Finite Group Databasebeta

← #25068654

Subgroups — #25068654

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143755C212yesmaximal, complemented
2#19133509C211yesmaximal, characteristic, complemented
3#19133504C211yesmaximal, characteristic, complemented
4#19133439C212yesmaximal, complemented
5#19133432C212yesmaximal, complemented
6#19133419C211yesmaximal, characteristic, complemented
7#19133414C211yesmaximal, characteristic, complemented
8C2×#14582650C211yesmaximal, characteristic, complemented
9#19133008C212yesmaximal, complemented
10#19132884C211yesmaximal, characteristic, complemented
11C43×#3168C211yesmaximal, characteristic
12#14583030C2212yes—
13Q8×C43⋊C8C2212yes—
14#14582977C2212yes—
15#14582971—22no—
16D4×C43⋊C8—22no—
17D4×C43⋊C8C2212yes—
18#14582960—22no—
19#14582952C2211yescharacteristic
20#14582926—22no—
21C2×C4⋊(C43⋊C8)C2212yes—
22C4×#10621877C2211yescharacteristic
23#14582650C2211yescharacteristic
24#14582650C2211yescharacteristic
25#14582650C2212yes—
26Q8⋊(C43⋊C8)C2212yes—
27Q8⋊(C43⋊C8)C2212yes—
28D4⋊(C43⋊C8)C2212yes—
29D4⋊(C43⋊C8)C2212yes—
30#14582621C2211yescharacteristic
31#14582621C2211yescharacteristic
32#14582620C2211yescharacteristic
33#14582620C2211yescharacteristic
34C43×#529C2212yes—
35C43×#499C411yescharacteristic
36C43×#495C411yescharacteristic
37C43×#488C412yes—
38C43×#467C411yescharacteristic
39C43×#466C411yescharacteristic
40C43×#465C412yes—
41C4×Q16×C43C2211yescharacteristic
42C4×SD16×C43C2212yes—
43C4×D8×C43C2211yescharacteristic
44C2×C4×C8×C43C2211yescharacteristic
45C2×#10621877—21no—
46C2×#10621877—22no—
47C22×C43⋊C8—22no—
48C22×C43⋊C8—22no—
49C4⋊(C43⋊C8)—22no—
50C4⋊(C43⋊C8)—22no—
51C4⋊(C43⋊C8)—22no—
52C4⋊(C43⋊C8)D412yes—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55C22⋊(C43⋊C8)—22no—
56C22⋊(C43⋊C8)—22no—
57C22⋊(C43⋊C8)D412yes—
58#13063236—21no—
59#13063236—22no—
60C4×C43⋊C8—22no—
61C4×C43⋊C8C2311yescharacteristic
62C4×C43⋊C8C2311yescharacteristic
63C4×C43⋊C8C2311yescharacteristic
64C4×C43⋊C8C2311yescharacteristic
65C2×Q16×C43C2×C411yescharacteristic
66C2×SD16×C43C2×C412yes—
67C2×D8×C43C2×C411yescharacteristic
68C22×C8×C43C2×C411yescharacteristic
69C22×C8×C43C2×C411yescharacteristic
70#126×C43—22no—
71#125×C43C2×C412yes—
72#124×C43C2×C412yes—
73#123×C43—22no—
74C22⋊Q8×C43C2×C412yes—
75#121×C43C2×C412yes—
76C4×Q8×C43C2312yes—
77C4×D4×C43—22no—
78C4×D4×C43C2312yes—
79#117×C43—22no—
80C2×C42×C43C2311yescharacteristic
81#107×C43C2×C411yescharacteristic
82#107×C43C2×C411yescharacteristic
83#106×C43C2×C412yes—
84#103×C43C2×C412yes—
85#103×C43C2×C412yes—
86#102×C43C2×C412yes—
87#102×C43C2×C412yes—
88C4×C8×C43C2×C411yescharacteristic
89C4×C8×C43C2×C411yescharacteristic
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C2×Q8×C43C22×C412yes—
93C2×D4×C43—22no—
94C2×D4×C43C22×C412yes—
95C22×C4×C43—22no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99Q16×C43—22no—
100SD16×C43—42no—
101D8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—41no—
