Finite Group Databasebeta

← #25065918

Subgroups — #25065918

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143722C212yesmaximal
2#19143561C211yesmaximal, characteristic
3#19133381C212yesmaximal, complemented
4#19133372C212yesmaximal, complemented
5#19133364C212yesmaximal, complemented
6#19133361C212yesmaximal, complemented
7#19133346C212yesmaximal, complemented
8C2×#14582650C211yesmaximal, characteristic, complemented
9C43×#1568C211yesmaximal, characteristic, complemented
10C4×#10621898C2211yescharacteristic
11#14583029C411yescharacteristic
12#14583029C411yescharacteristic
13#14583027—22no—
14#14582978C411yescharacteristic
15#14582978C411yescharacteristic
16#14582972—22no—
17#14582970C412yes—
18#14582970C412yes—
19#14582967—22no—
20(C22⋊D43)⋊C8—22no—
21#14582955C2212yes—
22#14582952C2211yescharacteristic
23#14582951C2212yes—
24#14582950C2212yes—
25#14582921C2212yes—
26C2×C4⋊(C43⋊C8)C2212yes—
27C4⋊C8×D43C2212yes—
28C4×#10621872C2212yes—
29#14582651C2212yes—
30#14582651C2212yes—
31#14582650C2211yescharacteristic
32#14582650C2211yescharacteristic
33#14582650C2212yes—
34#14582649C2212yes—
35#14582649C2212yes—
36C43×#432C2212yes—
37C2×C4×C8×C43C2211yescharacteristic
38C43×#335C2212yes—
39C43×#334C2211yescharacteristic
40C43×#334C2211yescharacteristic
41C2×#10621898Q811yescharacteristic
42C2×#10621872—22no—
43C2×#10621872C2×C412yes—
44C2×#10621872C2×C412yes—
45C22×C43⋊C8—22no—
46C2×C8×D43—22no—
47C4×Dic86C2×C411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172C2×C411yescharacteristic
50C4×D172D411yescharacteristic
51C4×C22⋊D43C2×C412yes—
52C4×C22⋊D43D412yes—
53#13063284Q811yescharacteristic
54#13063282Q812yes—
55C42×D43C2312yes—
56C4⋊(C43⋊C8)—22no—
57C4⋊(C43⋊C8)C2×C411yescharacteristic
58C4⋊(C43⋊C8)C2×C411yescharacteristic
59C4⋊(C43⋊C8)C2312yes—
60C4⋊(C43⋊C8)C2312yes—
61Dic43⋊C8—22no—
62Dic43⋊C8—22no—
63Dic43⋊C8C2×C412yes—
64Dic43⋊C8C2×C412yes—
65C22⋊(C43⋊C8)C2×C412yes—
66(C2×D43)⋊C8—22no—
67(C2×D43)⋊C8—22no—
68(C2×D43)⋊C8C2×C412yes—
69(C2×D43)⋊C8C2×C412yes—
70#13063235—22no—
71#13063235C2×C412yes—
72#13063235C2×C412yes—
73C4×C43⋊C8C2312yes—
74C8×Dic43—22no—
75C22×C8×C43C2×C411yescharacteristic
76C22×C8×C43C2×C411yescharacteristic
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43C2312yes—
79C4⋊C8×C43C2312yes—
80C22⋊C8×C43—22no—
81#97×C43—22no—
82C4×C8×C43C2×C411yescharacteristic
83C4×C8×C43C2×C411yescharacteristic
84C4×C8×C43C2311yescharacteristic
85C4×C8×C43C2311yescharacteristic
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×Q811yescharacteristic
89C2×C22⋊D43C4⋊C412yes—
90#10621898—42no—
91C2×D172C4⋊C411yescharacteristic
92C2×C4×D43C22×C412yes—
93C2×C4×D43C2×D412yes—
94C2×C4×D43C2×Q812yes—
95C2×Dic86C4⋊C411yescharacteristic
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C2×C8×C43C22×C411yescharacteristic
101C2×C8×C43C22×C411yescharacteristic
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C22×C411yescharacteristic
