Finite Group Databasebeta

← #25012657

Subgroups — #25012657

Order 11008.

422 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143366C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582707C211yesmaximal, characteristic
4C2×#14582705C211yesmaximal, characteristic
5#19134765C211yesmaximal, characteristic, complemented
6#19132690C211yesmaximal, characteristic, complemented
7C43×#1382C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583367—21no—
10C22×C43⋊C16C2211yescharacteristic
11#14582993C411yescharacteristic
12#14582993C411yescharacteristic
13#14582986—21no—
14#14582986—21no—
15#14582981C411yescharacteristic
16#14582981C411yescharacteristic
17C2×#13063261C2211yescharacteristic
18C2×#13063260—21no—
19#14582922—21no—
20#14582893—21no—
21C2×C8×Dic43C2211yescharacteristic
22Dic43⋊C16—21no—
23Dic43⋊C16—21no—
24#14582707—22no—
25#14582705—22no—
26C22×C16×C43C2211yescharacteristic
27C2×#108×C43C2211yescharacteristic
28C43×#427C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347D412yes—
33#13063347Q812yes—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37C2×#10621877—21no—
38C22×C43⋊C8D411yescharacteristic
39#13063290—21no—
40#13063290—21no—
41#13063287—21no—
42#13063287—21no—
43(C22⋊D43)⋊C4—41no—
44(C22⋊D43)⋊C4—41no—
45#13063282—41no—
46C2×C4×Dic43D411yescharacteristic
47C42×D43—41no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50C2×C43⋊C16—21no—
51#13063261—21no—
52#13063261—21no—
53#13063260—42no—
54Dic43⋊C8—41no—
55Dic43⋊C8—41no—
56#13063248—21no—
57#13063248—21no—
58#13063245—21no—
59#13063245—21no—
60C8×Dic43C2×C411yescharacteristic
61C8×Dic43C2×C411yescharacteristic
62C8×Dic43D411yescharacteristic
63C8×Dic43D411yescharacteristic
64C2×M16×C43—21no—
65C22×C8×C43C2311yescharacteristic
66#117×C43—21no—
67C2×C16×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70#108×C43—21no—
71#108×C43—21no—
72#107×C43C2×C411yescharacteristic
73#107×C43C2×C411yescharacteristic
74#106×C43—21no—
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—41no—
77C22×Dic43SD1611yescharacteristic
78C22×Dic43SD1611yescharacteristic
79#10621898—22no—
80#10621898—22no—
81#10621898—41no—
82#10621898—41no—
83C2×D172—21no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×Dic86—21no—
88M16×C43—41no—
89M16×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×Q811yescharacteristic
95C2×C8×C43#4111yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C22⋊C4×C43—41no—
100C42×C43—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C4×Dic43C22⋊C411yescharacteristic
108C4×Dic43C22⋊C411yescharacteristic
109C4×Dic43D811yescharacteristic
110C4×Dic43D811yescharacteristic
111#10621877—41no—
112#10621877—41no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8C22⋊C411yescharacteristic
117C2×C43⋊C8C22⋊C411yescharacteristic
118Dic172—21no—
119Dic172C4⋊C412yes—
120D344—21no—
121D344C4⋊C412yes—
122#10621873—22no—
123#10621873—22no—
124C16×C43—41no—
125C43⋊C16—41no—
126C23×C43C2×SD1611yescharacteristic
127C22×D43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43C22⋊Q811yescharacteristic
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C22⋊D43—42no—
137C22⋊D43—42no—
138C2×Dic43—22no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43#10211yescharacteristic
142C2×Dic43#10211yescharacteristic
143C2×Dic43#10211yescharacteristic
144C2×Dic43#10211yescharacteristic
145D172—22no—
146D172—41no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43—82no—
150C4×D43—82no—
151Dic86—22no—
152Dic86—41no—
153C8×C43—81no—
154C8×C43C2×C4⋊C411yescharacteristic
155C8×C43#11711yescharacteristic
156C8×C43#12111yescharacteristic
157C8×C43C22⋊Q811yescharacteristic
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—81no—
161#12815—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43C2×#10211yescharacteristic
165C22×C43#46111yescharacteristic
166C22×C43#47611yescharacteristic
167C2×D43—42no—
168C2×D43—81no—
169C2×D43—81no—
170C4×C43—81no—
171C4×C43—81no—
172C4×C43#38011yescharacteristic
173C4×C43#41711yescharacteristic
174C4×C43#45911yescharacteristic
175C4×C43#47411yescharacteristic
176Dic43—21no—
177Dic43—21no—
178Dic43—21no—
179Dic43—42no—
180Dic43#35912yescomplemented
181C4×#135—431no—
182C2×C4⋊C16—431no—
