Finite Group Databasebeta

← #24986071

Subgroups — #24986071

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582950C211yesmaximal, characteristic
2C2×#14582921C211yesmaximal, characteristic
3C2×C4⋊C8×D43C211yesmaximal, characteristic
4#19132430C211yesmaximal, characteristic, complemented
5#19132429C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C22×C8×D43—21no—
10C2×C42×D43C2211yescharacteristic
11#14582950—22no—
12#14582950—22no—
13#14582921—22no—
14#14582921C414yes—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×Dic43⋊C8—21no—
18C2×Dic43⋊C8—21no—
19C2×Dic43⋊C8C412yes—
20C4⋊C8×D43—22no—
21C4⋊C8×D43C414yes—
22C2×(C2×D43)⋊C8C412yes—
23C2×C4×C43⋊C8C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4×C8×C43C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43Q811yescharacteristic
30C2×#10621872—24no—
31C2×#10621872—42no—
32C2×#10621872—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8C2×C412yes—
36C2×C8×D43—24no—
37C2×C8×D43—42no—
38C2×C8×D43—42no—
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C2×C4×Dic43Q811yescharacteristic
42C42×D43C2×C412yes—
43C42×D43C2×C412yes—
44C42×D43D412yes—
45C42×D43D412yes—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C412yes—
49C4⋊(C43⋊C8)C2×C412yes—
50Dic43⋊C8—24no—
51Dic43⋊C8—24no—
52Dic43⋊C8—24no—
53(C2×D43)⋊C8—24no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C22×C8×C43C2×C412yes—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43C2×C412yes—
63C4⋊C8×C43C2×C412yes—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C23×D43C4⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×Q811yescharacteristic
70C22×Dic43C4⋊C411yescharacteristic
71C22×Dic43C4⋊C411yescharacteristic
72C22×Dic43C4⋊C411yescharacteristic
73C2×C4×D43—22no—
74C2×C4×D43—22no—
75C2×C4×D43—42no—
76C2×C4×D43C4212yes—
77C2×C4×D43C22⋊C412yes—
78C2×C4×D43C22⋊C412yes—
79C2×C4×D43C22⋊C412yes—
80C2×C4×D43C4⋊C412yes—
81C2×C4×D43C4⋊C412yes—
82C2×C4×D43D812yes—
83C2×C4×D43SD1612yes—
84C2×C4×D43SD1612yes—
85C2×C4×D43Q1612yes—
86C2×C8×C43—22no—
87C2×C8×C43—22no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C42×C43C22×C411yescharacteristic
96C42×C43C22×C411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C4×Dic43C4212yes—
100C4×Dic43C22⋊C412yes—
101C4×Dic43C22⋊C412yes—
102C4×Dic43C22⋊C412yes—
103C4×Dic43C4⋊C412yes—
104C4×Dic43C4⋊C412yes—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114#10621872—48no—
115C8×D43—48no—
116C23×C43C2×C4⋊C411yescharacteristic
117C22×D43—22no—
118C22×D43—22no—
119C22×D43#9512yes—
120C22×D43#10612yes—
121C22×D43#10712yes—
122C2×C4×C43—22no—
123C2×C4×C43C2×C4211yescharacteristic
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43C2×C22⋊C411yescharacteristic
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43C2×C4⋊C411yescharacteristic
129C2×C4×C43#13112yes—
130C2×C4×C43#13112yes—
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×C4×C43C2×Q1611yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43#9512yes—
138C2×Dic43#9512yes—
139C2×Dic43#9512yes—
140C2×Dic43#10612yes—
141C2×Dic43#10712yes—
142C4×D43—22no—
143C4×D43—22no—
144C4×D43—24no—
145C4×D43—42no—
146C4×D43—42no—
147C4×D43#10214yes—
148C4×D43#10214yes—
149C4×D43#10314yes—
150C4×D43#10314yes—
151C8×C43—42no—
152C8×C43—42no—
153C8×C43—42no—
154C43⋊C8—42no—
155C43⋊C8—42no—
156C43⋊C8—42no—
157#7877—431nomaximal, Sylow
158C22×C43C2×#9511yescharacteristic
159C22×C43#42412yes—
160C22×C43C2×#10611yescharacteristic
161C22×C43C2×#10711yescharacteristic
162C22×C43#43012yes—
163C2×D43—24no—
164C2×D43—24no—
165C2×D43—22no—
166C2×D43—22no—
167C2×D43#34014yes—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43#40511yescharacteristic
171C4×C43#40511yescharacteristic
172C4×C43#40812yes—
173C4×C43C2×#10211yescharacteristic
174C4×C43C2×#10211yescharacteristic
175C4×C43C2×#10311yescharacteristic
176C4×C43C2×#10311yescharacteristic
177Dic43—22no—
178Dic43—22no—
179Dic43#34014yes—
180C2×#431—431no—
181C2×#423—431no—
182C22×C4⋊C8—431no—
183#1277—431no—
184#1277—431no—
185#1277—431no—
186#1277D4311yescharacteristic, complemented
187C2×C43#157012yes—
188C2×C43#157112yes—
189C2×C43#172911yescharacteristic
