Finite Group Databasebeta

← #24996646

Subgroups — #24996646

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134575C211yesmaximal, characteristic
2C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic
3#19132438C212yesmaximal
4#19132438C212yesmaximal
5C2×C43×#387C211yesmaximal, characteristic
6C2×C4⋊(C43⋊C8)—21no—
7C2×C22⋊(C43⋊C8)C2212yes—
8C2×C22⋊(C43⋊C8)C2212yes—
9C2×C4×C43⋊C8—21no—
10#14582654—21no—
11#14582654—21no—
12C22×C4⋊C4×C43C411yescharacteristic
13C22×C4⋊C4×C43C411yescharacteristic
14C22×C42×C43C2211yescharacteristic
15C43×#387—21no—
16C43×#387—21no—
17C43×#387—21no—
18C43×#387—21no—
19C2×#95×C43C411yescharacteristic
20C2×#95×C43C411yescharacteristic
21C2×#95×C43C2211yescharacteristic
22C2×#95×C43C2211yescharacteristic
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C4⋊(C43⋊C8)—42no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)—24no—
28C22⋊(C43⋊C8)Q814yes—
29C4×C43⋊C8—42no—
30C23×C4×C43C2×C411yescharacteristic
31C23×C4×C43C2×C411yescharacteristic
32C23×C4×C43C2×C411yescharacteristic
33C23×C4×C43C2×C411yescharacteristic
34C23×C4×C43C2×C411yescharacteristic
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43C2311yescharacteristic
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—42no—
43C2×C4⋊C4×C43C814yescomplemented
44C2×C42×C43—42no—
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57C24×C43C22×C411yescharacteristic
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C2×C812yes—
86C22×C4×C43C2×C812yes—
87C22×C4×C43C2×C812yes—
88C22×C4×C43M1612yes—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×Q812yes—
92C22×C4×C43#4112yes—
93C4⋊C4×C43—24no—
94C4⋊C4×C43—24no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—42no—
97C42×C43—22no—
98C42×C43—22no—
99C42×C43—41no—
100C42×C43—41no—
101C2×C43⋊C8—24no—
102C2×C43⋊C8—42no—
103C2×C43⋊C8—42no—
104C2×C43⋊C8—42no—
105C2×C43⋊C8—42no—
106C2×C43⋊C8—42no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43C2×C22⋊C411yescharacteristic
112C23×C43C4×Q812yes—
113C23×C43C22×C811yescharacteristic
114C23×C43C2×M1611yescharacteristic
115C23×C43#13112yes—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—44no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—82no—
151C2×C4×C43—82no—
152C2×C4×C43C22⋊C812yes—
153C2×C4×C43C22⋊C812yes—
154C2×C4×C43#9912yes—
155C2×C4×C43C22⋊Q812yes—
156C2×C4×C43#12411yescharacteristic
157C2×C4×C43C4⋊Q811yescharacteristic
158C43⋊C8—44no—
159C43⋊C8—82no—
160#9880—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—22no—
169C22×C43#39111yescharacteristic
170C22×C43C2×C22⋊C811yescharacteristic
171C22×C43#40811yescharacteristic
172C22×C43C2×#9911yescharacteristic
173C22×C43#41011yescharacteristic
174C22×C43#41311yescharacteristic
175C22×C43#41311yescharacteristic
176C22×C43C8×Q812yes—
177C22×C43#44612yes—
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—42no—
185C4×C43—42no—
186C4×C43—41no—
187C4×C43—81no—
188C4×C43—81no—
189C2×#387D4311yescharacteristic
190#1797—431no—
191C4×C22⋊C8—431no—
192#1280—432no—
193#1280—432no—
194C2×C43—22no—
195C2×C43—22no—
196C2×C43#145811yescharacteristic
197C2×C43#145911yescharacteristic
198C2×C43#146811yescharacteristic
199C2×C43#147311yescharacteristic
200C2×C43#198411yescharacteristic
201C2×C43#199611yescharacteristic
