Finite Group Databasebeta

← #24992722

Subgroups — #24992722

Order 11008.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144655C211yesmaximal, characteristic
2#19133186C211yesmaximal, characteristic, complemented
3#19133047C211yesmaximal, characteristic, complemented
4#19133034C211yesmaximal, characteristic, complemented
5#19132485C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#2922C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583223—21no—
10#14583194C411yescharacteristic
11#14583189C411yescharacteristic
12#14583099C411yescharacteristic
13#14583094C411yescharacteristic
14#14583044—21no—
15C4×#10621884—21no—
16C4×#10621882—21no—
17#14582952C2211yescharacteristic
18#14582923C2211yescharacteristic
19C4×#10621877C2211yescharacteristic
20#14582638—22no—
21Q8⋊(C43⋊C8)—21no—
22#14582628—22no—
23D4⋊(C43⋊C8)—21no—
24C4×#41×C43C2211yescharacteristic
25C43×#433—22no—
26C43×#431—22no—
27C43×#424—21no—
28C43×#408—21no—
29C4×M16×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621884—21no—
33C2×#10621882—21no—
34C2×#10621877—21no—
35C2×#10621877—21no—
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063313—21no—
39#13063299—21no—
40#13063299—21no—
41C4×D172—21no—
42C4×D172—21no—
43#13063258—21no—
44#13063256—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)C2×C411yescharacteristic
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49#13063249—21no—
50#13063246—21no—
51#13063245—21no—
52#13063245—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8—21no—
57C2×#41×C43D411yescharacteristic
58C2×M16×C43—21no—
59C22×C8×C43—21no—
60C4×Q8×C43C2×C411yescharacteristic
61C4×Q8×C43D411yescharacteristic
62C4×D4×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43C2×C411yescharacteristic
65C4×D4×C43D411yescharacteristic
66#117×C43—21no—
67#117×C43D411yescharacteristic
68C2×C42×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—24no—
71C22⋊C8×C43—24no—
72#97×C43D412yes—
73C4×C8×C43—21no—
74C4×C8×C43—21no—
75C4×C8×C43D412yes—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43C22⋊C411yescharacteristic
79C2×D4×C43—21no—
80C2×D4×C43C22⋊C411yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—41no—
88#10621898—81no—
89#10621898—81no—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—21no—
93C2×C4×D43—41no—
94C2×Dic86—21no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43C22⋊C411yescharacteristic
104C4⋊C4×C43C22⋊C411yescharacteristic
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C22⋊C4×C43—21no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115#10621884—42no—
116#10621882—42no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121#10621877—22no—
122#10621877—41no—
123#10621877—81no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C23×C43—21no—
129C23×C43#12311yescharacteristic
130C22×D43—41no—
131Q8×C43—21no—
132Q8×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—42no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C22⋊D43—82no—
157C2×Dic43—41no—
158D172—41no—
159D172—41no—
160D172—41no—
161D172—41no—
162D172—81no—
163C4×D43—81no—
164C4×D43—81no—
165Dic86—81no—
166C8×C43—42no—
167C8×C43—42no—
168C43⋊C8—42no—
169C43⋊C8—41no—
170C43⋊C8—41no—
171C43⋊C8—81no—
172#9213—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43#38611yescharacteristic
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43#42111yescharacteristic
190C4×C43#42111yescharacteristic
191C4×C43#44311yescharacteristic
192C4×C43#44411yescharacteristic
193C4×C43#47111yescharacteristic
194C4×C43#47211yescharacteristic
195Dic43—81no—
196#3106—431no—
197#2922D4311yescharacteristic, complemented
198#1525—431no—
199#1492—431no—
200#1489—431no—
201#1299—431no—
202#1278—431no—
203C2×C43—41no—
204C2×C43—81no—
205C2×C43#187611yescharacteristic
206C2×C43#189711yescharacteristic
207C2×C43#190711yescharacteristic
208D43—161no—
209#532—431no—
210C4×#41C2×D4311yescharacteristic
