Finite Group Databasebeta

← #25081937

Subgroups — #25081937

Order 11008.

644 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
1#19145723C211yesmaximal, characteristic
2#19144067C211yesmaximal, characteristic
3#19143676C211yesmaximal, characteristic, complemented
4#19134013C214yesmaximal, complemented
5#19133979C214yesmaximal, complemented
6#19133365C211yesmaximal, characteristic, complemented
7#19133276C211yesmaximal, characteristic, complemented
8#19133245C211yesmaximal, characteristic
9C2×C43×#477C211yesmaximal, characteristic, complemented
10C2×#13063356—21no—
11#14583449C2211yescharacteristic
12#14583295C2212yes—
13#14583247C2212yes—
14#14583217—22no—
15#14583186—22no—
16#14583121—22no—
17#14583109C2212yes—
18#14583099C2212yes—
19Q8×C43⋊C8—22no—
20Q8×C43⋊C8C2214yes—
21#14582952—22no—
22#14582952C2211yescharacteristic
23#14582952C2211yescharacteristic
24#14582923C2211yescharacteristic
25#14582898—21no—
26#14582649C2214yes—
27#14582648C2214yes—
28#14582646C2212yes—
29#14582642C2212yes—
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#477—22no—
33C43×#477C2214yes—
34C2×#107×C43—21no—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#103×C43—21no—
37C2×#10621898—21no—
38#13063356—44no—
39C2×#10621885—22no—
40C2×#10621884—22no—
41C2×#10621877—21no—
42#13063325C2311yescharacteristic
43#13063322C2311yescharacteristic
44#13063313—21no—
45#13063299—21no—
46#13063299—21no—
47C4×D172—21no—
48C4×D172—21no—
49#13063256—24no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—24no—
52C4⋊(C43⋊C8)D412yes—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55#13063248—22no—
56#13063245—22no—
57#13063245—24no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D412yes—
60C4×C43⋊C8—21no—
61C4×C43⋊C8—24no—
62C4×C43⋊C8C2312yes—
63C22×Q8×C43—21no—
64C22×Q8×C43D411yescharacteristic
65C22×C8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43C2312yes—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43D412yes—
73C4×Q8×C43C2312yes—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C42×C43—21no—
79C2×C42×C43C2311yescharacteristic
80#107×C43—24no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43C2312yes—
83#103×C43—24no—
84C2×Q8×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—22no—
87C2×Q8×C43—41no—
88C2×Q8×C43—82no—
89C2×Q8×C43SD1614yes—
90C2×Q8×C43C2×D412yes—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—41no—
98#10621898—42no—
99#10621898—42no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105C2×C8×C43—22no—
106C2×C8×C43—42no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43C2×D412yes—
115C42×C43—22no—
116C42×C43—22no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43C2411yescharacteristic
121#10621885—44no—
122#10621884—44no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127#10621877—42no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8C2×D414yes—
131C23×C43#12111yescharacteristic
132C22×D43—41no—
133Q8×C43—22no—
134Q8×C43—24no—
135Q8×C43—82no—
136Q8×C43—82no—
137Q8×C43C2×SD1614yes—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—81no—
145C2×C4×C43—82no—
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43C2×SD1612yes—
150C2×C4×C43#13512yes—
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C2×C4×C43C2×#4111yescharacteristic
154C22⋊D43—82no—
155C2×Dic43—41no—
156D172—41no—
157D172—41no—
158D172—42no—
159D172—81no—
160C4×D43—82no—
161Dic86—41no—
162Dic86—41no—
163C8×C43—42no—
164C43⋊C8—24no—
165C43⋊C8—42no—
166C43⋊C8—42no—
167#19403—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43#46512yes—
171C22×C43C2×#12111yescharacteristic
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C4×C43—21no—
176C4×C43—24no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—42no—
180C4×C43—82no—
181C4×C43#46512yes—
182C4×C43C22×SD1611yescharacteristic
183C4×C43C2×#13511yescharacteristic
184C4×C43#57812yes—
185Dic43—81no—
186#3227—431no—
187C2×#477D4311yescharacteristic, complemented
188#3037—431no—
189#2982—431no—
