Finite Group Databasebeta

← #25006170

Subgroups — #25006170

Order 11008.

440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139086C211yesmaximal, characteristic
2#19132923C211yesmaximal, characteristic, complemented
3#324×D43C211yesmaximal, characteristic, complemented
4#19132538C211yesmaximal, characteristic, complemented
5#19132538C211yesmaximal, characteristic, complemented
6#19132527C211yesmaximal, characteristic, complemented
7C43×#1318C211yesmaximal, characteristic, complemented
8C2×#13063296C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582861—21no—
11C22⋊C8×D43—21no—
12#14582827—21no—
13#14582827—21no—
14#14582802C411yescharacteristic
15#14582775—21no—
16#14582775—21no—
17#14582765C411yescharacteristic
18#14582764C2211yescharacteristic
19C4×(C2×D43)⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#390C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—41no—
32C2×C8×D43—41no—
33#13063296—41no—
34#13063296—41no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4D411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C4⋊C4×D43—41no—
40C4⋊C4×D43—41no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48(C2×D43)⋊C8—41no—
49(C2×D43)⋊C8—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×D4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2×C411yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C24×C43—21no—
63C23×D43C22⋊C411yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—41no—
90C2×C4×D43—81no—
91C2×C4×D43—81no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊C4×C43—81no—
96C22⋊C4×C43—81no—
97C42×C43—41no—
98C22⋊Dic43—42no—
99C22⋊Dic43—81no—
100C22⋊Dic43—81no—
101(C2×D43)⋊C4—42no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110#10621872—82no—
111C8×D43—82no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—22no—
123C22×D43—41no—
124C22×D43#9911yescharacteristic
125C22×D43#9911yescharacteristic
126D4×C43—81no—
127D4×C43—81no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43#13111yescharacteristic
138C2×C4×C43#13111yescharacteristic
139C22⋊D43—82no—
140C22⋊D43—82no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C4×D43—41no—
155C4×D43—41no—
156C4×D43—41no—
157C4×D43—41no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—81no—
161C4×D43—81no—
162C8×C43—81no—
163C8×C43—81no—
164C43⋊C8—81no—
165C43⋊C8—81no—
166#11553—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43—81no—
176C22×C43#40811yescharacteristic
177C22×C43C2×#9911yescharacteristic
178C22×C43#41311yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—42no—
185C2×D43—42no—
186C2×D43#35512yes—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—81no—
192Dic43—41no—
193Dic43—41no—
194Dic43—41no—
195Dic43—81no—
196Dic43—81no—
197#2504—431no—
198#1463—431no—
199C2×#324—431no—
200#1324—431no—
201#1324—431no—
202#1318—431no—
203#1318D4311yescharacteristic, complemented
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—161no—
207C2×C43#146811yescharacteristic
208C2×C43#212711yescharacteristic
209C2×C43C2×#35511yescharacteristic
210D43—22no—
211D43—41no—
212C2×#121—431no—
213C22×C4⋊C4—431no—
214#407—861no—
215C2×C22⋊C8—861no—
216#397—861no—
217#397—861no—
218#390—431no—
219#390C2×D4311yescharacteristic
220#386—861no—
221#386—861no—
222#382—431no—
223#382—431no—
224C4×C22⋊C4—431no—
225#324—431no—
226#324—431no—
227#324—861no—
228#324—861no—
229#324C2×D4311yescharacteristic
230#324C2×D4311yescharacteristic
231C43#1155311yescharacteristic, complemented, Sylow
232C22×D4—861no—
233C22×D4C4×D4311yescharacteristic
234C23×C4—431no—
235C23×C4—431no—
236C23×C4—431no—
237C2×M16—1721no—
238C22×C8—1721no—
239#121—1721no—
240#121—1721no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—1721no—
246C2×C4⋊C4—1721no—
247C2×C4⋊C4C22×D4311yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C42—431no—
255C2×C42C4×D4311yescharacteristic
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—861no—
259C22⋊C8—861no—
260C22⋊C8—1721no—
261C22⋊C8—1721no—
262#95—861no—
263#95—861no—
264#95—861no—
265#95—861no—
266#95—861no—
267C24—21no—
268C24—431no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—1721no—
274C2×D4—1721no—
275C2×D4—1722no—
276C2×D4—1722no—
277C22×C4—21no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—3441no—
292C22×C4—3441no—
293C22×C4—1721no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297M16—3442no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—3442no—
301C2×C8—1721no—
302C2×C8—1721no—
303C4⋊C4—41no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—3441no—
311C22⋊C4—3441no—
312C22⋊C4—1722no—
313C22⋊C4—1722no—
314C42—41no—
315C42—861no—
316C42—861no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—431no—
325C23—431no—
326C23—862no—
327C23—861no—
328C23—861no—
329C23—1721no—
330C23C22⋊C4×D4311yescharacteristic
331D4—81no—
332D4—81no—
333D4—3442no—
334D4—3442no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4#1306333111yescharacteristic
366C2×C4#1306333311yescharacteristic
367C8—81no—
368C8—81no—
369C8—3441no—
370C8—3441no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—432no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—861no—
385C22—861no—
386C22—1722no—
387C22—1722no—
388C22#1458286411yescharacteristic
389C22#99×D4311yescharacteristic
390C22#1458288011yescharacteristic
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—3441no—
397C4—3441no—
398C4—1721no—
399C4—1721no—
400C4—1721no—
401C2—21no—
402C2—21no—
403C2—161no—
404C2—862no—
405C2—1721no—
406C2#1913294011yescharacteristic
407C2#1913626111yescharacteristic
408C2#355×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC2×#13063296C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11553
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #19132923C2semidirect
3. #324×D43C2semidirect
4. #19132538C2semidirect
5. #19132538C2semidirect
6. #19132527C2semidirect
7. C43×#1318C2semidirect
203. #1318D43semidirect
231. C43#11553semidirect

Maximal subgroups

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

subgroupindex
#191390862
#191329232
#324×D432
#191325382
#191325272
C43×#13182
#1155343