Finite Group Databasebeta

← #25012868

Subgroups — #25012868

Order 11008.

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

normal subgroups only

This group has 566 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#19137178C211yesmaximal, characteristic
2#19134517C212yesmaximal
3#19132722C211yesmaximal, characteristic, complemented
4#19132721C212yesmaximal, complemented
5C43×#1394C211yesmaximal, characteristic, complemented
6C22×Q8×D43C2211yescharacteristic
7C2×#13063283C411yescharacteristic
8C2×#13063282C411yescharacteristic
9C2×#13063244C2212yes—
10C2×#13063243—22no—
11#14582862—22no—
12#14582806C2211yescharacteristic
13#14582805C411yescharacteristic
14#14582804C411yescharacteristic
15#14582803—22no—
16#14582761—22no—
17C2×#101×C43C2212yes—
18C43×#391C2211yescharacteristic
19C22×Dic86C2×C411yescharacteristic
20C22×Dic86D412yes—
21C2×Q8×D43—22no—
22C2×Q8×D43—21no—
23C2×Q8×D43—21no—
24C2×Q8×D43—42no—
25C2×Q8×D43—42no—
26C22×C4×D43C2×C411yescharacteristic
27C22×C4×D43D412yes—
28C2×#10621877—22no—
29#13063283—42no—
30#13063282—42no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37#13063244—22no—
38#13063244—22no—
39#13063243—44no—
40(C2×D43)⋊C8—44no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C43⋊#95—22no—
44C22×Q8×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48#101×C43—22no—
49#101×C43—22no—
50#95×C43—22no—
51C23×D43C22⋊C411yescharacteristic
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43#4112yes—
55C2×Q8×C43#4111yescharacteristic
56C2×Q8×C43#4111yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C22×C411yescharacteristic
60C22×C4×C43C2×D412yes—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43C22⋊C412yes—
64C22×Dic43C22⋊C411yescharacteristic
65Q8×D43—48no—
66Q8×D43—44no—
67Q8×D43—44no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—22no—
73C2×C4×D43—22no—
74C2×C4×D43—24no—
75C2×C4×D43—42no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×Dic86—22no—
79C2×Dic86—22no—
80C2×Dic86—24no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—42no—
84M16×C43—42no—
85M16×C43—42no—
86C2×C8×C43—42no—
87C4⋊C4×C43—41no—
88C42×C43—41no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91C4⋊Dic43—41no—
92Dic43⋊C4—42no—
93C4×Dic43—42no—
94C4×Dic43—41no—
95#10621877—42no—
96#10621877—42no—
97C2×C43⋊C8—42no—
98C23×C43C2×C22⋊C411yescharacteristic
99C22×D43—21no—
100C22×D43—21no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43#9912yes—
104Q8×C43—42no—
105Q8×C43—41no—
106Q8×C43—41no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43#11711yescharacteristic
117C2×C4×C43#11711yescharacteristic
118C2×C4×C43#12312yes—
119C2×C4×C43#12312yes—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—42no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43#9912yes—
131C4×D43—24no—
132C4×D43—24no—
133C4×D43—44no—
134C4×D43—44no—
135Dic86—44no—
136Dic86—44no—
137Dic86—42no—
138Dic86—42no—
139C8×C43—82no—
140C43⋊C8—82no—
141#12862—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43#38111yescharacteristic
145C22×C43C2×#9911yescharacteristic
146C22×C43C2×#9911yescharacteristic
147C2×D43—22no—
148C2×D43—22no—
149C2×D43—22no—
150C2×D43—42no—
151C2×D43—42no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—81no—
157C4×C43—81no—
158Dic43—22no—
159Dic43—42no—
160Dic43—81no—
161Dic43—81no—
162#2310—431no—
163#1784—432no—
164#1394—432no—
165#1394—431no—
166#1394D4311yescharacteristic, complemented