190#1678—434no—
191#1672—434no—
192#1570—431no—
193#1548—431no—
194#1540—431no—
195C2×C43—22no—
196C2×C43#304411yescharacteristic
197C2×C43C2×#46511yescharacteristic
198C2×C43#306811yescharacteristic
199D43—161no—
200C2×#137—861no—
201#532—431no—
202C2×C4⋊Q8C2×D4311yescharacteristic
203C2×C4×Q8C2×D4311yescharacteristic
204#498—432no—
205#486—432no—
206#481—862no—
207#477—22no—
208#477C2×D4314yes—
209#476—862no—
210#464—862no—
211#462—432no—
212#460—432no—
213C8×Q8—434no—
214C8×Q8—862no—
215#431—431no—
216#431—431no—
217#431—862no—
218C2×#107—21no—
219#423—431no—
220C2×C4⋊C8C2×D4311yescharacteristic
221#417—861no—
222C2×#103—21no—
223#334—434no—
224#333—434no—
225#332—432no—
226#331—432no—
227C43#1940311yescharacteristic, complemented, Sylow
228C2×#41—861no—
229C22×Q8—21no—
230C22×Q8C22⋊D4311yescharacteristic
231#137—1724no—
232C2×Q16—862no—
233C2×SD16—862no—
234C2×M16—861no—
235C22×C8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—431no—
240C4⋊Q8C22×D4312yes—
241#127—431no—
242#124—861no—
243#121—861no—
244#121—861no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C22⋊D4312yes—
248C4×Q8C22×D4312yes—
249C4×D4—861no—
250C4×D4—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4C22⋊D4311yescharacteristic
255C2×C42—21no—
256C2×C42C22×D4311yescharacteristic
257#107—24no—
258#106—864no—
259C4⋊C8—21no—
260C4⋊C8—432no—
261C4⋊C8—432no—
262C4⋊C8—432no—
263C4⋊C8—864no—
264C4⋊C8—861no—
265C4⋊C8C22×D4312yes—
266#103—24no—
267#103—862no—
268#102—864no—
269#102—862no—
270C22⋊C8—432no—
271C22⋊C8—861no—
272C4×C8—432no—
273C4×C8—864no—
274C4×C8—861no—
275#41—1722no—
276#41—1722no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—82no—
282C2×Q8—861no—
283C2×Q8#1062188414yes—
284C2×Q8C2×C22⋊D4312yes—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—1721no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—1721no—
293C22×C4D4×D4311yescharacteristic
294C22×C4#1062190011yescharacteristic
295C22×C4C2×C22⋊D4311yescharacteristic
296Q16—1724no—
297SD16—1724no—
298M16—1722no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—434no—
302C2×C8—862no—
303C2×C8—862no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4C2×C22⋊D4312yes—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—22no—
317C42—22no—
318C42D4×D4311yescharacteristic
319C42#1062190011yescharacteristic
320C42C2×C22⋊D4311yescharacteristic
321C42C23×D4311yescharacteristic
322C23—1721no—
323C23#1306329711yescharacteristic
324Q8—24no—
325Q8—22no—
326Q8—82no—
327Q8—82no—
328Q8—1721no—
329Q8—1721no—
330Q8C2×#1062188414yes—
331D4—3441no—
332D4—3442no—
333D4—1721no—
334D4—1721no—
335D4—1722no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—3442no—
345C2×C4—1721no—
346C2×C4#1306329711yescharacteristic
347C2×C4#1306329711yescharacteristic
348C2×C4#1306329711yescharacteristic
349C2×C4C2×#1062188412yes—
350C2×C4#1306334512yes—
351C2×C4C2×D4×D4311yescharacteristic
352C2×C4C22×C22⋊D4311yescharacteristic
353C2×C4C2×#1062190011yescharacteristic
354C8—42no—
355C8—864no—
356C8—1722no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22#1458313012yes—
364C22C2×#1306329711yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—24no—
369C4—42no—
370C4—82no—
371C4—3441no—
372C4#1458313012yes—
373C4C22×#1062188411yescharacteristic
374C4C2×#1306334511yescharacteristic
375C4#1458371212yes—
376C2—22no—
377C2—6881no—
378C2#1914412211yescharacteristic
379C2C2×#1458313011yescharacteristic
380C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#477C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenterC2×#477D43
hypocenterC43#19403
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #19143676C2semidirect
4. #19134013C2semidirect
5. #19133979C2semidirect
6. #19133365C2semidirect
7. #19133276C2semidirect
9. C2×C43×#477C2semidirect
187. C2×#477D43semidirect
227. C43#19403semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191440672
#191436762
#191340132
#191339792
#191333652
#191332762
#191332452
C2×C43×#4772
#1940343