Finite Group Databasebeta

← #25006810

Subgroups — #25006810

Order 11008.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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#19134332C211yesmaximal, characteristic
3#19132908C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063324C411yescharacteristic
10C2×#13063303—21no—
11C2×#13063283C2211yescharacteristic
12#14582949—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—
30C2×#10621872—41no—
31M16×D43—24no—
32M16×D43—42no—
33C2×C8×D43—41no—
34#13063324—41no—
35#13063324—41no—
36#13063303—42no—
37#13063303—42no—
38#13063283—41no—
39#13063283—41no—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×(C2×D43)⋊C4D411yescharacteristic
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—41no—
52C22⋊(C43⋊C8)—21no—
53C8×Dic43—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95C2×C411yescharacteristic
59C2×M16×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C4⋊C4×C43C2311yescharacteristic
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43C2×C411yescharacteristic
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—22no—
80C2×C4×D43D812yes—
81C2×C4×D43SD1612yes—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—42no—
85C2×Dic86—42no—
86M16×C43—22no—
87M16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100Dic43⋊C4—42no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—42no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108#10621877—22no—
109#10621877—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112#10621872—44no—
113C8×D43—44no—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43#10212yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43C2×D811yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43#9911yescharacteristic
145C2×Dic43#9911yescharacteristic
146C2×Dic43#10212yes—
147C2×Dic43#10412yes—
148C4×D43—22no—
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152Dic86—82no—
153Dic86—82no—
154C8×C43—42no—
155C8×C43—81no—
156C43⋊C8—42no—
157C43⋊C8—81no—
158#11700—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43C2×#9911yescharacteristic
162C22×C43C2×#10211yescharacteristic
163C22×C43C2×#10411yescharacteristic
164C2×D43—22no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—42no—
168C2×D43—81no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—81no—
174C4×C43—81no—
175Dic43—41no—
176Dic43—41no—
177Dic43—81no—
178Dic43—81no—
179Dic43#32712yes—
180Dic43#32712yes—
181#2621—431no—
182#1742—431no—
183#1458—431no—
184#1346—431no—
185#1346—431no—
186#1346—431no—
187#1346D4311yescharacteristic, complemented
188C2×C43—21no—
189C2×C43—21no—
190C2×C43C2×#32711yescharacteristic
191C2×C43#212311yescharacteristic
192C2×C43#213511yescharacteristic
193D43—42no—
194C22×M16—861no—
195C2×C4⋊Q8—431no—
196C2×C22⋊Q8—861no—
197C2×#117—431no—
198#431—861no—
199#398—431no—
200#398—861no—
201#398C2×D4311yescharacteristic
202#397—431no—
203#397—431no—
204#397—861no—
205#391—861no—
206#382—431no—
207#343—431no—
208#343—861no—
209#343C2×D4311yescharacteristic
210#324—431no—
211#324C2×D4311yescharacteristic
212#323—861no—
213C43#1170011yescharacteristic, complemented, Sylow
214C22×Q8—861no—
215C23×C4—431no—
216C2×M16—21no—
217C2×M16—864no—
218C2×M16—861no—
219C2×M16—1721no—
220C2×M16—1722no—
221C22×C8—1721no—
222C4⋊Q8—1721no—
223C4⋊Q8—1721no—
224C22⋊Q8—1722no—
225C22⋊Q8—1722no—
226#117—1721no—
227#117—1721no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—431no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4C4×D4311yescharacteristic
235C2×C4⋊C4C22×D4311yescharacteristic
236C2×C22⋊C4—431no—
237C2×C22⋊C4—431no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C42—431no—
241C2×C42—431no—
242C4⋊C8—1721no—
243C22⋊C8—21no—
244C22⋊C8—861no—
245C4×C8—1721no—
246#95—21no—
247#95—431no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95C4×D4311yescharacteristic
253C24—431no—
254C2×Q8—1722no—
255C2×Q8—1721no—
256C2×Q8—1721no—
257C2×Q8—1722no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—432no—
262C22×C4—432no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—862no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273M16—22no—
274M16—41no—
275M16—862no—
276M16—1724no—
277M16—1721no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—1724no—
281C2×C8—1721no—
282C2×C8—1721no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1722no—
290C4⋊C4—1722no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1722no—
296C22⋊C4—1722no—
297C42—861no—
298C42—861no—
299C42—861no—
300C42—861no—
301C23—432no—
302C23—861no—
303C23—861no—
304C23—1721no—
305C23—1721no—
306C23C22⋊C4×D4311yescharacteristic
307Q8—3442no—
308Q8—3442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—432no—
324C2×C4—432no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4D8×D4311yescharacteristic
340C2×C4SD16×D4311yescharacteristic
341C8—42no—
342C8—81no—
343C8—3441no—
344C8—1722no—
345C22—21no—
346C22—21no—
347C22—862no—
348C22—3441no—
349C22—1722no—
350C22—1721no—
351C22—1721no—
352C22#99×D4311yescharacteristic
353C22#102×D4311yescharacteristic
354C22#104×D4311yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—432no—
362C4—432no—
363C4—3441no—
364C4—3441no—
365C4—1721no—
366C4—1721no—
367C2—21no—
368C2—21no—
369C2—1722no—
370C2#327×D4311yescharacteristic
371C2#1913624711yescharacteristic
372C2#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#11700
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
187. #1346D43semidirect
213. C43#11700semidirect

Maximal subgroups

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

subgroupindex
#191403632
#191343322
#191329082
#191326022
#191326012
#191326002
C43×#13462
#1170043