Finite Group Databasebeta

← #25066086

Subgroups — #25066086

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143704C212yesmaximal, complemented
2C4×#13063347C211yesmaximal, characteristic
3#19133418C212yesmaximal, complemented
4#19133413C212yesmaximal, complemented
5#19133394C214yesmaximal, complemented
6#19132980C212yesmaximal, complemented
7#19132878C211yesmaximal, characteristic, complemented
8C2×C43×#334C211yesmaximal, characteristic, complemented
9C2×#13063347C411yescharacteristic
10C4×#10621898C2212yes—
11#14583023C2214yes—
12C4×Dic172C411yescharacteristic
13C4×Dic172C2211yescharacteristic
14C4×#10621873C412yes—
15C4×#10621873C2212yes—
16C4×D344C411yescharacteristic
17C4×D344C2211yescharacteristic
18#14582964C2214yes—
19C8×C22⋊D43—24no—
20#14582952C2211yescharacteristic
21#14582952C2211yescharacteristic
22#14582951—22no—
23#14582937C411yescharacteristic
24C4⋊C8×D43—22no—
25#14582896C412yes—
26#14582629C2214yes—
27#14582626C2214yes—
28#14582620C2212yes—
29C8×C43⋊C8C2212yes—
30C2×C4⋊C8×C43C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#334C2212yes—
33C43×#334C2212yes—
34C2×#10621898C2×C412yes—
35#13063347C818yescomplemented
36C2×Dic172C2×C411yescharacteristic
37C2×#10621873C2×C412yes—
38C2×D344C2×C411yescharacteristic
39C2×C8×D43—24no—
40C4×Dic86C2×C412yes—
41C4×Dic86C2312yes—
42C4×D172C2×C412yes—
43C4×D172C2312yes—
44C4×C22⋊D43—22no—
45C4×C22⋊D43—22no—
46#13063284C2×C412yes—
47#13063282—22no—
48C42×D43—22no—
49#13063259C2×C411yescharacteristic
50#13063259C2×C411yescharacteristic
51#13063257C2×C412yes—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D412yes—
54Dic43⋊C8—24no—
55#13063250C2×C412yes—
56#13063250C2×C412yes—
57#13063247C2×C412yes—
58#13063247C2×C412yes—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61(C2×D43)⋊C8—24no—
62C4×C43⋊C8C2312yes—
63C4×C43⋊C8C2312yes—
64C8×Dic43—24no—
65C22×C8×C43—22no—
66C22×C8×C43C2×C411yescharacteristic
67C22×C8×C43C2×C411yescharacteristic
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—22no—
70C4⋊C8×C43C2314yes—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—22no—
79#10621898—24no—
80#10621898C2×C818yescomplemented
81C2×D172C22×C412yes—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×Dic86C22×C412yes—
86C2×C8×C43—22no—
87C2×C8×C43—24no—
88C2×C8×C43—82no—
89C2×C8×C43C2×C814yescomplemented
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97C42×C43C2411yescharacteristic
98C22⋊Dic43—22no—
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101C4⋊Dic43C22×C412yes—
102C4⋊Dic43C22×C412yes—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C4×Dic43—22no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8C2×D414yes—
110Dic172C2×C814yescomplemented
111D344C2×C814yescomplemented
112#10621873C2×C818yescomplemented
113C8×D43—84no—
114C23×C43C4×D411yescharacteristic
115C22×D43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—41no—
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43C4×D411yescharacteristic
121C2×C4×C43C22×C812yes—
122C2×C4×C43#13112yes—
123C2×C4×C43C23×C411yescharacteristic
124C2×C4×C43C22×D411yescharacteristic
125C2×C4×C43C2×#4111yescharacteristic
126C22⋊D43—28no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130D172—22no—
131D172C22×C814yes—
132C4×D43—28no—
133C4×D43—42no—
134C4×D43—42no—
135C4×D43—82no—
136Dic86—22no—
137Dic86C22×C814yes—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43—44no—
141C8×C43C22×C812yes—
142C8×C43C22×C812yes—
143C43⋊C8—24no—
144C43⋊C8—42no—
145#17858—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43C8×D412yes—
149C22×C43C2×C4×D411yescharacteristic
150C2×D43—24no—
151C2×D43—42no—
152C2×D43—42no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43C8×D412yes—
157C4×C43C23×C811yescharacteristic
158C4×C43C2×#13111yescharacteristic
159C4×C43#57712yes—
160Dic43—24no—
161Dic43—42no—
162Dic43—42no—
163#2988—432no—
164C4×#135—431no—
165#1580—432no—
166#1579—432no—
167C8×SD16—434no—
168C2×#334D4311yescharacteristic, complemented
169#1477—432no—
170#1450—431no—
171C2×C43—22no—
172C2×C43C2×C8×D411yescharacteristic
173C2×C43#295211yescharacteristic