190C2×C43C2×#34011yescharacteristic
191C2×C43#173811yescharacteristic
192D43—24no—
193C22×M16—861no—
194C23×C8—861no—
195C22×C42—431no—
196#431—862no—
197#431—862no—
198#423—434no—
199#423—862no—
200C2×C4⋊C8—431no—
201C2×C4⋊C8—431no—
202C2×C4⋊C8—434no—
203C2×C4⋊C8—432no—
204C2×C4⋊C8—862no—
205C2×C4⋊C8—861no—
206C2×C4⋊C8—861no—
207C2×C4⋊C8C2×D4311yescharacteristic
208C2×C4⋊C8C2×D4311yescharacteristic
209C2×C22⋊C8—432no—
210C2×C4×C8—431no—
211C2×C4×C8C2×D4311yescharacteristic
212C43#787711yescharacteristic, complemented, Sylow
213C23×C4—431no—
214C23×C4—431no—
215C23×C4—431no—
216C2×M16—864no—
217C2×M16—1722no—
218C2×M16—1722no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—432no—
222C22×C8—864no—
223C22×C8—861no—
224C22×C8—861no—
225C22×C8—1722no—
226C22×C8—1722no—
227C22×C8C4×D4312yes—
228C2×C42—431no—
229C2×C42—431no—
230C2×C42—431no—
231C2×C42—432no—
232C2×C42—432no—
233C2×C42—432no—
234C2×C42—432no—
235C2×C42C22×D4311yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—432no—
239C4⋊C8—432no—
240C4⋊C8—864no—
241C4⋊C8—864no—
242C4⋊C8—864no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8C4×D4312yes—
246C4⋊C8C4×D4312yes—
247C22⋊C8—864no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—861no—
251C4×C8—861no—
252C24—431no—
253C22×C4—431no—
254C22×C4—432no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4—432no—
259C22×C4—432no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—432no—
263C22×C4—432no—
264C22×C4—432no—
265C22×C4—432no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4—1722no—
269C22×C4C2×C4×D4311yescharacteristic
270C22×C4D4×D4311yescharacteristic
271C22×C4Q8×D4311yescharacteristic
272M16—1728no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—862no—
283C2×C8—862no—
284C2×C8—862no—
285C2×C8—862no—
286C2×C8—862no—
287C2×C8—1728no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C2×C8—1721no—
292C42—432no—
293C42—432no—
294C42—432no—
295C42—432no—
296C42—432no—
297C42—432no—
298C42C2×C4×D4311yescharacteristic
299C42C2×C4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42D4×D4311yescharacteristic
302C23—432no—
303C23—432no—
304C23—432no—
305C23—862no—
306C23—862no—
307C23C4⋊C4×D4311yescharacteristic
308C2×C4—22no—
309C2×C4—432no—
310C2×C4—432no—
311C2×C4—432no—
312C2×C4—434no—
313C2×C4—434no—
314C2×C4—434no—
315C2×C4—434no—
316C2×C4—432no—
317C2×C4—432no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—864no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4C42×D4311yescharacteristic
326C2×C4C22⋊C4×D4311yescharacteristic
327C2×C4C22⋊C4×D4311yescharacteristic
328C2×C4C22⋊C4×D4311yescharacteristic
329C2×C4C4⋊C4×D4311yescharacteristic
330C2×C4C4⋊C4×D4311yescharacteristic
331C2×C4#1306333112yes—
332C2×C4#1306333312yes—
333C2×C4D8×D4311yescharacteristic
334C2×C4SD16×D4311yescharacteristic
335C2×C4SD16×D4311yescharacteristic
336C2×C4Q16×D4311yescharacteristic
337C8—42no—
338C8—42no—
339C8—42no—
340C8—1722no—
341C8—1722no—
342C8—1722no—
343C22—434no—
344C22—862no—
345C22—862no—
346C22—864no—
347C22—864no—
348C22#95×D4311yescharacteristic
349C22#1458292412yes—
350C22#106×D4311yescharacteristic
351C22#107×D4311yescharacteristic
352C22#1458294612yes—
353C4—21no—
354C4—21no—
355C4—434no—
356C4—862no—
357C4—862no—
358C4#1458285311yescharacteristic
359C4#1458285611yescharacteristic
360C4#1458286412yes—
361C4#102×D4311yescharacteristic
362C4#102×D4311yescharacteristic
363C4#103×D4311yescharacteristic
364C4#103×D4311yescharacteristic
365C2—864no—
366C2#1913336412yes—
367C2#1913336812yes—
368C2#1913429011yescharacteristic
369C2#340×D4311yescharacteristic
370C2#1913432011yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socleC23×C43C2×C4⋊C4
prime radicalC23×D43C4⋊C4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#7877
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. #19132430C2semidirect
5. #19132429C2semidirect
6. #19132429C2semidirect
7. C43×#1277C2semidirect
186. #1277D43semidirect
212. C43#7877semidirect

Maximal subgroups

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

subgroupindex
C2×#145829502
C2×#145829212
C2×C4⋊C8×D432
#191324302
#191324292
C43×#12772
#787743