Finite Group Databasebeta

← #25015058

Subgroups — #25015058

Order 11008.

478 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#19145019C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582707C211yesmaximal, characteristic, complemented
4C2×#14582706C211yesmaximal, characteristic, complemented
5C2×#14582705C211yesmaximal, characteristic, complemented
6#108×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×#359C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063345—21no—
10#14583445—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583284C411yescharacteristic
13#14583282C411yescharacteristic
14#14583280—21no—
15#14583277C411yescharacteristic
16#14583274C411yescharacteristic
17#14583270—21no—
18C2×#13063261C2211yescharacteristic
19M16×Dic43—21no—
20C2×C8×Dic43C2211yescharacteristic
21Dic43⋊C16—21no—
22Dic43⋊C16—21no—
23#14582707—22no—
24#14582706—22no—
25#14582705—22no—
26#14582663—21no—
27C2×#135×C43C2211yescharacteristic
28C22×C16×C43C2211yescharacteristic
29C2×#108×C43C2211yescharacteristic
30C43×#359—22no—
31C2×#10621898—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37#13063345—42no—
38C2×Dic172C2×C411yescharacteristic
39C2×#10621885—21no—
40C2×#10621873—21no—
41C2×#10621883—21no—
42C2×#10621884—21no—
43C2×D344C2×C411yescharacteristic
44C2×#10621882—21no—
45C2×#10621877—21no—
46C22×C43⋊C8D411yescharacteristic
47#13063323—21no—
48#13063321—21no—
49#13063314—21no—
50#13063312—21no—
51#13063297—41no—
52#13063297—41no—
53C4×C22⋊D43—41no—
54C4×C22⋊D43—41no—
55C2×C4×Dic43D411yescharacteristic
56C2×C43⋊C16—21no—
57C2×C43⋊C16—21no—
58C2×C43⋊C16—21no—
59#13063261—21no—
60#13063261D412yescomplemented
61#13063235—41no—
62C8×Dic43—41no—
63C8×Dic43C2×C411yescharacteristic
64C8×Dic43C2×C411yescharacteristic
65C8×Dic43D411yescharacteristic
66C8×Dic43D411yescharacteristic
67C2×#41×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72C2×Q16×C43C2×C411yescharacteristic
73C2×SD16×C43—21no—
74C2×D8×C43C2×C411yescharacteristic
75C2×M16×C43—21no—
76C22×C8×C43C2311yescharacteristic
77C2×C16×C43—21no—
78C2×C16×C43—21no—
79C2×C16×C43—21no—
80#108×C43—21no—
81#108×C43D412yescomplemented
82#41×C43—41no—
83#41×C43—41no—
84#41×C43—41no—
85#41×C43—41no—
86C2×Q8×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C22×Dic43SD1611yescharacteristic
95C22×Dic43SD1611yescharacteristic
96#10621898—41no—
97#10621898—41no—
98#10621898—41no—
99#10621898—41no—
100C2×D172—21no—
101C2×C4×D43—41no—
102C2×Dic86—21no—
103Q16×C43—21no—
104Q16×C43—21no—
105SD16×C43—41no—
106SD16×C43—41no—
107D8×C43—21no—
108D8×C43—21no—
109M16×C43—22no—
110M16×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43C22×C411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43#4111yescharacteristic
117C2×C8×C43#4111yescharacteristic
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120#10621885—42no—
121#10621884—42no—
122#10621883—42no—
123#10621882—42no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128C4×Dic43C22⋊C411yescharacteristic
129C4×Dic43C22⋊C411yescharacteristic
130C4×Dic43D811yescharacteristic
131C4×Dic43D811yescharacteristic
132#10621877—22no—
133#10621877—41no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8C22⋊C411yescharacteristic
