Finite Group Databasebeta

← #25102046

Subgroups — #25102046

Order 11008.

688 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135210C212yesmaximal
2#19135203C212yesmaximal
3#19135161C212yesmaximal, complemented
4#19135154C212yesmaximal, complemented
5#19134452C211yesmaximal, characteristic, complemented
6#19134452C211yesmaximal, characteristic, complemented
7#19134361C211yesmaximal, characteristic
8#19134361C211yesmaximal, characteristic
9#19134341C211yesmaximal, characteristic, complemented
10C4×#13063236C211yesmaximal, characteristic, complemented
11C43×#2298C211yesmaximal, characteristic
12C2×C4⋊(C43⋊C8)C2212yes—
13C2×C4⋊(C43⋊C8)C2212yes—
14C2×C22⋊(C43⋊C8)C2212yes—
15C2×C22⋊(C43⋊C8)C2212yes—
16C2×#13063236C2211yescharacteristic
17C2×#13063236C2211yescharacteristic
18C2×#13063236C2212yes—
19C2×C4×C43⋊C8C2212yes—
20C2×C4×C43⋊C8C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582654C2212yes—
23#14582654C2212yes—
24#14582654C2212yes—
25#14582654C2212yes—
26#14582654C2212yes—
27#14582654C2212yes—
28C2×#117×C43C2211yescharacteristic
29C43×#388C412yes—
30C43×#388C412yes—
31C43×#387C412yes—
32C43×#387C412yes—
33C4×C4⋊C4×C43C2211yescharacteristic
34C4×C4⋊C4×C43C2211yescharacteristic
35C4×C22⋊C4×C43C2211yescharacteristic
36C4×C22⋊C4×C43C2211yescharacteristic
37C43×#376C2211yescharacteristic
38C43×C43C2211yescharacteristic
39C22×C43⋊C8C2312yes—
40C22×C43⋊C8C2312yes—
41C22×C43⋊C8C2312yes—
42C22×C43⋊C8C2312yes—
43C4⋊(C43⋊C8)—24no—
44C4⋊(C43⋊C8)—24no—
45C22⋊(C43⋊C8)—24no—
46C22⋊(C43⋊C8)—24no—
47#13063236—22no—
48#13063236—22no—
49#13063236—24no—
50C4×C43⋊C8—22no—
51C4×C43⋊C8—22no—
52C4×C43⋊C8—24no—
53C23×C4×C43C2311yescharacteristic
54#117×C43—22no—
55#117×C43—22no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C412yes—
59C2×C4⋊C4×C43C2×C412yes—
60C2×C22⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43C2×C412yes—
63C2×C22⋊C4×C43C2×C412yes—
64C2×C42×C43C2×C412yes—
65C2×C42×C43C2×C412yes—
66C2×C42×C43C2311yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C2×C42×C43C2311yescharacteristic
69C2×C42×C43C2311yescharacteristic
70C2×C42×C43C2311yescharacteristic
71C2×C42×C43C2311yescharacteristic
72#95×C43C2×C412yes—
73#95×C43C2×C412yes—
74#95×C43C2×C412yes—
75#95×C43C2×C412yes—
76#95×C43C2×C412yes—
77#95×C43C2×C412yes—
78C24×C43C22×C411yescharacteristic
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43C22×C412yes—
84C22×C4×C43C22×C412yes—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C22×C412yes—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C412yes—
92C22×C4×C43C2411yescharacteristic
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—42no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—42no—
101C42×C43—24no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—22no—
105C42×C43—22no—
106C42×C43—22no—
107C42×C43—22no—
108C42×C43—42no—
109C42×C43#4112yes—
110C42×C43#4112yes—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8#4114yes—
122C2×C43⋊C8#4114yes—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43C23×C411yescharacteristic
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43#11712yes—
152C2×C4×C43#11712yes—
153C2×C4×C43#13114yes—
154C2×C4×C43C2×#4112yes—
155C2×C4×C43C2×#4112yes—
156C2×C4×C43C2×#4111yescharacteristic
157C2×C4×C43C2×#4111yescharacteristic
158C43⋊C8—24no—
159C43⋊C8—24no—
160C43⋊C8—42no—
161C43⋊C8—42no—
162#21434—431nomaximal, Sylow
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43C2×#11711yescharacteristic
169C22×C43C4×#4111yescharacteristic
170C22×C43C4×#4111yescharacteristic
171C22×C43C2×#13112yes—
172C22×C43#56812yes—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—24no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—42no—
179C4×C43—42no—
180C4×C43—42no—
181C4×C43—41no—
182C4×C43#52912yes—
183C4×C43#52912yes—
184#2298D4311yescharacteristic
185#1924—432no—
186#1923—432no—
187#1917—432no—
188#1916—432no—
189#1768—431no—
190#1768—431no—
191#1750—431no—
192#1750—431no—
193#1744—431no—
194C4×#97—431no—
195C2×C43—81no—
196C2×C43#229811yescharacteristic
197C2×C43#292211yescharacteristic
198C2×C43#292311yescharacteristic
