Finite Group Databasebeta

← #24990932

Subgroups — #24990932

Order 11008.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135370C211yesmaximal, characteristic
2#19133353C211yesmaximal, characteristic
3#19133024C211yesmaximal, characteristic
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic
5#19132490C211yesmaximal, characteristic
6#19132433C211yesmaximal, characteristic
7Q8×M16×C43C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9C2×#13063260—21no—
10#14582923C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582663—21no—
14#14582651—22no—
15Q8⋊(C43⋊C8)—21no—
16Q8⋊(C43⋊C8)—21no—
17Q8⋊(C43⋊C8)C411yescharacteristic
18Q8⋊(C43⋊C8)C411yescharacteristic
19Q8⋊(C43⋊C8)C411yescharacteristic
20Q8⋊(C43⋊C8)C411yescharacteristic
21C2×C4×Q8×C43C2211yescharacteristic
22C43×#446—21no—
23C43×#446—22no—
24C8×Q8×C43—21no—
25C43×#423—21no—
26C43×#423C2211yescharacteristic
27C4×M16×C43—21no—
28C4×M16×C43C2211yescharacteristic
29C2×#10621877—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063260—42no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)C2×C411yescharacteristic
38C4⋊(C43⋊C8)C2×C411yescharacteristic
39C22⋊(C43⋊C8)—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8C2×C411yescharacteristic
43C4×C43⋊C8C2×C411yescharacteristic
44C22×Q8×C43Q811yescharacteristic
45C2×M16×C43—21no—
46C2×M16×C43D411yescharacteristic
47C2×M16×C43D411yescharacteristic
48C4×Q8×C43—21no—
49C4×Q8×C43—21no—
50C4×Q8×C43C2×C411yescharacteristic
51C4×Q8×C43C2×C411yescharacteristic
52C4×Q8×C43D411yescharacteristic
53C4×Q8×C43D411yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43Q811yescharacteristic
56C2×C42×C43—21no—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—22no—
59C4⋊C8×C43—22no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43D412yes—
62#97×C43—22no—
63#97×C43—21no—
64C4×C8×C43—22no—
65C4×C8×C43—21no—
66C2×Q8×C43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43C4⋊C411yescharacteristic
70C2×Q8×C43C4⋊C411yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×Q811yescharacteristic
75C22×C4×C43#4111yescharacteristic
76M16×C43—21no—
77M16×C43—21no—
78M16×C43—21no—
79M16×C43—41no—
80M16×C43—41no—
81M16×C43Q1612yes—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—22no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43C4⋊C411yescharacteristic
91C4⋊C4×C43C4⋊C411yescharacteristic
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43C22×C411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43#4111yescharacteristic
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—42no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43C22⋊Q811yescharacteristic
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—42no—
116Q8×C43#10812yescomplemented
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—81no—
126C2×C4×C43C2×C4⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43C22⋊Q811yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×Q1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C8×C43—22no—
137C8×C43—41no—
138C8×C43—42no—
139C43⋊C8—22no—
140C43⋊C8—41no—
141C43⋊C8—41no—
142C43⋊C8—41no—
143C43⋊C8—81no—
144C43⋊C8—81no—
145#8907—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#38511yescharacteristic
149C22×C43#47711yescharacteristic
150C22×C43#47911yescharacteristic
151C4×C43—21no—
152C4×C43—22no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#10811yescharacteristic
159C4×C43#43011yescharacteristic
160C4×C43C4×Q1611yescharacteristic
161C4×C43#44011yescharacteristic
162C4×C43#44911yescharacteristic
163C4×C43#45111yescharacteristic
164Q8×M16D4311yescharacteristic
165#1950—431no—
166#1567—431no—
167#1487—431no—
168C2×Q8⋊C8—431no—
169#1301—431no—
170#1278—431no—
171C2×C43—21no—
