Finite Group Databasebeta

← #25065861

Subgroups — #25065861

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143261C212yesmaximal
2#19133384C212yesmaximal, complemented
3#19133380C212yesmaximal, complemented
4#19133375C212yesmaximal, complemented
5#19133362C212yesmaximal, complemented
6#19133358C211yesmaximal, characteristic, complemented
7#19133347C212yesmaximal, complemented
8#19133343C211yesmaximal, characteristic, complemented
9C43×#2965C211yesmaximal, characteristic
10#14582960—22no—
11#14582960—22no—
12#14582956C2212yes—
13#14582956C2212yes—
14#14582952C2212yes—
15#14582952C2212yes—
16#14582923C2212yes—
17C2×C4⋊(C43⋊C8)C2212yes—
18#14582866—22no—
19#14582855—22no—
20#14582652C2212yes—
21#14582652C2212yes—
22#14582652C2212yes—
23#14582652C2212yes—
24#14582650C2211yescharacteristic
25#14582650C2211yescharacteristic
26#14582650C2212yes—
27#14582650C2211yescharacteristic
28#14582650C2211yescharacteristic
29#14582650C2212yes—
30C4×#41×C43C2211yescharacteristic
31C43×#446C411yescharacteristic
32C43×#446C411yescharacteristic
33C43×#436C411yescharacteristic
34C43×#436C411yescharacteristic
35C43×#435C412yes—
36C43×#435C412yes—
37C43×#431C2211yescharacteristic
38C43×#431C2212yes—
39C4×M16×C43C2212yes—
40C2×C4×C8×C43C2211yescharacteristic
41C2×#10621877—22no—
42C22×C43⋊C8—22no—
43C4⋊(C43⋊C8)—22no—
44C4⋊(C43⋊C8)—22no—
45C4⋊(C43⋊C8)C2312yes—
46C4⋊(C43⋊C8)C2312yes—
47C4⋊(C43⋊C8)C2312yes—
48C4⋊(C43⋊C8)C2312yes—
49C22⋊(C43⋊C8)—22no—
50C22⋊(C43⋊C8)—22no—
51C22⋊(C43⋊C8)—22no—
52C22⋊(C43⋊C8)—22no—
53#13063236—22no—
54#13063236—22no—
55C4×C43⋊C8—22no—
56C4×C43⋊C8—22no—
57C2×#41×C43D411yescharacteristic
58C2×M16×C43C2×C412yes—
59C2×M16×C43C2×C412yes—
60C22×C8×C43C2×C411yescharacteristic
61C22×C8×C43C2×C411yescharacteristic
62C4×Q8×C43C2×C411yescharacteristic
63C4×Q8×C43Q811yescharacteristic
64C4×D4×C43C2×C412yes—
65C4×D4×C43C2×C411yescharacteristic
66C4×D4×C43Q812yes—
67C4×D4×C43Q811yescharacteristic
68#117×C43D412yes—
69#117×C43D411yescharacteristic
70C2×C42×C43C2312yes—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43C2×C412yes—
73C4⋊C8×C43C2×C412yes—
74C4⋊C8×C43C2×C411yescharacteristic
75C4⋊C8×C43C2×C411yescharacteristic
76C22⋊C8×C43C2×C412yes—
77C22⋊C8×C43C2×C412yes—
78C22⋊C8×C43C2×C412yes—
79#97×C43C2×C412yes—
80#97×C43C2×C412yes—
81C4×C8×C43C2×C411yescharacteristic
82C4×C8×C43C2×C411yescharacteristic
83C4×C8×C43C2311yescharacteristic
84C4×C8×C43C2311yescharacteristic
85C4×C8×C43C2312yes—
86#41×C43—42no—
87C2×Q8×C43C4⋊C411yescharacteristic
88C2×D4×C43C4⋊C412yes—
89C2×D4×C43C4⋊C411yescharacteristic
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C412yes—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×Q812yes—
95C22×C4×C43C2×Q811yescharacteristic
96M16×C43—24no—
97M16×C43—42no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C2×C8×C43C22×C411yescharacteristic
101C2×C8×C43C22×C411yescharacteristic
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C22×C412yes—
104C2×C8×C43C22×C412yes—
105C2×C8×C43C22×C411yescharacteristic
106C4⋊C4×C43C4⋊C412yes—
107C4⋊C4×C43C4⋊C411yescharacteristic