199C2×C43#296812yes—
200C2×C43#296912yes—
201C2×#117C2×D4311yescharacteristic
202C2×C4⋊C8—432no—
203C2×C4⋊C8—432no—
204C2×C22⋊C8—432no—
205C2×C22⋊C8—432no—
206C2×#97—432no—
207C2×#97—431no—
208C2×#97—431no—
209C2×C4×C8—432no—
210C2×C4×C8—431no—
211C2×C4×C8—431no—
212#388Dic4312yes—
213#388Dic4312yes—
214#387Dic4312yes—
215#387Dic4312yes—
216C4×C4⋊C4C2×D4311yescharacteristic
217C4×C4⋊C4C2×D4311yescharacteristic
218C4×C22⋊C4C2×D4311yescharacteristic
219C4×C22⋊C4C2×D4311yescharacteristic
220#376C2×D4311yescharacteristic
221C43C2×D4311yescharacteristic
222#336—432no—
223#336—432no—
224#336—432no—
225#336—432no—
226#336—432no—
227#336—432no—
228C43#2143411yescharacteristic, complemented, Sylow
229C23×C4C22×D4311yescharacteristic
230C22×C8—432no—
231C22×C8—432no—
232C22×C8—432no—
233C22×C8—432no—
234#117—22no—
235#117—22no—
236C2×C4⋊C4C2×Dic4311yescharacteristic
237C2×C4⋊C4C2×Dic4311yescharacteristic
238C2×C4⋊C4C2×Dic4312yes—
239C2×C4⋊C4C2×Dic4312yes—
240C2×C22⋊C4C2×Dic4311yescharacteristic
241C2×C22⋊C4C2×Dic4311yescharacteristic
242C2×C22⋊C4C2×Dic4312yes—
243C2×C22⋊C4C2×Dic4312yes—
244C2×C42C2×Dic4312yes—
245C2×C42C2×Dic4312yes—
246C2×C42C22×D4311yescharacteristic
247C2×C42C22×D4311yescharacteristic
248C2×C42C22×D4311yescharacteristic
249C2×C42C22×D4311yescharacteristic
250C2×C42C22×D4311yescharacteristic
251C2×C42C22×D4311yescharacteristic
252C4⋊C8—864no—
253C4⋊C8—864no—
254C22⋊C8—864no—
255C22⋊C8—864no—
256#97—864no—
257#97—862no—
258#97—862no—
259C4×C8—864no—
260C4×C8—862no—
261C4×C8—862no—
262#95C2×Dic4312yes—
263#95C2×Dic4312yes—
264#95C2×Dic4312yes—
265#95C2×Dic4312yes—
266#95C2×Dic4312yes—
267#95C2×Dic4312yes—
268C24C22×Dic4311yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4C22×Dic4312yes—
274C22×C4C22×Dic4312yes—
275C22×C4C22×Dic4311yescharacteristic
276C22×C4C22×Dic4312yes—
277C22×C4C22×Dic4311yescharacteristic
278C22×C4C22×Dic4311yescharacteristic
279C22×C4C22×Dic4311yescharacteristic
280C22×C4C22×Dic4311yescharacteristic
281C22×C4C22×Dic4312yes—
282C22×C4C23×D4311yescharacteristic
283C2×C8—434no—
284C2×C8—434no—
285C2×C8—862no—
286C2×C8—862no—
287C2×C8—862no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8—862no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8—862no—
294C2×C8—862no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—24no—
298C4⋊C4—42no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—24no—
302C22⋊C4—42no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—21no—
309C42—21no—
310C42—42no—
311C42#1062189812yes—
312C42#1062189812yes—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—22no—
317C23—22no—
318C23C23×Dic4311yescharacteristic
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4#1306328412yes—
342C2×C4#1306328412yes—
343C2×C4#1306333214yes—
344C2×C4#41×D4312yes—
345C2×C4#41×D4312yes—
346C2×C4C2×#1062189811yescharacteristic
347C2×C4C2×#1062189811yescharacteristic
348C8—864no—
349C8—864no—
350C8—1722no—
351C8—1722no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—42no—
356C22—42no—
357C22C2×#1306328411yescharacteristic
358C22#41×Dic4311yescharacteristic
359C22#41×Dic4311yescharacteristic
360C22C2×#1306333212yes—
361C22#1458366612yes—
362C4—22no—
363C4—22no—
364C4—24no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—42no—
369C4—42no—
370C4—42no—
371C4#1458342712yes—
372C4#1458342712yes—
373C2—81no—
374C2#1913709311yescharacteristic
375C2#1914323911yescharacteristic
376C2#1914324611yescharacteristic
377C2#1914359112yes—
378C2#1914360012yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#2298C2
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenter#2298D43
hypocenterC43#21434
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
3. #19135161C2semidirect
4. #19135154C2semidirect
5. #19134452C2semidirect
6. #19134452C2semidirect
9. #19134341C2semidirect
10. C4×#13063236C2semidirect
228. C43#21434semidirect

Maximal subgroups

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

subgroupindex
#191352102
#191352032
#191351612
#191351542
#191344522
#191343612
#191343412
C4×#130632362
C43×#22982
#2143443