Finite Group Databasebeta

← #24992365

Subgroups — #24992365

Order 11008.

902 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 135 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#19142882C211yesmaximal, characteristic
2C2×#14582762C211yesmaximal, characteristic
3C2×#14582637C212yesmaximal, complemented
4#19132475C212yesmaximal, complemented
5C43×#1779C211yesmaximal, characteristic
6C2×#13063304C412yescomplemented
7C2×#13063304C2211yescharacteristic
8C22×C22⋊Dic43—21no—
9#14582772—21no—
10#14582772—22no—
11#14582762—24no—
12#14582759C412yescomplemented
13#14582759C2211yescharacteristic
14#14582755—21no—
15C2×C43⋊#95—21no—
16C2×C43⋊#95C2212yes—
17#14582637—24no—
18C24×C4×C43C2211yescharacteristic
19C2×C22⋊C8×C43—22no—
20C2×C22⋊C8×C43C2212yes—
21C22×Dic86C2×C411yescharacteristic
22C23×Dic43—22no—
23#13063304—22no—
24#13063304—22no—
25#13063304—44no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—24no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—44no—
36C43⋊#95—24no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—21no—
40C43⋊#95D414yes—
41C25×C43D411yescharacteristic
42C23×C4×C43—22no—
43C23×C4×C43—22no—
44C23×C4×C43—44no—
45C23×C4×C43C2×C412yes—
46C23×C4×C43D411yescharacteristic
47C23×C4×C43D412yes—
48C23×C4×C43C2311yescharacteristic
49C22×C8×C43—22no—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—44no—
53C24×C43—24no—
54C24×C43—21no—
55C24×C43—21no—
56C24×C43—22no—
57C24×C43—22no—
58C24×C43—42no—
59C24×C43C22⋊C412yes—
60C24×C43C2×D411yescharacteristic
61C22×C4×C43—24no—
62C22×C4×C43—24no—
63C22×C4×C43—24no—
64C22×C4×C43—24no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43—42no—
71C22×C4×C43—48no—
72C22×C4×C43—48no—
73C22×C4×C43C22⋊C412yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D412yes—
77C22×C4×C43#4112yes—
78C22×Dic43—21no—
79C22×Dic43—22no—
80C22×Dic43—21no—
81C22×Dic43—24no—
82C22×Dic43—44no—
83C22×Dic43—44no—
84C22×Dic43—42no—
85C22×Dic43—42no—
86C2×Dic86—22no—
87C2×Dic86—42no—
88C2×C8×C43—44no—
89C2×C8×C43—42no—
90C22⋊Dic43—44no—
91C22⋊Dic43—48no—
92C22⋊Dic43—44no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—42no—
96C4⋊Dic43—22no—
97C4⋊Dic43—42no—
98Dic43⋊C4—44no—
99Dic43⋊C4—42no—
100C23×C43—22no—
101C23×C43—22no—
102C23×C43—24no—
103C23×C43—24no—
104C23×C43—22no—
105C23×C43—22no—
106C23×C43—22no—
107C23×C43—22no—
108C23×C43—22no—
109C23×C43—22no—
110C23×C43—48no—
111C23×C43—48no—
112C23×C43—42no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43#9914yes—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#12011yescharacteristic
119C23×C43#12311yescharacteristic
120C23×C43#13512yes—
121C23×C43#13712yes—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—48no—
130C2×C4×C43—48no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43C4×D412yes—
134C2×C4×C43#12112yes—
135C2×Dic43—44no—
136C2×Dic43—44no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—44no—
145C2×Dic43—84no—
146C2×Dic43—84no—
147Dic86—82no—
148C8×C43—82no—
149#9154—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—24no—
155C22×C43—24no—
156C22×C43—24no—
157C22×C43—24no—
158C22×C43—24no—
159C22×C43—48no—
160C22×C43—48no—
161C22×C43—42no—
162C22×C43—42no—
163C22×C43—42no—
164C22×C43—42no—
165C22×C43#38611yescharacteristic
166C22×C43C2×#9912yes—
167C22×C43#41611yescharacteristic
168C22×C43#41911yescharacteristic
169C22×C43#42112yes—
170C22×C43#45212yes—
171C22×C43#48512yes—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—42no—
175Dic43—84no—
176Dic43—81no—
177Dic43—81no—
178Dic43—82no—
179#2848—431no—