108C4⋊C4×C43C4⋊C412yes—
109C4⋊C4×C43C4⋊C411yescharacteristic
110C22⋊C4×C43C4⋊C412yes—
111C22⋊C4×C43C4⋊C412yes—
112C22⋊C4×C43C4⋊C412yes—
113C42×C43C22×C411yescharacteristic
114C42×C43C22×C412yes—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D412yes—
117C42×C43C2×Q812yes—
118C42×C43C2×Q811yescharacteristic
119C42×C43C2411yescharacteristic
120#10621877—44no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—44no—
126C23×C43C2×C4⋊C411yescharacteristic
127C23×C43C2×C4⋊C412yes—
128Q8×C43—41no—
129D4×C43—42no—
130D4×C43—41no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43C2×C4⋊C411yescharacteristic
141C2×C4×C43C2×C4⋊C412yes—
142C2×C4×C43C2×C4⋊C411yescharacteristic
143C2×C4×C43C2×C4⋊C412yes—
144C2×C4×C43C2×C4⋊C411yescharacteristic
145C2×C4×C43C2×C4⋊C412yes—
146C2×C4×C43C23×C411yescharacteristic
147C2×C4×C43C22×D411yescharacteristic
148C2×C4×C43C22×Q811yescharacteristic
149C8×C43—21no—
150C8×C43—22no—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—22no—
154C8×C43#13112yes—
155C43⋊C8—42no—
156C43⋊C8—42no—
157C43⋊C8—42no—
158C43⋊C8—42no—
159#17831—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—22no—
162C22×C43—22no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—22no—
166C22×C43C22×C4⋊C411yescharacteristic
167C4×C43—21no—
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—22no—
174C4×C43C2×#13111yescharacteristic
175C4×C43#56811yescharacteristic
176C4×C43#57512yes—
177#2965D4311yescharacteristic
178#2925—432no—
179#1574—432no—
180#1573—432no—
181#1572—432no—
182#1569—432no—
183#1568—431no—
184#1565—432no—
185#1564—431no—
186C2×C43—41no—
187C2×C43—42no—
188C2×C43#290611yescharacteristic
189C2×C43#291111yescharacteristic
190C2×C43#291611yescharacteristic
191C4×#41C2×D4311yescharacteristic
192#446Dic4311yescharacteristic
193#446Dic4311yescharacteristic
194#436Dic4311yescharacteristic
195#436Dic4311yescharacteristic
196#435Dic4312yes—
197#435Dic4312yes—
198#433—862no—
199#433—862no—
200#432—432no—
201#432—432no—
202#431—432no—
203#431—432no—
204#431C2×D4311yescharacteristic
205#431C2×D4312yes—
206#423—432no—
207C2×C4⋊C8—432no—
208#408—862no—
209#405—862no—
210C4×M16C2×D4312yes—
211C2×C4×C8C2×D4311yescharacteristic
212#335—432no—
213#335—432no—
214#335—432no—
215#335—432no—
216#334—431no—
217#334—431no—
218#334—432no—
219#334—431no—
220#334—431no—
221#334—432no—
222C43#1783111yescharacteristic, complemented, Sylow
223C2×#41D17211yescharacteristic
224C2×M16—862no—
225C2×M16C2×Dic4312yes—
226C2×M16C2×Dic4312yes—
227C22×C8—862no—
228C22×C8C2×Dic4311yescharacteristic
229C22×C8C2×Dic4311yescharacteristic
230C4×Q8Dic8611yescharacteristic
231C4×Q8C2×Dic4311yescharacteristic
232C4×D4Dic8611yescharacteristic
233C4×D4Dic8612yes—
234C4×D4C2×Dic4312yes—
235C4×D4C2×Dic4311yescharacteristic
236#117D17212yes—
237#117D17211yescharacteristic
238C2×C42C22×D4311yescharacteristic
239C2×C42C22×D4312yes—
240C4⋊C8—432no—
241C4⋊C8—432no—
242C4⋊C8—432no—
243C4⋊C8—432no—
244C4⋊C8—862no—
245C4⋊C8—862no—
246C4⋊C8C2×Dic4312yes—
247C4⋊C8C2×Dic4312yes—
248C4⋊C8C2×Dic4311yescharacteristic
