Finite Group Databasebeta

← #25005850

Subgroups — #25005850

Order 11008.

488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C4×#13063306C211yesmaximal, characteristic
2#19132916C211yesmaximal, characteristic
3#19132544C212yesmaximal, complemented
4#19132524C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic
6C2×#13063306C411yescharacteristic
7C22×C4×Dic43C411yescharacteristic
8#14582952—21no—
9#14582787—21no—
10#14582780—21no—
11#14582779C411yescharacteristic
12#14582771C2211yescharacteristic
13#14582760C2211yescharacteristic
14C4×Dic43⋊C4—21no—
15C4×C22⋊Dic43—21no—
16C4×C22⋊Dic43C411yescharacteristic
17#14582623—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C23×Dic43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25#13063306—22no—
26#13063306C814yescomplemented
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43C2×C411yescharacteristic
32C2×C22⋊Dic43C2×C411yescharacteristic
33C2×C4×Dic43—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43—41no—
37C2×C4×Dic43—41no—
38C4⋊(C43⋊C8)—41no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×D4×C43C2×C411yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C22×C8×C43—41no—
50C4×D4×C43—41no—
51C4×D4×C43—41no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2311yescharacteristic
55C2×C42×C43D411yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C22×C411yescharacteristic
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43C2×C812yes—
63C2×D4×C43M1612yes—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—42no—
84C22×Dic43C2×C812yescomplemented
85C2×C8×C43—42no—
86C2×C8×C43—82no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C42×C43—21no—
91C42×C43—21no—
92C22⋊Dic43—24no—
93C22⋊Dic43—21no—
94C22⋊Dic43—41no—
95C22⋊Dic43—42no—
96C22⋊Dic43C2×C812yescomplemented
97Dic43⋊C4—24no—
98Dic43⋊C4—42no—
99C4×Dic43—42no—
100C4×Dic43—42no—
101C4×Dic43—41no—
102C4×Dic43—41no—
103C2×C43⋊C8—42no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43C22⋊C812yes—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43C22×C811yescharacteristic
115C23×C43C2×M1611yescharacteristic
116D4×C43—42no—
117D4×C43—42no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—81no—
131C2×C4×C43C22⋊C812yes—
132C2×C4×C43#9911yescharacteristic
133C2×C4×C43#9911yescharacteristic
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C8×C43—82no—
151C43⋊C8—82no—
152#11472—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—22no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—42no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—81no—
167C22×C43C2×C22⋊C811yescharacteristic
168C22×C43C2×#9911yescharacteristic
169C22×C43#41311yescharacteristic
170C4×C43—21no—
171C4×C43—22no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43#35212yes—
176Dic43—42no—
177Dic43—42no—
178Dic43—42no—
179Dic43—81no—
180C4×#123—431no—
181#1460—431no—
182#1459D4311yescharacteristic
183#1326—432no—
184#1317—432no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—41no—
188C2×C43—41no—
189C2×C43—42no—
190C2×C43#145911yescharacteristic
191C2×C43C2×#35211yescharacteristic
192C2×C43#212011yescharacteristic
193C2×#123—431no—
194C2×C4×D4C2×D4311yescharacteristic
195C22×C42—431no—
196#431—861no—
197C2×C22⋊C8—21no—
198#388—861no—
199#387—861no—
200#386—431no—
201#385—431no—
202#381—431no—
203C4×C4⋊C4—861no—
204C4×C22⋊C4—431no—
205C4×C22⋊C4—861no—
206#324—21no—
207#323—432no—
208#323—861no—
209#323C2×D4312yes—
210C43#1147211yescharacteristic, complemented, Sylow
211C22×D4C4×D4311yescharacteristic
212C23×C4—431no—
213C23×C4—431no—
214C23×C4C4×D4311yescharacteristic
215C23×C4C22⋊D4311yescharacteristic
216C22×C8—41no—
217#123—434no—
218#123—862no—
219C4×D4—41no—
220C4×D4—41no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C22⋊C4—431no—
225C2×C22⋊C4—431no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4D17211yescharacteristic
229C2×C22⋊C4C22×D4311yescharacteristic
230C2×C42—861no—
231C2×C42—861no—
232C2×C42—861no—
233C2×C42—1721no—
234C2×C42—1721no—
235C2×C42D17211yescharacteristic
236C4⋊C8—1721no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239C22⋊C8—862no—
240C4×C8—1721no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95—861no—
245#95—861no—
246C24(C2×D43)⋊C411yescharacteristic
247C24C2×C4×D4311yescharacteristic
248C2×D4—41no—
249C2×D4—41no—
250C2×D4C8×D4312yes—
251C2×D4#1062187212yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—432no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—1722no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4—1721no—
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4(C2×D43)⋊C411yescharacteristic
271C22×C4C2×D17211yescharacteristic
272C22×C4C2×C22⋊D4311yescharacteristic
273C2×C8—42no—
274C2×C8—82no—
275C2×C8—1722no—
276C4⋊C4—41no—
277C4⋊C4—864no—
278C4⋊C4—1722no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—432no—
282C22⋊C4—864no—
283C22⋊C4—861no—
284C22⋊C4—1722no—
285C22⋊C4—1721no—
286C42—21no—
287C42—21no—
288C42—1722no—
289C42—1722no—
290C42—1721no—
291C42—1721no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23(C2×D43)⋊C812yes—
301C23C2×(C2×D43)⋊C411yescharacteristic
302C23C2×C8×D4311yescharacteristic
303C23C2×#1062187211yescharacteristic
304D4—42no—
305D4—42no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
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—81no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4(C2×D43)⋊C812yes—
336C2×C4#1306323911yescharacteristic
337C2×C4#1306323911yescharacteristic
338C8—82no—
339C8—3442no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22C2×(C2×D43)⋊C811yescharacteristic
355C22C2×#1306323911yescharacteristic
356C22#1458288111yescharacteristic
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3441no—
363C4—1722no—
364C4—1722no—
365C4—1722no—
366C4#1458268812yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—42no—
372C2#1913291111yescharacteristic
373C2C2×#1458268811yescharacteristic
374C2#1913623711yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC23×C43C22×C8
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1459C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1459D43
hypocenterC43#11472
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #19132544C2semidirect
4. #19132524C2semidirect
26. #13063306C8semidirect
84. C22×Dic43C2×C8semidirect
96. C22⋊Dic43C2×C8semidirect
210. C43#11472semidirect

Maximal subgroups

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

subgroupindex
C4×#130633062
#191329162
#191325442
#191325242
C43×#14592
#1147243