Finite Group Databasebeta

← #25013733

Subgroups — #25013733

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143471C211yesmaximal, characteristic
2C2×#14582706C211yesmaximal, characteristic
3C2×#14582703C211yesmaximal, characteristic, complemented
4#19135511C211yesmaximal, characteristic, complemented
5#19132704C211yesmaximal, characteristic, complemented
6#19132685C211yesmaximal, characteristic, complemented
7C2×C43×#510C211yesmaximal, characteristic
8#14583382—21no—
9C22×C43⋊C16C2211yescharacteristic
10#14583000—22no—
11Q16×Dic43—21no—
12D8×Dic43—21no—
13C2×#13063261C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15#14582908—21no—
16#14582900—21no—
17C2×#13063244—21no—
18#14582854C2211yescharacteristic
19#14582706—22no—
20#14582703—22no—
21C2×#135×C43C2211yescharacteristic
22C22×Q16×C43C2211yescharacteristic
23C43×#510—22no—
24C43×#510C414yescomplemented
25C2×Q32×C43—21no—
26C2×SD32×C43—21no—
27C2×M32×C43C2211yescharacteristic
28C2×#10621877—21no—
29C2×#10621877D411yescharacteristic
30Q8×Dic43—22no—
31D4×Dic43—22no—
32D4×Dic43—42no—
33#13063284—41no—
34#13063284D411yescharacteristic
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—41no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16—21no—
40#13063261—21no—
41#13063261—21no—
42#13063259—21no—
43#13063259D412yes—
44#13063249—22no—
45#13063249—41no—
46#13063249—41no—
47#13063246—22no—
48#13063244—42no—
49#13063235—21no—
50C8×Dic43—21no—
51C2×#41×C43—21no—
52C22×Q8×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43C2×C412yes—
56#135×C43D412yes—
57C2×Q16×C43—21no—
58C2×Q16×C43—21no—
59C2×Q16×C43—21no—
60C2×Q16×C43—21no—
61C2×Q16×C43—21no—
62C2×Q16×C43C2×C412yescomplemented
63C2×Q16×C43D411yescharacteristic
64C2×SD16×C43—21no—
65C2×D8×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67Q32×C43—24no—
68SD32×C43—24no—
69M32×C43—21no—
70M32×C43C2×C412yescomplemented
71C2×C16×C43—21no—
72#41×C43—22no—
73#41×C43—22no—
74#41×C43—41no—
75#41×C43—41no—
76C2×Q8×C43—22no—
77C2×Q8×C43—21no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C2×D4×C43—21no—
84C2×D4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—42no—
89C22×Dic43—41no—
90Q16×C43—22no—
91Q16×C43—22no—
92Q16×C43—21no—
93Q16×C43—41no—
94Q16×C43—41no—
95Q16×C43C22⋊C412yes—
96SD16×C43—22no—
97SD16×C43—22no—
98D8×C43—21no—
99D8×C43C22⋊C412yes—
100C2×C8×C43C22×C411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C2×C8×C43#4111yescharacteristic
106C22⋊Dic43—21no—
107C22⋊Dic43—42no—
108C4⋊Dic43—22no—
109C4⋊Dic43—42no—
110C4⋊Dic43—41no—
111C4⋊Dic43D811yescharacteristic
112C4⋊Dic43D811yescharacteristic
113C4×Dic43—21no—
114C4×Dic43—42no—
115#10621877—21no—
116#10621877—21no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—41no—
121C16×C43—22no—
122C43⋊C16—41no—
123C23×C43—41no—
124C23×C43AGL(1,ℤ/8)11yescharacteristic
125Q8×C43—22no—
126Q8×C43—41no—
127Q8×C43—42no—
128Q8×C43—42no—
129Q8×C43—81no—
130Q8×C43—81no—
131D4×C43—22no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43C2×D811yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—42no—
150C2×Dic43—162no—
151C2×Dic43—161no—
152C8×C43C2×C22⋊C411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12311yescharacteristic
156C43⋊C8—41no—
157C43⋊C8—81no—
158#13023—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—42no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43#44211yescharacteristic
165C22×C43#44711yescharacteristic
166C22×C43#46311yescharacteristic
167C4×C43—42no—
168C4×C43—82no—
169C4×C43#38611yescharacteristic
170C4×C43C4×D811yescharacteristic
171C4×C43#44911yescharacteristic
172C4×C43#45911yescharacteristic
173Dic43—41no—
174Dic43—41no—
175Dic43—82no—
176C2×#510D4311yescharacteristic
177#2951—431no—
178C2×#359—431no—
179C2×#358—431no—
180#1979—431no—
181#1387—431no—
182#1379—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—82no—
186C2×C43#187911yescharacteristic