172C2×C43—21no—
173C2×C43#185511yescharacteristic
174C2×C43#186111yescharacteristic
175C2×C43#186311yescharacteristic
176C2×C4×Q8C2×D4311yescharacteristic
177#446—21no—
178#446—22no—
179C8×Q8—21no—
180#431—431no—
181C2×#108—861no—
182#423—21no—
183#423—431no—
184#423C2×D4311yescharacteristic
185C2×C4⋊C8—431no—
186C4×M16—21no—
187C4×M16C2×D4311yescharacteristic
188C2×C4×C8—431no—
189#341—861no—
190#335—862no—
191Q8⋊C8—431no—
192Q8⋊C8—431no—
193Q8⋊C8—431no—
194Q8⋊C8—431no—
195Q8⋊C8—861no—
196Q8⋊C8—861no—
197C43#890711yescharacteristic, complemented, Sylow
198C22×Q8Dic8611yescharacteristic
199C2×M16—21no—
200C2×M16—861no—
201C2×M16C22⋊D4311yescharacteristic
202C2×M16C22⋊D4311yescharacteristic
203C22×C8—861no—
204C22×C8—861no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C4×D4311yescharacteristic
208C4×Q8C4×D4311yescharacteristic
209C4×Q8C22⋊D4311yescharacteristic
210C4×Q8C22⋊D4311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Dic8611yescharacteristic
213C2×C42—21no—
214C2×C42C22×D4311yescharacteristic
215#108—1722no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—431no—
220C4⋊C8—431no—
221C4⋊C8—861no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C4⋊C8—861no—
225C4⋊C8C22⋊D4312yes—
226C22⋊C8—861no—
227#97—22no—
228#97—21no—
229C4×C8—22no—
230C4×C8—21no—
231C4×C8—431no—
232C4×C8—431no—
233C4×C8—861no—
234C4×C8—861no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8Dic43⋊C411yescharacteristic
239C2×Q8Dic43⋊C411yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic8611yescharacteristic
243C22×C4#1062189811yescharacteristic
244C22×C4C2×C22⋊D4311yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—1721no—
251M16—1721no—
252M16#1062188512yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—861no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—1722no—
261C2×C8—1721no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4Dic43⋊C411yescharacteristic
271C4⋊C4Dic43⋊C411yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C2×C4×D4311yescharacteristic
277C42#1062189811yescharacteristic
278C42C2×C22⋊D4311yescharacteristic
279C42C2×C22⋊D4311yescharacteristic
280C23#1306330411yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#1306326012yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×Dic43⋊C411yescharacteristic
296C2×C4C4×C22⋊D4311yescharacteristic
297C2×C4C4×C22⋊D4311yescharacteristic
298C2×C4#1306329411yescharacteristic
299C2×C4#1306330411yescharacteristic
300C2×C4#1306330811yescharacteristic
301C2×C4C2×#1062188511yescharacteristic
302C2×C4#1306334511yescharacteristic
303C2×C4#1306335011yescharacteristic
304C2×C4#1306335611yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—862no—
309C8—3441no—
310C8—3441no—
311C8—1721no—
312C8—1721no—
313C8—1721no—
314C22—21no—
315C22—21no—
316C22#1458277211yescharacteristic
317C22#1458319411yescharacteristic
318C22#1458320611yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#1306326011yescharacteristic
327C4#1458294711yescharacteristic
328C4C4×#1062188511yescharacteristic
329C4#1458299711yescharacteristic
330C4#1458304411yescharacteristic
331C4#1458305511yescharacteristic
332C2—21no—
333C2—21no—
334C2#1913480011yescharacteristic
335C2#1913483511yescharacteristic
336C2#1913484911yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingQ8×M16×C43C2
socleC22×C43#385
prime radicalC23×C43C22⋊Q8
cosocleC2×C42×C43C23
hypercenterQ8×M16D43
hypocenterC43#8907
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
116. Q8×C43#108semidirect
197. C43#8907semidirect
285. Q8#13063260semidirect

Maximal subgroups

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

subgroupindex
#191353702
#191333532
#191330242
C2×Q8⋊(C43⋊C8)2
#191324902
#191324332
Q8×M16×C432
#890743