Finite Group Databasebeta

← #24990590

Subgroups — #24990590

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134782C212yesmaximal
2C2×#14582625C211yesmaximal, characteristic
3#19132848C211yesmaximal, characteristic
4#19132473C212yesmaximal
5C43×#2316C211yesmaximal, characteristic
6C22×C4⋊Dic43C2211yescharacteristic
7C2×#13063258—22no—
8C2×C22⋊(C43⋊C8)C2212yes—
9C2×C43⋊#95—21no—
10C2×C43⋊#95—21no—
11C2×C43⋊#95C2211yescharacteristic
12#14582661—22no—
13#14582625C414yescomplemented
14C2×#117×C43—21no—
15C22×C4⋊C4×C43C2211yescharacteristic
16C43×#389—22no—
17C43×#389—22no—
18C43×#380—21no—
19C43×#380C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C22×C43⋊C8—22no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—42no—
25#13063258—44no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)C2×C414yes—
28C43⋊#95—22no—
29C43⋊#95—42no—
30C43⋊#95—42no—
31C23×C4×C43D411yescharacteristic
32C23×C4×C43D411yescharacteristic
33C23×C4×C43C2311yescharacteristic
34#117×C43—42no—
35#117×C43—42no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43C2×C412yes—
43C2×C4⋊C4×C43D412yes—
44C2×C4⋊C4×C43D412yes—
45C2×C4⋊C4×C43Q812yes—
46C2×C22⋊C4×C43—22no—
47C2×C42×C43—22no—
48#95×C43—22no—
49#95×C43—22no—
50C24×C43C2×D411yescharacteristic
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C4⋊C412yes—
64C22×C4×C43C4⋊C412yes—
65C22×C4×C43D812yes—
66C22×C4×C43Q1612yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D412yes—
69C22×C4×C43C2×Q811yescharacteristic
70C22×C4×C43#4112yes—
71C22×Dic43—22no—
72C22×Dic43—22no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—41no—
84C22×Dic43—41no—
85C4⋊C4×C43—24no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—42no—
89C4⋊C4×C43—42no—
90C4⋊C4×C43—42no—
91C4⋊C4×C43—81no—
92C4⋊C4×C43—81no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—42no—
95C42×C43—44no—
96C4⋊Dic43—24no—
97C4⋊Dic43—42no—
98C2×C43⋊C8—24no—
99C2×C43⋊C8—42no—
100C2×C43⋊C8—42no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43C2×C4⋊C411yescharacteristic
106C23×C43#12011yescharacteristic
107C23×C43#12311yescharacteristic
108C23×C43C2×D811yescharacteristic
109C23×C43C2×Q1611yescharacteristic
110C23×C43AGL(1,ℤ/8)11yescharacteristic
111C23×C43#13711yescharacteristic
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—81no—
134C2×C4×C43#10714yescomplemented
135C2×C4×C43C4×D412yes—
136C2×C4×C43C22⋊Q812yes—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C43⋊C8—44no—
152#8856—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#38511yescharacteristic
166C22×C43C2×#10711yescharacteristic
167C22×C43#42811yescharacteristic
168C22×C43#44711yescharacteristic
169C22×C43#45111yescharacteristic
170C22×C43#45411yescharacteristic
171C22×C43#45611yescharacteristic
172C22×C43B(4,𝔽2)11yescharacteristic
173C22×C43#45811yescharacteristic
174C22×C43#48011yescharacteristic
175C22×C43#48411yescharacteristic
176C4×C43—24no—
177C4×C43—22no—
178C4×C43—22no—
179C4×C43—42no—
180C4×C43—82no—
181C4×C43—82no—
182Dic43—82no—
183Dic43—82no—
184#2316D4311yescharacteristic
185#1852—432no—
186C2×#324—431no—
187#1441—431no—
188#1294—432no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43#159811yescharacteristic
194C2×C43#160511yescharacteristic
195C2×C43#161011yescharacteristic
196C2×C43#161711yescharacteristic
197C2×C43#185211yescharacteristic
198C2×C43#185711yescharacteristic
199C2×C43#186711yescharacteristic
200C2×#117—21no—
201C22×C4⋊C4—431no—
202C22×C4⋊C4C2×D4311yescharacteristic
203C2×#107—862no—
204C2×C22⋊C8—432no—
205#389—22no—
206#389—22no—
207#380—21no—
208#380C2×D4312yes—
209C2×#95—431no—
210C2×#95—861no—
211C2×#95—861no—
212#340—862no—
213#324—434no—
214C43#885611yescharacteristic, complemented, Sylow
215C23×C4—861no—
216C23×C4—861no—
217C23×C4C22⋊D4311yescharacteristic
218C23×C4C22⋊D4311yescharacteristic
219C23×C4C22×D4311yescharacteristic
220C22×C8—862no—
221#117—42no—
222#117—42no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—1722no—
231C2×C4⋊C4Dic8612yes—
232C2×C4⋊C4C4×D4312yes—
233C2×C4⋊C4C22⋊D4312yes—
234C2×C4⋊C4C22⋊D4312yes—
235C2×C22⋊C4—22no—
236C2×C42—22no—
237#107—1724no—
238C22⋊C8—434no—
239C22⋊C8—862no—
240#95—22no—
241#95—22no—
242#95—862no—
243#95—1722no—
244#95—1722no—
245C24C2×C22⋊D4311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—862no—
259C22×C4—862no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4—1721no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4—1721no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4Dic43⋊C412yes—
273C22×C4Dic43⋊C412yes—
274C22×C4#1062188212yes—
275C22×C4#1062188512yes—
276C22×C4C2×Dic8611yescharacteristic
277C22×C4C2×C4×D4311yescharacteristic
278C22×C4#1062189812yes—
279C22×C4C2×C22⋊D4312yes—
280C2×C8—864no—
281C2×C8—1722no—
282C2×C8—1722no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—864no—
292C4⋊C4—1722no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C42—44no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C2×Dic43⋊C411yescharacteristic
301C23#1306329411yescharacteristic
302C23#1306330811yescharacteristic
303C23C2×#1062188211yescharacteristic
304C23C2×#1062188511yescharacteristic
305C23#1306335111yescharacteristic
306C23#1306335611yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4#1306325814yescomplemented
344C2×C4C4×C22⋊D4312yes—
345C2×C4#1306330412yes—
346C8—1724no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1458277211yescharacteristic
360C22C2×#1306325811yescharacteristic
361C22#1458293911yescharacteristic
362C22#1458303311yescharacteristic
363C22#1458305511yescharacteristic
364C22#1458307211yescharacteristic
365C22#1458308211yescharacteristic
366C22#1458308611yescharacteristic
367C22#1458308911yescharacteristic
368C22#1458321211yescharacteristic
369C22#1458323411yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—3442no—
377C4—3442no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1913353011yescharacteristic
383C2#1913356911yescharacteristic
384C2#1913359811yescharacteristic
385C2#1913363711yescharacteristic
386C2#1913478311yescharacteristic
387C2#1913481011yescharacteristic
388C2#1913487611yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2316C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2316D43
hypocenterC43#8856
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
13. #14582625C4semidirect
134. C2×C4×C43#107semidirect
214. C43#8856semidirect
343. C2×C4#13063258semidirect

Maximal subgroups

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

subgroupindex
#191347822
C2×#145826252
#191328482
#191324732
C43×#23162
#885643