Finite Group Databasebeta

← #25007263

Subgroups — #25007263

Order 11008.

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

normal subgroups only

This group has 486 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#19134672C211yesmaximal, characteristic, complemented
3#19132596C212yesmaximal, complemented
4#19132593C212yesmaximal
5C43×#1464C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic, complemented
7C2×C4×C22⋊D43—21no—
8#14582829C411yescharacteristic, complemented
9#14582824C2211yescharacteristic
10#14582821—21no—
11#14582816C411yescharacteristic, complemented
12#14582815—21no—
13#14582808C2211yescharacteristic
14#14582762—21no—
15C4×C4⋊Dic43C411yescharacteristic, complemented
16C4×(C2×D43)⋊C4—21no—
17#14582666—21no—
18#14582666C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#323C2212yes—
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×C22⋊Dic43—22no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×C4×Dic43—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—41no—
42C43⋊#95—41no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46#117×C43—41no—
47#117×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43C2311yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56#97×C43—41no—
57C24×C43C2×D411yescharacteristic
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×C43C22×C411yescharacteristic
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—
75C22×Dic43—42no—
76C2×D172—42no—
77C2×D172—41no—
78C2×C4×D43—42no—
79C2×C4×D43—42no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C8×C43—42no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C22⋊Dic43—42no—
92C22⋊Dic43—42no—
93C22⋊Dic43—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98C4⋊Dic43—42no—
99C4⋊Dic43—41no—
100Dic43⋊C4—42no—
101C4×Dic43—42no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43AGL(1,ℤ/8)12yes—
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—21no—
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#9911yescharacteristic
131C2×C4×C43#9911yescharacteristic
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—
142C2×Dic43—82no—
143C2×Dic43—82no—
144C2×Dic43—82no—
145D172—42no—
146D172—42no—
147C4×D43—82no—
148C4×D43—82no—
149C8×C43—82no—
150#11798—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—22no—
154C22×C43—42no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—81no—
158C22×C43C2×#9911yescharacteristic
159C22×C43#41811yescharacteristic
160C22×C43#42111yescharacteristic
161C2×D43—42no—
162C2×D43—42no—
163C2×D43—42no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175Dic43—42no—
176Dic43—81no—
177Dic43—81no—
178Dic43—162no—
179#2392—431no—
180#1820—431no—
181#1464D4311yescharacteristic, complemented
182#1344—432no—
183#1343—432no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—42no—
187C2×C43#151011yescharacteristic
188C2×C43#212011yescharacteristic
189C2×C43#212611yescharacteristic
190D43—82no—
191C2×C4×D4—431no—
192C2×C4×D4—861no—
193C2×#117C2×D4311yescharacteristic
194#432—21no—
195#398—431no—
196#397—431no—
197#396—861no—
198#394—431no—
199#394—861no—
200#392—431no—
201#381—861no—
202C4×C4⋊C4—431no—
203C4×C22⋊C4—861no—
204#342—432no—
205#342—861no—
206#324—21no—
207#323C2×D4312yes—
208C43#1179811yescharacteristic, complemented, Sylow
209C22×D4—431no—
210C22×D4—861no—
211C23×C4—861no—
212C23×C4D17211yescharacteristic
213C4×D4—1721no—
214C4×D4—1721no—
215C4×D4—1724no—
216#117—41no—
217#117—41no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C4×D4311yescharacteristic
222C2×C4⋊C4C22⋊D4311yescharacteristic
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—862no—
229C2×C22⋊C4D17211yescharacteristic
230C2×C22⋊C4C22×D4311yescharacteristic
231C2×C42—861no—
232C2×C42C4×D4311yescharacteristic
233C2×C42C22⋊D4311yescharacteristic
234C4⋊C8—41no—
235C22⋊C8—22no—
236#97—41no—
237#95—431no—
238#95—431no—
239#95—861no—
240#95—861no—
241#95—1721no—
242#95—1721no—
243C24—861no—
244C24C2×D17211yescharacteristic
245C2×D4—1721no—
246C2×D4—1722no—
247C2×D4—1722no—
248C2×D4—1722no—
249C2×D4—1722no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—1722no—
258C22×C4—1722no—
259C22×C4—1722no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4(C2×D43)⋊C411yescharacteristic
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4(C2×D43)⋊C411yescharacteristic
266C22×C4C2×C4×D4311yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268C2×C8—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—1721no—
272C4⋊C4—1722no—
273C4⋊C4—1722no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—1722no—
277C22⋊C4—1722no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C22⋊C4—1722no—
281C22⋊C4—1722no—
282C22⋊C4—1722no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—1722no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—862no—
293C23—1721no—
294C23—1721no—
295C23—1721no—
296C23—1721no—
297C23—1721no—
298C23—1721no—
299C23C2×(C2×D43)⋊C411yescharacteristic
300C23#1306335312yes—
301D4—1722no—
302D4—1722no—
303D4—1728no—
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—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—862no—
320C2×C4—3442no—
321C2×C4—3442no—
322C2×C4—3442no—
323C2×C4—3442no—
324C2×C4—3442no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4#1306323911yescharacteristic
334C2×C4#1306323911yescharacteristic
335C8—82no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—3441no—
344C22—3441no—
345C22—3441no—
346C22—3441no—
347C22—1722no—
348C22—1722no—
349C22—1722no—
350C22C2×#1306323911yescharacteristic
351C22#1458290511yescharacteristic
352C22#1458291511yescharacteristic
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3441no—
361C4—3441no—
362C4—1722no—
363C4—6882no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—3442no—
368C2#1913312511yescharacteristic
369C2#1913623711yescharacteristic
370C2#1913625811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11798
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. #19134672C2semidirect
3. #19132596C2semidirect
5. C43×#1464C2semidirect
6. C2×C4×D172C4semidirect
8. #14582829C4semidirect
11. #14582816C4semidirect
15. C4×C4⋊Dic43C4semidirect
181. #1464D43semidirect
208. C43#11798semidirect

Maximal subgroups

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

subgroupindex
#191378312
#191346722
#191325962
#191325932
C43×#14642
#1179843