Finite Group Databasebeta

← #25084495

Subgroups — #25084495

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145718C211yesmaximal, characteristic
2#19145545C211yesmaximal, characteristic, complemented
3#19145154C211yesmaximal, characteristic
4C2×#14583297C211yesmaximal, characteristic, complemented
5#19144989C211yesmaximal, characteristic
6#19144976C211yesmaximal, characteristic, complemented
7#19134255C212yesmaximal, complemented
8#19134241C212yesmaximal, complemented
9#19134196C212yesmaximal, complemented
10#19134192C212yesmaximal, complemented
11C8×M16×C43C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583449C2211yescharacteristic
14C2×#13063325C2211yescharacteristic
15C2×#13063325C2211yescharacteristic
16#14583304C2212yes—
17#14583297—22no—
18#14583297C2212yes—
19#14583297C2212yes—
20#14583297C2211yescharacteristic
21#14583279C2212yes—
22#14583272C2211yescharacteristic
23#14583268—22no—
24#14583259—22no—
25#14583250C2212yes—
26#14583250C2212yes—
27#14583250C2212yes—
28#14583250C2211yescharacteristic
29#14583250C2212yes—
30#14583246C2212yes—
31#14583246C2211yescharacteristic
32#14583246C2212yes—
33#14583213—22no—
34#14583180—22no—
35#14583128—22no—
36#14583110—22no—
37#14583057—22no—
38C4×#10621873—22no—
39C2×#13063257—22no—
40#14582909—22no—
41#14582901—22no—
42C43×#431C2211yescharacteristic
43C4×M16×C43C2211yescharacteristic
44C2×C4×C8×C43C2211yescharacteristic
45C43×#322C2212yes—
46C82×C43C2212yes—
47C2×#10621898—21no—
48C22×Dic86—21no—
49C22×Dic86—21no—
50C2×Dic172—24no—
51C2×#10621873—22no—
52#13063325—21no—
53#13063325—21no—
54#13063325—21no—
55#13063325—21no—
56#13063325—21no—
57#13063325—21no—
58#13063325C2312yes—
59#13063325C2312yes—
60#13063325C2311yescharacteristic
61#13063325C2311yescharacteristic
62#13063325C2311yescharacteristic
63#13063322C2311yescharacteristic
64#13063317—21no—
65#13063313—21no—
66#13063304—21no—
67#13063304—21no—
68#13063299—21no—
69#13063299—21no—
70C4×Dic86—21no—
71C4×Dic86—21no—
72C4×D172—21no—
73C4×D172—21no—
74#13063284—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79#13063259—24no—
80#13063257—24no—
81#13063257—24no—
82#13063257—22no—
83#13063250—24no—
84#13063250—22no—
85#13063250—24no—
86#13063250—24no—
87#13063250—24no—
88#13063247—22no—
89#13063247—24no—
90#13063247—24no—
91C2×M16×C43D412yes—
92C22×C8×C43D412yes—
93C2×C42×C43C2311yescharacteristic
94C4⋊C8×C43D412yes—
95C22⋊C8×C43D412yes—
96#97×C43D412yes—
97C4×C8×C43D412yes—
98C4×C8×C43C2311yescharacteristic
99C4×C8×C43C2311yescharacteristic
100C4×C8×C43C2312yes—
101C4×C8×C43C2312yes—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C2×C22⋊D43—41no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108#10621898—44no—
109C2×D172—21no—
110C2×D172—21no—
111C2×D172—21no—
112C2×C4×D43—41no—
113C2×Dic86—21no—
114C2×Dic86—22no—
115C2×Dic86—21no—
116C2×Dic86—22no—
117C2×Dic86—21no—
118C2×Dic86—44no—
119C2×Dic86—41no—
120C2×Dic86—41no—
121C2×Dic86—82no—
122M16×C43—24no—
123C2×C8×C43—24no—
124C2×C8×C43C2×D412yes—
125C2×C8×C43C2×D414yes—
126C2×C8×C43C2×D414yes—
127C2×C8×C43C2×D412yes—