183C2×#359—431no—
184C2×#359—431no—
185#1848—431no—
186#1382—431no—
187#1382D4311yescharacteristic, complemented
188C2×C43—21no—
189C2×C43—21no—
190C2×C43#180211yescharacteristic
191C2×C43C2×#35911yescharacteristic
192C2×C43#214311yescharacteristic
193D43—82no—
194C2×#135—431no—
195C4×#41—861no—
196C22×C16—431no—
197C22×C16C2×D4311yescharacteristic
198C4×Q16—431no—
199C4×Q16—431no—
200C4×SD16—861no—
201C4×SD16—861no—
202C4×D8—431no—
203C4×D8—431no—
204C2×#108—431no—
205C2×#108—861no—
206C2×#108C2×D4311yescharacteristic
207#427C2×D4311yescharacteristic
208#423—861no—
209#416—861no—
210C2×C4×C8—431no—
211C4⋊C16—861no—
212C4⋊C16—861no—
213#359—862no—
214#359—862no—
215C43#1281511yescharacteristic, complemented, Sylow
216C2×#41—861no—
217#135—432no—
218#135—432no—
219#135—861no—
220#135—861no—
221C2×Q16—431no—
222C2×SD16—861no—
223C2×D8—431no—
224C2×M16—21no—
225C2×M16—861no—
226C22×C8—431no—
227C22×C8C22×D4311yescharacteristic
228C4×Q8—861no—
229C4×Q8—861no—
230C4×D4—861no—
231C4×D4—861no—
232C4×D4—1721no—
233C4×D4—1721no—
234#117—21no—
235#117—1721no—
236C2×C42—431no—
237C2×C42—1721no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—861no—
242C2×C16—861no—
243C2×C16—861no—
244#108—21no—
245#108—21no—
246#108—861no—
247#108—861no—
248#108—1722no—
249#107C4×D4311yescharacteristic
250#107C4×D4311yescharacteristic
251#106—21no—
252C4⋊C8—1721no—
253C4⋊C8—1721no—
254#103—861no—
255#103—861no—
256#102—861no—
257#102—861no—
258C4×C8—431no—
259C4×C8—431no—
260C4×C8—431no—
261C4×C8—431no—
262#41—862no—
263#41—862no—
264#41—1721no—
265#41—1721no—
266C2×Q8—861no—
267C2×D4—861no—
268C2×D4—1721no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—1721no—
272C22×C4—1721no—
273C22×C4—1721no—
274C22×C4D4×D4311yescharacteristic
275Q16—432no—
276Q16—861no—
277SD16—862no—
278SD16—862no—
279D8—432no—
280D8—861no—
281M16—41no—
282M16—41no—
283M16—1721no—
284M16—1721no—
285C2×C8—41no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—1721no—
291C2×C8C2×C4×D4311yescharacteristic
292C2×C8#1062189811yescharacteristic
293C2×C8#1062189811yescharacteristic
294C2×C8D4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8Q8×D4311yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—41no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C42—41no—
305C42—431no—
306C42—431no—
307C42—431no—
308C42—431no—
309C42—1721no—
310C42—1721no—
311C16—41no—
312C16—1721no—
313C23—1721no—
314C23SD16×D4311yescharacteristic
315Q8—862no—
316Q8—1721no—
317D4—862no—
318D4—1722no—
319D4—1722no—
320D4—1721no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—862no—
328C2×C4—3442no—
329C2×C4—3442no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4C22⋊C4×D4311yescharacteristic
335C2×C4#1306329811yescharacteristic
336C2×C4#1306330311yescharacteristic
337C2×C4D8×D4311yescharacteristic
338C2×C4#1306335211yescharacteristic
339C2×C4#1306335711yescharacteristic
340C8—81no—
341C8—861no—
342C8—861no—
343C8—3441no—
344C8C4⋊C4×D4311yescharacteristic
345C8#1306328211yescharacteristic
346C8#1306329811yescharacteristic
347C8#1306330311yescharacteristic
348C22—21no—
349C22—21no—
350C22—3441no—
351C22—3441no—
352C22—1722no—
353C22#102×D4311yescharacteristic
354C22#1458310311yescharacteristic
355C22#1458318811yescharacteristic
356C4—81no—
357C4—81no—
358C4—432no—
359C4—861no—
360C4—861no—
361C4—861no—
362C4—1722no—
363C4#1458275811yescharacteristic
364C4#1458289911yescharacteristic
365C4#1458309311yescharacteristic
366C4#1458317811yescharacteristic
367C2—21no—
368C2—21no—
369C2—3442no—
370C2#1913459411yescharacteristic
371C2#359×D4311yescharacteristic
372C2#1913632111yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1382C2
socleC22×C43C2×#102
prime radicalC2×#13063347C22
cosocleC22×C8×C43C23
hypercenter#1382D43
hypocenterC43#12815
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×Dic43⋊C16C2semidirect
5. #19134765C2semidirect
6. #19132690C2semidirect
7. C43×#1382C2semidirect
180. Dic43#359semidirect
187. #1382D43semidirect
215. C43#12815semidirect

Maximal subgroups

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

subgroupindex
#191433662
C2×Dic43⋊C162
C2×#145827072
C2×#145827052
#191347652
#191326902
C43×#13822
#1281543