138C2×C43⋊C8C22⋊C411yescharacteristic
139Dic172—21no—
140Dic172—21no—
141D344—21no—
142D344—21no—
143#10621873—41no—
144#10621873—41no—
145C16×C43—41no—
146C43⋊C16—41no—
147C23×C43—41no—
148C23×C43C2×SD1611yescharacteristic
149C22×D43—41no—
150Q8×C43—41no—
151Q8×C43—41no—
152D4×C43—41no—
153D4×C43—41no—
154D4×C43—81no—
155D4×C43—81no—
156C2×C4×C43—41no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C22⋊D43—82no—
166C22⋊D43—81no—
167C22⋊D43—81no—
168C22⋊D43—82no—
169C2×Dic43—22no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#10211yescharacteristic
173C2×Dic43#10211yescharacteristic
174C2×Dic43#10211yescharacteristic
175C2×Dic43#10211yescharacteristic
176D172—41no—
177D172—41no—
178C4×D43—81no—
179C4×D43—81no—
180Dic86—41no—
181Dic86—41no—
182C8×C43—42no—
183C8×C43C4×D411yescharacteristic
184C8×C43C4×D411yescharacteristic
185C8×C43#12411yescharacteristic
186C8×C43#12711yescharacteristic
187C43⋊C8—21no—
188C43⋊C8—21no—
189C43⋊C8—42no—
190#13251—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43C2×#10211yescharacteristic
197C22×C43#46011yescharacteristic
198C22×C43#46011yescharacteristic
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C4×C43—81no—
203C4×C43#39011yescharacteristic
204C4×C43#41811yescharacteristic
205C4×C43#45911yescharacteristic
206C4×C43#45911yescharacteristic
207Dic43—21no—
208Dic43—21no—
209Dic43—21no—
210Dic43—81no—
211Dic43#35912yescomplemented
212#3147—431no—
213C2×C4⋊C16—431no—
214C2×#359—431no—
215C2×#359—431no—
216C2×#359—431no—
217C2×#359D4311yescharacteristic, complemented
218C4×#108—431no—
219C2×C43—21no—
220C2×C43—21no—
221C2×C43—161no—
222C2×C43#198211yescharacteristic
223C2×C43C2×#35911yescharacteristic
224C2×C43#214311yescharacteristic
225D43—161no—
226C2×#135—431no—
227C2×#135—861no—
228C2×#135C2×D4311yescharacteristic
229#532—861no—
230C22×C16—431no—
231C22×C16C2×D4311yescharacteristic
232#495—431no—
233#495—431no—
234#495—861no—
235#494—431no—
236#493—431no—
237#492—861no—
238C2×#108—431no—
239C2×#108C2×D4311yescharacteristic
240C4×M16—861no—
241C2×C4×C8—431no—
242C4⋊C16—861no—
243C4⋊C16—861no—
244#359—22no—
245#359—862no—
246#359—862no—
247#359—862no—
248#341—861no—
249C43#1325111yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41—861no—
252#135—21no—
253#135—21no—
254#135—21no—
255#135—21no—
256#135—861no—
257#135—861no—
258#135—861no—
259#135—861no—
260#135—1722no—
261#135—1722no—
262C2×Q16—431no—
263C2×Q16—861no—
264C2×Q16C4×D4311yescharacteristic
265C2×SD16—21no—
266C2×SD16—861no—
267C2×SD16—861no—
268C2×SD16—861no—
269C2×D8—431no—
270C2×D8—861no—
271C2×D8C4×D4311yescharacteristic
272C2×M16—21no—
273C2×M16—861no—
274C22×C8—431no—
275C22×C8C22×D4311yescharacteristic
276C4⋊Q8—861no—
277#127—861no—
278#124—861no—
279#124—861no—
280#121—1721no—
281#121—1721no—
282C4×D4—1721no—
283C4×D4—1721no—
284C2×C42—431no—
285C2×C16—21no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—861no—
289C2×C16—861no—
290C2×C16—861no—
291#108—21no—
292#108—432no—
293#108—861no—
294#108C22⋊D4312yescomplemented
295#97—1721no—
296C4×C8—431no—
297C4×C8—431no—
298C4×C8—431no—
299C4×C8—431no—
