Finite Group Databasebeta

← #25005753

Subgroups — #25005753

Order 11008.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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#19136998C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic
3#19132540C212yesmaximal, complemented
4#19132538C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7C22×C4×Dic43C411yescharacteristic
8#14582952—21no—
9#14582768C411yescharacteristic
10#14582768C2211yescharacteristic
11#14582764C411yescharacteristic
12#14582764C2211yescharacteristic
13#14582757—21no—
14#14582757—21no—
15C4×Dic43⋊C4—21no—
16C4×Dic43⋊C4—21no—
17#14582625C2212yes—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C23×Dic43—21no—
24#13063284—41no—
25#13063284—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—22no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C814yescomplemented
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43C2×C411yescharacteristic
39C4⋊(C43⋊C8)—41no—
40C22⋊(C43⋊C8)—22no—
41C4×C43⋊C8—41no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C23×C4×C43C2×C411yescharacteristic
47#117×C43—41no—
48#117×C43—41no—
49C2×C4⋊C4×C43C2×C411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C4⋊C8×C43—41no—
56C22⋊C8×C43—22no—
57C4×C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C2×C812yes—
66C22×C4×C43M1612yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—24no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—42no—
76C22×Dic43—42no—
77C2×C8×C43—42no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—42no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93C4×Dic43—24no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C4×Dic43—41no—
97C4×Dic43—41no—
98C4×Dic43C2×C812yes—
99C4×Dic43C2×C812yes—
100C2×C43⋊C8—42no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43C22⋊C812yes—
106C23×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43C22⋊C812yes—
122C2×C4×C43#9911yescharacteristic
123C2×C4×C43#9911yescharacteristic
124C2×C4×C43#10112yes—
125C2×C4×C43C22×C811yescharacteristic
126C2×C4×C43C2×M1611yescharacteristic
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—48no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C8×C43—82no—
141C43⋊C8—82no—
142#11447—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43C2×C22⋊C811yescharacteristic
151C22×C43C2×#9911yescharacteristic
152C22×C43C2×#10111yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43#32412yes—
160C4×C43#32412yes—
161Dic43—24no—
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165#2285—431no—
166#1458—431no—
167#1458D4311yescharacteristic
168#1325—432no—
169#1324—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—42no—
173C2×C43C2×#32411yescharacteristic
174C2×C43#212611yescharacteristic
175C2×C43#213211yescharacteristic
176C2×#117—431no—
177C2×#117C2×D4311yescharacteristic
178C22×C42—431no—
179#431—21no—
180#431—861no—
181#384—431no—
182#384—431no—
183#382—431no—
184#382—431no—
185#380—861no—
186#380—861no—
187C4×C4⋊C4—861no—
188C4×C4⋊C4—861no—
189#324—432no—
190#324C2×D4312yes—
191#323—21no—
192#323—861no—
193C43#1144711yescharacteristic, complemented, Sylow
194C23×C4—861no—
195C23×C4C4×D4311yescharacteristic
196#117—41no—
197#117—41no—
198#117—1721no—
199#117—1721no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4C4×D4311yescharacteristic
207C2×C4⋊C4C22×D4311yescharacteristic
208C2×C22⋊C4—861no—
209C2×C22⋊C4D17211yescharacteristic
210C2×C22⋊C4C22⋊D4311yescharacteristic
211C2×C42—434no—
212C2×C42—431no—
213C2×C42—431no—
214C2×C42—862no—
215C2×C42—861no—
216C2×C42—861no—
217C2×C42D17211yescharacteristic
218C2×C42C22⋊D4311yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—1721no—
221C22⋊C8—22no—
222C22⋊C8—862no—
223C4×C8—41no—
224C4×C8—1721no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229C24(C2×D43)⋊C411yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—861no—
234C22×C4—864no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4C8×D4312yes—
241C22×C4#1062187212yes—
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4C2×D17211yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248C2×C8—42no—
249C2×C8—1722no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C4⋊C4—1722no—
257C4⋊C4—1722no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—1722no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—432no—
266C42—432no—
267C42—864no—
268C42—861no—
269C42—861no—
270C42—1721no—
271C42—1721no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23(C2×D43)⋊C812yes—
277C23C2×(C2×D43)⋊C411yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—1728no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4(C2×D43)⋊C812yes—
306C2×C4#1306323911yescharacteristic
307C2×C4#1306323911yescharacteristic
308C2×C4#1306324312yes—
309C2×C4C2×C8×D4311yescharacteristic
310C2×C4C2×#1062187211yescharacteristic
311C8—82no—
312C8—3442no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22C2×(C2×D43)⋊C811yescharacteristic
321C22C2×#1306323911yescharacteristic
322C22C2×#1306324311yescharacteristic
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—864no—
330C4—3441no—
331C4—3441no—
332C4—1722no—
333C4#1458262412yes—
334C4#1458262412yes—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C2×#1458262411yescharacteristic
339C2#1913625811yescharacteristic
340C2#1913627811yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1458C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1458D43
hypocenterC43#11447
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
4. #19132538C2semidirect
36. C2×C4×Dic43C8semidirect
193. C43#11447semidirect

Maximal subgroups

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

subgroupindex
#191369982
#191329092
#191325402
#191325382
C43×#14582
#1144743