Finite Group Databasebeta

← #24991701

Subgroups — #24991701

Order 11008.

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

normal subgroups only

This group has 566 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#19137831C211yesmaximal, characteristic
2#19133019C212yesmaximal, complemented
3#19132909C211yesmaximal, characteristic, complemented
4#19132496C212yesmaximal, complemented
5C43×#2921C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7C2×C4×C22⋊D43—21no—
8#14582952C2212yes—
9#14582829C411yescharacteristic
10#14582824C411yescharacteristic
11#14582821—21no—
12#14582816C411yescharacteristic
13#14582815—21no—
14#14582808C411yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16C4×(C2×D43)⋊C4—21no—
17#14582626—24no—
18#14582625—21no—
19#14582623—21no—
20C2×#117×C43C2211yescharacteristic
21C43×#433—24no—
22C43×#423C2212yes—
23C43×#407—21no—
24C4×M16×C43—21no—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28C4×D172—22no—
29C4×D172—22no—
30C4×C22⋊D43—44no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×C4×Dic43—21no—
40C4⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—22no—
42C4×C43⋊C8—22no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95C2×C411yescharacteristic
46C43⋊#95C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C2×M16×C43—22no—
49#117×C43—22no—
50#117×C43—22no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—22no—
58C4⋊C8×C43D414yescomplemented
59C22⋊C8×C43—24no—
60#97×C43—22no—
61C4×C8×C43—22no—
62C24×C43C22⋊C411yescharacteristic
63C23×D43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—42no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C2×D172—22no—
81C2×D172—42no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—42no—
85C2×C4×D43—42no—
86M16×C43—42no—
87M16×C43—42no—
88C2×C8×C43—24no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—22no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43C2×D412yes—
96C42×C43#4112yes—
97C22⋊Dic43—42no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—42no—
102C4⋊Dic43—22no—
103C4⋊Dic43—42no—
104Dic43⋊C4—42no—
105C4×Dic43—42no—
106C2×C43⋊C8—42no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43C2×C22⋊C411yescharacteristic
113C22×D43—22no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C4×D412yes—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12112yes—
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43#13512yes—
136C2×C4×C43AGL(1,ℤ/8)12yes—
137C22⋊D43—48no—
138C2×Dic43—22no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147D172—24no—
148D172—42no—
149C4×D43—82no—
150C4×D43—82no—
151C8×C43—44no—
152C43⋊C8—82no—
153#9036—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—42no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—81no—
161C22×C43#38611yescharacteristic
162C22×C43#41611yescharacteristic
163C22×C43#41811yescharacteristic
164C2×D43—42no—
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43#44912yes—
177C4×C43#48212yes—
178Dic43—42no—
179Dic43—81no—
180Dic43—81no—
181#2921D4311yescharacteristic, complemented
182#2392—431no—
183#1486—432no—
184#1458—431no—
185#1303—432no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—81no—
189C2×C43#187511yescharacteristic
190C2×C43#188411yescharacteristic
191C2×C43#189111yescharacteristic
192D43—82no—
193C2×C4×D4—431no—
194C2×C4×D4—861no—
195C2×#117C2×D4311yescharacteristic
196#433—24no—
197#431—432no—
198#423C2×D4312yes—
199#407—21no—
200C4×M16—21no—
201#398—431no—
202#397—431no—
203#396—861no—
204#394—431no—
205#394—861no—
206#392—431no—
207C4×C4⋊C4—431no—
208C4×C22⋊C4—861no—
209D4⋊C8—864no—
210#324—861no—
211#323—861no—
212C43#903611yescharacteristic, complemented, Sylow
213C22×D4—431no—
214C22×D4—861no—
215C23×C4—861no—
216C23×C4C22⋊D4311yescharacteristic
217C2×M16—22no—
218C4×D4—862no—
219C4×D4—862no—
220C4×D4—1724no—
221#117—22no—
222#117—22no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4C4×D4311yescharacteristic
227C2×C4⋊C4D17211yescharacteristic
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4C4×D4311yescharacteristic
234C2×C22⋊C4D17211yescharacteristic
235C2×C42—861no—
236C2×C42C22⋊D4311yescharacteristic
237C2×C42C22×D4311yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—862no—
240C4⋊C8C22⋊D4314yescomplemented
241C22⋊C8—24no—
242C22⋊C8—862no—
243#97—22no—
244C4×C8—22no—
245C4×C8—862no—
246#95—431no—
247#95—431no—
248#95—861no—
249#95—861no—
250C24—861no—
251C24(C2×D43)⋊C411yescharacteristic
252C2×D4—862no—
253C2×D4—1722no—
254C2×D4—1722no—
255C2×D4—1722no—
256C2×D4—1722no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1722no—
267C22×C4—1722no—
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4(C2×D43)⋊C411yescharacteristic
271C22×C4C2×C4×D4311yescharacteristic
272C22×C4C2×D17211yescharacteristic
273C22×C4C2×C22⋊D4311yescharacteristic
274M16—42no—
275M16—42no—
276C2×C8—24no—
277C2×C8—1722no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—862no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—1722no—
286C22⋊C4—1722no—
287C22⋊C4—1722no—
288C22⋊C4—1722no—
289C22⋊C4—1722no—
290C42—21no—
291C42—21no—
292C42—1722no—
293C42#1062189812yes—
294C42C2×C22⋊D4312yes—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23—862no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23C2×(C2×D43)⋊C411yescharacteristic
308D4—864no—
309D4—1722no—
310D4—1728no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—862no—
323C2×C4—3442no—
324C2×C4—3442no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4C4×C22⋊D4312yes—
334C2×C4#1306329411yescharacteristic
335C2×C4#1306329912yes—
336C2×C4#1306330811yescharacteristic
337C2×C4#1306334512yes—
338C2×C4#1306335012yes—
339C8—44no—
340C8—3442no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—3441no—
349C22—3441no—
350C22—3441no—
351C22—3441no—
352C22—1722no—
353C22—1722no—
354C22—1722no—
355C22#1458277811yescharacteristic
356C22#1458289311yescharacteristic
357C22#1458290311yescharacteristic
358C4—22no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—3441no—
364C4—3441no—
365C4—1722no—
366C4#1458304412yes—
367C4#1458322312yes—
368C2—21no—
369C2—21no—
370C2—81no—
371C2—3442no—
372C2#1913491711yescharacteristic
373C2#1913497811yescharacteristic
374C2#1913501311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2921C2
socleC22×C43#386
prime radical#14582808C4
cosocleC2×C42×C43C23
hypercenter#2921D43
hypocenterC43#9036
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #19133019C2semidirect
3. #19132909C2semidirect
4. #19132496C2semidirect
5. C43×#2921C2semidirect
58. C4⋊C8×C43D4semidirect
181. #2921D43semidirect
212. C43#9036semidirect
240. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191378312
#191330192
#191329092
#191324962
C43×#29212
#903643