Finite Group Databasebeta

← #24992401

Subgroups — #24992401

Order 11008.

450 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#19143615C211yesmaximal, characteristic
2#19134405C211yesmaximal, characteristic
3#19133190C211yesmaximal, characteristic, complemented
4#19133107C211yesmaximal, characteristic, complemented
5#19132487C211yesmaximal, characteristic, complemented
6#19132466C211yesmaximal, characteristic, complemented
7C43×#3116C211yesmaximal, characteristic
8Q8×C43⋊C8—21no—
9#14582977—22no—
10#14582977—21no—
11#14582956—21no—
12#14582956C2211yescharacteristic
13C2×#13063252—21no—
14C4×#10621877—21no—
15C4×#10621877C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17#14582745C2211yescharacteristic
18#14582658—21no—
19#14582641—21no—
20#14582641—21no—
21#14582636—22no—
22C43×#533C2211yescharacteristic
23C4×#41×C43C2211yescharacteristic
24C43×#485—21no—
25C43×#477C411yescharacteristic, complemented
26C43×#476C411yescharacteristic, complemented
27C43×#462C411yescharacteristic, complemented
28C43×#461C411yescharacteristic, complemented
29C43×#452—21no—
30C43×#441—21no—
31C43×#440—21no—
32C43×#432C2211yescharacteristic
33C2×#10621877—22no—
34C2×#10621877—21no—
35C2×#10621877—21no—
36C2×C4×Dic43—21no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)—21no—
39#13063252—24no—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)D412yes—
42#13063236—21no—
43#13063236—21no—
44#13063236D411yescharacteristic
45#13063236D411yescharacteristic
46C4×C43⋊C8—22no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C2×#41×C43D411yescharacteristic
52C2×Q16×C43—21no—
53C2×SD16×C43—21no—
54C4⋊Q8×C43C2×C411yescharacteristic
55C4⋊Q8×C43C2×C411yescharacteristic
56#125×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43D411yescharacteristic
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43C2×C411yescharacteristic
66C4×D4×C43D411yescharacteristic
67#117×C43—21no—
68#117×C43—21no—
69#117×C43D411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72#107×C43—21no—
73#106×C43—21no—
74C4⋊C8×C43C2×C411yescharacteristic
75C4⋊C8×C43C2×C411yescharacteristic
76#103×C43—21no—
77#103×C43—21no—
78#103×C43—21no—
79#102×C43—21no—
80C22⋊C8×C43—21no—
81#97×C43—21no—
82#41×C43—22no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43C22⋊C411yescharacteristic
87C2×D4×C43—21no—
88C2×D4×C43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×Dic43—41no—
96Q16×C43—42no—
97SD16×C43—42no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43C22⋊C411yescharacteristic
109C4⋊C4×C43C22⋊C411yescharacteristic
110C22⋊C4×C43—21no—
111C22⋊C4×C43—21no—
112C22⋊C4×C43—21no—
113C22⋊C4×C43—41no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43—41no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C4×Dic43—22no—
123C4×Dic43—41no—
124#10621877—22no—
125#10621877—42no—
126#10621877—44no—
127#10621877—41no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—41no—
132C23×C43—21no—
133C23×C43#12111yescharacteristic
134Q8×C43—21no—
135Q8×C43—41no—
136Q8×C43—41no—
137Q8×C43—81no—
138Q8×C43#10412yes—
139D4×C43—21no—
140D4×C43—21no—
141D4×C43—42no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×Dic43—42no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C8×C43—41no—
164C8×C43—41no—
165C43⋊C8—22no—
166C43⋊C8—42no—
167C43⋊C8—41no—
168C43⋊C8—42no—
169#9160—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43#38611yescharacteristic
177C4×C43—21no—
178C4×C43—22no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—81no—
186C4×C43—81no—
187C4×C43C2×#10411yescharacteristic
188C4×C43#42111yescharacteristic
189Dic43—82no—
190#3116D4311yescharacteristic
191#2971—431no—
192#1759—431no—
193#1526—431no—
194#1506—431no—
195#1300—431no—
196#1291—431no—
197C2×C43—41no—
198C2×C43—81no—
199C2×C43#187111yescharacteristic
200C2×C43#190211yescharacteristic
201C2×C43#190611yescharacteristic