104C2×C8×C43C22×C411yescharacteristic
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C22×C411yescharacteristic
108C4⋊C4×C43—22no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43C22×C412yes—
113C4⋊C4×C43C22×C412yes—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—22no—
119C42×C43—22no—
120C42×C43C22×C411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C42×C43C2411yescharacteristic
124#10621877—42no—
125#10621877—82no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—82no—
131C2×C43⋊C8—82no—
132C2×C43⋊C8C2×D412yes—
133C2×C43⋊C8C2×D412yes—
134C23×C43—22no—
135C23×C43C4×D411yescharacteristic
136Q8×C43—22no—
137Q8×C43—22no—
138D4×C43—22no—
139D4×C43—22no—
140D4×C43—44no—
141C2×C4×C43—22no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C23×C411yescharacteristic
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C2×#4111yescharacteristic
156C8×C43—21no—
157C8×C43—21no—
158C8×C43—21no—
159C8×C43#13112yes—
160C43⋊C8—22no—
161C43⋊C8—22no—
162C43⋊C8—41no—
163C43⋊C8—41no—
164C43⋊C8—42no—
165C43⋊C8—42no—
166#18093—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43#44412yes—
173C22×C43C2×C4×D411yescharacteristic
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—42no—
179C4×C43—42no—
180C4×C43—42no—
181C4×C43C2×#13111yescharacteristic
182C4×C43#56811yescharacteristic
183C4×C43#57712yes—
184#3168D4311yescharacteristic
185#2994—432no—
186#1594—431no—
187#1593—431no—
188#1583—432no—
189#1582—432no—
190#1580—431no—
191#1579—431no—
192C2×#334—431no—
193#1483—432no—
194#1451—431no—
195C2×C43—22no—
196C2×C43—82no—
197C2×C43#293511yescharacteristic
198C2×C43#295211yescharacteristic
199C2×C43C2×#44411yescharacteristic
200#529C2×D4312yes—
201#499Dic4311yescharacteristic
202#495Dic4311yescharacteristic
203#488Dic4312yes—
204#467Dic4311yescharacteristic
205#466Dic4311yescharacteristic
206#465Dic4312yes—
207#446—432no—
208C8×Q8—432no—
209C4×Q16C2×D4311yescharacteristic
210C4×SD16C2×D4312yes—
211C4×D8C2×D4311yescharacteristic
212#436—432no—
213#435—862no—
214C8×D4—432no—
215C8×D4—862no—
216#433—862no—
217#431—431no—
218#424—862no—
219C2×C4⋊C8—432no—
220C4×M16—431no—
221C2×C4×C8C2×D4311yescharacteristic
222#334—431no—
223#334—432no—
224#334—431no—
225Q8⋊C8—432no—
226Q8⋊C8—432no—
227D4⋊C8—432no—
228D4⋊C8—432no—
229#322—431no—
230#322—431no—
231#322—431no—
232#322—431no—
233C43#1809311yescharacteristic, complemented, Sylow
234C2×Q16C2×Dic4311yescharacteristic
235C2×SD16C2×Dic4312yes—
236C2×D8C2×Dic4311yescharacteristic
237C2×M16—862no—
238C2×M16—861no—
239C22×C8—862no—
240C22×C8—862no—
241C22×C8C2×Dic4311yescharacteristic
242C22×C8C2×Dic4311yescharacteristic
243#126—22no—
244#125C2×Dic4312yes—
245#124C2×Dic4312yes—
246#123—22no—
247C22⋊Q8C2×Dic4312yes—
248#121C2×Dic4312yes—
249C4×Q8C22×D4312yes—
250C4×D4—22no—
251C4×D4C22×D4312yes—
252#117—22no—
253C2×C42C22×D4311yescharacteristic
254#107C2×Dic4311yescharacteristic
255#107C2×Dic4311yescharacteristic
256#106C2×Dic4312yes—
257C4⋊C8—432no—
