Finite Group Databasebeta

← #25007518

Subgroups — #25007518

Order 11008.

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

normal subgroups only

This group has 438 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#19140075C211yesmaximal, characteristic
2C2×#14582625C211yesmaximal, characteristic, complemented
3#19132621C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C43×#1821C211yesmaximal, characteristic, complemented
6C2×#13063299C411yescharacteristic
7C2×C22⋊(C43⋊C8)—21no—
8#14582838C411yescharacteristic
9#14582838C2211yescharacteristic
10#14582816C411yescharacteristic
11#14582816C2211yescharacteristic
12#14582789—21no—
13#14582789—21no—
14#14582778—21no—
15#14582778—21no—
16C4×C22⋊Dic43C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C43⋊C8—41no—
26#13063299—41no—
27#13063299—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C22⋊Dic43—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×C4×Dic43—21no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—22no—
48C2×C4⋊C4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43C2311yescharacteristic
54C22⋊C8×C43—41no—
55C22⋊C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C23×D43—21no—
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—41no—
66C22×C4×C43—81no—
67C22×C4×C43—81no—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—41no—
82C2×D172—81no—
83M16×C43—42no—
84M16×C43—42no—
85C2×C8×C43—42no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊Dic43—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—81no—
95(C2×D43)⋊C4—81no—
96C4⋊Dic43—41no—
97C4×Dic43—81no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—82no—
100C23×C43—22no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43#9911yescharacteristic
105C23×C43#9911yescharacteristic
106C23×C43C2×C22⋊C411yescharacteristic
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C2×C4×C43—21no—
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—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43#13512yes—
134C22⋊D43—82no—
135C22⋊D43—82no—
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—41no—
145D172—82no—
146C8×C43—82no—
147C43⋊C8—82no—
148#11852—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—42no—
157C22×C43—42no—
158C22×C43#35512yes—
159C22×C43C2×#9911yescharacteristic
160C22×C43#41611yescharacteristic
161C22×C43#42111yescharacteristic
162C2×D43—81no—
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C4×C43—22no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175Dic43—81no—
176Dic43—81no—
177Dic43—81no—
178#2591—431no—
179#1821D4311yescharacteristic, complemented
180C2×#324—431no—
181#1353—432no—
182#1345—432no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—22no—
186C2×C43—41no—
187C2×C43#151611yescharacteristic
188C2×C43#212111yescharacteristic
189C2×C43C2×#35511yescharacteristic
190D43—161no—
191C2×#121—431no—
192C22×C4⋊C4C2×D4311yescharacteristic
193#407—21no—
194C2×C22⋊C8—861no—
195#400—431no—
196#400—431no—
197#394—431no—
198#394—431no—
199#388—861no—
200#388—861no—
201#386—861no—
202#386—861no—
203C4×C22⋊C4—431no—
204#343—21no—
205#343C2×D4312yes—
206#324—432no—
207#324—861no—
208C43#1185211yescharacteristic, complemented, Sylow
209C22×D4—431no—
210C22×D4—861no—
211C23×C4C4×D4311yescharacteristic
212C23×C4D17211yescharacteristic
213C23×C4C22⋊D4311yescharacteristic
214C2×M16—22no—
215C22×C8—1721no—
216#121—1721no—
217#121—1721no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4C4×D4311yescharacteristic
222C2×C4⋊C4D17211yescharacteristic
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C4⋊C4C22×D4311yescharacteristic
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C42—861no—
232C22⋊C8—41no—
233C22⋊C8—41no—
234C22⋊C8—862no—
235C22⋊C8—1721no—
236#95—431no—
237#95—431no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242C24—861no—
243C24(C2×D43)⋊C411yescharacteristic
244C2×D4—3441no—
245C2×D4—1721no—
246C2×D4—1722no—
247C2×D4—1722no—
248C2×D4—1721no—
249C2×D4—1721no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—81no—
259C22×C4—81no—
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—42no—
270M16—42no—
271C2×C8—42no—
272C2×C8—3442no—
273C2×C8—1722no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—1721no—
279C22⋊C4—3441no—
280C22⋊C4—3441no—
281C22⋊C4—1722no—
282C22⋊C4—1722no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C42—3441no—
286C23—21no—
287C23—21no—
288C23—22no—
289C23—41no—
290C23—1721no—
291C23—1721no—
292C23—1721no—
293C23—1721no—
294C23—1721no—
295C23—1721no—
296C23—1721no—
297C23#1306323911yescharacteristic
298C23#1306323911yescharacteristic
299C23C2×(C2×D43)⋊C411yescharacteristic
300D4—3442no—
301D4—3442no—
302D4—3442no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
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#1306334512yes—
332C8—82no—
333C8—3442no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—3441no—
344C22—3441no—
345C22—3441no—
346C22—3441no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22#1458269512yes—
351C22C2×#1306323911yescharacteristic
352C22#1458289311yescharacteristic
353C22#1458291711yescharacteristic
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3441no—
361C4—3441no—
362C4—3441no—
363C2—21no—
364C2—21no—
365C2—22no—
366C2—41no—
367C2—6881no—
368C2#1913314911yescharacteristic
369C2#1913624211yescharacteristic
370C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1821C2
socleC22×C43C2×#99
prime radicalC2×#13063299C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1821D43
hypocenterC43#11852
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. C2×#14582625C2semidirect
3. #19132621C2semidirect
4. #19132597C2semidirect
5. C43×#1821C2semidirect
179. #1821D43semidirect
208. C43#11852semidirect

Maximal subgroups

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

subgroupindex
#191400752
C2×#145826252
#191326212
#191325972
C43×#18212
#1185243