Finite Group Databasebeta

← #25006160

Subgroups — #25006160

Order 11008.

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

normal subgroups only

This group has 398 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#19139079C211yesmaximal, characteristic
2#19132923C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132538C211yesmaximal, characteristic, complemented
5#19132538C211yesmaximal, characteristic, complemented
6#19132529C211yesmaximal, characteristic, complemented
7C43×#1319C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582861—21no—
11C22⋊C8×D43—21no—
12#14582840—21no—
13#14582840—21no—
14#14582806C411yescharacteristic
15#14582765C411yescharacteristic
16#14582764C2211yescharacteristic
17#14582761—21no—
18#14582761—21no—
19C4×(C2×D43)⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#391C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621872—41no—
31C2×C8×D43—41no—
32#13063301—41no—
33#13063301—41no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4D411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C4⋊C4×D43—41no—
40C4⋊C4×D43—41no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×C4×Dic43C2×C411yescharacteristic
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—41no—
47(C2×D43)⋊C8—41no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×Q8×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C23×D43C22⋊C411yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—41no—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C42×C43—41no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—42no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104#10621872—82no—
105C8×D43—82no—
106C23×C43C2×C22⋊C411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—22no—
110C22×D43—41no—
111C22×D43#9911yescharacteristic
112C22×D43#9911yescharacteristic
113Q8×C43—81no—
114Q8×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43#13111yescharacteristic
128C2×C4×C43#13111yescharacteristic
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—42no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C4×D43—41no—
142C4×D43—41no—
143C4×D43—41no—
144C4×D43—41no—
145C4×D43—42no—
146C4×D43—42no—
147C4×D43—81no—
148C4×D43—81no—
149C8×C43—81no—
150C8×C43—81no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#11551—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#40811yescharacteristic
157C22×C43C2×#9911yescharacteristic
158C22×C43#41311yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—42no—
165C2×D43—42no—
166C2×D43#35412yes—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—81no—
172C4×C43—81no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43—81no—
177Dic43—81no—
178#2503—431no—
179#1463—431no—
180C2×#324—431no—
181#1324—431no—
182#1324—431no—
183#1319—431no—
184#1319D4311yescharacteristic, complemented
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#146811yescharacteristic
188C2×C43C2×#35411yescharacteristic
189C2×C43#213311yescharacteristic
190D43—22no—
191D43—41no—
192C2×C22⋊Q8—431no—
193C22×C4⋊C4—431no—
194#407—861no—
195C2×C22⋊C8—861no—
196#400—861no—
197#400—861no—
198#391—431no—
199#391C2×D4311yescharacteristic
200#382—431no—
201#382—431no—
202#381—861no—
203#381—861no—
204C4×C22⋊C4—431no—
205#324—431no—
206#324—431no—
207#324—861no—
208#324—861no—
209#324C2×D4311yescharacteristic
210#324C2×D4311yescharacteristic
211C43#1155111yescharacteristic, complemented, Sylow
212C22×Q8C4×D4311yescharacteristic
213C23×C4—431no—
214C23×C4—431no—
215C23×C4—431no—
216C2×M16—1721no—
217C22×C8—1721no—
218C22⋊Q8—1721no—
219C22⋊Q8—1721no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—1721no—
226C2×C4⋊C4—1721no—
227C2×C4⋊C4C22×D4311yescharacteristic
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C42—431no—
231C2×C42C4×D4311yescharacteristic
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—861no—
235C22⋊C8—861no—
236C22⋊C8—1721no—
237C22⋊C8—1721no—
238#95—21no—
239#95—21no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95—861no—
247C24—431no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—1721no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273M16—3442no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—3442no—
277C2×C8—1721no—
278C2×C8—1721no—
279C4⋊C4—41no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C4⋊C4—1722no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C22⋊C4—1722no—
288C42—41no—
289C42—861no—
290C42—861no—
291C23—431no—
292C23—431no—
293C23—862no—
294C23—861no—
295C23—861no—
296C23—1721no—
297C23C22⋊C4×D4311yescharacteristic
298Q8—81no—
299Q8—81no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4#1306333111yescharacteristic
333C2×C4#1306333311yescharacteristic
334C8—81no—
335C8—81no—
336C8—3441no—
337C8—3441no—
338C22—21no—
339C22—21no—
340C22—432no—
341C22—861no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—1722no—
347C22—1722no—
348C22#1458286411yescharacteristic
349C22#99×D4311yescharacteristic
350C22#1458288011yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—3441no—
358C4—3441no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C2—21no—
363C2—21no—
364C2—862no—
365C2—1721no—
366C2#1913294011yescharacteristic
367C2#354×D4311yescharacteristic
368C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11551
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #19132538C2semidirect
5. #19132538C2semidirect
6. #19132529C2semidirect
7. C43×#1319C2semidirect
184. #1319D43semidirect
211. C43#11551semidirect

Maximal subgroups

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

subgroupindex
#191390792
#191329232
#324×D432
#191325382
#191325292
C43×#13192
#1155143