258C4⋊C8—432no—
259C4⋊C8—432no—
260C4⋊C8—862no—
261C4⋊C8—862no—
262C4⋊C8—862no—
263#103C2×Dic4312yes—
264#103C2×Dic4312yes—
265#102C2×Dic4312yes—
266#102C2×Dic4312yes—
267C22⋊C8—432no—
268C22⋊C8—862no—
269C22⋊C8—862no—
270#97—862no—
271#97—861no—
272C4×C8—431no—
273C4×C8—431no—
274C4×C8—431no—
275C4×C8—431no—
276C4×C8—862no—
277C4×C8C2×Dic4311yescharacteristic
278C4×C8C2×Dic4311yescharacteristic
279C4×C8C22×D4311yescharacteristic
280C4×C8C22×D4311yescharacteristic
281C2×Q8C22×Dic4312yes—
282C2×D4—22no—
283C2×D4C22×Dic4312yes—
284C22×C4—22no—
285C22×C4D4×D4311yescharacteristic
286C22×C4#1062190011yescharacteristic
287C22×C4C22×Dic4311yescharacteristic
288Q16—22no—
289SD16—42no—
290D8—22no—
291M16—3442no—
292M16—1722no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—432no—
296C2×C8—432no—
297C2×C8—862no—
298C2×C8—862no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—3442no—
302C2×C8—3442no—
303C2×C8C22×Dic4311yescharacteristic
304C2×C8C22×Dic4311yescharacteristic
305C2×C8C22×Dic4311yescharacteristic
306C2×C8C22×Dic4311yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4C22×Dic4312yes—
312C4⋊C4C22×Dic4312yes—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C42—22no—
319C42D4×D4311yescharacteristic
320C42#1062190011yescharacteristic
321C42C22×Dic4311yescharacteristic
322C42C23×D4311yescharacteristic
323C23—22no—
324C23D4×Dic4311yescharacteristic
325Q8—22no—
326Q8—22no—
327D4—22no—
328D4—22no—
329D4—44no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4D4×Dic4311yescharacteristic
340C2×C4D4×Dic4311yescharacteristic
341C2×C4D4×Dic4311yescharacteristic
342C2×C4C23×Dic4311yescharacteristic
343C2×C4C2×D4×D4311yescharacteristic
344C2×C4C2×#1062190011yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—862no—
349C8—862no—
350C8—1721no—
351C8—1721no—
352C8—1722no—
353C8—1722no—
354C8#1306333212yes—
355C22—21no—
356C22—21no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22#1458302112yes—
361C22C2×D4×Dic4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—42no—
367C4—42no—
368C4—42no—
369C4C2×#1306333211yescharacteristic
370C4#1458366611yescharacteristic
371C4#1458370612yes—
372C2—22no—
373C2—82no—
374C2#1914333911yescharacteristic
375C2#1914347911yescharacteristic
376C2C2×#1458302111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3168C2
socleC22×C43C2×C4×D4
prime radicalC43×#466C4
cosocleC42×C43C24
hypercenter#3168D43
hypocenterC43#18093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #19143755C2semidirect
2. #19133509C2semidirect
3. #19133504C2semidirect
4. #19133439C2semidirect
5. #19133432C2semidirect
6. #19133419C2semidirect
7. #19133414C2semidirect
8. C2×#14582650C2semidirect
9. #19133008C2semidirect
10. #19132884C2semidirect
233. C43#18093semidirect

Maximal subgroups

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

subgroupindex
#191437552
#191335092
#191335042
#191334392
#191334322
#191334192
#191334142
C2×#145826502
#191330082
#191328842
C43×#31682
#1809343