Finite Group Databasebeta

← #25150211

Subgroups — #25150211

Order 11008.

1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C2×#14583505C211yesmaximal, characteristic, complemented
2C2×#14583275C211yesmaximal, characteristic, complemented
3#19140346C211yesmaximal, characteristic, complemented
4#19135592C214yesmaximal, complemented
5#19135561C211yesmaximal, characteristic, complemented
6#19135419C211yesmaximal, characteristic, complemented
7#19134940C214yesmaximal, complemented
8#19134364C211yesmaximal, characteristic, complemented
9C2×C43×#490C211yesmaximal, characteristic, complemented
10C22×#10621882C2214yes—
11#14583505—24no—
12#14583505—24no—
13C2×#13063322C2211yescharacteristic
14C2×#13063310—22no—
15C2×#13063300—22no—
16C2×#13063300C2212yes—
17C2×#13063296C2212yes—
18C2×#13063287C2212yes—
19C2×#13063282C2211yescharacteristic
20#14583275—24no—
21C2×#13063247C2214yes—
22C2×(C2×D43)⋊C8C2212yes—
23C2×C4×C43⋊C8C2211yescharacteristic
24#14582813—22no—
25#14582807—22no—
26#14582802C2212yes—
27#14582765C2211yescharacteristic
28#14582661C2214yes—
29#14582653C2212yes—
30C2×#127×C43C2211yescharacteristic
31C2×#125×C43C2211yescharacteristic
32C43×#490—24no—
33C2×#102×C43C2214yes—
34C2×#97×C43C2211yescharacteristic
35C22×D172—22no—
36C22×D172—22no—
37C22×D172C2312yes—
38C22×C22⋊D43—22no—
39C22×C4×D43—22no—
40C22×C4×D43C2311yescharacteristic
41C2×#10621882—28no—
42C2×#10621882—28no—
43C2×#10621882—44no—
44C22×C43⋊C8C2312yes—
45#13063322—22no—
46#13063322D414yescomplemented
47#13063310—216no—
48#13063300—216no—
49#13063300—24no—
50#13063300—24no—
51#13063296—44no—
52#13063287—24no—
53#13063287—24no—
54#13063282—22no—
55#13063282—22no—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4D412yes—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—24no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4D412yes—
63C2×C4×Dic43C2311yescharacteristic
64#13063247—44no—
65(C2×D43)⋊C8—24no—
66C4×C43⋊C8—22no—
67C43⋊#95—22no—
68C22×D4×C43—22no—
69C22×D4×C43C2312yes—
70C22×C8×C43C2312yes—
71#127×C43—22no—
72#127×C43—22no—
73#125×C43—22no—
74#125×C43D414yescomplemented
75C2×C4⋊C4×C43—22no—
76C2×C4⋊C4×C43C2312yes—
77C2×C42×C43C2311yescharacteristic
78#102×C43—28no—
79#97×C43—22no—
80C24×C43—22no—
81C23×D43—22no—
82C23×D43C2×D411yescharacteristic
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—24no—
86C2×D4×C43—24no—
87C2×D4×C43—44no—
88C2×D4×C43—84no—
89C22×C4×C43—22no—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2411yescharacteristic
92C2×C22⋊D43—44no—
93C2×C22⋊D43—84no—
94C22×Dic43—22no—
95C22×Dic43C2×D412yes—
96C22×Dic43C2×D411yescharacteristic
97C2×D172—22no—
98C2×D172—28no—
99C2×D172—28no—
100C2×D172—24no—
101C2×D172—24no—
102C2×D172—84no—
103C2×D172—84no—
104C2×D172C2×D414yes—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43—22no—
108C2×C4×D43—22no—
109C2×C4×D43—28no—
110C2×C4×D43—84no—
111C2×C8×C43—22no—
112C2×C8×C43—22no—
113C2×C8×C43—22no—
114C4⋊C4×C43—28no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43C2×D414yes—
117C42×C43C2×D412yes—