202#533C2×D4311yescharacteristic
203C4×#41C2×D4311yescharacteristic
204#485—21no—
205#477Dic4311yescharacteristic, complemented
206#476Dic4311yescharacteristic, complemented
207#462Dic4311yescharacteristic, complemented
208#461Dic4311yescharacteristic, complemented
209#452—21no—
210C8×Q8—861no—
211#441—21no—
212#440—21no—
213#436—862no—
214#436—861no—
215#432—431no—
216#432—861no—
217#432C2×D4311yescharacteristic
218C2×#104—861no—
219C4×M16—431no—
220C4×M16—431no—
221C4×M16—861no—
222#376—431no—
223#339—861no—
224#330—861no—
225#330—861no—
226#328—862no—
227C43#916011yescharacteristic, complemented, Sylow
228C2×#41C22⋊D4311yescharacteristic
229C2×Q16—21no—
230C2×SD16—21no—
231C2×M16—862no—
232C2×M16—861no—
233C2×M16—861no—
234C4⋊Q8C2×Dic4311yescharacteristic
235C4⋊Q8C2×Dic4311yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×Dic4311yescharacteristic
242C4×Q8C22⋊D4311yescharacteristic
243C4×D4—21no—
244C4×D4—21no—
245C4×D4C2×Dic4311yescharacteristic
246C4×D4C22⋊D4311yescharacteristic
247#117—21no—
248#117—21no—
249#117C22⋊D4311yescharacteristic
250C2×C42—21no—
251C2×C42—861no—
252C2×C42C22×D4311yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—862no—
256C4⋊C8—861no—
257C4⋊C8C2×Dic4311yescharacteristic
258C4⋊C8C2×Dic4311yescharacteristic
259#104—864no—
260#103—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264C22⋊C8—21no—
265C22⋊C8—432no—
266C22⋊C8—862no—
267#97—21no—
268#97—431no—
269#97—431no—
270#97—861no—
271#97—861no—
272C4×C8—862no—
273C4×C8—861no—
274C4×C8—861no—
275#95—861no—
276#95—861no—
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊Dic4311yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊Dic4311yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—1721no—
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190011yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—862no—
294M16—1722no—
295M16—1724no—
296M16—1721no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—862no—
302C2×C8—1721no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊Dic4311yescharacteristic
312C4⋊C4C22⋊Dic4311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—862no—
322C42—1721no—
323C42D4×D4311yescharacteristic
324C42#1062190011yescharacteristic
325C42C22×Dic4311yescharacteristic
326C42C2×C22⋊D4311yescharacteristic
327C23—21no—
328C23#1306329711yescharacteristic
329Q8—21no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#1306325212yes—
334D4—21no—
335D4—21no—
336D4—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1722no—
352C2×C4C2×C22⋊Dic4311yescharacteristic
353C2×C4D4×Dic4311yescharacteristic
354C2×C4D4×Dic4311yescharacteristic
355C2×C4#1306329311yescharacteristic
356C2×C4#1306329711yescharacteristic
357C2×C4#1306330611yescharacteristic
358C8—41no—
359C8—41no—
360C8—862no—
361C8—1721no—
362C8—1722no—
363C8—1722no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22#1458277911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—3442no—
382C4C2×#1306325211yescharacteristic
383C4#1458291611yescharacteristic
384C2—41no—
385C2—81no—
386C2#1913489811yescharacteristic
387C2#1913507011yescharacteristic
388C2#1913509811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3116C2
socleC22×C43#386
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#3116D43
hypocenterC43#9160
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
3. #19133190C2semidirect
4. #19133107C2semidirect
5. #19132487C2semidirect
6. #19132466C2semidirect
25. C43×#477C4semidirect
26. C43×#476C4semidirect
27. C43×#462C4semidirect
28. C43×#461C4semidirect
205. #477Dic43semidirect
206. #476Dic43semidirect
207. #462Dic43semidirect
208. #461Dic43semidirect
227. C43#9160semidirect

Maximal subgroups

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

subgroupindex
#191436152
#191344052
#191331902
#191331072
#191324872
#191324662
C43×#31162
#916043