Finite Group Databasebeta

← #24991699

Subgroups — #24991699

Order 11008.

566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 111 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#19143233C211yesmaximal, characteristic, complemented
2#19137831C211yesmaximal, characteristic
3#19133021C212yesmaximal, complemented
4#19132497C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7C2×C4×C22⋊D43—21no—
8#14582960—24no—
9#14582923C2212yes—
10#14582863—21no—
11C4×#10621877—21no—
12#14582829C411yescharacteristic
13#14582824C411yescharacteristic
14#14582821—21no—
15#14582816C411yescharacteristic
16#14582815—21no—
17#14582808C411yescharacteristic
18C4×C4⋊Dic43C2211yescharacteristic
19C4×(C2×D43)⋊C4—21no—
20#14582628—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#431C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28C2×#10621877—22no—
29C4×D172—22no—
30C4×D172—22no—
31C4×C22⋊D43—44no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—22no—
42C4⋊(C43⋊C8)D414yescomplemented
43C22⋊(C43⋊C8)—24no—
44#13063236—22no—
45C4×C43⋊C8—22no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95C2×C411yescharacteristic
49C43⋊#95C2×C411yescharacteristic
50C23×C4×C43D411yescharacteristic
51#117×C43—22no—
52#117×C43—22no—
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—22no—
60C22⋊C8×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—
86C2×C8×C43—42no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—22no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43C2×D412yes—
94C42×C43#4112yes—
95C22⋊Dic43—42no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100C4⋊Dic43—22no—
101C4⋊Dic43—42no—
102Dic43⋊C4—42no—
103C4×Dic43—42no—
104#10621877—42no—
105#10621877—42no—
106C2×C43⋊C8—24no—
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—82no—
152C43⋊C8—44no—
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#2921—431no—
182#2392—431no—
183#1486—432no—
184#1458D4311yescharacteristic, complemented
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—864no—
197#431C2×D4312yes—
198#423—432no—
199#407—861no—
200C4×M16—861no—
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—21no—
211#323—21no—
212C43#903611yescharacteristic, complemented, Sylow
213C22×D4—431no—
214C22×D4—861no—
215C23×C4—861no—
216C23×C4D17211yescharacteristic
217C2×M16—862no—
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⋊C4C22⋊D4311yescharacteristic
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⋊C4C22⋊D4311yescharacteristic
235C2×C42—861no—
236C2×C42D17211yescharacteristic
237C2×C42C22×D4311yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—434no—
240C4⋊C8—862no—
241C22⋊C8—22no—
242C22⋊C8—864no—
243#97—862no—
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—1722no—
275M16—1722no—
276C2×C8—42no—
277C2×C8—864no—
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—
293C42D4×D4312yes—
294C42#1062190012yes—
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×C4(C22⋊D43)⋊C412yes—
334C2×C4#1306329511yescharacteristic
335C2×C4#1306329712yes—
336C2×C4#1306330911yescharacteristic
337C2×C4#1306334712yes—
338C2×C4#1306335312yes—
339C8—82no—
340C8—1724no—
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#1458277611yescharacteristic
356C22#1458289611yescharacteristic
357C22#1458290511yescharacteristic
358C4—22no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—3441no—
364C4—3441no—
365C4—1722no—
366C4#1458304612yes—
367C4#1458322412yes—
368C2—21no—
369C2—21no—
370C2—81no—
371C2—3442no—
372C2#1913491511yescharacteristic
373C2#1913497611yescharacteristic
374C2#1913501111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1458C2
socleC22×C43#386
prime radical#14582808C4
cosocleC2×C42×C43C23
hypercenter#1458D43
hypocenterC43#9036
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
1. #19143233C2semidirect
3. #19133021C2semidirect
4. #19132497C2semidirect
5. C43×#1458C2semidirect
42. C4⋊(C43⋊C8)D4semidirect
184. #1458D43semidirect
212. C43#9036semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191378312
#191330212
#191324972
C43×#14582
#903643