Finite Group Databasebeta

← #25007299

Subgroups — #25007299

Order 11008.

388 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140363C211yesmaximal, characteristic
2#19134677C211yesmaximal, characteristic
3#19132928C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1346C211yesmaximal, characteristic, complemented
8C2×#13063324C411yescharacteristic
9C2×#13063303—21no—
10C2×#13063283C2211yescharacteristic
11#14582953—21no—
12#14582862—21no—
13#14582832—21no—
14#14582829C2211yescharacteristic
15#14582828—21no—
16#14582826C411yescharacteristic
17#14582825C411yescharacteristic
18#14582803—21no—
19#14582763C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582622—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28C22×C4×D43D411yescharacteristic
29C2×#10621877—21no—
30#13063324—41no—
31#13063324—41no—
32#13063303—42no—
33#13063303—42no—
34#13063283—41no—
35#13063283—41no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4C2×C411yescharacteristic
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—41no—
48C22⋊(C43⋊C8)—21no—
49(C2×D43)⋊C8—41no—
50(C2×D43)⋊C8—41no—
51#13063235—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—41no—
80C2×Dic86—42no—
81C2×Dic86—42no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84M16×C43—41no—
85M16×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98Dic43⋊C4—42no—
99Dic43⋊C4—42no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106#10621877—41no—
107#10621877—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—41no—
115C22×D43—41no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43#9911yescharacteristic
143C2×Dic43#9911yescharacteristic
144C4×D43—41no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148Dic86—82no—
149Dic86—82no—
150C8×C43—81no—
151C8×C43—81no—
152C43⋊C8—81no—
153C43⋊C8—81no—
154#11807—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43C2×#9911yescharacteristic
158C22×C43#41811yescharacteristic
159C22×C43#42111yescharacteristic
160C2×D43—42no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—81no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—81no—
170C4×C43—81no—
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43—81no—
176Dic43—81no—
177#2621—431no—
178#1822—431no—
179#1464—431no—
180#1346—431no—
181#1346—431no—
182#1346—431no—
183#1346D4311yescharacteristic, complemented
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#151011yescharacteristic
187C2×C43#212311yescharacteristic
188C2×C43#213511yescharacteristic
189D43—81no—
190C2×C4⋊Q8—431no—
191C2×C22⋊Q8—861no—
192C2×#117—431no—
193#432—861no—
194#407—861no—
195#398—431no—
196#398—861no—
197#398C2×D4311yescharacteristic
198#397—431no—
199#397—431no—
200#397—861no—
201#391—861no—
202#382—431no—
203#343—431no—
204#343—861no—
205#343C2×D4311yescharacteristic
206#324—431no—
207#324C2×D4311yescharacteristic
208#323—861no—
209C43#1180711yescharacteristic, complemented, Sylow
210C22×Q8—861no—
211C23×C4—431no—
212C2×M16—21no—
213C2×M16—861no—
214C4⋊Q8—1721no—
215C4⋊Q8—1721no—
216C22⋊Q8—1722no—
217C22⋊Q8—1722no—
218#117—1721no—
219#117—1721no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4C4×D4311yescharacteristic
227C2×C4⋊C4C22×D4311yescharacteristic
228C2×C22⋊C4—431no—
229C2×C22⋊C4—431no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C42—431no—
233C2×C42—431no—
234C4⋊C8—1721no—
235C22⋊C8—21no—
236C22⋊C8—861no—
237C22⋊C8—1721no—
238C22⋊C8—1721no—
239#97—1721no—
240#95—21no—
241#95—431no—
242#95—861no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95C4×D4311yescharacteristic
247C24—431no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1722no—
251C2×Q8—1722no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—1721no—
264C22×C4C2×C4×D4311yescharacteristic
265C22×C4D4×D4311yescharacteristic
266C22×C4D4×D4311yescharacteristic
267M16—41no—
268M16—41no—
269M16—1721no—
270M16—1721no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1721no—
274C2×C8—1721no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C22⋊C4—1722no—
288C22⋊C4—1722no—
289C42—861no—
290C42—861no—
291C42—861no—
292C42—861no—
293C23—861no—
294C23—861no—
295C23—861no—
296C23—1721no—
297C23—1721no—
298C23C22⋊C4×D4311yescharacteristic
299Q8—3442no—
300Q8—3442no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4#1306334911yescharacteristic
332C2×C4#1306335211yescharacteristic
333C8—81no—
334C8—81no—
335C8—3441no—
336C8—3441no—
337C22—21no—
338C22—21no—
339C22—3441no—
340C22—1722no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22#99×D4311yescharacteristic
345C22#1458290211yescharacteristic
346C22#1458291411yescharacteristic
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—861no—
354C4—861no—
355C4—3441no—
356C4—3441no—
357C4—1721no—
358C4—1721no—
359C2—21no—
360C2—21no—
361C2—3441no—
362C2#1913312211yescharacteristic
363C2#1913624711yescharacteristic
364C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43#11807
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #19132602C2semidirect
5. #19132601C2semidirect
6. #19132600C2semidirect
7. C43×#1346C2semidirect
183. #1346D43semidirect
209. C43#11807semidirect

Maximal subgroups

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

subgroupindex
#191403632
#191346772
#191329282
#191326022
#191326012
#191326002
C43×#13462
#1180743