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#181911yescharacteristic
170C2×C43#213311yescharacteristic
171C2×C43#213311yescharacteristic
172D43—42no—
173C23×Q8—431no—
174C2×#117—431no—
175C2×#117—431no—
176C2×#101—432no—
177C2×#101—862no—
178C2×#101C2×D4312yes—
179#407—862no—
180#391—431no—
181#391—431no—
182#391—431no—
183#391—862no—
184#391C2×D4311yescharacteristic
185#381—862no—
186C43#1286211yescharacteristic, complemented, Sylow
187C22×Q8—431no—
188C22×Q8—432no—
189C22×Q8—862no—
190C22×Q8—861no—
191C22×Q8—861no—
192C22×Q8—1722no—
193C22×Q8—1722no—
194C22×Q8C22×D4311yescharacteristic
195C23×C4—431no—
196C23×C4—432no—
197C2×M16—22no—
198C2×M16—862no—
199#117—1722no—
200#117—1722no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4C4×D4311yescharacteristic
204C2×C22⋊C4—861no—
205C2×C22⋊C4—861no—
206C2×C42—431no—
207C2×C42—861no—
208C2×C42C4×D4311yescharacteristic
209#101—22no—
210#101—22no—
211#101—862no—
212#101—862no—
213#101—1724no—
214C22⋊C8—1724no—
215#95—22no—
216#95—862no—
217#95—862no—
218#95—862no—
219C24—431no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—864no—
223C2×Q8—861no—
224C2×Q8—861no—
225C2×Q8—862no—
226C2×Q8—862no—
227C2×Q8—1721no—
228C2×Q8—1721no—
229C2×Q8—1722no—
230C2×Q8—1728no—
231C2×Q8—1724no—
232C2×Q8—1724no—
233C2×Q8#1062189812yes—
234C2×Q8#1062190011yescharacteristic
235C2×Q8#1062190211yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—431no—
239C22×C4—432no—
240C22×C4—862no—
241C22×C4—862no—
242C22×C4—864no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—862no—
246C22×C4—862no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—1722no—
250C22×C4C2×C4×D4311yescharacteristic
251C22×C4D4×D4312yes—
252M16—42no—
253M16—42no—
254M16—1722no—
255M16—1722no—
256C2×C8—42no—
257C2×C8—1722no—
258C4⋊C4—41no—
259C4⋊C4—1721no—
260C4⋊C4—1722no—
261C22⋊C4—1722no—
262C22⋊C4—1722no—
263C42—41no—
264C42—1721no—
265C42—1722no—
266C23—432no—
267C23—861no—
268C23—861no—
269C23—1721no—
270C23—1721no—
271C23C22⋊C4×D4311yescharacteristic
272Q8—42no—
273Q8—41no—
274Q8—41no—
275Q8—1724no—
276Q8—1724no—
277Q8—1722no—
278Q8—1722no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—432no—
289C2×C4—864no—
290C2×C4—864no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—1724no—
297C2×C4—1724no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1722no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4#1306328211yescharacteristic
304C2×C4#1306328311yescharacteristic
305C2×C4#1306330712yes—
306C2×C4#1306331012yes—
307C8—82no—
308C8—3442no—
309C22—21no—
310C22—21no—
311C22—862no—
312C22—862no—
313C22—862no—
314C22—1722no—
315C22—1722no—
316C22#1458276111yescharacteristic
317C22#99×D4311yescharacteristic
318C22#99×D4311yescharacteristic
319C4—22no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—862no—
326C4—3441no—
327C4—3441no—
328C4—1722no—
329C2—21no—
330C2—21no—
331C2—1722no—
332C2#1913466811yescharacteristic
333C2#1913628111yescharacteristic
334C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1394C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC22×Q8×C43C23
hypercenter#1394D43
hypocenterC43#12862
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #19132722C2semidirect
4. #19132721C2semidirect
5. C43×#1394C2semidirect
166. #1394D43semidirect
186. C43#12862semidirect

Maximal subgroups

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

subgroupindex
#191371782
#191345172
#191327222
#191327212
C43×#13942
#1286243