Finite Group Databasebeta

← #24996696

Subgroups — #24996696

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142980C211yesmaximal, characteristic
2#19134449C211yesmaximal, characteristic
3#97×Dic43C211yesmaximal, characteristic
4#19132477C211yesmaximal, characteristic
5#19132477C211yesmaximal, characteristic
6#19132476C211yesmaximal, characteristic
7C43×#1295C211yesmaximal, characteristic
8C2×Dic43⋊C8—21no—
9C2×#13063236C2211yescharacteristic
10C2×#13063236C2211yescharacteristic
11C2×#13063235—21no—
12C2×C8×Dic43—21no—
13#14582798C411yescharacteristic
14#14582798C411yescharacteristic
15#14582795C411yescharacteristic
16#14582795C411yescharacteristic
17#14582786—21no—
18#14582786—21no—
19#14582782—21no—
20#14582782—21no—
21#14582765C2211yescharacteristic
22C42×Dic43C2211yescharacteristic
23#14582653—21no—
24C2×#97×C43C2211yescharacteristic
25C2×#97×C43C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43D411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41Dic43⋊C8—24no—
42#13063236—21no—
43#13063236—21no—
44#13063236—21no—
45#13063236Q812yes—
46#13063235—24no—
47C8×Dic43—24no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#97×C43—21no—
60#97×C43—21no—
61#97×C43—21no—
62#97×C43Q812yes—
63#95×C43—21no—
64#95×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×C8×C43—22no—
77C2×C8×C43—22no—
78C2×C8×C43—22no—
79C2×C8×C43—22no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C42×C43C2×Q811yescharacteristic
85C42×C43C2×Q811yescharacteristic
86C42×C43#4111yescharacteristic
87C42×C43#4111yescharacteristic
88C4⋊Dic43—42no—
89C4⋊Dic43—42no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94C4×Dic43—22no—
95C4×Dic43—22no—
96C4×Dic43—22no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43C4×Q811yescharacteristic
120C2×C4×C43C4×Q811yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C2×C4×C43C22⋊Q811yescharacteristic
123C2×C4×C43#12411yescharacteristic
124C2×C4×C43C4⋊Q811yescharacteristic
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43#10412yes—
141C2×Dic43#10412yes—
142C2×Dic43#10412yes—
143C8×C43—24no—
144C8×C43—42no—
145C43⋊C8—24no—
146C43⋊C8—42no—
147#9892—431nomaximal, Sylow
148C22×C43#39111yescharacteristic
149C22×C43#41311yescharacteristic
150C22×C43#41311yescharacteristic
151C22×C43C2×#10411yescharacteristic
152C22×C43C2×#10411yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C22×C43#42111yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—81no—
162C4×C43—81no—
163Dic43—22no—
164Dic43—22no—
165Dic43—22no—
166Dic43—41no—
167Dic43—81no—
168Dic43—81no—
169#2864—431no—
170#1767—431no—
171C4×#97—431no—
172#1295—431no—
173#1295—431no—
174#1295—431no—
175#1295D4311yescharacteristic
176C2×C43#152411yescharacteristic
177C2×C43#152411yescharacteristic
178C2×C43#152911yescharacteristic
179C2×C43#153211yescharacteristic
180C2×C43#198611yescharacteristic
181C2×C43#199411yescharacteristic
182C2×C43#199811yescharacteristic
183C2×C4⋊C8—861no—
184C2×#97—431no—
185C2×#97—431no—
186C2×#97—861no—
187C2×#97C2×D4311yescharacteristic
188C2×#97C2×D4311yescharacteristic
189C2×C4×C8—861no—
190#389—431no—
191#389—431no—
192#389—431no—
193#389—431no—
194#387—861no—
195#387—861no—
196#387—861no—
197#387—861no—
198#382—431no—
199#382C2×D4311yescharacteristic
200C43—431no—
201#336—861no—
202C43#989211yescharacteristic, complemented, Sylow
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—861no—
206C22×C8—861no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C4×D4311yescharacteristic
214C2×C4⋊C4C4×D4311yescharacteristic
215C2×C42—431no—
216C2×C42—431no—
217C2×C42—431no—
218C2×C42—431no—
219C2×C42—431no—
220C2×C42—431no—
221C2×C42C22×D4311yescharacteristic
222C4⋊C8—864no—
223#97—21no—
224#97—21no—
225#97—21no—
226#97—432no—
227#97—864no—
228#97—861no—
229#97—861no—
230#97—861no—
231#97Dic8612yes—
232C4×C8—864no—
233#95—21no—
234#95—21no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95—861no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—862no—
259C2×C8—862no—
260C2×C8—862no—
261C2×C8—862no—
262C2×C8—1721no—
263C2×C8—1721no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1722no—
269C4⋊C4—1722no—
270C4⋊C4—1722no—
271C4⋊C4—1722no—
272C42—862no—
273C42—862no—
274C42—862no—
275C42—1721no—
276C42—1721no—
277C42—1721no—
278C42C2×Dic8611yescharacteristic
279C42#1062189811yescharacteristic
280C42#1062190011yescharacteristic
281C42Q8×D4311yescharacteristic
282C23C22⋊C4×D4311yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—432no—
296C2×C4—432no—
297C2×C4—432no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4#1306329011yescharacteristic
314C2×C4C4×Dic8611yescharacteristic
315C2×C4#1306330211yescharacteristic
316C2×C4#1306330311yescharacteristic
317C2×C4#1306331111yescharacteristic
318C2×C4#1306332411yescharacteristic
319C8—24no—
320C8—42no—
321C8—864no—
322C8—1722no—
323C22#1458280311yescharacteristic
324C22#1458288011yescharacteristic
325C22#1458288211yescharacteristic
326C22#104×D4311yescharacteristic
327C22#104×D4311yescharacteristic
328C22#104×D4311yescharacteristic
329C22#1458291411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—862no—
339C4—862no—
340C4—862no—
341C4—3441no—
342C4—3441no—
343C4—1721no—
344C2#1913318011yescharacteristic
345C2#1913318211yescharacteristic
346C2#1913319911yescharacteristic
347C2#1913321411yescharacteristic
348C2#1913553711yescharacteristic
349C2#1913557011yescharacteristic
350C2#1913558611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#9892
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
202. C43#9892semidirect

Maximal subgroups

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

subgroupindex
#191429802
#191344492
#97×Dic432
#191324772
#191324762
C43×#12952
#989243