Finite Group Databasebeta

← #25015000

Subgroups — #25015000

Order 11008.

426 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583329C211yesmaximal, characteristic
2C2×#14582728C211yesmaximal, characteristic, complemented
3C2×#14582706C211yesmaximal, characteristic, complemented
4C2×#14582705C211yesmaximal, characteristic, complemented
5C2×C4×C43⋊C16C211yesmaximal, characteristic, complemented
6#19135483C211yesmaximal, characteristic, complemented
7C43×#1974C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583329—22no—
10#14583329—22no—
11C2×#13063271C411yescharacteristic, complemented
12C2×#13063269C411yescharacteristic, complemented
13C2×#13063268C411yescharacteristic, complemented
14C2×#13063266C411yescharacteristic, complemented
15C22×C43⋊C16C2211yescharacteristic
16C22×C43⋊C16C2211yescharacteristic
17C2×#13063261C2211yescharacteristic
18C2×#13063253—21no—
19#14582865—21no—
20#14582728—22no—
21#14582706—22no—
22#14582705—22no—
23C4×C43⋊C16—22no—
24C2×#135×C43C2211yescharacteristic
25C2×#108×C43C2211yescharacteristic
26C2×#104×C43—21no—
27C43×#408—21no—
28C2×C4×C8×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37C2×#10621877—21no—
38#13063271—22no—
39#13063269—22no—
40#13063268—22no—
41#13063266—22no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16C2×C411yescharacteristic
45C2×C43⋊C16C2×C411yescharacteristic
46C2×C43⋊C16D412yes—
47C2×C43⋊C16D412yes—
48C2×C43⋊C16D412yes—
49#13063261—21no—
50#13063261—21no—
51#13063253—42no—
52(C2×D43)⋊C8—42no—
53C2×#41×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43—21no—
57#135×C43—21no—
58C2×Q16×C43C2×C411yescharacteristic
59C2×SD16×C43—21no—
60C2×D8×C43C2×C411yescharacteristic
61C2×M16×C43—21no—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C2×C42×C43D411yescharacteristic
65#108×C43—21no—
66#108×C43—21no—
67#104×C43—42no—
68C22⋊C8×C43—42no—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71#41×C43—41no—
72#41×C43—41no—
73#41×C43—41no—
74#41×C43—41no—
75C2×Q8×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—41no—
78C22×C4×C43—21no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89Q16×C43—21no—
90Q16×C43—21no—
91SD16×C43—41no—
92SD16×C43—41no—
93D8×C43—21no—
94D8×C43—21no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—41no—
100C2×C8×C43D812yes—
101C2×C8×C43C22×C411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43#4111yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C42×C43—21no—
108C42×C43D812yes—
109#10621877—41no—
110#10621877—41no—
111C2×C43⋊C8—41no—
112Dic172—21no—
113Dic172—21no—
114D344—21no—
115D344—21no—
116#10621873—41no—
117#10621873—41no—
118C43⋊C16—22no—
119C43⋊C16C22⋊C412yes—
120C43⋊C16C22⋊C412yes—
121C23×C43—41no—
122C23×C43#13511yescharacteristic
123C22×D43—41no—
124Q8×C43—41no—
125Q8×C43—41no—
126D4×C43—41no—
127D4×C43—41no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43—24no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12711yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×D811yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—41no—
144D172—41no—
145D172—41no—
146C4×D43—81no—
147C4×D43—81no—
148Dic86—41no—
149Dic86—41no—
150C8×C43—22no—
151C8×C43—81no—
152C8×C43C2×C22⋊C411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12411yescharacteristic
156C43⋊C8—81no—
157#13241—431nomaximal, Sylow
158C22×C43—22no—
159C22×C43—82no—
160C22×C43—81no—
161C22×C43C4×D811yescharacteristic
162C22×C43#46611yescharacteristic
163C22×C43#49511yescharacteristic
164C2×D43—82no—
165C2×D43—81no—
166C4×C43—24no—
167C4×C43—81no—
168C4×C43#39011yescharacteristic
169C4×C43C4×D811yescharacteristic
170C4×C43#46611yescharacteristic
171C4×C43#49311yescharacteristic
172Dic43—81no—
173C2×#508—431no—
174C2×#368—431no—
175C2×#359—431no—
176C2×#359—431no—
177C2×C4×C16—431no—
178#1974—431no—
179#1974D4311yescharacteristic, complemented
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—161no—
183C2×C43#197011yescharacteristic
184C2×C43#217812yes—
185D43—161no—
