Finite Group Databasebeta

← #25104572

Subgroups — #25104572

Order 11008.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583251C211yesmaximal, characteristic
2C4⋊Q8×Dic43C211yesmaximal, characteristic
3#19137162C211yesmaximal, characteristic
4#19135397C211yesmaximal, characteristic
5#19135272C214yesmaximal
6#19134722C211yesmaximal, characteristic
7#19134414C214yesmaximal
8C4×C8×Dic43C211yesmaximal, characteristic
9C43×#1990C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11C2×Q8×Dic43—21no—
12C2×#13063290C2212yes—
13#14583251C418yescomplemented
14C2×#13063250C2214yes—
15C2×#13063248C2214yes—
16C2×C4×C43⋊C8C2211yescharacteristic
17C2×C8×Dic43C2212yes—
18C2×C8×Dic43C2212yes—
19#14582806—21no—
20#14582804C2212yes—
21#14582798—21no—
22#14582798C2212yes—
23#14582795—21no—
24#14582795—21no—
25#14582769C2211yescharacteristic
26C4⋊C4×Dic43—21no—
27C4⋊C4×Dic43—21no—
28C4⋊C4×Dic43—21no—
29C4⋊C4×Dic43C2212yes—
30C42×Dic43C2211yescharacteristic
31#14582661C2214yes—
32C2×C4⋊Q8×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×#384C2211yescharacteristic
35C43×#340C2214yes—
36C22×Dic86C2312yes—
37C22×C43⋊C8C2312yes—
38#13063325—22no—
39#13063325C2×C414yes—
40Q8×Dic43—44no—
41#13063290—28no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43C2312yes—
48C2×Dic43⋊C4—22no—
49C2×C4×Dic43—22no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55C2×C4×Dic43C2311yescharacteristic
56C2×C4×Dic43C2311yescharacteristic
57#13063250—28no—
58#13063248C2×C4116yes—
59C4×C43⋊C8C2×C414yes—
60C8×Dic43—24no—
61C8×Dic43—24no—
62C43⋊#95—22no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C22×Q8×C43—21no—
67C22×C8×C43C2312yes—
68C4⋊Q8×C43—22no—
69C4⋊Q8×C43C2×C414yes—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2312yes—
74C2×C4⋊C4×C43C2312yes—
75C2×C42×C43C2311yescharacteristic
76C4×C8×C43—22no—
77C2×Q8×C43—24no—
78C2×Q8×C43—42no—
79C2×Q8×C43—42no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2411yescharacteristic
85C22×Dic43—22no—
86C22×Dic43—22no—
87C22×Dic43C2×D411yescharacteristic
88C22×Dic43C2×D411yescharacteristic
89C22×Dic43C2×D411yescharacteristic
90C22×Dic43C2×D411yescharacteristic
91C2×Dic86—24no—
92C2×Dic86—24no—
93C2×Dic86—22no—
94C2×Dic86C22×C414yes—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43#4114yes—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—24no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43C22×C414yes—
104C42×C43C22×C412yes—
105C42×C43#4112yes—
106C4⋊Dic43—24no—
107C4⋊Dic43—24no—
108C4⋊Dic43—24no—
109C4⋊Dic43—42no—
110C4⋊Dic43—42no—
111C4⋊Dic43—44no—
112Dic43⋊C4—44no—
113C4×Dic43—22no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116C4×Dic43—44no—
117C4×Dic43—44no—
118C4×Dic43SD1614yes—
119C4×Dic43Q1614yes—
120C4×Dic43#4114yes—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8C22×C414yes—
124C23×C43C22×D411yescharacteristic
125Q8×C43—48no—
126C2×C4×C43—24no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C4×D412yes—
133C2×C4×C43C4×D412yes—
134C2×C4×C43C2×SD1612yes—
135C2×C4×C43C2×Q1612yes—
136C2×C4×C43#13512yes—
137C2×C4×C43#13512yes—
138C2×C4×C43C23×C411yescharacteristic
139C2×C4×C43C2×#4112yes—
140C2×C4×C43C2×#4111yescharacteristic
141C2×C4×C43C2×#4112yes—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—24no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43#12412yes—
155C2×Dic43#12412yes—
156C2×Dic43C2×SD1612yes—
157C2×Dic43C2×SD1612yes—
158C2×Dic43C2×Q1612yes—
159C2×Dic43C2×Q1612yes—
160Dic86—28no—
161Dic86—44no—
162C8×C43—24no—
163C43⋊C8—24no—
164C4×#487—431nomaximal, Sylow
165C22×C43C2×C4×D411yescharacteristic
166C22×C43C2×#12411yescharacteristic
167C22×C43#53211yescharacteristic
168C22×C43C22×SD1611yescharacteristic
169C22×C43C22×Q1611yescharacteristic
170C22×C43C2×#13511yescharacteristic
171C22×C43C2×#13511yescharacteristic
172C4×C43—44no—
173C4×C43—82no—
174C4×C43C4×SD1614yes—
175C4×C43C4×Q1614yes—
176C4×C43C4×#4112yes—
177C4×C43#52912yes—
178Dic43—22no—
179Dic43—22no—
180Dic43—22no—
181Dic43—44no—
182Dic43—82no—
183Dic43#48714yescomplemented
184C2×#487—431no—
185C4×C4⋊Q8—431no—
186C4×C4⋊Q8—431no—