118C42×C43C2×D412yes—
119C22⋊Dic43—44no—
120C22⋊Dic43—84no—
121#10621882—416no—
122(C2×D43)⋊C4—28no—
123(C2×D43)⋊C4—28no—
124(C2×D43)⋊C4—24no—
125C4⋊Dic43—24no—
126Dic43⋊C4—24no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8#4114yes—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—44no—
136C23×C43—44no—
137C23×C43C22×D411yescharacteristic
138C22×D43—21no—
139C22×D43—24no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—24no—
143C22×D43—42no—
144C22×D43—42no—
145C22×D43—44no—
146C22×D43—44no—
147D4×C43—44no—
148D4×C43—44no—
149D4×C43—88no—
150C2×C4×C43—24no—
151C2×C4×C43—24no—
152C2×C4×C43—44no—
153C2×C4×C43#12014yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C2×#4112yes—
157C2×C4×C43H(5,𝔽2)12yes—
158C22⋊D43—88no—
159C2×Dic43—22no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—24no—
164C2×Dic43—42no—
165C2×Dic43—44no—
166D172—28no—
167D172—44no—
168D172—88no—
169D172—88no—
170C4×D43—42no—
171C4×D43—42no—
172C4×D43—88no—
173C8×C43—42no—
174C43⋊C8—24no—
175#25608—431nomaximal, Sylow
176C22×C43—84no—
177C22×C43—82no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—84no—
181C22×C43C2×#12011yescharacteristic
182C22×C43#53211yescharacteristic
183C22×C43#53511yescharacteristic
184C22×C43#57614yes—
185C2×D43—42no—
186C2×D43—41no—
187C2×D43—44no—
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—44no—
191C2×D43—44no—
192C2×D43—84no—
193C2×D43—84no—
194C4×C43—24no—
195C4×C43—44no—
196C4×C43#54612yes—
197C4×C43#55012yes—
198Dic43—41no—
199Dic43—42no—
200Dic43—82no—
201C2×#540—431no—
202C2×#493—431no—
203C2×#490D4311yescharacteristic, complemented
204#2619—431no—
205#1999—434no—
206#1991—431no—
207#1961—431no—
208#1879—434no—
209#1750—431no—
210C2×C43—162no—
211C2×C43#243111yescharacteristic
212C2×C43#300812yes—
213C2×C43#317612yes—
214C2×C43#322012yes—
215D43—81no—
216D43—84no—
217C22×D8—434no—
218#540—864no—
219#540—864no—
220C2×#127—431no—
221C2×#127C2×D4311yescharacteristic
222C2×#125C2×D4311yescharacteristic
223C2×#123—862no—
224C2×#121—432no—
225C2×#121—432no—
226C2×#121—862no—
227C2×C4×D4—432no—
228C2×#117—431no—
229#493—864no—
230#490—24no—
231C2×#102—434no—
232C2×#102C2×D4314yes—
233C2×C22⋊C8—432no—
234C2×#97C2×D4311yescharacteristic
235C2×C4×C8—431no—
236#394—862no—
237#392—862no—
238#390—432no—
239#382—431no—
240#340—434no—
241#336—432no—
242C43#2560811yescharacteristic, complemented, Sylow
243C22×D4—22no—
244C22×D4—432no—
245C22×D4—862no—
246C22×D4—862no—
247C22×D4—862no—
248C22×D4C22×D4312yes—
249C23×C4—431no—
250C23×C4—862no—
251C2×D8—868no—
252C2×D8—868no—
253C2×D8—1724no—
254C22×C8—432no—
255C22×C8C22×D4312yes—
256#127—22no—
257#127—22no—
258#127—434no—
259#127—862no—
260#125—22no—
261#125C22⋊D4314yescomplemented
262#123—8616no—
263#121—864no—
264#121—8616no—
265#121—864no—
266#121—1724no—
267C4×D4—864no—
268C4×D4—864no—
269#117—862no—
270#117—862no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—432no—
273C2×C4⋊C4—432no—
274C2×C4⋊C4C22×D4312yes—
275C2×C22⋊C4—432no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—864no—
