Finite Group Databasebeta

← #24995973

Subgroups — #24995973

Order 11008.

502 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145021C211yesmaximal, characteristic
2#19134757C211yesmaximal, characteristic, complemented
3#19133156C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic, complemented
5#19133154C211yesmaximal, characteristic, complemented
6#19132879C211yesmaximal, characteristic, complemented
7C43×#1517C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C2×#13063345—21no—
10#14583449C2211yescharacteristic
11#14583281—21no—
12#14583281—21no—
13#14583278C411yescharacteristic, complemented
14#14583275C411yescharacteristic, complemented
15#14583273C411yescharacteristic, complemented
16#14583271C411yescharacteristic, complemented
17#14582952C2211yescharacteristic
18C2×#13063258—21no—
19C2×#13063256—21no—
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582765C2211yescharacteristic
22#14582634—22no—
23#14582633—22no—
24#14582632—22no—
25#14582621—21no—
26C8×C43⋊C8—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#382C2211yescharacteristic
30C43×#327—22no—
31C2×#10621898—21no—
32#13063345—42no—
33#13063345—42no—
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621885—21no—
38C2×#10621883—21no—
39C2×#10621883—21no—
40C2×#10621884—21no—
41C2×#10621884—21no—
42C2×#10621882—21no—
43C2×#10621882—21no—
44C22×C43⋊C8D411yescharacteristic
45C22×C43⋊C8D411yescharacteristic
46#13063325C2×C411yescharacteristic
47#13063322C2×C411yescharacteristic
48#13063313—21no—
49#13063299—21no—
50#13063299—21no—
51C4×D172—21no—
52C4×D172—21no—
53C2×C4⋊Dic43—21no—
54#13063258—42no—
55#13063256—42no—
56C4⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58C4×C43⋊C8—21no—
59C4×C43⋊C8C2×C411yescharacteristic
60C4×C43⋊C8C2×C411yescharacteristic
61C4×C43⋊C8D411yescharacteristic
62C4×C43⋊C8D411yescharacteristic
63C43⋊#95—21no—
64C43⋊#95—21no—
65C2×#41×C43—21no—
66C4⋊Q8×C43C2×C411yescharacteristic
67#127×C43C2×C411yescharacteristic
68#124×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77C4×C8×C43—21no—
78#95×C43—21no—
79#95×C43—21no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—41no—
95C22×Dic43—41no—
96#10621898—41no—
97#10621898—41no—
98#10621898—41no—
99#10621898—41no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105C2×C8×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116#10621885—42no—
117#10621885—42no—
118#10621884—42no—
119#10621884—42no—
120#10621883—42no—
121#10621883—42no—
122#10621882—42no—
123#10621882—42no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—41no—
129C4⋊Dic43—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8C22⋊C411yescharacteristic
132C2×C43⋊C8C22⋊C411yescharacteristic
133C2×C43⋊C8C22⋊C411yescharacteristic
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8D812yes—
136C2×C43⋊C8D812yes—
137C2×C43⋊C8SD1612yes—
138C2×C43⋊C8SD1612yes—
139C23×C43—41no—
140C23×C43#12711yescharacteristic
141C22×D43—41no—
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—81no—
147D4×C43—81no—
148D4×C43—81no—
149D4×C43—81no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12411yescharacteristic
164C2×C4×C43C2×D811yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43C2×SD1611yescharacteristic
167C2×C4×C43C2×SD1611yescharacteristic
168C22⋊D43—81no—
169C22⋊D43—81no—
170C2×Dic43—41no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174D172—41no—
175D172—41no—
176D172—81no—
177D172—81no—
178C4×D43—81no—
179C4×D43—81no—
180Dic86—41no—
181Dic86—41no—
182C8×C43—42no—
183C43⋊C8—42no—
184C43⋊C8#10212yes—
185C43⋊C8#10212yes—
186C43⋊C8#10212yes—
187C43⋊C8#10212yes—
188#9756—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43#39011yescharacteristic
195C22×C43#49211yescharacteristic
196C22×C43#49311yescharacteristic
197C2×D43—81no—
198C2×D43—81no—
199C2×D43—81no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—81no—
205C4×C43—161no—
206C4×C43C2×#10211yescharacteristic
207C4×C43C2×#10211yescharacteristic
208C4×C43#48611yescharacteristic
209C4×C43#48611yescharacteristic
210Dic43—81no—
211Dic43—161no—
212#3147—431no—
213#1846—431no—
214#1517—431no—
215#1517—431no—
216#1517—431no—
217#1517D4311yescharacteristic, complemented
218#1450—431no—
219C2×C43—21no—
220C2×C43—21no—
221C2×C43—161no—
222C2×C43#195711yescharacteristic
223C2×C43#197611yescharacteristic
224C2×C43#197611yescharacteristic
225D43—161no—
226C2×#135—861no—
227C2×#135—861no—