300C4×C8—1721no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—1721no—
306#41—1721no—
307#41—1721no—
308#41—1721no—
309C2×Q8—21no—
310C2×Q8—861no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—861no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C22×C4—41no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—1721no—
321C22×C4D4×D4311yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—861no—
325Q16—861no—
326Q16—1722no—
327SD16—41no—
328SD16—41no—
329SD16—1722no—
330SD16—1722no—
331SD16—1721no—
332SD16—1721no—
333D8—21no—
334D8—21no—
335D8—861no—
336D8—861no—
337D8—1722no—
338M16—22no—
339M16—41no—
340M16—862no—
341M16—1721no—
342C2×C8—41no—
343C2×C8—431no—
344C2×C8—431no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—1721no—
348C2×C8C2×C4×D4311yescharacteristic
349C2×C8#1062189811yescharacteristic
350C2×C8D4×D4311yescharacteristic
351C2×C8D4×D4311yescharacteristic
352C2×C8#1062190011yescharacteristic
353C2×C8C2×C22⋊D4311yescharacteristic
354C4⋊C4—1721no—
355C4⋊C4—1721no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C42—431no—
361C42—431no—
362C42—431no—
363C42—431no—
364C16—41no—
365C16—1721no—
366C23—41no—
367C23—1721no—
368C23SD16×D4311yescharacteristic
369Q8—41no—
370Q8—41no—
371Q8—1721no—
372Q8—1721no—
373D4—41no—
374D4—41no—
375D4—81no—
376D4—81no—
377D4—3442no—
378D4—3442no—
379D4—3441no—
380D4—3441no—
381D4—1721no—
382D4—1721no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—431no—
387C2×C4—431no—
388C2×C4—431no—
389C2×C4—431no—
390C2×C4—862no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4C22⋊C4×D4311yescharacteristic
396C2×C4#1306329711yescharacteristic
397C2×C4#1306329811yescharacteristic
398C2×C4D8×D4311yescharacteristic
399C2×C4#1306334911yescharacteristic
400C2×C4#1306335211yescharacteristic
401C8—42no—
402C8—861no—
403C8—861no—
404C8—1722no—
405C8(C22⋊D43)⋊C411yescharacteristic
406C8C4×C22⋊D4311yescharacteristic
407C8#1306331111yescharacteristic
408C8#1306332111yescharacteristic
409C22—21no—
410C22—21no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22#102×D4311yescharacteristic
418C22#1458309711yescharacteristic
419C22#1458309811yescharacteristic
420C4—81no—
421C4—432no—
422C4—861no—
423C4—861no—
424C4—861no—
425C4—3441no—
426C4#1458279911yescharacteristic
427C4#1458290211yescharacteristic
428C4#1458309211yescharacteristic
429C4#1458309311yescharacteristic
430C2—21no—
431C2—21no—
432C2—161no—
433C2—6881no—
434C2#1913552011yescharacteristic
435C2#359×D4311yescharacteristic
436C2#1913632111yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#359C2
socleC22×C43C2×#102
prime radical#19145019C2
cosocleC22×C8×C43C23
hypercenterC2×#359D43
hypocenterC43#13251
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×Dic43⋊C16C2semidirect
3. C2×#14582707C2semidirect
4. C2×#14582706C2semidirect
5. C2×#14582705C2semidirect
6. #108×Dic43C2semidirect
7. C2×C43×#359C2semidirect
60. #13063261D4semidirect
81. #108×C43D4semidirect
211. Dic43#359semidirect
217. C2×#359D43semidirect
249. C43#13251semidirect
294. #108C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450192
C2×Dic43⋊C162
C2×#145827072
C2×#145827062
C2×#145827052
#108×Dic432
C2×C43×#3592
#1325143