249C4⋊C8C2×Dic4311yescharacteristic
250C22⋊C8—862no—
251C22⋊C8—862no—
252C22⋊C8—862no—
253C22⋊C8—862no—
254C22⋊C8C2×Dic4312yes—
255C22⋊C8C2×Dic4312yes—
256C22⋊C8C2×Dic4312yes—
257#97—862no—
258#97—862no—
259#97C2×Dic4312yes—
260#97C2×Dic4312yes—
261C4×C8—862no—
262C4×C8—862no—
263C4×C8C2×Dic4311yescharacteristic
264C4×C8C2×Dic4311yescharacteristic
265C4×C8C22×D4311yescharacteristic
266C4×C8C22×D4311yescharacteristic
267C4×C8C22×D4312yes—
268#41—42no—
269C2×Q8C4⋊Dic4311yescharacteristic
270C2×D4C4⋊Dic4312yes—
271C2×D4C4⋊Dic4311yescharacteristic
272C22×C4C2×Dic8611yescharacteristic
273C22×C4C2×Dic8612yes—
274C22×C4C2×D17211yescharacteristic
275C22×C4C2×D17212yes—
276C22×C4C22×Dic4311yescharacteristic
277C22×C4C22×Dic4312yes—
278M16—24no—
279M16—42no—
280M16—1724no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—862no—
284C2×C8—862no—
285C2×C8—862no—
286C2×C8—862no—
287C2×C8—1724no—
288C2×C8C22×Dic4311yescharacteristic
289C2×C8C22×Dic4311yescharacteristic
290C2×C8C22×Dic4311yescharacteristic
291C2×C8C22×Dic4312yes—
292C2×C8C22×Dic4312yes—
293C2×C8C22×Dic4311yescharacteristic
294C4⋊C4C4⋊Dic4312yes—
295C4⋊C4C4⋊Dic4311yescharacteristic
296C4⋊C4C4⋊Dic4312yes—
297C4⋊C4C4⋊Dic4311yescharacteristic
298C22⋊C4C4⋊Dic4312yes—
299C22⋊C4C4⋊Dic4312yes—
300C22⋊C4C4⋊Dic4312yes—
301C42C2×Dic8611yescharacteristic
302C42C2×Dic8612yes—
303C42C2×D17211yescharacteristic
304C42C2×D17212yes—
305C42C22×Dic4311yescharacteristic
306C42C22×Dic4312yes—
307C42C23×D4311yescharacteristic
308C23C2×C4⋊Dic4311yescharacteristic
309C23C2×C4⋊Dic4312yes—
310Q8—41no—
311D4—42no—
312D4—41no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4C2×C4⋊Dic4311yescharacteristic
323C2×C4C2×C4⋊Dic4312yes—
324C2×C4C2×C4⋊Dic4311yescharacteristic
325C2×C4C2×C4⋊Dic4312yes—
326C2×C4C2×C4⋊Dic4311yescharacteristic
327C2×C4C2×C4⋊Dic4312yes—
328C2×C4C23×Dic4311yescharacteristic
329C2×C4C22×D17211yescharacteristic
330C2×C4C22×Dic8611yescharacteristic
331C8—21no—
332C8—22no—
333C8—21no—
334C8—21no—
335C8—22no—
336C8—1722no—
337C8—1722no—
338C8—1722no—
339C8—1722no—
340C8#1306333212yes—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—22no—
347C22C22×C4⋊Dic4311yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—22no—
355C4C2×#1306333211yescharacteristic
356C4#1458366611yescharacteristic
357C4#1458369912yes—
358C2—42no—
359C2—41no—
360C2#1914316311yescharacteristic
361C2#1914318511yescharacteristic
362C2#1914320611yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2965C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#41×C43D4
cosocleC42×C43C24
hypercenter#2965D43
hypocenterC43#17831
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #19133384C2semidirect
3. #19133380C2semidirect
4. #19133375C2semidirect
5. #19133362C2semidirect
6. #19133358C2semidirect
7. #19133347C2semidirect
8. #19133343C2semidirect
222. C43#17831semidirect

Maximal subgroups

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

subgroupindex
#191432612
#191333842
#191333802
#191333752
#191333622
#191333582
#191333472
#191333432
C43×#29652
#1783143