187C2×C43#219411yescharacteristic
188C2×C43#219511yescharacteristic
189C2×#135C2×D4311yescharacteristic
190C22×Q16C2×D4311yescharacteristic
191#520—861no—
192#510—22no—
193#510Dic4314yescomplemented
194C2×Q32—21no—
195C2×SD32—21no—
196C2×M32C2×D4311yescharacteristic
197C22×C16—431no—
198#440—862no—
199C4×Q16—861no—
200C4×D8—861no—
201C2×#108—431no—
202C2×#107—431no—
203#419—861no—
204#417—861no—
205C2×#101—861no—
206#405—431no—
207#359—862no—
208#358—862no—
209C43#1302311yescharacteristic, complemented, Sylow
210C2×#41—21no—
211C22×Q8—21no—
212#135—21no—
213#135—21no—
214#135C2×Dic4312yes—
215#135C22⋊D4312yes—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16C2×Dic4312yescomplemented
222C2×Q16C22⋊D4311yescharacteristic
223C2×SD16—21no—
224C2×D8C22⋊D4311yescharacteristic
225C2×M16—431no—
226C2×M16—861no—
227C22×C8C22×D4311yescharacteristic
228C4×Q8—862no—
229C4×D4—862no—
230C4×D4—1722no—
231#117—431no—
232#117—1721no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—1721no—
235Q32—24no—
236SD32—24no—
237M32—21no—
238M32C2×Dic4312yescomplemented
239C2×C16—21no—
240C2×C16—861no—
241C2×C16—861no—
242C2×C16—861no—
243#108—861no—
244#108—861no—
245#107—432no—
246#107—861no—
247#103—862no—
248#103—1721no—
249#103—1721no—
250#102—862no—
251#101—1722no—
252#97—861no—
253C4×C8—861no—
254#41—22no—
255#41—22no—
256#41—41no—
257#41—41no—
258C2×Q8—22no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—1722no—
270C22×C4—1721no—
271C22×C4D4×D4311yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—21no—
275Q16—41no—
276Q16—41no—
277Q16C22⋊Dic4312yes—
278SD16—22no—
279SD16—22no—
280D8—21no—
281D8C22⋊Dic4312yes—
282M16—861no—
283M16—861no—
284M16—1721no—
285M16—1721no—
286C2×C8—861no—
287C2×C8—1721no—
288C2×C8D4×D4311yescharacteristic
289C2×C8#1062190011yescharacteristic
290C2×C8#1062190011yescharacteristic
291C2×C8C22×Dic4311yescharacteristic
292C2×C8C2×C22⋊D4311yescharacteristic
293C2×C8C2×C22⋊D4311yescharacteristic
294C4⋊C4—431no—
295C4⋊C4—431no—
296C4⋊C4—862no—
297C4⋊C4—1722no—
298C4⋊C4—1721no—
299C22⋊C4—861no—
300C22⋊C4—1722no—
301C42—861no—
302C42—1722no—
303C16—22no—
304C16—1721no—
305C23—41no—
306C23#1306334911yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—42no—
310Q8—42no—
311Q8—81no—
312Q8—81no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—1722no—
326C2×C4—6881no—
327C2×C4—6882no—
328C2×C4D4×Dic4311yescharacteristic
329C2×C4#1306329311yescharacteristic
330C2×C4#1306329711yescharacteristic
331C2×C4D8×D4311yescharacteristic
332C2×C4#1306334411yescharacteristic
333C2×C4#1306334911yescharacteristic
334C8—3441no—
335C8—1721no—
336C8C2×C22⋊Dic4311yescharacteristic
337C8D4×Dic4311yescharacteristic
338C8#1306329711yescharacteristic
339C8#1306330611yescharacteristic
340C22—21no—
341C22—21no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22#1458301111yescharacteristic
346C22#1458303111yescharacteristic
347C22#1458311211yescharacteristic
348C4—42no—
349C4—82no—
350C4—3442no—
351C4—1721no—
352C4—1721no—
353C4#1458277911yescharacteristic
354C4D8×Dic4311yescharacteristic
355C4#1458304111yescharacteristic
356C4#1458309211yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1913494511yescharacteristic
361C2#1913656311yescharacteristic
362C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#510C2
socleC22×C43#447
prime radicalC2×#135×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#510D43
hypocenterC43#13023
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
3. C2×#14582703C2semidirect
4. #19135511C2semidirect
5. #19132704C2semidirect
6. #19132685C2semidirect
24. C43×#510C4semidirect
62. C2×Q16×C43C2×C4semidirect
70. M32×C43C2×C4semidirect
193. #510Dic43semidirect
209. C43#13023semidirect
221. C2×Q16C2×Dic43semidirect
238. M32C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191434712
C2×#145827062
C2×#145827032
#191355112
#191327042
#191326852
C2×C43×#5102
#1302343