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2411yescharacteristic
132C22⋊Dic43—41no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135C4⋊Dic43—22no—
136C4⋊Dic43—21no—
137C4⋊Dic43—22no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43—22no—
143C4⋊Dic43—22no—
144C4⋊Dic43—21no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151C4×Dic43—41no—
152Dic172—84no—
153#10621873—44no—
154C23×C43#12711yescharacteristic
155C22×D43—41no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43#12711yescharacteristic
159C2×C4×C43#12711yescharacteristic
160C2×C4×C43#12711yescharacteristic
161C2×C4×C43#13514yes—
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C22⋊D43—82no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—82no—
172C2×Dic43—82no—
173D172—42no—
174D172—42no—
175D172—42no—
176C4×D43—82no—
177Dic86—44no—
178Dic86—42no—
179Dic86—42no—
180Dic86—42no—
181Dic86—44no—
182Dic86—82no—
183Dic86—82no—
184C8×C43—24no—
185C8×C43—22no—
186C8×C43—24no—
187C8×C43#13714yes—
188#19626—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43#49512yes—
192C22×C43C2×#12711yescharacteristic
193C2×D43—81no—
194C2×D43—81no—
195C2×D43—81no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43#49512yes—
199C4×C43C2×#13512yes—
200C4×C43C2×#13712yes—
201C4×C43#57712yes—
202Dic43—82no—
203Dic43—81no—
204Dic43—81no—
205Dic43—82no—
206Dic43—81no—
207#3226—431no—
208#3209—431no—
209#3167—431no—
210C2×#498—431no—
211#3141—431no—
212#3139—431no—
213#1720—432no—
214#1718—432no—
215#1708—432no—
216#1707—432no—
217C8×M16D4311yescharacteristic, complemented
218C2×C43—22no—
219C2×C43C2×#49511yescharacteristic
220C2×C43#315211yescharacteristic
221C2×C43#315411yescharacteristic
222D43—161no—
223#533—431no—
224#532—431no—
225C2×C4⋊Q8—431no—
226C2×C4⋊Q8—431no—
227#500—432no—
228#498—432no—
229#498—432no—
230#498—431no—
231#498—862no—
232#494—432no—
233#492—431no—
234#491—862no—
235#489—862no—
236#487—432no—
237#487—432no—
238#487—432no—
239#487—431no—
240#487—432no—
241#486—432no—
242#486—431no—
243#486—432no—
244#480—862no—
245#474—862no—
246#465—862no—
247#462—862no—
248#451—862no—
249C4×SD16—862no—
250#431C2×D4311yescharacteristic
251C2×#106—862no—
252#419—862no—
253#417—862no—
254C4×M16C2×D4311yescharacteristic
255C2×C4×C8C2×D4311yescharacteristic
256#322C2×D4312yes—
257C82C2×D4312yes—
258C43#1962611yescharacteristic, complemented, Sylow
259C2×#41—861no—
260C22×Q8—861no—
261C22×Q8—861no—
262C2×Q16—864no—
263C2×SD16—862no—
264C2×M16D17212yes—
265C22×C8D17212yes—
266C4⋊Q8—432no—
267C4⋊Q8—432no—
268C4⋊Q8—431no—
269C4⋊Q8—431no—
270C4⋊Q8—431no—
271C4⋊Q8—861no—
272C4⋊Q8—861no—
273C4⋊Q8—861no—
274C4⋊Q8—861no—
275C4⋊Q8—861no—
276C4⋊Q8—861no—
277#127—431no—
278#125—861no—
279#124—861no—
280C22⋊Q8—861no—
281C22⋊Q8—861no—
282#121—861no—
283#121—861no—
284C4×Q8—861no—
285C4×Q8—861no—
286C4×D4—861no—
287C4×D4—861no—
288#117—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—861no—
291C2×C4⋊C4—861no—
292C2×C4⋊C4—861no—
293C2×C42C22×D4311yescharacteristic
294#107—864no—
295#106—864no—
296#106—864no—
297#106—862no—
298C4⋊C8D17212yes—
