Finite Group Databasebeta

← #24991688

Subgroups — #24991688

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143232C211yesmaximal, characteristic
2#19137865C211yesmaximal, characteristic
3#19133024C211yesmaximal, characteristic, complemented
4#19132907C211yesmaximal, characteristic
5#19132497C211yesmaximal, characteristic, complemented
6#19132496C211yesmaximal, characteristic, complemented
7C43×#1487C211yesmaximal, characteristic, complemented
8C2×#13063282C2211yescharacteristic
9#14582959—22no—
10#14582959—22no—
11#14582952C2211yescharacteristic
12#14582923C2211yescharacteristic
13#14582862—21no—
14M16×Dic43—21no—
15#14582837C411yescharacteristic
16#14582834C411yescharacteristic
17#14582832—21no—
18#14582821—21no—
19#14582818C411yescharacteristic
20#14582810C411yescharacteristic
21C4×Dic43⋊C4—21no—
22C4×C4⋊Dic43C2211yescharacteristic
23C4×(C2×D43)⋊C4—21no—
24Q8⋊(C43⋊C8)—22no—
25#14582624—21no—
26#14582622—21no—
27C2×C4×Q8×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33#13063282—21no—
34#13063282—21no—
35#13063282—21no—
36#13063282—21no—
37C2×C4⋊Dic43—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4C2×C411yescharacteristic
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43D411yescharacteristic
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D412yes—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—24no—
53#13063235—22no—
54C4×C43⋊C8—21no—
55C8×Dic43—22no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95C2×C411yescharacteristic
61C43⋊#95C2×C411yescharacteristic
62C22×Q8×C43C2×C411yescharacteristic
63C2×M16×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D412yes—
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77C23×D43C22⋊C411yescharacteristic
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—42no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97M16×C43—41no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C42×C43—41no—
106C42×C43—41no—
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—42no—
116(C2×D43)⋊C4—42no—
117C4⋊Dic43—42no—
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122Dic43⋊C4—42no—
123Dic43⋊C4—42no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128#10621877—41no—
129#10621877—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—41no—
132C23×C43C2×C22⋊C411yescharacteristic
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—41no—
137C22×D43—41no—
138Q8×C43—22no—
139Q8×C43—22no—
140Q8×C43—41no—
141Q8×C43—41no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12311yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×C4×C43#13711yescharacteristic
160C2×Dic43—22no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—41no—
177C8×C43—42no—
178C8×C43—81no—
179C43⋊C8—42no—
180C43⋊C8—81no—
181#9034—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43#38611yescharacteristic
185C22×C43#41611yescharacteristic
186C22×C43#41911yescharacteristic
187C2×D43—42no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—81no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—81no—
198C4×C43#45211yescharacteristic
199C4×C43#45211yescharacteristic
200C4×C43#48511yescharacteristic
201C4×C43#48511yescharacteristic
202Dic43—42no—
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206Dic43—81no—
207#2921—431no—
208#2396—431no—
209#1487—431no—
210#1487D4311yescharacteristic, complemented
211#1458—431no—
212#1303—431no—
213#1303—431no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43#187311yescharacteristic
217C2×C43#188411yescharacteristic
218C2×C43#189111yescharacteristic
219D43—81no—
220C2×C4×Q8C2×D4311yescharacteristic
221C2×#117—431no—
222#433—862no—
223#433—862no—
224#431—431no—
225#431C2×D4311yescharacteristic
226#423—431no—
227#423C2×D4311yescharacteristic
228#407—861no—
229C4×M16—861no—
230#400—431no—
231#399—431no—
232#398—861no—
233#396—861no—
234#395—431no—
235#393—431no—
236C4×C4⋊C4—431no—
237C4×C4⋊C4—861no—
238C4×C22⋊C4—861no—
239Q8⋊C8—22no—
240Q8⋊C8—862no—
241#324—861no—
242#323—861no—
243C43#903411yescharacteristic, complemented, Sylow
244C22×Q8C4×D4311yescharacteristic
245C23×C4—431no—
246C2×M16—21no—
247C2×M16—861no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252#117—861no—
253#117—861no—
254#117—861no—
255#117—861no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4C4×D4311yescharacteristic
263C2×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42—21no—
268C2×C42—431no—
269C2×C42—861no—
270C2×C42C22×D4311yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275C4⋊C8—861no—
276C4⋊C8C22⋊D4312yes—
277C22⋊C8—21no—
278C22⋊C8—864no—
279C22⋊C8—861no—
280#97—862no—
281C4×C8—21no—
282C4×C8—862no—
283C4×C8—861no—
284#95—431no—
285#95—431no—
286#95—861no—
287#95—861no—
288#95—861no—
289#95—861no—
290C24—431no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—42no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4C2×C4×D4311yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310M16—41no—
311M16—41no—
312M16—1721no—
313M16—1721no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—862no—
317C2×C8—1721no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—1722no—
327C4⋊C4—1722no—
328C4⋊C4—1722no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C42—41no—
336C42—41no—
337C42—861no—
338C42—861no—
339C42—1721no—
340C42—1721no—
341C42#1062189811yescharacteristic
342C42D4×D4311yescharacteristic
343C42#1062190011yescharacteristic
344C42C2×C22⋊D4311yescharacteristic
345C23—861no—
346C23—861no—
347C23—861no—
348C23—1721no—
349C23—1721no—
350C23C22⋊C4×D4311yescharacteristic
351Q8—22no—
352Q8—22no—
353Q8—41no—
354Q8—41no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—862no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4(C22⋊D43)⋊C411yescharacteristic
381C2×C4C4×C22⋊D4311yescharacteristic
382C2×C4#1306329311yescharacteristic
383C2×C4#1306329611yescharacteristic
384C2×C4#1306329811yescharacteristic
385C2×C4#1306330711yescharacteristic
386C2×C4#1306334611yescharacteristic
387C2×C4#1306334811yescharacteristic
388C2×C4#1306335411yescharacteristic
389C2×C4#1306335711yescharacteristic
390C8—42no—
391C8—81no—
392C8—3441no—
393C8—1722no—
394C22—21no—
395C22—21no—
396C22—3441no—
397C22—1722no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22#1458277511yescharacteristic
402C22#1458289411yescharacteristic
403C22#1458290611yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—3441no—
411C4—1722no—
412C4—1721no—
413C4—1721no—
414C4—1721no—
415C4#1458305811yescharacteristic
416C4#1458306011yescharacteristic
417C4#1458323811yescharacteristic
418C4#1458323911yescharacteristic
419C2—21no—
420C2—21no—
421C2—3441no—
422C2#1913490411yescharacteristic
423C2#1913497511yescharacteristic
424C2#1913501011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1487C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1487D43
hypocenterC43#9034
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #19133024C2semidirect
5. #19132497C2semidirect
6. #19132496C2semidirect
7. C43×#1487C2semidirect
210. #1487D43semidirect
243. C43#9034semidirect

Maximal subgroups

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

subgroupindex
#191432322
#191378652
#191330242
#191329072
#191324972
#191324962
C43×#14872
#903443