Finite Group Databasebeta

← #24991821

Subgroups — #24991821

Order 11008.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19143338C211yesmaximal, characteristic, complemented
3#19135515C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic, complemented
5#19132434C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1480C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583449C2211yescharacteristic
10#14583302C411yescharacteristic, complemented
11#14583275C411yescharacteristic, complemented
12#14583247C411yescharacteristic, complemented
13#14583245C411yescharacteristic, complemented
14#14583133—22no—
15C4×#10621882—22no—
16#14582976—21no—
17#14582969—22no—
18#14582964—21no—
19C2×#13063252—21no—
20C2×#13063252—21no—
21#14582865—21no—
22C4×#10621877C2211yescharacteristic
23C2×C4×C43⋊C8C2211yescharacteristic
24C4×C4⋊Dic43C2211yescharacteristic
25#14582634—22no—
26C43×#532C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×D4⋊C8—21no—
30C43×D4⋊C8—21no—
31C2×#10621898—21no—
32C2×#10621882—22no—
33#13063331—42no—
34#13063331—42no—
35C2×#10621877D411yescharacteristic
36C2×#10621877D411yescharacteristic
37C2×#10621872—22no—
38C22×C43⋊C8—21no—
39C2×C8×D43—22no—
40#13063325C2×C411yescharacteristic
41#13063322C2×C411yescharacteristic
42#13063313—21no—
43#13063299—21no—
44#13063299D412yes—
45C4×D172—21no—
46C4×D172D412yes—
47C2×C4⋊Dic43—21no—
48C2×C4×Dic43—21no—
49#13063258—22no—
50#13063252—42no—
51#13063252—42no—
52#13063246—22no—
53#13063245—22no—
54(C2×D43)⋊C8—22no—
55(C2×D43)⋊C8—22no—
56#13063236—21no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8C2×C411yescharacteristic
60C4×C43⋊C8C2×C411yescharacteristic
61C43⋊#95—21no—
62C2×#41×C43—21no—
63C22×C8×C43—21no—
64C4⋊Q8×C43C2×C411yescharacteristic
65#127×C43C2×C411yescharacteristic
66#124×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D411yescharacteristic
75C4⋊C8×C43D411yescharacteristic
76C22⋊C8×C43—21no—
77C4×C8×C43—21no—
78#41×C43—41no—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82C2×Q8×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C22⋊D43—22no—
92C22×Dic43—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172C22⋊C412yes—
100C2×C4×D43—22no—
101C2×Dic86—21no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115#10621882—44no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118C4⋊Dic43—21no—
119C4⋊Dic43—22no—
120C4⋊Dic43—41no—
121C4⋊Dic43C22⋊C412yes—
122C4×Dic43—41no—
123C4×Dic43—41no—
124#10621877—21no—
125#10621877—21no—
126#10621877—21no—
127#10621877D812yescomplemented
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—42no—
133#10621872—44no—
134C8×D43—44no—
135C23×C43—41no—
136C23×C43#12111yescharacteristic
137C22×D43—22no—
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—42no—
141D4×C43—41no—
142D4×C43—41no—
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—81no—
146D4×C43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12311yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C22⋊D43—42no—
164C22⋊D43—42no—
165C2×Dic43—22no—
166C2×Dic43—42no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169D172—42no—
170D172—41no—
171D172—41no—
172D172—41no—
173D172—41no—
174C4×D43—42no—
175C4×D43—42no—
176Dic86—41no—
177Dic86—41no—
178C8×C43—41no—
179C8×C43—41no—
180C8×C43—81no—
181C43⋊C8—22no—
182C43⋊C8—22no—
183C43⋊C8—41no—
184C43⋊C8—41no—
185#9053—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43#38611yescharacteristic
192C22×C43#45911yescharacteristic
193C22×C43#46311yescharacteristic
194C2×D43—42no—
195C2×D43—42no—
196C2×D43—42no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—81no—
201C4×C43C4×D811yescharacteristic
202C4×C43#44211yescharacteristic
203C4×C43#44311yescharacteristic
204C4×C43#44411yescharacteristic
205C4×C43#44711yescharacteristic
206C4×C43#44911yescharacteristic
207Dic43—42no—
208Dic43—82no—
209#3169—431no—
210#2935—431no—
211#1980—431no—
212#1502—431no—
213#1480D4311yescharacteristic, complemented
214#1279—431no—
215#1278—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—161no—
219C2×C43#187611yescharacteristic
220C2×C43#187911yescharacteristic
221C2×C43#188411yescharacteristic
222D43—82no—
223C2×#131—861no—
224#532—431no—