202C2×C43#199811yescharacteristic
203C22×C4⋊C4Dic4311yescharacteristic
204C22×C4⋊C4Dic4311yescharacteristic
205C22×C42C2×D4311yescharacteristic
206C2×C4⋊C8—861no—
207C2×C22⋊C8—432no—
208C2×C22⋊C8—432no—
209C2×C4×C8—861no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214C2×#95Dic4311yescharacteristic
215C2×#95Dic4311yescharacteristic
216C2×#95C2×D4311yescharacteristic
217C2×#95C2×D4311yescharacteristic
218#336—861no—
219#336—861no—
220C43#988011yescharacteristic, complemented, Sylow
221C23×C4C2×Dic4311yescharacteristic
222C23×C4C2×Dic4311yescharacteristic
223C23×C4C2×Dic4311yescharacteristic
224C23×C4C2×Dic4311yescharacteristic
225C23×C4C2×Dic4311yescharacteristic
226C23×C4C2×Dic4311yescharacteristic
227C23×C4C22×D4311yescharacteristic
228C22×C8—862no—
229C22×C8—862no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4C43⋊C814yescomplemented
237C2×C42—42no—
238C2×C42C22⋊D4311yescharacteristic
239C2×C42C22⋊D4311yescharacteristic
240C2×C42C22⋊D4311yescharacteristic
241C2×C42C22⋊D4311yescharacteristic
242C4⋊C8—1722no—
243C22⋊C8—434no—
244C22⋊C8—862no—
245C22⋊C8—864no—
246C4×C8—1722no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24C22×Dic4311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C2×C43⋊C812yes—
280C22×C4C2×C43⋊C812yes—
281C22×C4C2×C43⋊C812yes—
282C22×C4#1062187712yes—
283C22×C4C22⋊Dic4311yescharacteristic
284C22×C4C22⋊Dic4311yescharacteristic
285C22×C4C22⋊Dic4311yescharacteristic
286C22×C4C22⋊Dic4311yescharacteristic
287C22×C4Q8×D4312yes—
288C22×C4#1062190212yes—
289C22×C4C2×C22⋊D4311yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291C2×C8—864no—
292C2×C8—1722no—
293C2×C8—1722no—
294C2×C8—1722no—
295C2×C8—1722no—
296C2×C8—1722no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C22⋊Dic4311yescharacteristic
310C23Q8×Dic4312yes—
311C23C22×C43⋊C811yescharacteristic
312C23C2×#1062187711yescharacteristic
313C23#1306333212yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4C22⋊(C43⋊C8)12yes—
351C2×C4C22⋊(C43⋊C8)12yes—
352C2×C4#1306324012yes—
353C2×C4#1306330112yes—
354C2×C4#1306331411yescharacteristic
355C2×C4#1306332311yescharacteristic
356C8—3442no—
357C8—1724no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22#1458280611yescharacteristic
367C22C2×C22⋊(C43⋊C8)11yescharacteristic
368C22#1458286611yescharacteristic
369C22C2×#1306324011yescharacteristic
370C22#1458287311yescharacteristic
371C22#1458288311yescharacteristic
372C22#1458288311yescharacteristic
373C22Q8×C43⋊C812yes—
374C22#1458303012yes—
375C4—22no—
376C4—21no—
377C4—22no—
378C4—21no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—42no—
383C4—42no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2#1913290911yescharacteristic
389C2#1913291311yescharacteristic
390C2#1913294311yescharacteristic
391C2#1913296411yescharacteristic
392C2#1913553211yescharacteristic
393C2#1913558111yescharacteristic
394C2#1913558911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#387C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenterC2×#387D43
hypocenterC43#9880
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
43. C2×C4⋊C4×C43C8semidirect
220. C43#9880semidirect
236. C2×C4⋊C4C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191345752
C4×C22⋊(C43⋊C8)2
#191324382
C2×C43×#3872
#988043