Finite Group Databasebeta

← #24992609

Subgroups — #24992609

Order 11008.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143157C211yesmaximal, characteristic
2#19140419C211yesmaximal, characteristic
3#19133281C211yesmaximal, characteristic, complemented
4#19133279C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132453C211yesmaximal, characteristic, complemented
7C43×#1286C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063325C2211yescharacteristic
10C2×#13063282C2211yescharacteristic
11#14582952C2211yescharacteristic
12#14582924—22no—
13#14582924—22no—
14#14582923C2211yescharacteristic
15#14582922—21no—
16#14582839C412yes—
17#14582836C412yes—
18#14582820—21no—
19#14582812—21no—
20#14582798—21no—
21#14582756—21no—
22#14582646—22no—
23#14582644—22no—
24#14582624—21no—
25#14582622—21no—
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C43×#382C2211yescharacteristic
29C22×Dic86—21no—
30C22×C4×D43D411yescharacteristic
31C2×#10621877—21no—
32C2×#10621872—22no—
33M16×D43—42no—
34M16×D43—42no—
35C2×C8×D43—22no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325—21no—
40#13063282—21no—
41#13063282—21no—
42#13063282—21no—
43#13063282—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43C2×C412yes—
47C2×Dic43⋊C4C2×C411yescharacteristic
48C2×Dic43⋊C4D411yescharacteristic
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4C2×C411yescharacteristic
51C2×(C2×D43)⋊C4D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)D412yes—
56Dic43⋊C8—24no—
57C22⋊(C43⋊C8)—21no—
58C4×C43⋊C8—21no—
59C43⋊#95—22no—
60C43⋊#95—22no—
61C2×M16×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43D412yes—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69#95×C43—21no—
70#95×C43C2×C412yes—
71C23×D43C22⋊C411yescharacteristic
72C22×C4×C43—22no—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—22no—
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43SD1612yes—
85C2×C4×D43Q1612yes—
86C2×Dic86—41no—
87C2×Dic86—41no—
88C2×Dic86—82no—
89M16×C43—41no—
90M16×C43—41no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43#4111yescharacteristic
98C42×C43#4111yescharacteristic
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—82no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—82no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113C4×Dic43—21no—
114C4×Dic43—21no—
115#10621877—41no—
116#10621877—41no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—41no—
119#10621872—44no—
120C8×D43—44no—
121C23×C43C2×C22⋊C411yescharacteristic
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43#10312yes—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43C2×Q1611yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43#10312yes—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—22no—
156Dic86—82no—
157Dic86—82no—
158C8×C43—42no—
159C8×C43—81no—
160C43⋊C8—42no—
161C43⋊C8—81no—
162#9193—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#38611yescharacteristic
166C22×C43C2×#10311yescharacteristic
167C22×C43#41711yescharacteristic
168C2×D43—22no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—42no—
172C2×D43—81no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—82no—
178C4×C43#45011yescharacteristic
179C4×C43#45111yescharacteristic
180C4×C43#48311yescharacteristic
181C4×C43#48411yescharacteristic
182Dic43—22no—
183Dic43—41no—
184Dic43—41no—
185Dic43—82no—
186#2905—431no—
187#2628—431no—
188#1549—431no—
189#1549—431no—
190#1458—431no—
191#1286—431no—
192#1286D4311yescharacteristic, complemented
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#187211yescharacteristic
196C2×C43#191011yescharacteristic
197C2×C43#191511yescharacteristic
198D43—42no—
199C22×M16—861no—
200C2×C4⋊Q8—431no—
201C2×#117—431no—
202#431—431no—
203#431C2×D4311yescharacteristic
204#424—862no—
205#424—862no—
206#423—431no—
207#423—861no—
208#423C2×D4311yescharacteristic
209#400—432no—
210#399—432no—
211#395—861no—
212#393—861no—
213#389—861no—
214#382C2×D4311yescharacteristic
215#380—861no—
216#332—862no—
217#332—862no—
218#324—861no—
219#323—861no—
220C43#919311yescharacteristic, complemented, Sylow
221C22×Q8—861no—
222C23×C4—431no—
223C2×M16—21no—
224C2×M16—862no—
225C2×M16—861no—
226C2×M16—1722no—
227C2×M16—1722no—
228C22×C8—862no—
229C4⋊Q8—861no—
230C4⋊Q8—861no—
231C4⋊Q8—861no—
232C4⋊Q8—861no—
233#117—861no—
234#117—861no—
235#117—861no—
236#117—861no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—862no—
242C2×C4⋊C4—861no—
243C2×C22⋊C4—431no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4—862no—
246C2×C42—431no—
247C2×C42C22×D4311yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—432no—
251C4⋊C8—864no—
252C4⋊C8—861no—
253C4⋊C8—861no—
254C4⋊C8D17212yes—
255C22⋊C8—21no—
256C22⋊C8—861no—
257C4×C8—21no—
258C4×C8—861no—
259#95—21no—
260#95—862no—
261#95—862no—
262#95C4×D4312yes—
263C24—431no—
264C2×Q8—3442no—
265C2×Q8—1721no—
266C2×Q8—1721no—
267C22×C4—22no—
268C22×C4—431no—
269C22×C4—432no—
270C22×C4—432no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—862no—
278C22×C4C2×C4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281M16—41no—
282M16—41no—
283M16—1724no—
284M16—1721no—
285M16—1721no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—862no—
289C2×C8—1724no—
290C2×C8—1721no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—862no—
298C4⋊C4—862no—
299C4⋊C4—3442no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—3442no—
307C42—861no—
308C42—861no—
309C42C2×D17211yescharacteristic
310C42#1062189811yescharacteristic
311C42D4×D4311yescharacteristic
312C42#1062190211yescharacteristic
313C23—432no—
314C23—861no—
315C23—861no—
316C23—1721no—
317C23—1721no—
318C23C22⋊C4×D4311yescharacteristic
319Q8—3442no—
320Q8—3442no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—432no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4#1306328711yescharacteristic
341C2×C4C4×D17211yescharacteristic
342C2×C4#1306329511yescharacteristic
343C2×C4#1306329811yescharacteristic
344C2×C4#1306330011yescharacteristic
345C2×C4#1306331011yescharacteristic
346C2×C4SD16×D4311yescharacteristic
347C2×C4Q16×D4311yescharacteristic
348C2×C4#1306334911yescharacteristic
349C2×C4#1306335411yescharacteristic
350C8—42no—
351C8—81no—
352C8—3441no—
353C8—1722no—
354C22—21no—
355C22—21no—
356C22—862no—
357C22—3441no—
358C22—1722no—
359C22—1721no—
360C22—1721no—
361C22#1458277711yescharacteristic
362C22#103×D4311yescharacteristic
363C22#1458289711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—862no—
370C4—3442no—
371C4—1721no—
372C4—1721no—
373C4#1458305111yescharacteristic
374C4#1458305611yescharacteristic
375C4#1458323111yescharacteristic
376C4#1458323611yescharacteristic
377C2—21no—
378C2—21no—
379C2—1722no—
380C2#1913490111yescharacteristic
381C2#1913512111yescharacteristic
382C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1286C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1286D43
hypocenterC43#9193
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
3. #19133281C2semidirect
4. #19133279C2semidirect
6. #19132453C2semidirect
7. C43×#1286C2semidirect
192. #1286D43semidirect
220. C43#9193semidirect

Maximal subgroups

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

subgroupindex
#191431572
#191404192
#191332812
#191332792
#191329072
#191324532
C43×#12862
#919343