Finite Group Databasebeta

← #25012495

Subgroups — #25012495

Order 11008.

732 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136270C212yesmaximal, complemented
2#19136260C211yesmaximal, characteristic
3#19135118C212yesmaximal, complemented
4#19134979C211yesmaximal, characteristic
5C43×#3550C211yesmaximal, characteristic
6#14583666C2211yescharacteristic
7#14582916—21no—
8#14582908—22no—
9#14582873C2211yescharacteristic
10#14582873C2212yes—
11#14582694—21no—
12#14582694—24no—
13#14582692—21no—
14#14582659—21no—
15#14582655—22no—
16C43×#563—21no—
17C43×#563C412yescomplemented
18C43×#559—21no—
19Q82×C43C412yescomplemented
20C43×#556—22no—
21D4×Q8×C43—22no—
22C43×#542—24no—
23C43×#536—21no—
24C43×#536C2212yes—
25C43×#533—21no—
26C43×#532C2211yescharacteristic
27#13063332—42no—
28C2×#10621877—22no—
29C2×#10621877—21no—
30#13063284—22no—
31#13063284—21no—
32#13063252—42no—
33#13063249—44no—
34#13063240—22no—
35#13063240—22no—
36#13063240—22no—
37C2×#41×C43D411yescharacteristic
38C2×#41×C43C2311yescharacteristic
39C22×Q8×C43—21no—
40C22×Q8×C43D412yes—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43—21no—
43C4⋊Q8×C43—22no—
44C4⋊Q8×C43—24no—
45C4⋊Q8×C43C2×C411yescharacteristic
46C4⋊Q8×C43C2×C414yes—
47#127×C43D411yescharacteristic
48#126×C43—24no—
49#126×C43—24no—
50#125×C43—22no—
51#124×C43—22no—
52#124×C43—24no—
53#124×C43C2×C411yescharacteristic
54#124×C43D411yescharacteristic
55#124×C43D414yes—
56#123×C43—22no—
57#123×C43—22no—
58#123×C43—22no—
59#123×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—24no—
63C22⋊Q8×C43—24no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—22no—
66#121×C43—22no—
67C4×Q8×C43—22no—
68C4×Q8×C43—22no—
69C4×Q8×C43—24no—
70C4×D4×C43—24no—
71C4×D4×C43—22no—
72#117×C43—22no—
73#117×C43—21no—
74#117×C43D412yes—
75C2×C42×C43D411yescharacteristic
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—22no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—42no—
84C2×Q8×C43—42no—
85C2×Q8×C43—81no—
86C2×Q8×C43—81no—
87C2×Q8×C43C22⋊C414yes—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×Q8×C43C22×C411yescharacteristic
90C2×D4×C43—22no—
91C2×D4×C43—21no—
92C2×D4×C43C22⋊C411yescharacteristic
93C2×D4×C43C2×D412yes—
94C2×D4×C43C2×D411yescharacteristic
95C22×C4×C43—22no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D412yes—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—24no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—24no—
108C4⋊C4×C43—24no—
109C4⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—24no—
112C22⋊C4×C43—22no—
113C22⋊C4×C43—24no—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—24no—
117C42×C43—24no—
118C42×C43—22no—
119C42×C43—21no—
120C42×C43C22⋊C411yescharacteristic
121C42×C43C22⋊C411yescharacteristic
122C42×C43C22⋊C414yes—
123C22⋊Dic43—42no—
124C22⋊Dic43—41no—
125C4⋊Dic43—42no—
126C4⋊Dic43—41no—
127C4×Dic43—41no—
128C4×Dic43—42no—
129#10621877—22no—
130#10621877—42no—
131#10621877—41no—
132C2×C43⋊C8—24no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43#12012yes—
136C23×C43#12011yescharacteristic
137Q8×C43—41no—
138Q8×C43—44no—
139Q8×C43—41no—
140Q8×C43—44no—
141Q8×C43—42no—
142Q8×C43—42no—
143Q8×C43—82no—
144D4×C43—41no—
145D4×C43—42no—
146D4×C43—41no—
147D4×C43—44no—
148D4×C43—81no—
149C2×C4×C43—21no—
150C2×C4×C43—22no—
151C2×C4×C43—21no—
152C2×C4×C43—22no—
153C2×C4×C43—21no—
154C2×C4×C43—24no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—24no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—82no—
162C2×C4×C43—82no—
163C2×C4×C43C2×C22⋊C412yes—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43#12011yescharacteristic
166C2×Dic43—82no—
167C2×Dic43—81no—
168C43⋊C8—42no—
169#12779—431nomaximal, Sylow
170C22×C43—22no—
171C22×C43—21no—
172C22×C43—41no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—41no—
176C22×C43#37911yescharacteristic
177C4×C43—22no—
178C4×C43—21no—
179C4×C43—22no—
180C4×C43—41no—
181C4×C43—44no—
182C4×C43—41no—
183C4×C43—44no—
184C4×C43B(4,𝔽2)11yescharacteristic