186C2×#135—431no—
187C2×#135C2×D4311yescharacteristic
188#508—862no—
189#508—862no—
190C2×Q32—431no—
191C2×SD32—431no—
192C2×SD32—431no—
193C2×D16—431no—
194C22×C16—431no—
195C22×C16—431no—
196C2×#108—431no—
197C2×#108C2×D4311yescharacteristic
198C2×#104—21no—
199C2×#104—861no—
200#408—21no—
201#408—861no—
202C2×C4×C8C2×D4311yescharacteristic
203#368—862no—
204#359—862no—
205#359—862no—
206C4×C16—862no—
207C43#1324111yescharacteristic, complemented, Sylow
208C2×#41—21no—
209C2×#41—861no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—861no—
215#135—861no—
216#135—861no—
217#135—861no—
218C2×Q16—431no—
219C2×Q16C4×D4311yescharacteristic
220C2×SD16—21no—
221C2×SD16—861no—
222C2×D8—431no—
223C2×D8C4×D4311yescharacteristic
224C2×M16—21no—
225C2×M16—861no—
226C22×C8C22⋊D4311yescharacteristic
227C22×C8C22×D4311yescharacteristic
228C2×C42C22⋊D4311yescharacteristic
229Q32—862no—
230SD32—862no—
231SD32—862no—
232D16—862no—
233C2×C16—431no—
234C2×C16—431no—
235C2×C16—432no—
236C2×C16—432no—
237C2×C16—432no—
238C2×C16—861no—
239C2×C16—861no—
240#108—21no—
241#108—21no—
242#108—861no—
243#108—861no—
244#104—42no—
245#104—1722no—
246C22⋊C8—42no—
247C22⋊C8—1722no—
248C4×C8—21no—
249C4×C8—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—1721no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258C2×Q8—21no—
259C2×Q8—861no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—861no—
263C2×D4—1721no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—1721no—
267C22×C4C2×C22⋊D4311yescharacteristic
268Q16—21no—
269Q16—21no—
270Q16—861no—
271Q16—861no—
272SD16—41no—
273SD16—41no—
274SD16—1721no—
275SD16—1721no—
276D8—21no—
277D8—21no—
278D8—861no—
279D8—861no—
280M16—41no—
281M16—41no—
282M16—1721no—
283M16—1721no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—1721no—
288C2×C8#1062188212yes—
289C2×C8C2×C4×D4311yescharacteristic
290C2×C8#1062189811yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8D4×D4311yescharacteristic
294C2×C8#1062190011yescharacteristic
295C42—21no—
296C42#1062188212yes—
297C16—432no—
298C16—432no—
299C16—862no—
300C23—41no—
301C23—1721no—
302C23#1306334511yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—1721no—
306Q8—1721no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—3441no—
312D4—3441no—
313D4—1721no—
314D4—1721no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4C4×C22⋊D4311yescharacteristic
324C2×C4#1306329711yescharacteristic
325C2×C4#1306332111yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4C2×#1062188211yescharacteristic
328C2×C4#1306334511yescharacteristic
329C8—22no—
330C8—81no—
331C8—3441no—
332C8C22⋊C4×D4311yescharacteristic
333C8(C22⋊D43)⋊C411yescharacteristic
334C8#1306329811yescharacteristic
335C8#1306331111yescharacteristic
336C22—22no—
337C22—82no—
338C22—81no—
339C22—3442no—
340C22—3441no—
341C22C4×#1062188211yescharacteristic
342C22#1458313311yescharacteristic
343C22#1458328111yescharacteristic
344C4—24no—
345C4—81no—
346C4—3441no—
347C4#1458279911yescharacteristic
348C4C4×#1062188211yescharacteristic
349C4#1458313311yescharacteristic
350C4#1458327511yescharacteristic
351C2—21no—
352C2—21no—
353C2—161no—
354C2—6881no—
355C2#1913546011yescharacteristic
356C2#1913647412yes—
subgroupG/H
centerC2×C4C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1974C2
socleC22×C43C4×D8
prime radicalC2×#14583329C2
cosocleC22×C8×C43C23
hypercenter#1974D43
hypocenterC43#13241
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#14582728C2semidirect
3. C2×#14582706C2semidirect
4. C2×#14582705C2semidirect
5. C2×C4×C43⋊C16C2semidirect
6. #19135483C2semidirect
7. C43×#1974C2semidirect
11. C2×#13063271C4semidirect
12. C2×#13063269C4semidirect
13. C2×#13063268C4semidirect
14. C2×#13063266C4semidirect
179. #1974D43semidirect
207. C43#13241semidirect

Maximal subgroups

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

subgroupindex
C2×#145833292
C2×#145827282
C2×#145827062
C2×#145827052
C2×C4×C43⋊C162
#191354832
C43×#19742
#1324143