Finite Group Databasebeta

← #24985019

Subgroups — #24985019

Order 11008.

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

normal subgroups only

This group has 550 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#19142926C211yesmaximal, characteristic
2#19134357C211yesmaximal, characteristic, complemented
3#19132419C212yesmaximal, complemented
4#19132415C212yesmaximal, complemented
5C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C411yescharacteristic
8C2×C22⋊(C43⋊C8)—21no—
9C2×#13063236—21no—
10#14582801C411yescharacteristic
11#14582801C2211yescharacteristic
12#14582797C411yescharacteristic
13#14582797C2211yescharacteristic
14#14582790—21no—
15#14582790—21no—
16#14582778—21no—
17#14582759C411yescharacteristic
18#14582654C2212yes—
19C22×C42×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C2×C4×C8×C43—21no—
22C43×#336C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C43⋊C8—22no—
26#13063308—44no—
27#13063299—42no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C22⋊(C43⋊C8)—24no—
40#13063236—42no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C22×C8×C43—22no—
48C2×C42×C43—42no—
49C2×C42×C43C2×C411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43C2311yescharacteristic
53C22⋊C8×C43—24no—
54C4×C8×C43—42no—
55C24×C43C22⋊C411yescharacteristic
56C23×D43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C2×D172—22no—
79C2×D172—41no—
80C2×D172—41no—
81C2×C8×C43—24no—
82C2×C8×C43—42no—
83C2×C8×C43—42no—
84C42×C43—22no—
85C42×C43—22no—
86C42×C43—41no—
87C42×C43—41no—
88C22⋊Dic43—42no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94C4⋊Dic43—22no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97Dic43⋊C4—42no—
98Dic43⋊C4—42no—
99C2×C43⋊C8—24no—
100C2×C43⋊C8—42no—
101C2×C43⋊C8—42no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43#10412yes—
109C23×C43C2×C22⋊C411yescharacteristic
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—44no—
133C2×C4×C43#9912yes—
134C2×C4×C43#10412yes—
135C2×C4×C43#13112yes—
136C2×C4×C43#13512yes—
137C2×C4×C43AGL(1,ℤ/8)12yes—
138C22⋊D43—84no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148D172—82no—
149C8×C43—44no—
150C43⋊C8—44no—
151#7674—431nomaximal, Sylow
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43#40811yescharacteristic
160C22×C43C2×#9911yescharacteristic
161C22×C43#41311yescharacteristic
162C22×C43#41611yescharacteristic
163C22×C43#41811yescharacteristic
164C22×C43C2×#10411yescharacteristic
165C22×C43C2×#10411yescharacteristic
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—41no—
179Dic43—81no—
180Dic43—81no—
181Dic43—81no—
182#2854—431no—
183#1749—431no—
184C4×C22⋊C8D4311yescharacteristic, complemented
185#1271—432no—
186#1270—432no—
187C2×C43—42no—
188C2×C43#146811yescharacteristic
189C2×C43#148411yescharacteristic
190C2×C43#149411yescharacteristic
191C2×C43#150111yescharacteristic
192C2×C43#150711yescharacteristic
193C2×C43#152411yescharacteristic
194C2×C43#155311yescharacteristic
195D43—161no—
196C2×#123—861no—
197C2×#121—431no—
198C22×C42C2×D4311yescharacteristic
199C2×C22⋊C8—21no—
200C2×C22⋊C8—861no—
201C2×#97—861no—
202C2×C4×C8—21no—
203#390—431no—
204#390—431no—
205#389—431no—
206#389—431no—
207#388—861no—
208#388—861no—
209#386—861no—
210#380—431no—
211#336—432no—
212#336C2×D4312yes—
213C43#767411yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C22×D4—861no—
216C23×C4C4×D4311yescharacteristic
217C23×C4D17211yescharacteristic
218C23×C4C22⋊D4311yescharacteristic
219C22×C8—22no—
220C22×C8—862no—
221#123—1724no—
222#121—1722no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C42—42no—
235C2×C42C4×D4311yescharacteristic
236C2×C42D17211yescharacteristic
237C2×C42C22⋊D4311yescharacteristic
238C2×C42C22×D4311yescharacteristic
239C22⋊C8—24no—
240C22⋊C8—864no—
241#97—1722no—
242C4×C8—42no—
243#95—861no—
244#95—861no—
245#95—861no—
246C24—861no—
247C24(C2×D43)⋊C411yescharacteristic
248C2×D4—862no—
249C2×D4—1721no—
250C2×D4—1721no—
251C2×D4—1722no—
252C2×D4—1722no—
253C2×D4—1722no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4C2×C4×D4311yescharacteristic
270C22×C4C2×D17211yescharacteristic
271C22×C4C2×C22⋊D4311yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—864no—
276C2×C8—1722no—
277C2×C8—1722no—
278C4⋊C4—862no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C22⋊C4—1722no—
286C22⋊C4—1722no—
287C22⋊C4—1722no—
288C22⋊C4—1722no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—1721no—
300C23—1721no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23#1306325312yes—
307C23C2×(C2×D43)⋊C411yescharacteristic
308D4—3442no—
309D4—3444no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4#1306323912yes—
336C2×C4#1306325112yes—
337C2×C4#1306333112yes—
338C2×C4#1306334712yes—
339C2×C4#1306335012yes—
340C8—44no—
341C8—1724no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—3441no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22#1458286511yescharacteristic
357C22C2×#1306323911yescharacteristic
358C22#1458288111yescharacteristic
359C22#1458289611yescharacteristic
360C22#1458290311yescharacteristic
361C22C2×#1306325111yescharacteristic
362C22C2×#1306325311yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—3441no—
370C4—3441no—
371C4—3441no—
372C2—42no—
373C2—6881no—
374C2#1913294111yescharacteristic
375C2#1913301111yescharacteristic
376C2#1913305611yescharacteristic
377C2#1913308711yescharacteristic
378C2#1913311011yescharacteristic
379C2#1913318411yescharacteristic
380C2#1913329811yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C4
cosocleC2×C42×C43C23
hypercenterC4×C22⋊C8D43
hypocenterC43#7674
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #19134357C2semidirect
3. #19132419C2semidirect
4. #19132415C2semidirect
5. C4×C22⋊C8×C43C2semidirect
184. C4×C22⋊C8D43semidirect
213. C43#7674semidirect

Maximal subgroups

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

subgroupindex
#191429262
#191343572
#191324192
#191324152
C4×C22⋊C8×C432
#767443