Finite Group Databasebeta

← #24990929

Subgroups — #24990929

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#19143546C211yesmaximal, characteristic
2#19135368C211yesmaximal, characteristic
3#19133023C211yesmaximal, characteristic
4C2×#14582631C211yesmaximal, characteristic
5#19132490C211yesmaximal, characteristic
6#19132432C211yesmaximal, characteristic
7C43×#1567C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583028—22no—
10#14583026—21no—
11#14583023—21no—
12#14582952C2211yescharacteristic
13C2×#13063260—21no—
14#14582922—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17M16×Dic43—21no—
18#14582663—21no—
19#14582631C411yescharacteristic
20#14582631C411yescharacteristic
21#14582631C411yescharacteristic
22#14582631C411yescharacteristic
23#14582629—21no—
24#14582629—21no—
25C43×#423C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C43×#335—22no—
29C22×Dic86Q811yescharacteristic
30C2×#10621877D411yescharacteristic
31C2×#10621877D411yescharacteristic
32C22×C43⋊C8—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86C2×C411yescharacteristic
36C4×Dic86C2×C411yescharacteristic
37C4×Dic86D411yescharacteristic
38C4×Dic86D411yescharacteristic
39C2×C4⋊Dic43Q811yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×C4×Dic43—21no—
42#13063260—42no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C411yescharacteristic
46C4⋊(C43⋊C8)C2×C411yescharacteristic
47Dic43⋊C8—22no—
48Dic43⋊C8—22no—
49C22⋊(C43⋊C8)—21no—
50#13063236—21no—
51#13063235—22no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8—21no—
54C8×Dic43—22no—
55C2×M16×C43—21no—
56C2×M16×C43—21no—
57C22×C8×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43D412yes—
63C4×C8×C43—21no—
64C4×C8×C43C2×C411yescharacteristic
65C4×C8×C43C2×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×Q811yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—22no—
72C2×Dic86—21no—
73C2×Dic86—41no—
74C2×Dic86C4⋊C411yescharacteristic
75C2×Dic86C4⋊C411yescharacteristic
76M16×C43—41no—
77M16×C43—41no—
78M16×C43—41no—
79M16×C43—41no—
80C2×C8×C43—21no—
81C2×C8×C43—21no—
82C2×C8×C43—22no—
83C2×C8×C43—42no—
84C2×C8×C43—41no—
85C42×C43C22×C411yescharacteristic
86C42×C43C2×D411yescharacteristic
87C42×C43C2×D411yescharacteristic
88C42×C43#4111yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43C4⋊C411yescharacteristic
91C4⋊Dic43C4⋊C411yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100#10621877—21no—
101#10621877—21no—
102#10621877—21no—
103#10621877Q1612yes—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43C22⋊Q811yescharacteristic
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43C2×C4⋊C411yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43#12011yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43C2×Q1611yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—42no—
130C2×Dic43—81no—
131Dic86—21no—
132Dic86—21no—
133Dic86—21no—
134Dic86—42no—
135Dic86#10812yescomplemented
136C8×C43—22no—
137C8×C43—41no—
138C8×C43—42no—
139C8×C43—81no—
140C43⋊C8—22no—
141C43⋊C8—41no—
142C43⋊C8—41no—
143C43⋊C8—41no—
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—21no—
153C4×C43—21no—
154C4×C43C2×#10811yescharacteristic
155C4×C43#43011yescharacteristic
156C4×C43C4×Q1611yescharacteristic
157C4×C43#44011yescharacteristic
158C4×C43#44911yescharacteristic
159C4×C43#45111yescharacteristic
160Dic43—22no—
161Dic43—41no—
162Dic43—41no—
163Dic43—41no—
164Q8×M16—431no—
165#1950—431no—
166#1567D4311yescharacteristic
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×Q8—431no—
177#446—861no—
178#446—862no—
179C8×Q8—861no—
180#431—431no—
181C2×#108—861no—
182#423—861no—
183#423C2×D4311yescharacteristic
184#423C2×D4311yescharacteristic
185C2×C4⋊C8—431no—
186C4×M16—431no—
187C4×M16—861no—
188C2×C4×C8C2×D4311yescharacteristic
189#341—861no—
190#335—22no—
191Q8⋊C8—431no—
192Q8⋊C8—431no—
193Q8⋊C8—431no—
194Q8⋊C8—431no—
195Q8⋊C8—861no—
196Q8⋊C8—861no—
197C43#890711yescharacteristic, complemented, Sylow
198C22×Q8—431no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—431no—
202C2×M16—431no—
203C22×C8—21no—
204C22×C8—861no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×Q8—431no—
208C4×Q8—431no—
209C4×Q8—861no—
210C4×Q8—861no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C42—861no—
214C2×C42C22×D4311yescharacteristic
215#108—1722no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—431no—
220C4⋊C8—431no—
221C4⋊C8—862no—
222C4⋊C8—862no—
223C4⋊C8—861no—
224C4⋊C8—861no—
225C4⋊C8C22⋊D4312yes—
226C22⋊C8—861no—
227#97—862no—
228#97—861no—
229C4×C8—21no—
230C4×C8—862no—
231C4×C8—861no—
232C4×C8—861no—
233C4×C8C4×D4311yescharacteristic
234C4×C8C4×D4311yescharacteristic
235C2×Q8—431no—
236C2×Q8—431no—
237C2×Q8—862no—
238C2×Q8—861no—
239C2×Q8—1721no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4#1062189811yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4Q8×D4311yescharacteristic
245M16—41no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—432no—
250M16—861no—
251M16—861no—
252M16—861no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—861no—
261C2×C8—861no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C42—861no—
273C42—861no—
274C42—861no—
275C42—861no—
276C42C2×C4×D4311yescharacteristic
277C42D4×D4311yescharacteristic
278C42#1062190211yescharacteristic
279C42C2×C22⋊D4311yescharacteristic
280C23#1306330311yescharacteristic
281Q8—432no—
282Q8—861no—
283Q8—861no—
284Q8—861no—
285Q8—1722no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—3441no—
294C2×C4—1722no—
295C2×C4C4⋊C4×D4311yescharacteristic
296C2×C4C4×C22⋊D4311yescharacteristic
297C2×C4#1306328711yescharacteristic
298C2×C4#1306329311yescharacteristic
299C2×C4#1306330111yescharacteristic
300C2×C4#1306331011yescharacteristic
301C2×C4Q16×D4311yescharacteristic
302C2×C4#1306334411yescharacteristic
303C2×C4#1306334911yescharacteristic
304C2×C4#1306335711yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—81no—
309C8—862no—
310C8—3441no—
311C8—1721no—
312C8—1721no—
313C8—1721no—
314C22—21no—
315C22—21no—
316C22#1458277011yescharacteristic
317C22#1458319311yescharacteristic
318C22#1458320511yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—862no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4#108×D4311yescharacteristic
327C4#1458294611yescharacteristic
328C4#1458299311yescharacteristic
329C4#1458299811yescharacteristic
330C4#1458304111yescharacteristic
331C4#1458305311yescharacteristic
332C2—21no—
333C2—21no—
334C2#1913479811yescharacteristic
335C2#1913483411yescharacteristic
336C2#1913484611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1567C2
socleC22×C43#385
prime radicalC23×C43C22⋊Q8
cosocleC2×C42×C43C23
hypercenter#1567D43
hypocenterC43#8907
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
135. Dic86#108semidirect
197. C43#8907semidirect

Maximal subgroups

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

subgroupindex
#191435462
#191353682
#191330232
C2×#145826312
#191324902
#191324322
C43×#15672
#890743