
354C2#1913626611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1740C2
socleC22×C43C2×#99
prime radical#19140345C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1740D43
hypocenterC43#11693
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #19132909C2semidirect
3. #19132591C2semidirect
4. C43×#1740C2semidirect
5. C2×#13063322C4semidirect
9. #14582816C4semidirect
13. #14582765C4semidirect
171. #1740D43semidirect
197. C43#11693semidirect

Maximal subgroups

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

subgroupindex
#191403452
#191329092
#191325912
C43×#17402
#1169343