Finite Group Databasebeta

← #25065635

Subgroups — #25065635

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143713C212yesmaximal
2C4×#13063331C211yesmaximal, characteristic
3#19133359C214yesmaximal, complemented
4#19133355C212yesmaximal, complemented
5#19133349C212yesmaximal, complemented
6#19133345C212yesmaximal, complemented
7#19133343C211yesmaximal, characteristic, complemented
8C2×C43×#334C211yesmaximal, characteristic, complemented
9C2×#13063331C411yescharacteristic
10C2×#13063331C411yescharacteristic
11C4×#10621898C2211yescharacteristic
12#14583026—22no—
13#14582976—22no—
14#14582970—24no—
15#14582955C2214yes—
16#14582952C2212yes—
17#14582921C2214yes—
18#14582854C411yescharacteristic
19#14582854C411yescharacteristic
20#14582853C412yes—
21#14582853C412yes—
22C4×#10621877C2211yescharacteristic
23C4×#10621872C2212yes—
24C4×C8×D43C2212yes—
25#14582652C2212yes—
26#14582651C2214yes—
27#14582650C2211yescharacteristic
28#14582650C2211yescharacteristic
29#14582649C2214yes—
30C2×C4⋊C8×C43C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#334C2212yes—
33C43×#334C2212yes—
34C2×#10621898C2×C411yescharacteristic
35#13063331—24no—
36#13063331—24no—
37C2×#10621877C2×C411yescharacteristic
38C2×#10621877C2×C411yescharacteristic
39C2×#10621872—24no—
40C2×#10621872C2×C412yes—
41C2×#10621872C2×C412yes—
42C2×C8×D43C2×C412yes—
43C2×C8×D43C2×C412yes—
44C4×Dic86D411yescharacteristic
45C4×Dic86Q811yescharacteristic
46C4×D172D411yescharacteristic
47C4×D172Q811yescharacteristic
48C4×C22⋊D43D412yes—
49C4×C22⋊D43Q812yes—
50#13063284C2×C411yescharacteristic
51#13063282C2×C412yes—
52C42×D43C2312yes—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55Dic43⋊C8—24no—
56C22⋊(C43⋊C8)—22no—
57(C2×D43)⋊C8—24no—
58#13063236C2×C412yes—
59#13063235—24no—
60#13063235C2×C412yes—
61#13063235C2×C412yes—
62C4×C43⋊C8—22no—
63C4×C43⋊C8C2312yes—
64C8×Dic43C2×C412yes—
65C8×Dic43C2×C412yes—
66C22×C8×C43—22no—
67C22×C8×C43C2×C411yescharacteristic
68C22×C8×C43C2×C411yescharacteristic
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—22no—
71C4⋊C8×C43C2314yes—
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C4×C8×C43C2311yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×Q811yescharacteristic
79C2×C22⋊D43C4⋊C412yes—
80#10621898—22no—
81#10621898—22no—
82C2×D172C4⋊C411yescharacteristic
83C2×C4×D43C22×C412yes—
84C2×C4×D43C2×D412yes—
85C2×C4×D43C2×Q812yes—
86C2×Dic86C4⋊C411yescharacteristic
87C2×C8×C43—22no—
88C2×C8×C43—24no—
89C2×C8×C43—82no—
90C2×C8×C43M1614yescomplemented
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C22×C411yescharacteristic
95C42×C43C22×C411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43C2×Q811yescharacteristic
98C42×C43C2411yescharacteristic
99C22⋊Dic43C4⋊C412yes—
100(C2×D43)⋊C4C4⋊C412yes—
101(C2×D43)⋊C4C4⋊C412yes—
102C4⋊Dic43C4⋊C411yescharacteristic
103C4⋊Dic43C4⋊C411yescharacteristic
104Dic43⋊C4C4⋊C412yes—
105Dic43⋊C4C4⋊C412yes—
106C4×Dic43C22×C412yes—
107C4×Dic43C2×D412yes—
108C4×Dic43C2×Q812yes—
109#10621877—22no—
110#10621877M1614yescomplemented
111C2×C43⋊C8—22no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8C22×C412yes—
114C2×C43⋊C8C22×C412yes—
115#10621872—24no—
116#10621872—24no—
117#10621872—84no—
118C8×D43—24no—
119C8×D43—24no—
120C23×C43C2×C4⋊C411yescharacteristic
121C22×D43C2×C4⋊C412yes—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43C2×C4⋊C411yescharacteristic
125C2×C4×C43C2×C4⋊C411yescharacteristic
126C2×C4×C43C2×C4⋊C411yescharacteristic
127C2×C4×C43C2×M1612yes—
128C2×C4×C43C2×M1612yes—
129C2×C4×C43C23×C411yescharacteristic
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C22×Q811yescharacteristic
132C22⋊D43—24no—
133C2×Dic43C2×C4⋊C412yes—
134C2×Dic43C2×C4⋊C412yes—
135C2×Dic43C2×C4⋊C412yes—
136D172—22no—
137C4×D43—22no—
138C4×D43—22no—
139C4×D43—24no—
140C4×D43—42no—
141Dic86—22no—
142C8×C43—21no—
143C8×C43—21no—
144C8×C43—44no—
145C8×C43C2×M1612yes—
146C8×C43C2×M1612yes—
147C43⋊C8—22no—
148C43⋊C8—42no—
149C43⋊C8—42no—
150C43⋊C8C2×M1614yes—
151#17798—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43#42312yes—
155C22×C43C22×C4⋊C411yescharacteristic
156C2×D43—22no—
157C2×D43—22no—
158C2×D43—22no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43#42312yes—
163C4×C43C22×M1611yescharacteristic
164C4×C43C22×M1611yescharacteristic
165C4×C43#57712yes—