299#103—864no—
300#103—864no—
301#103—864no—
302#103—862no—
303#103—864no—
304#102—864no—
305#102—862no—
306#102—864no—
307C22⋊C8D17212yes—
308#97D17212yes—
309C4×C8D17212yes—
310C4×C8C22×D4311yescharacteristic
311C4×C8C22×D4312yes—
312C4×C8C22×D4312yes—
313C4×C8C22×D4311yescharacteristic
314#41—1724no—
315C2×Q8—861no—
316C2×Q8—862no—
317C2×Q8—861no—
318C2×Q8—862no—
319C2×Q8—861no—
320C2×Q8—3442no—
321C2×Q8—1724no—
322C2×Q8—1721no—
323C2×Q8—1721no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—1721no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4C2×D17211yescharacteristic
332C22×C4C2×D17211yescharacteristic
333C22×C4C2×D17211yescharacteristic
334Q16—3444no—
335SD16—1724no—
336M16—24no—
337C2×C8—24no—
338C2×C8C2×D17212yes—
339C2×C8C2×D17214yes—
340C2×C8C2×D17214yes—
341C2×C8C2×D17212yes—
342C4⋊C4—862no—
343C4⋊C4—861no—
344C4⋊C4—862no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—862no—
350C4⋊C4—862no—
351C4⋊C4—861no—
352C4⋊C4—1721no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C4⋊C4—1721no—
356C4⋊C4—1721no—
357C4⋊C4—1721no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C42—1721no—
362C42C2×D17211yescharacteristic
363C42C2×D17211yescharacteristic
364C42C2×D17211yescharacteristic
365C42C23×D4311yescharacteristic
366C23—1721no—
367C23#1306332211yescharacteristic
368Q8—3442no—
369Q8—3442no—
370Q8—1724no—
371Q8—1722no—
372Q8—1722no—
373Q8—1722no—
374Q8—1724no—
375D4—3442no—
376D4—1722no—
377D4—1722no—
378D4—1722no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—3442no—
382C2×C4—3442no—
383C2×C4—3442no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4#1306332211yescharacteristic
390C2×C4#1306332211yescharacteristic
391C2×C4#1306332211yescharacteristic
392C2×C4#1306334714yes—
393C2×C4C22×D17211yescharacteristic
394C2×C4C22×D17211yescharacteristic
395C2×C4C22×D17211yescharacteristic
396C8—24no—
397C8—22no—
398C8—24no—
399C8#1306335814yes—
400C22—21no—
401C22—21no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22#1458328312yes—
406C22C2×#1306332211yescharacteristic
407C4—21no—
408C4—21no—
409C4—3441no—
410C4—3442no—
411C4—3441no—
412C4—3442no—
413C4—3441no—
414C4#1458328312yes—
415C4C2×#1306334712yes—
416C4C2×#1306335812yes—
417C4#1458371112yes—
418C2—22no—
419C2—6881no—
420C2C2×#1458328311yescharacteristic
421C2#1914505411yescharacteristic
422C2#1914507111yescharacteristic
subgroupG/H
centerC22C2×#13063322
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC8×M16×C43C2
socleC22×C43C2×#127
prime radical#14583449C22
hypercenterC8×M16D43
hypocenterC43#19626
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #19145545C2semidirect
4. C2×#14583297C2semidirect
6. #19144976C2semidirect
7. #19134255C2semidirect
8. #19134241C2semidirect
9. #19134196C2semidirect
10. #19134192C2semidirect
11. C8×M16×C43C2semidirect
217. C8×M16D43semidirect
258. C43#19626semidirect

Maximal subgroups

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

subgroupindex
#191457182
#191455452
#191451542
C2×#145832972
#191449892
#191449762
#191342552
#191342412
#191341962
#191341922
C8×M16×C432
#1962643