211#482—861no—
212#477—431no—
213#476—431no—
214#460—431no—
215#459—431no—
216#449—861no—
217C4×SD16—861no—
218C4×D8—861no—
219#433—22no—
220#431—22no—
221#431—431no—
222#424—21no—
223#423—431no—
224#408—21no—
225C4×M16—431no—
226C4×M16C2×D4311yescharacteristic
227C2×C4×C8C2×D4311yescharacteristic
228#329—862no—
229Q8⋊C8—861no—
230D4⋊C8—861no—
231D4⋊C8—862no—
232C43#921311yescharacteristic, complemented, Sylow
233C2×#41—861no—
234C2×#41C22⋊D4311yescharacteristic
235C2×SD16—861no—
236C2×D8—861no—
237C2×M16—21no—
238C2×M16—861no—
239C2×M16—861no—
240C22×C8—21no—
241C4⋊Q8—431no—
242#127—431no—
243#124—861no—
244#121—861no—
245#121—861no—
246C4×Q8C4×D4311yescharacteristic
247C4×Q8D17211yescharacteristic
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—861no—
251C4×D4—861no—
252C4×D4C4×D4311yescharacteristic
253C4×D4D17211yescharacteristic
254#117—21no—
255#117C22⋊D4311yescharacteristic
256C2×C42—21no—
257C2×C42C22×D4311yescharacteristic
258#107—861no—
259#106—861no—
260C4⋊C8—24no—
261C4⋊C8—431no—
262C4⋊C8—431no—
263C4⋊C8—861no—
264C4⋊C8—861no—
265#103—861no—
266#102—861no—
267#102—861no—
268#102—861no—
269C22⋊C8—24no—
270C22⋊C8—861no—
271#97—861no—
272#97C22⋊D4312yes—
273C4×C8—21no—
274C4×C8—21no—
275C4×C8—861no—
276C4×C8—861no—
277C4×C8C22⋊D4312yes—
278#41—41no—
279#41—41no—
280#41—3441no—
281#41—3441no—
282C2×Q8—861no—
283C2×Q8(C2×D43)⋊C411yescharacteristic
284C2×D4—21no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—1721no—
289C2×D4(C2×D43)⋊C411yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—1721no—
294C22×C4#1062189811yescharacteristic
295C22×C4#1062189811yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297SD16—1722no—
298D8—1722no—
299M16—41no—
300M16—41no—
301M16—862no—
302M16—3441no—
303M16—1721no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—861no—
309C2×C8—861no—
310C2×C8—1721no—
311C2×C8—1721no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4(C2×D43)⋊C411yescharacteristic
317C4⋊C4(C2×D43)⋊C411yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×C4×D4311yescharacteristic
327C42C2×D17211yescharacteristic
328C42C2×C22⋊D4311yescharacteristic
329C42C2×C22⋊D4311yescharacteristic
330C23—21no—
331C23—1721no—
332C23#1306330811yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—3441no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—3441no—
340D4—3442no—
341D4—1721no—
342D4—1721no—
343D4—1721no—
344D4—1721no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—1721no—
362C2×C4C2×(C2×D43)⋊C411yescharacteristic
363C2×C4C4×C22⋊D4311yescharacteristic
364C2×C4C4×C22⋊D4311yescharacteristic
365C2×C4#1306329411yescharacteristic
366C2×C4#1306329911yescharacteristic
367C2×C4#1306329911yescharacteristic
368C8—42no—
369C8—42no—
370C8—3441no—
371C8—1722no—
372C8—1721no—
373C8—1721no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3441no—
381C22—3441no—
382C22—3441no—
383C22#1458277811yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3441no—
391C4#1458291711yescharacteristic
392C4#1458291711yescharacteristic
393C4#1458301411yescharacteristic
394C4#1458301911yescharacteristic
395C4#1458316211yescharacteristic
396C4#1458316911yescharacteristic
397C2—41no—
398C2—81no—
399C2—6881no—
400C2#1913492211yescharacteristic
401C2#1913504311yescharacteristic
402C2#1913510311yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2922C2
socleC22×C43#386
prime radical#19144655C2
cosocleC2×C42×C43C23
hypercenter#2922D43
hypocenterC43#9213
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #19133186C2semidirect
3. #19133047C2semidirect
4. #19133034C2semidirect
5. #19132485C2semidirect
6. #19132432C2semidirect
7. C43×#2922C2semidirect
197. #2922D43semidirect
232. C43#9213semidirect

Maximal subgroups

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

subgroupindex
#191446552
#191331862
#191330472
#191330342
#191324852
#191324322
C43×#29222
#921343