228#532—431no—
229#532C2×D4311yescharacteristic
230#495—861no—
231#495—861no—
232#494—431no—
233#493—431no—
234#492—431no—
235#492—431no—
236#431—431no—
237#431C2×D4311yescharacteristic
238C2×#107—861no—
239C2×#106—861no—
240C2×C4×C8—431no—
241#382—431no—
242#382C2×D4311yescharacteristic
243#327—22no—
244#327—862no—
245#327—862no—
246#327—862no—
247#322—861no—
248C82—861no—
249C43#975611yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41—861no—
252#135—1722no—
253#135—1722no—
254#135—1722no—
255#135—1722no—
256C2×Q16—861no—
257C2×Q16—861no—
258C2×SD16—861no—
259C2×SD16—861no—
260C2×SD16—861no—
261C2×SD16—861no—
262C2×D8—861no—
263C2×D8—861no—
264C22×C8—431no—
265C22×C8—431no—
266C4⋊Q8—431no—
267C4⋊Q8C4×D4311yescharacteristic
268#127—431no—
269#127C4×D4311yescharacteristic
270#124—21no—
271#124—861no—
272#121—21no—
273#121—21no—
274#121—861no—
275#121—861no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—861no—
279C4×D4—861no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—861no—
282C2×C42C22×D4311yescharacteristic
283#107—1722no—
284#106—1722no—
285C4⋊C8—21no—
286C4⋊C8—861no—
287C22⋊C8—432no—
288C22⋊C8C22⋊D4312yes—
289C4×C8—21no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—431no—
293C4×C8—431no—
294C4×C8—861no—
295#95—21no—
296#95—21no—
297#95—861no—
298#95—861no—
299#41—41no—
300#41—41no—
301#41—41no—
302#41—41no—
303#41—1721no—
304#41—1721no—
305#41—1721no—
306#41—1721no—
307C2×Q8—21no—
308C2×Q8—861no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—861no—
314C2×D4—861no—
315C2×D4—861no—
316C2×D4—1721no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—1721no—
320C22×C4—1721no—
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324Q16—1722no—
325Q16—1722no—
326SD16—1722no—
327SD16—1722no—
328SD16—1722no—
329SD16—1722no—
330D8—1722no—
331D8—1722no—
332C2×C8—22no—
333C2×C8—431no—
334C2×C8—431no—
335C2×C8—431no—
336C2×C8—431no—
337C2×C8—432no—
338C2×C8—432no—
339C2×C8—432no—
340C2×C8—432no—
341C2×C8—862no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—1721no—
349C4⋊C4—1721no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C42C2×C4×D4311yescharacteristic
355C42#1062189811yescharacteristic
356C42D4×D4311yescharacteristic
357C42#1062190011yescharacteristic
358C23—41no—
359C23—1721no—
360C23#1306332111yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—1721no—
364Q8—1721no—
365D4—41no—
366D4—41no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371D4—3441no—
372D4—3441no—
373D4—3441no—
374D4—3441no—
375D4—1721no—
376D4—1721no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—3441no—
386C2×C4—3441no—
387C2×C4—3441no—
388C2×C4—3441no—
389C2×C4—3441no—
390C2×C4—1721no—
391C2×C4C22⋊C4×D4311yescharacteristic
392C2×C4(C22⋊D43)⋊C411yescharacteristic
393C2×C4C4×C22⋊D4311yescharacteristic
394C2×C4#1306329711yescharacteristic
395C2×C4#1306329811yescharacteristic
396C2×C4#1306331111yescharacteristic
397C2×C4D8×D4311yescharacteristic
398C2×C4D8×D4311yescharacteristic
399C2×C4SD16×D4311yescharacteristic
400C2×C4SD16×D4311yescharacteristic
401C8—42no—
402C8—432no—
403C8—432no—
404C8—432no—
405C8—432no—
406C8—1722no—
407C22—21no—
408C22—21no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—3441no—
413C22—3441no—
414C22—3441no—
415C22#1458279911yescharacteristic
416C22#1458327011yescharacteristic
417C22#1458327411yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—161no—
424C4—3441no—
425C4—6881no—
426C4#102×D4311yescharacteristic
427C4#102×D4311yescharacteristic
428C4#1458324411yescharacteristic
429C4#1458324411yescharacteristic
430C2—21no—
431C2—21no—
432C2—161no—
433C2—6881no—
434C2#1913539911yescharacteristic
435C2#1913549011yescharacteristic
436C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1517C2
socleC22×C43#390
prime radical#19145021C2
cosocleC2×C42×C43C23
hypercenter#1517D43
hypocenterC43#9756
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #19134757C2semidirect
3. #19133156C2semidirect
4. #19133155C2semidirect
5. #19133154C2semidirect
6. #19132879C2semidirect
7. C43×#1517C2semidirect
13. #14583278C4semidirect
14. #14583275C4semidirect
15. #14583273C4semidirect
16. #14583271C4semidirect
217. #1517D43semidirect
249. C43#9756semidirect

Maximal subgroups

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

subgroupindex
#191450212
#191347572
#191331562
#191331552
#191331542
#191328792
C43×#15172
#975643