Finite Group Databasebeta

← #25007114

Subgroups — #25007114

Order 11008.

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

normal subgroups only

This group has 470 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#19140282C211yesmaximal, characteristic
2#19134334C211yesmaximal, characteristic, complemented
3#19132626C212yesmaximal, complemented
4#19132599C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic, complemented
6C22×#10621877—21no—
7C2×#13063313C411yescharacteristic
8#14582819C2211yescharacteristic
9#14582816C2211yescharacteristic
10#14582811C411yescharacteristic
11#14582808C411yescharacteristic
12#14582799—21no—
13#14582790—21no—
14#14582789—21no—
15#14582778—21no—
16#14582745C411yescharacteristic
17#14582668—21no—
18#14582668C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C22×D172C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26C2×#10621877—24no—
27C2×#10621877—22no—
28C2×#10621877—41no—
29C2×#10621877—42no—
30C22×C43⋊C8—41no—
31#13063313—41no—
32#13063313—41no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—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—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47#117×C43—41no—
48#117×C43—41no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C4⋊C8×C43—41no—
56C22⋊C8×C43—22no—
57#97×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C23×D43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—22no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C2×C22⋊D43—42no—
72C2×C22⋊D43—42no—
73C2×C22⋊D43—81no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×D172—41no—
78C2×D172—81no—
79C2×Dic86—41no—
80C2×Dic86—81no—
81C2×C8×C43—42no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C22⋊Dic43—81no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—81no—
98Dic43⋊C4—81no—
99C4×Dic43—42no—
100#10621877—24no—
101#10621877—44no—
102#10621877—42no—
103C2×C43⋊C8—44no—
104C2×C43⋊C8—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43#10412yes—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
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—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43#9911yescharacteristic
135C2×C4×C43#9911yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C22⋊D43—84no—
139C2×Dic43—22no—
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—
149Dic86—82no—
150C8×C43—82no—
151C43⋊C8—44no—
152#11765—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—22no—
156C22×C43—42no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—81no—
160C22×C43C2×#9911yescharacteristic
161C22×C43#41711yescharacteristic
162C22×C43C2×#10411yescharacteristic
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178Dic43—42no—
179Dic43—81no—
180Dic43—81no—
181#2610—431no—
182#1742—431no—
183#1464D4311yescharacteristic, complemented
184#1354—432no—
185#1345—432no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—42no—
189C2×C43#150411yescharacteristic
190C2×C43#212211yescharacteristic
191C2×C43#213211yescharacteristic
192D43—161no—
193C22×M16—861no—
194C2×#124—431no—
195C2×#117C2×D4311yescharacteristic
196#432—21no—
197#395—431no—
198#394—431no—
199#393—431no—
200#392—431no—
201#390—861no—
202#388—861no—
203#388—861no—
204#386—861no—
205#376—431no—
206#343—432no—
207#343—861no—
208#324C2×D4312yes—
209#323—21no—
210C43#1176511yescharacteristic, complemented, Sylow
211C22×Q8—431no—
212C22×D4—431no—
213C22×D4—861no—
214C23×C4D17211yescharacteristic
215C2×M16—864no—
216C2×M16—862no—
217C2×M16—1721no—
218C2×M16—1722no—
219C22×C8—1721no—
220#124—1721no—
221#124—1721no—
222#117—41no—
223#117—41no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4D17211yescharacteristic
226C2×C4⋊C4C22×D4311yescharacteristic
227C2×C22⋊C4—861no—
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×C42C4×D4311yescharacteristic
237C2×C42C22⋊D4311yescharacteristic
238C4⋊C8—41no—
239C22⋊C8—22no—
240#97—41no—
241#95—431no—
242#95—431no—
243#95—861no—
244#95—861no—
245#95—861no—
246C24—861no—
247C24(C2×D43)⋊C411yescharacteristic
248C2×Q8—3441no—
249C2×Q8—1721no—
250C2×D4—3441no—
251C2×D4—3441no—
252C2×D4—1721no—
253C2×D4—1722no—
254C2×D4—1722no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4(C2×D43)⋊C411yescharacteristic
266C22×C4C2×C4×D4311yescharacteristic
267C22×C4C2×D17211yescharacteristic
268C22×C4C2×C22⋊D4311yescharacteristic
269M16—864no—
270M16—1724no—
271M16—1722no—
272C2×C8—42no—
273C2×C8—1724no—
274C2×C8—1722no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—3441no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—3441no—
281C22⋊C4—3441no—
282C22⋊C4—1722no—
283C22⋊C4—1722no—
284C22⋊C4—1721no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C22⋊C4—1721no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—1722no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—1721no—
298C23—1721no—
299C23—1721no—
300C23—1721no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23#1306325112yes—
305C23C2×(C2×D43)⋊C411yescharacteristic
306Q8—3442no—
307D4—3442no—
308D4—3444no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
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—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—862no—
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#1306323911yescharacteristic
335C2×C4#1306323911yescharacteristic
336C2×C4#1306335311yescharacteristic
337C2×C4#1306335811yescharacteristic
338C8—82no—
339C8—1724no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22C2×#1306323911yescharacteristic
355C22#1458290111yescharacteristic
356C22C2×#1306325111yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—3441no—
366C4—3441no—
367C4—1722no—
368C2—21no—
369C2—21no—
370C2—42no—
371C2—6881no—
372C2#1913310011yescharacteristic
373C2#1913624411yescharacteristic
374C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radical#14582808C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11765
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19134334C2semidirect
3. #19132626C2semidirect
4. #19132599C2semidirect
5. C43×#1464C2semidirect
183. #1464D43semidirect
210. C43#11765semidirect

Maximal subgroups

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

subgroupindex
#191402822
#191343342
#191326262
#191325992
C43×#14642
#1176543