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×Q811yescharacteristic
107C42×C43C2411yescharacteristic
108C22⋊Dic43C4⋊C412yes—
109(C2×D43)⋊C4C4⋊C412yes—
110(C2×D43)⋊C4C4⋊C412yes—
111C4⋊Dic43C4⋊C411yescharacteristic
112C4⋊Dic43C4⋊C411yescharacteristic
113Dic43⋊C4C4⋊C412yes—
114Dic43⋊C4C4⋊C412yes—
115C4×Dic43C22×C412yes—
116C4×Dic43C2×D412yes—
117C4×Dic43C2×Q812yes—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—82no—
121C2×C43⋊C8C22×C412yes—
122C2×C43⋊C8C22×C412yes—
123#10621872—24no—
124#10621872—42no—
125#10621872—82no—
126C8×D43—82no—
127C23×C43C2×C4⋊C411yescharacteristic
128C22×D43C2×C4⋊C412yes—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43C2×C4⋊C411yescharacteristic
134C2×C4×C43C2×C4⋊C411yescharacteristic
135C2×C4×C43C2×C4⋊C411yescharacteristic
136C2×C4×C43C23×C411yescharacteristic
137C2×C4×C43C22×D411yescharacteristic
138C2×C4×C43C22×Q811yescharacteristic
139C22⋊D43—24no—
140C2×Dic43C2×C4⋊C412yes—
141C2×Dic43C2×C4⋊C412yes—
142C2×Dic43C2×C4⋊C412yes—
143D172—41no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—22no—
148C4×D43—42no—
149Dic86—41no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—42no—
154C8×C43—42no—
155C8×C43#13112yes—
156C43⋊C8—22no—
157C43⋊C8—22no—
158C43⋊C8—42no—
159C43⋊C8—42no—
160#17838—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43#43012yes—
164C22×C43C22×C4⋊C411yescharacteristic
165C2×D43—22no—
166C2×D43—22no—
167C2×D43—22no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43C2×#13111yescharacteristic
173C4×C43#56811yescharacteristic
174C4×C43#57712yes—
175Dic43—22no—
176Dic43—22no—
177Dic43—22no—
178#2990—432no—
179#2965—431no—
180#1573—432no—
181#1572—432no—
182#1570—432no—
183#1569—432no—
184#1568D4311yescharacteristic, complemented
185#1565—432no—
186C2×#334—431no—
187C2×C43—22no—
188C2×C43#290611yescharacteristic
189C2×C43#291211yescharacteristic
190C2×C43C2×#43011yescharacteristic
191D43—42no—
192C4×#41—431no—
193#446—431no—
194#446—431no—
195#446—862no—
196#436—431no—
197#436—431no—
198#435—432no—
199#435—432no—
200#435—862no—
201#435—862no—
202C8×D4—862no—
203#432—432no—
204#432C2×D4312yes—
205#431—431no—
206#431—432no—
207#431—432no—
208#423—432no—
209C2×C4⋊C8—432no—
210C2×C4⋊C8—432no—
211C4×M16—432no—
212C2×C4×C8C2×D4311yescharacteristic
213#335—432no—
214#335—432no—
215#335C2×D4312yes—
216#334—432no—
217#334—432no—
218#334—431no—
219#334—431no—
220#334—432no—
221#334C2×D4311yescharacteristic
222#334C2×D4311yescharacteristic
223C43#1783811yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×M16—432no—
226C2×M16—432no—
227C2×M16—862no—
228C22×C8—862no—
229C22×C8—862no—
230C22×C8C4×D4311yescharacteristic
231C22×C8C4×D4311yescharacteristic
232C4×Q8—431no—
233C4×Q8—431no—
234C4×D4—432no—
235C4×D4—432no—
236C4×D4—431no—
237C4×D4—431no—
238#117—431no—
239#117—432no—
240C2×C42—432no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—432no—
243C4⋊C8—432no—
244C4⋊C8—431no—
