Finite Group Databasebeta

← #25007286

Subgroups — #25007286

Order 11008.

472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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#19137831C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic, complemented
3#19132600C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C43×#1822C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7C2×C4×C22⋊D43—21no—
8#14582956—21no—
9#14582829C2211yescharacteristic
10#14582824C411yescharacteristic
11#14582821—21no—
12#14582816C2211yescharacteristic
13#14582815—21no—
14#14582808C411yescharacteristic
15C4×C4⋊Dic43C411yescharacteristic
16C4×(C2×D43)⋊C4—21no—
17#14582625C2212yes—
18#14582623—21no—
19C2×#117×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C4×D43—21no—
26C4×D172—41no—
27C4×D172—41no—
28C4×C22⋊D43—44no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×C4×Dic43—21no—
38C4⋊(C43⋊C8)—41no—
39C22⋊(C43⋊C8)—22no—
40#13063236—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C2×M16×C43—22no—
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
55C22⋊C8×C43—41no—
56C22⋊C8×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C23×D43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43—41no—
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C2×C22⋊D43—42no—
70C2×C22⋊D43—42no—
71C2×C22⋊D43—42no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×D172—42no—
76C2×D172—41no—
77C2×C4×D43—42no—
78C2×C4×D43—42no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81M16×C43—42no—
82M16×C43—42no—
83C2×C8×C43—42no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C22⋊Dic43—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—42no—
97C4⋊Dic43—42no—
98C4⋊Dic43—41no—
99Dic43⋊C4—42no—
100C4×Dic43—42no—
101C2×C43⋊C8—42no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43C2×C22⋊C411yescharacteristic
108C22×D43—22no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
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—42no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43#9911yescharacteristic
130C2×C4×C43#9911yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)12yes—
132C22⋊D43—48no—
133C2×Dic43—22no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142D172—42no—
143D172—42no—
144C4×D43—82no—
145C4×D43—82no—
146C8×C43—82no—
147C43⋊C8—82no—
148#11804—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—42no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43C2×#9911yescharacteristic
157C22×C43#41811yescharacteristic
158C22×C43#42111yescharacteristic
159C2×D43—42no—
160C2×D43—42no—
161C2×D43—42no—
162C2×D43—81no—
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C4×C43—22no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173Dic43—42no—
174Dic43—81no—
175Dic43—81no—
176#2392—431no—
177#1822D4311yescharacteristic, complemented
178#1464—431no—
179#1346—432no—
180#1345—432no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—81no—
184C2×C43#151011yescharacteristic
185C2×C43#212011yescharacteristic
186C2×C43#213211yescharacteristic
187D43—82no—
188C2×C4×D4—431no—
189C2×C4×D4—861no—
190C2×#117C2×D4311yescharacteristic
191#432—861no—
192#407—21no—
193#398—431no—
194#397—431no—
195#396—861no—
196#394—431no—
197#394—861no—
198#392—431no—
199C4×C4⋊C4—431no—
200C4×C22⋊C4—861no—
201#343—21no—
202#343C2×D4312yes—
203#324—432no—
204#323—861no—
205C43#1180411yescharacteristic, complemented, Sylow
206C22×D4—431no—
207C22×D4—861no—
208C23×C4—861no—
209C23×C4C22⋊D4311yescharacteristic
210C2×M16—22no—
211C4×D4—1721no—
212C4×D4—1721no—
213C4×D4—1724no—
214#117—41no—
215#117—41no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C4⋊C4C22×D4311yescharacteristic
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4C4×D4311yescharacteristic
227C2×C22⋊C4D17211yescharacteristic
228C2×C42—861no—
229C2×C42C4×D4311yescharacteristic
230C2×C42D17211yescharacteristic
231C4⋊C8—1721no—
232C22⋊C8—41no—
233C22⋊C8—41no—
234C22⋊C8—862no—
235#97—1721no—
236#95—431no—
237#95—431no—
238#95—861no—
239#95—861no—
240C24—861no—
241C24(C2×D43)⋊C411yescharacteristic
242C2×D4—1721no—
243C2×D4—1722no—
244C2×D4—1722no—
245C2×D4—1722no—
246C2×D4—1722no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—1722no—
255C22×C4—1722no—
256C22×C4—1721no—
257C22×C4—1721no—
258C22×C4(C2×D43)⋊C411yescharacteristic
259C22×C4(C2×D43)⋊C411yescharacteristic
260C22×C4(C2×D43)⋊C411yescharacteristic
261C22×C4C2×C4×D4311yescharacteristic
262C22×C4C2×D17211yescharacteristic
263C22×C4C2×C22⋊D4311yescharacteristic
264M16—42no—
265M16—42no—
266C2×C8—42no—
267C2×C8—1722no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—1721no—
271C4⋊C4—1722no—
272C4⋊C4—1722no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—1722no—
276C22⋊C4—1722no—
277C22⋊C4—1722no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—1722no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—862no—
291C23—1721no—
292C23—1721no—
293C23—1721no—
294C23—1721no—
295C23—1721no—
296C23—1721no—
297C23C2×(C2×D43)⋊C411yescharacteristic
298D4—1722no—
299D4—1722no—
300D4—1728no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—862no—
316C2×C4—3442no—
317C2×C4—3442no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4#1306323911yescharacteristic
327C2×C4#1306323911yescharacteristic
328C2×C4#1306335012yes—
329C8—82no—
330C8—3442no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—3441no—
339C22—3441no—
340C22—3441no—
341C22—3441no—
342C22—1722no—
343C22—1722no—
344C22—1722no—
345C22C2×#1306323911yescharacteristic
346C22#1458290311yescharacteristic
347C22#1458291711yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3441no—
356C4—3441no—
357C4—1722no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—3442no—
362C2#1913312311yescharacteristic
363C2#1913623711yescharacteristic
364C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1822C2
socleC22×C43C2×#99
prime radical#14582808C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1822D43
hypocenterC43#11804
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. #19132929C2semidirect
3. #19132600C2semidirect
4. #19132597C2semidirect
5. C43×#1822C2semidirect
177. #1822D43semidirect
205. C43#11804semidirect

Maximal subgroups

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

subgroupindex
#191378312
#191329292
#191326002
#191325972
C43×#18222
#1180443