225#532C2×D4311yescharacteristic
226#500—431no—
227#493—431no—
228#486—431no—
229#486—431no—
230#466—862no—
231C4×D8—862no—
232#436—861no—
233#435—862no—
234C8×D4—861no—
235#431C2×D4311yescharacteristic
236C2×C4⋊C8C2×D4311yescharacteristic
237C2×#104—861no—
238C2×#104—861no—
239#408—861no—
240C4×M16—431no—
241C2×C4×C8—431no—
242C4×C4⋊C4—431no—
243#327—862no—
244D4⋊C8—21no—
245D4⋊C8—21no—
246C43#905311yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C2×#41—861no—
249C2×D8—862no—
250#131—1722no—
251#131—1722no—
252C2×M16—431no—
253C2×M16—431no—
254C2×M16—862no—
255C22×C8—21no—
256C22×C8—862no—
257C22×C8—861no—
258C4⋊Q8—431no—
259C4⋊Q8C4×D4311yescharacteristic
260#127—431no—
261#127C4×D4311yescharacteristic
262#124—21no—
263#124—861no—
264#121—21no—
265#121—21no—
266#121—432no—
267#121—861no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—432no—
271C4×D4—861no—
272C2×C4⋊C4—861no—
273C2×C42—861no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8C22⋊D4311yescharacteristic
279C4⋊C8C22⋊D4311yescharacteristic
280#104—1722no—
281#104—1722no—
282#102—862no—
283#102—862no—
284C22⋊C8—21no—
285C22⋊C8—862no—
286C22⋊C8—862no—
287#97—861no—
288C4×C8—21no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—861no—
292C4×C8—861no—
293#95—861no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—1721no—
299#41—1721no—
300#41—1721no—
301#41—1721no—
302C2×Q8—21no—
303C2×Q8—861no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—432no—
309C2×D4—862no—
310C2×D4—861no—
311C2×D4—861no—
312C22×C4—41no—
313C22×C4—862no—
314C22×C4—1721no—
315C22×C4#1062189811yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318D8—1724no—
319M16—432no—
320M16—861no—
321M16—861no—
322M16—861no—
323M16—1724no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—861no—
330C2×C8—861no—
331C2×C8—861no—
332C2×C8—861no—
333C2×C8—1724no—
334C2×C8—1722no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—432no—
338C4⋊C4—862no—
339C4⋊C4—861no—
340C4⋊C4—1721no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—862no—
344C22⋊C4—862no—
345C42—1721no—
346C42—1721no—
347C42C2×C4×D4311yescharacteristic
348C42D4×D4311yescharacteristic
349C42#1062190011yescharacteristic
350C42C2×C22⋊D4311yescharacteristic
351C23—41no—
352C23—862no—
353C23#1306329811yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—1721no—
357Q8—1721no—
358D4—42no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4—1721no—
369D4—1721no—
370D4—1721no—
371D4—1721no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—862no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4C4×C22⋊D4311yescharacteristic
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329611yescharacteristic
389C2×C4#1306330711yescharacteristic
390C2×C4D8×D4311yescharacteristic
391C2×C4#1306334611yescharacteristic
392C2×C4#1306334911yescharacteristic
393C2×C4#1306335211yescharacteristic
394C8—41no—
395C8—41no—
396C8—81no—
397C8—862no—
398C8—862no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—1722no—
407C22—1722no—
408C22—1722no—
409C22#1458277511yescharacteristic
410C22#1458309311yescharacteristic
411C22#1458311311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—81no—
416C4—3442no—
417C4—1722no—
418C4#1458297911yescharacteristic
419C4#1458300811yescharacteristic
420C4#1458301411yescharacteristic
421C4#1458301911yescharacteristic
422C4#1458303111yescharacteristic
423C4#1458304311yescharacteristic
424C2—21no—
425C2—21no—
426C2—161no—
427C2—3442no—
428C2#1913492511yescharacteristic
429C2#1913494011yescharacteristic
430C2#1913497511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1480C2
socleC22×C43#386
prime radical#19145170C2
cosocleC2×C42×C43C23
hypercenter#1480D43
hypocenterC43#9053
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #19143338C2semidirect
3. #19135515C2semidirect
4. #19133091C2semidirect
5. #19132434C2semidirect
6. #19132431C2semidirect
7. C43×#1480C2semidirect
10. #14583302C4semidirect
11. #14583275C4semidirect
12. #14583247C4semidirect
13. #14583245C4semidirect
127. #10621877D8semidirect
213. #1480D43semidirect
246. C43#9053semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191433382
#191355152
#191330912
#191324342
#191324312
C43×#14802
#905343