245C4⋊C8—431no—
246C4⋊C8—432no—
247C4⋊C8—432no—
248C4⋊C8—862no—
249C4⋊C8—862no—
250C4⋊C8—862no—
251C4⋊C8C22×D4312yes—
252C4⋊C8C22×D4312yes—
253C22⋊C8—22no—
254C22⋊C8—432no—
255C22⋊C8—432no—
256C22⋊C8—432no—
257C22⋊C8—862no—
258C22⋊C8—862no—
259#97—22no—
260#97—432no—
261#97—432no—
262#97—862no—
263C4×C8—432no—
264C4×C8—862no—
265C4×C8C4×D4311yescharacteristic
266C4×C8C4×D4311yescharacteristic
267C4×C8C22×D4311yescharacteristic
268C4×C8C22×D4311yescharacteristic
269#41—1722no—
270C2×Q8—431no—
271C2×D4—432no—
272C2×D4—431no—
273C22×C4—432no—
274C22×C4—432no—
275C22×C4—432no—
276C22×C4C2×C4×D4311yescharacteristic
277C22×C4D4×D4311yescharacteristic
278C22×C4Q8×D4311yescharacteristic
279M16—864no—
280M16—3442no—
281M16—1722no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—432no—
287C2×C8—432no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8—3442no—
291C2×C8—3442no—
292C2×C8C2×C4×D4311yescharacteristic
293C2×C8C2×C4×D4311yescharacteristic
294C2×C8C2×C4×D4311yescharacteristic
295C2×C8C2×C4×D4311yescharacteristic
296C4⋊C4—432no—
297C4⋊C4—432no—
298C4⋊C4—431no—
299C4⋊C4—431no—
300C22⋊C4—432no—
301C22⋊C4—432no—
302C22⋊C4—432no—
303C42—432no—
304C42—432no—
305C42—432no—
306C42C2×C4×D4311yescharacteristic
307C42D4×D4311yescharacteristic
308C42Q8×D4311yescharacteristic
309C42C23×D4311yescharacteristic
310C23—432no—
311C23C4⋊C4×D4311yescharacteristic
312Q8—1721no—
313D4—864no—
314D4—1721no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—432no—
320C2×C4—432no—
321C2×C4—432no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—1722no—
327C2×C4C4⋊C4×D4311yescharacteristic
328C2×C4C4⋊C4×D4311yescharacteristic
329C2×C4C4⋊C4×D4311yescharacteristic
330C2×C4C22×C4×D4311yescharacteristic
331C2×C4C2×D4×D4311yescharacteristic
332C2×C4C2×Q8×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—42no—
337C8—42no—
338C8—862no—
339C8—862no—
340C8—1722no—
341C8—1722no—
342C8#1306333312yes—
343C22—21no—
344C22—21no—
345C22—862no—
346C22—862no—
347C22—862no—
348C22#1458294612yes—
349C22C2×C4⋊C4×D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—862no—
355C4—862no—
356C4—862no—
357C4C2×#1306333311yescharacteristic
358C4#1458366511yescharacteristic
359C4#1458370612yes—
360C2—22no—
361C2—1722no—
362C2#1914316411yescharacteristic
363C2#1914318711yescharacteristic
364C2C2×#1458294611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898Q8
cosocleC42×C43C24
hypercenter#1568D43
hypocenterC43#17838
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
3. #19133381C2semidirect
4. #19133372C2semidirect
5. #19133364C2semidirect
6. #19133361C2semidirect
7. #19133346C2semidirect
8. C2×#14582650C2semidirect
9. C43×#1568C2semidirect
184. #1568D43semidirect
223. C43#17838semidirect

Maximal subgroups

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

subgroupindex
#191437222
#191435612
#191333812
#191333722
#191333642
#191333612
#191333462
C2×#145826502
C43×#15682
#1783843