185C4×C43#45811yescharacteristic
186Dic43—162no—
187Dic43—161no—
188#3550D4311yescharacteristic
189#2129—432no—
190#2126—431no—
191#1909—432no—
192#1884—431no—
193C2×C43—21no—
194C2×C43—42no—
195C2×C43—41no—
196C2×C43—81no—
197C2×C43#179011yescharacteristic
198#568—431no—
199#563—21no—
200#563Dic4312yescomplemented
201#559—21no—
202Q82Dic4312yescomplemented
203#556—22no—
204D4×Q8—22no—
205#542—24no—
206#536—21no—
207#536C2×D4312yes—
208#533—21no—
209#532C2×D4311yescharacteristic
210#421—861no—
211#419—862no—
212#410—432no—
213#410—431no—
214#354—861no—
215#354—864no—
216#353—861no—
217#339—861no—
218H(3,ℤ/4)—862no—
219C43#1277911yescharacteristic, complemented, Sylow
220C2×#41C22⋊D4311yescharacteristic
221C2×#41C22×D4311yescharacteristic
222C22×Q8—21no—
223C22×Q8C22⋊D4312yes—
224#131—1722no—
225C2×M16—862no—
226C2×M16—861no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—22no—
230C4⋊Q8—24no—
231C4⋊Q8C2×Dic4311yescharacteristic
232C4⋊Q8C2×Dic4314yes—
233#127C22⋊D4311yescharacteristic
234#126—24no—
235#126—24no—
236#125—22no—
237#124—22no—
238#124—24no—
239#124C2×Dic4311yescharacteristic
240#124C22⋊D4311yescharacteristic
241#124C22⋊D4314yes—
242#123—22no—
243#123—22no—
244#123—22no—
245#123—22no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8—24no—
249C22⋊Q8—24no—
250C22⋊Q8—22no—
251C22⋊Q8—22no—
252#121—22no—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×Q8—24no—
256C4×D4—24no—
257C4×D4—22no—
258#117—22no—
259#117—21no—
260#117—862no—
261#117—861no—
262#117C22⋊D4312yes—
263C2×C42C22⋊D4311yescharacteristic
264#104—1722no—
265#103—1724no—
266#99—862no—
267#99—862no—
268#99—862no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—81no—
279C2×Q8—81no—
280C2×Q8C22⋊Dic4314yes—
281C2×Q8C22⋊Dic4311yescharacteristic
282C2×Q8C22×Dic4311yescharacteristic
283C2×D4—22no—
284C2×D4—21no—
285C2×D4C22⋊Dic4311yescharacteristic
286C2×D4C2×C22⋊D4312yes—
287C2×D4C2×C22⋊D4311yescharacteristic
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C2×C22⋊D4312yes—
294M16—862no—
295M16—1722no—
296M16—1721no—
297C2×C8—864no—
298C2×C8—1721no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—24no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—1722no—
309C4⋊C4—1721no—
310C22⋊C4—22no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—24no—
316C22⋊C4—22no—
317C22⋊C4—1722no—
318C22⋊C4—1721no—
319C42—24no—
320C42—22no—
321C42—21no—
322C42—1721no—
323C42—1722no—
324C42C22⋊Dic4311yescharacteristic
325C42C22⋊Dic4311yescharacteristic
326C42C22⋊Dic4314yes—
327C23—21no—
328C23#1306329412yes—
329C23#1306329411yescharacteristic
330Q8—41no—
331Q8—44no—
332Q8—41no—
333Q8—44no—
334Q8—42no—
335Q8—42no—
336Q8—82no—
337D4—41no—
338D4—42no—
339D4—41no—
340D4—44no—
341D4—81no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—24no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—3442no—
357C2×C4—3441no—
358C2×C4C2×C22⋊Dic4312yes—
359C2×C4C2×C22⋊Dic4311yescharacteristic
360C2×C4#1306329411yescharacteristic
361C8—1722no—
362C22—22no—
363C22—21no—
364C22—41no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22#1458275511yescharacteristic
369C4—22no—
370C4—21no—
371C4—22no—
372C4—41no—
373C4—44no—
374C4—41no—
375C4—44no—
376C4—6882no—
377C4—6881no—
378C4#1458308611yescharacteristic
379C4#1458308911yescharacteristic
380C2—21no—
381C2—42no—
382C2—41no—
383C2—81no—
384C2#1913454311yescharacteristic
subgroupG/H
centerC2#19134543
commutatorC2×Q8×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#3550C2
socleC2×C43#1790
prime radicalC43×#532C22
cosocleC2×#41×C43C23
hypercenter#3550D43
hypocenterC43#12779
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #19136270C2semidirect
3. #19135118C2semidirect
17. C43×#563C4semidirect
19. Q82×C43C4semidirect
200. #563Dic43semidirect
202. Q82Dic43semidirect
219. C43#12779semidirect

Maximal subgroups

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

subgroupindex
#191362702
#191362602
#191351182
#191349792
C43×#35502
#1277943