187#1990D4311yescharacteristic
188#1956—431no—
189#1933—434no—
190#1834—431no—
191C4×#103—434no—
192C42×C8—431no—
193C2×C43C4×#12411yescharacteristic
194C2×C43C2×C4×SD1611yescharacteristic
195C2×C43C2×C4×Q1611yescharacteristic
196C2×C43C2×#48711yescharacteristic
197C2×C43#313111yescharacteristic
198C2×C43#316711yescharacteristic
199C2×C43#317011yescharacteristic
200C2×C4⋊Q8—431no—
201C2×C4⋊Q8C2×D4311yescharacteristic
202C2×C4×Q8—432no—
203C2×C4×Q8—861no—
204#487—438no—
205C2×#103—434no—
206C2×#103—434no—
207C2×C4×C8—431no—
208C2×C4×C8—432no—
209C2×C4×C8—432no—
210C2×C4×C8C2×D4311yescharacteristic
211#391—432no—
212#391—861no—
213#389—432no—
214#389—861no—
215#389—861no—
216#389—861no—
217#384—431no—
218#384C2×D4311yescharacteristic
219C4×C4⋊C4—432no—
220C4×C4⋊C4—861no—
221C4×C4⋊C4—861no—
222C4×C4⋊C4—861no—
223C43—431no—
224#340—434no—
225#340C2×D4314yes—
226C43C4×#48711yescharacteristic, complemented, Sylow
227C22×Q8—21no—
228C22×Q8—432no—
229C22×C8—432no—
230C22×C8C22×D4312yes—
231C4⋊Q8—22no—
232C4⋊Q8—434no—
233C4⋊Q8—862no—
234C4⋊Q8C4×D4314yes—
235C4×Q8—868no—
236C4×Q8—1724no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—862no—
244C2×C4⋊C4—862no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4C22×D4312yes—
248C2×C4⋊C4C22×D4312yes—
249C2×C42—431no—
250C2×C42—431no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—431no—
254C2×C42—431no—
255C2×C42—862no—
256C2×C42—862no—
257C2×C42C22×D4311yescharacteristic
258#103—4316no—
259#103—868no—
260C4×C8—22no—
261C4×C8—434no—
262C4×C8—864no—
263C4×C8—864no—
264#95—862no—
265#95—862no—
266#95—862no—
267#95—862no—
268C2×Q8—24no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—434no—
272C2×Q8—862no—
273C2×Q8—864no—
274C2×Q8—864no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4C23×D4311yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—434no—
289C2×C8—862no—
290C2×C8—862no—
291C2×C8#1062190214yes—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—24no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—864no—
298C4⋊C4—864no—
299C4⋊C4—864no—
300C4⋊C4—1724no—
301C4⋊C4—1724no—
302C4⋊C4—1722no—
303C4⋊C4—1722no—
304C4⋊C4C2×C4×D4314yes—
305C42—434no—
306C42—434no—
307C42—434no—
308C42—862no—
309C42—862no—
310C42—862no—
311C42—1724no—
312C42—1724no—
313C42C2×C4×D4312yes—
314C42#1062190012yes—
315C23C2×D4×D4311yescharacteristic
316Q8—48no—
317Q8—868no—
318Q8—1724no—
319C2×C4—24no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—432no—
328C2×C4—432no—
329C2×C4—432no—
330C2×C4—432no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—864no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4(C22⋊D43)⋊C412yes—
344C2×C4(C22⋊D43)⋊C412yes—
345C2×C4SD16×D4312yes—
346C2×C4Q16×D4312yes—
347C2×C4#1306334412yes—
348C2×C4#1306334612yes—
349C2×C4C22×C4×D4311yescharacteristic
350C2×C4#41×D4312yes—
351C2×C4C2×#1062190011yescharacteristic
352C2×C4C2×#1062190212yes—
353C8—24no—
354C8—864no—
355C22C2×(C22⋊D43)⋊C411yescharacteristic
356C22#124×D4311yescharacteristic
357C22#1458345011yescharacteristic
358C22C2×SD16×D4311yescharacteristic
359C22C2×Q16×D4311yescharacteristic
360C22C2×#1306334411yescharacteristic
361C22C2×#1306334611yescharacteristic
362C4—44no—
363C4—82no—
364C4—434no—
365C4—862no—
366C4—862no—
367C4—862no—
368C4—3442no—
369C4—1724no—
370C4#1458299014yes—
371C4#1458299114yes—
372C4C4×#1062190212yes—
373C4#1458343512yes—
374C2#1913713811yescharacteristic
375C2C2×#1458299011yescharacteristic
376C2C2×#1458299111yescharacteristic
377C2#487×D4311yescharacteristic
378C2#1914491411yescharacteristic
379C2#1914515611yescharacteristic
380C2#1914518211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1990C2
socle, prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#1990D43
hypocenterC43C4×#487
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
13. #14583251C4semidirect
183. Dic43#487semidirect
226. C43C4×#487semidirect

Maximal subgroups

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

subgroupindex
C2×#145832512
C4⋊Q8×Dic432
#191371622
#191353972
#191352722
#191347222
#191344142
C4×C8×Dic432
C43×#19902
C4×#48743