166Dic43—22no—
167Dic43—22no—
168Dic43—22no—
169#2989—432no—
170C4×#131—431no—
171#1569—434no—
172#1568—432no—
173#1566—432no—
174#1565—432no—
175#1564—431no—
176C2×#334D4311yescharacteristic, complemented
177C2×C43—22no—
178C2×C43C2×#42311yescharacteristic
179C2×C43#291211yescharacteristic
180C2×C43#291611yescharacteristic
181D43—42no—
182C2×#131—431no—
183C2×#131—431no—
184C4×#41—431no—
185#446—862no—
186#436—862no—
187#435—864no—
188#432—434no—
189#431—432no—
190#423—434no—
191C2×C4⋊C8C2×D4312yes—
192#405—431no—
193#405—431no—
194#405—432no—
195#405—432no—
196C4×M16—431no—
197C4×M16—432no—
198C2×C4×C8—432no—
199C2×C4×C8C2×D4311yescharacteristic
200#335—434no—
201#335—432no—
202#334—434no—
203#334—431no—
204#334—431no—
205#334C2×D4312yes—
206#334C2×D4312yes—
207C43#1779811yescharacteristic, complemented, Sylow
208C2×#41—431no—
209#131—864no—
210#131—864no—
211C2×M16—431no—
212C2×M16—431no—
213C2×M16—432no—
214C2×M16—432no—
215C2×M16—864no—
216C22×C8—22no—
217C22×C8—432no—
218C22×C8—432no—
219C22×C8C4×D4311yescharacteristic
220C22×C8C4×D4311yescharacteristic
221C4×Q8—431no—
222C4×Q8—431no—
223C4×D4—432no—
224C4×D4—432no—
225C4×D4—431no—
226C4×D4—431no—
227#117—431no—
228#117—432no—
229C2×C42—432no—
230C2×C42C22×D4311yescharacteristic
231C4⋊C8—22no—
232C4⋊C8—432no—
233C4⋊C8—432no—
234C4⋊C8—864no—
235C4⋊C8C22×D4314yes—
236C22⋊C8—864no—
237C22⋊C8—862no—
238#97—432no—
239#97—432no—
240#97—432no—
241#97—864no—
242C4×C8—432no—
243C4×C8—432no—
244C4×C8—432no—
245C4×C8—862no—
246C4×C8C4×D4311yescharacteristic
247C4×C8C4×D4311yescharacteristic
248C4×C8C22×D4311yescharacteristic
249C4×C8C22×D4311yescharacteristic
250#41—862no—
251#41—862no—
252C2×Q8—431no—
253C2×D4—432no—
254C2×D4—431no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4C2×C4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260C22×C4Q8×D4311yescharacteristic
261M16—434no—
262M16—864no—
263M16—862no—
264M16—864no—
265M16—3444no—
266C2×C8—22no—
267C2×C8—24no—
268C2×C8—82no—
269C2×C8—432no—
270C2×C8—432no—
271C2×C8—864no—
272C2×C8—864no—
273C2×C8—862no—
274C2×C8—862no—
275C2×C8#1062187214yescomplemented
276C2×C8C2×C4×D4311yescharacteristic
277C2×C8C2×C4×D4311yescharacteristic
278C2×C8C2×C4×D4311yescharacteristic
279C2×C8C2×C4×D4311yescharacteristic
280C4⋊C4—432no—
281C4⋊C4—432no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C22⋊C4—432no—
285C22⋊C4—432no—
286C22⋊C4—432no—
287C42—432no—
288C42—432no—
289C42—432no—
290C42C2×C4×D4311yescharacteristic
291C42D4×D4311yescharacteristic
292C42Q8×D4311yescharacteristic
293C42C23×D4311yescharacteristic
294C23—432no—
295C23C4⋊C4×D4311yescharacteristic
296Q8—862no—
297D4—864no—
298D4—862no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—432no—
302C2×C4—432no—
303C2×C4—432no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—864no—
307C2×C4—1722no—
308C2×C4C4⋊C4×D4311yescharacteristic
309C2×C4C4⋊C4×D4311yescharacteristic
310C2×C4C4⋊C4×D4311yescharacteristic
311C2×C4M16×D4312yes—
312C2×C4C2×#1062187212yes—
313C2×C4C22×C4×D4311yescharacteristic
314C2×C4C2×D4×D4311yescharacteristic
315C2×C4C2×Q8×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—44no—
319C8—434no—
320C8—862no—
321C8—1722no—
322C8—1722no—
323C8C2×#1062187212yes—
324C8C2×#1062187212yes—
325C22—21no—
326C22—21no—
327C22—862no—
328C22—862no—
329C22—862no—
330C22#1458292112yes—
331C22C2×C4⋊C4×D4311yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—862no—
336C4—862no—
337C4—862no—
338C4#1458292112yes—
339C4C2×M16×D4311yescharacteristic
340C4C22×#1062187211yescharacteristic
341C4#1458370512yes—
342C2—22no—
343C2—1722no—
344C2C2×#1458292111yescharacteristic
345C2#1914318611yescharacteristic
346C2#1914320311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#334C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenterC2×#334D43
hypocenterC43#17798
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
3. #19133359C2semidirect
4. #19133355C2semidirect
5. #19133349C2semidirect
6. #19133345C2semidirect
7. #19133343C2semidirect
8. C2×C43×#334C2semidirect
90. C2×C8×C43M16semidirect
110. #10621877M16semidirect
176. C2×#334D43semidirect
207. C43#17798semidirect
275. C2×C8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437132
C4×#130633312
#191333592
#191333552
#191333492
#191333452
#191333432
C2×C43×#3342
#1779843