279C2×C22⋊C4—862no—
280C2×C42—431no—
281C2×C42C22×D4311yescharacteristic
282#102—28no—
283#102—1724no—
284C22⋊C8—864no—
285#97—22no—
286C4×C8—862no—
287#95—862no—
288C24—22no—
289C24—431no—
290C24—862no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—44no—
296C2×D4—84no—
297C2×D4—434no—
298C2×D4—868no—
299C2×D4—868no—
300C2×D4—862no—
301C2×D4—864no—
302C2×D4—864no—
303C2×D4—3444no—
304C2×D4—3444no—
305C2×D4—3444no—
306C2×D4—1724no—
307C22×C4—22no—
308C22×C4—432no—
309C22×C4—431no—
310C22×C4—868no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—862no—
316C22×C4—3444no—
317C22×C4D4×D4312yes—
318C22×C4C23×D4311yescharacteristic
319D8—17216no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—434no—
324C2×C8—862no—
325C2×C8—862no—
326C4⋊C4—28no—
327C4⋊C4—22no—
328C4⋊C4—864no—
329C4⋊C4—864no—
330C4⋊C4C2×C22⋊D4314yes—
331C22⋊C4—868no—
332C22⋊C4—868no—
333C22⋊C4—864no—
334C22⋊C4—3444no—
335C22⋊C4—1724no—
336C42—861no—
337C42—861no—
338C42D4×D4312yes—
339C42C2×C22⋊D4312yes—
340C23—42no—
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—864no—
346C23—861no—
347C23—864no—
348C23—861no—
349C23—861no—
350C23—1724no—
351C23—1724no—
352C23—1722no—
353C23—1722no—
354C23C2×D4×D4311yescharacteristic
355D4—44no—
356D4—44no—
357D4—88no—
358D4—868no—
359D4—3448no—
360D4—3448no—
361D4—3448no—
362D4—1724no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—44no—
366C2×C4—862no—
367C2×C4—861no—
368C2×C4—864no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—3448no—
372C2×C4—1724no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4#1306329314yes—
377C2×C4C2×D4×D4311yescharacteristic
378C2×C4C22×C22⋊D4311yescharacteristic
379C2×C4#41×D4312yes—
380C2×C4#1306337112yes—
381C8—42no—
382C8—864no—
383C22—84no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22—84no—
388C22—3444no—
389C22—3444no—
390C22—1722no—
391C22—1721no—
392C22—1724no—
393C22—1722no—
394C22—1724no—
395C22—1722no—
396C22—1724no—
397C22C2×#1306329311yescharacteristic
398C22#1458344811yescharacteristic
399C22#1458346711yescharacteristic
400C22#1458370314yes—
401C4—24no—
402C4—44no—
403C4—3442no—
404C4—1721no—
405C4—1722no—
406C4#1458354212yes—
407C4#1458356812yes—
408C2—162no—
409C2—3444no—
410C2—3441no—
411C2#1913821711yescharacteristic
412C2#1914386212yes—
413C2#1914524412yes—
414C2#1914564612yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#490C2
socleC23×C43C22×D4
hypercenterC2×#490D43
hypocenterC43#25608
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#14583505C2semidirect
2. C2×#14583275C2semidirect
3. #19140346C2semidirect
4. #19135592C2semidirect
5. #19135561C2semidirect
6. #19135419C2semidirect
7. #19134940C2semidirect
8. #19134364C2semidirect
9. C2×C43×#490C2semidirect
46. #13063322D4semidirect
74. #125×C43D4semidirect
203. C2×#490D43semidirect
242. C43#25608semidirect
261. #125C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835052
C2×#145832752
#191403462
#191355922
#191355612
#191354192
#191349402
#191343642
C2×C43×#4902
#2560843