174C2×C43#295711yescharacteristic
175D43—44no—
176C2×#135—431no—
177C4×#41—432no—
178C8×Q8—434no—
179C4×Q16—431no—
180C4×Q16—431no—
181C4×SD16—432no—
182C4×SD16—432no—
183C4×D8—431no—
184C4×D8—431no—
185C8×D4—434no—
186C8×D4—864no—
187#431—431no—
188#431—431no—
189#431—862no—
190#427—431no—
191C2×C4⋊C8—862no—
192C2×C4⋊C8C2×D4312yes—
193#416—432no—
194C2×C4×C8C2×D4311yescharacteristic
195#334C2×D4312yes—
196#334C2×D4312yes—
197Q8⋊C8—434no—
198D4⋊C8—434no—
199#322—432no—
200C82—432no—
201C43#1785811yescharacteristic, complemented, Sylow
202C2×#41—432no—
203#135—438no—
204C2×Q16—431no—
205C2×SD16—432no—
206C2×D8—431no—
207C22×C8—22no—
208C22×C8—864no—
209C22×C8C4×D4311yescharacteristic
210C22×C8C4×D4311yescharacteristic
211C4×Q8—432no—
212C4×Q8—432no—
213C4×D4—432no—
214C4×D4—432no—
215C4×D4—862no—
216C4×D4—862no—
217#117—432no—
218#117—862no—
219C2×C42—862no—
220C2×C42C22×D4311yescharacteristic
221#107—431no—
222#107—431no—
223#106—432no—
224C4⋊C8—22no—
225C4⋊C8—432no—
226C4⋊C8—864no—
227C4⋊C8—861no—
228C4⋊C8C22×D4314yes—
229#103—432no—
230#103—432no—
231#102—432no—
232#102—432no—
233C22⋊C8—432no—
234C22⋊C8—864no—
235C22⋊C8—861no—
236C4×C8—432no—
237C4×C8—432no—
238C4×C8—864no—
239C4×C8C4×D4311yescharacteristic
240C4×C8C4×D4311yescharacteristic
241C4×C8C22×D4311yescharacteristic
242C4×C8C22×D4311yescharacteristic
243#41—438no—
244#41—864no—
245C2×Q8—432no—
246C2×D4—432no—
247C2×D4—862no—
248C22×C4—862no—
249C22×C4—862no—
250C22×C4—862no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4#1062190211yescharacteristic
254Q16—434no—
255SD16—438no—
256D8—434no—
257C2×C8—22no—
258C2×C8—24no—
259C2×C8—82no—
260C2×C8—434no—
261C2×C8—862no—
262C2×C8—3444no—
263C2×C8C8×D4314yescomplemented
264C2×C8C2×C4×D4311yescharacteristic
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8C2×C4×D4311yescharacteristic
267C2×C8C2×C4×D4311yescharacteristic
268C4⋊C4—432no—
269C4⋊C4—432no—
270C4⋊C4—862no—
271C4⋊C4—862no—
272C22⋊C4—862no—
273C22⋊C4—862no—
274C22⋊C4—862no—
275C42—862no—
276C42—862no—
277C42—862no—
278C42C2×C4×D4311yescharacteristic
279C42D4×D4311yescharacteristic
280C42#1062190211yescharacteristic
281C42C23×D4311yescharacteristic
282C23—862no—
283C23#1306328711yescharacteristic
284Q8—434no—
285Q8—862no—
286D4—434no—
287D4—868no—
288D4—862no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—862no—
292C2×C4—868no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—3442no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4#1306328711yescharacteristic
299C2×C4#1306328711yescharacteristic
300C2×C4#1306328711yescharacteristic
301C2×C4C2×C8×D4312yes—
302C2×C4#1306333312yes—
303C2×C4C22×C4×D4311yescharacteristic
304C2×C4C2×D4×D4311yescharacteristic
305C2×C4C2×#1062190211yescharacteristic
306C8—21no—
307C8—21no—
308C8—44no—
309C8—864no—
310C8—1722no—
311C8C2×C8×D4312yes—
312C8C2×C8×D4312yes—
313C22—21no—
314C22—21no—
315C22—864no—
316C22—1722no—
317C22—1722no—
318C22#1458296412yes—
319C22C2×#1306328711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—864no—
324C4—1722no—
325C4—1722no—
326C4#1458296412yes—
327C4C22×C8×D4311yescharacteristic
328C4C2×#1306333311yescharacteristic
329C4#1458370512yes—
330C2—22no—
331C2—1724no—
332C2C2×#1458296411yescharacteristic
333C2#1914347811yescharacteristic
334C2#1914351111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC2×C43×#334C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C4
cosocleC42×C43C24
hypercenterC2×#334D43
hypocenterC43#17858
LCSG ▷ 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
1. #19143704C2semidirect
3. #19133418C2semidirect
4. #19133413C2semidirect
5. #19133394C2semidirect
6. #19132980C2semidirect
7. #19132878C2semidirect
8. C2×C43×#334C2semidirect
35. #13063347C8semidirect
80. #10621898C2×C8semidirect
89. C2×C8×C43C2×C8semidirect
110. Dic172C2×C8semidirect
111. D344C2×C8semidirect
112. #10621873C2×C8semidirect
168. C2×#334D43semidirect
201. C43#17858semidirect
263. C2×C8C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437042
C4×#130633472
#191334182
#191334132
#191333942
#191329802
#191328782
C2×C43×#3342
#1785843