180C2×#381—431no—
181#1779D4311yescharacteristic
182C2×#328—432no—
183#1294—432no—
184C2×C43—22no—
185C2×C43—22no—
186C2×C43—44no—
187C2×C43#151112yes—
188C2×C43#151612yes—
189C2×C43#187311yescharacteristic
190C2×C43#189711yescharacteristic
191C2×C43#189811yescharacteristic
192C24×C4C2×D4311yescharacteristic
193C2×C22⋊Q8—431no—
194C2×C22⋊Q8—432no—
195C22×C22⋊C4—861no—
196C2×C22⋊C8—22no—
197C2×C22⋊C8C2×D4312yes—
198#385—861no—
199#385—862no—
200#381—864no—
201#380—431no—
202#380—432no—
203#379—861no—
204C2×#95—432no—
205C2×#95—861no—
206#328—864no—
207C43#915411yescharacteristic, complemented, Sylow
208C25D17211yescharacteristic
209C22×Q8—431no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—44no—
213C23×C4—862no—
214C23×C4C4×D4312yes—
215C23×C4D17211yescharacteristic
216C23×C4C22⋊D4312yes—
217C23×C4C22×D4311yescharacteristic
218C22×C8—22no—
219C22⋊Q8—862no—
220C22⋊Q8—862no—
221C22⋊Q8—1724no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—432no—
224C2×C4⋊C4—862no—
225C2×C4⋊C4—861no—
226C2×C22⋊C4—864no—
227C2×C22⋊C4—862no—
228C2×C22⋊C4—862no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—1724no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—44no—
235#95—434no—
236#95—864no—
237#95—862no—
238#95—862no—
239#95—861no—
240C24—24no—
241C24—21no—
242C24—21no—
243C24—22no—
244C24—22no—
245C24—42no—
246C24(C2×D43)⋊C412yes—
247C24C2×D17211yescharacteristic
248C2×Q8—862no—
249C2×Q8—1722no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—48no—
261C22×C4—48no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—864no—
266C22×C4—1724no—
267C22×C4—1724no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4(C2×D43)⋊C412yes—
271C22×C4C2×C4×D4311yescharacteristic
272C22×C4D4×D4312yes—
273C22×C4#1062190012yes—
274C22×C4C2×C22⋊D4311yescharacteristic
275C2×C8—44no—
276C2×C8—42no—
277C4⋊C4—862no—
278C4⋊C4—1722no—
279C4⋊C4—1724no—
280C4⋊C4—1722no—
281C22⋊C4—1728no—
282C22⋊C4—1724no—
283C22⋊C4—1724no—
284C22⋊C4—1721no—
285C22⋊C4—1721no—
286C22⋊C4—1722no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#1306323914yes—
304C23C2×(C2×D43)⋊C411yescharacteristic
305C23#1306329511yescharacteristic
306C23#1306330911yescharacteristic
307C23#1306334712yes—
308C23#1306335812yes—
309Q8—3442no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—3444no—
322C2×C4—3444no—
323C2×C4—1724no—
324C2×C4—1724no—
325C2×C4—1724no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4(C22⋊D43)⋊C412yes—
334C2×C4#1306329712yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—24no—
341C22—24no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1458277611yescharacteristic
352C22C2×#1306323912yes—
353C22#1458289611yescharacteristic
354C22#1458290911yescharacteristic
355C22#1458291512yes—
356C22#1458306312yes—
357C22#1458324112yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—3444no—
362C4—3441no—
363C4—3441no—
364C4—3442no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1913312912yes—
369C2#1913315212yes—
370C2#1913490511yescharacteristic
371C2#1913504111yescharacteristic
372C2#1913504611yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1779C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#1779D43
hypocenterC43#9154
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#14582637C2semidirect
4. #19132475C2semidirect
6. C2×#13063304C4semidirect
12. #14582759C4semidirect
207. C43#9154semidirect

Maximal subgroups

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

subgroupindex
#191428822
C2×#145827622
C2×#145826372
#191324752
C43×#17792
#915443