Finite Group Databasebeta

← #24991464

Subgroups — #24991464

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144627C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic
4C4×#13063248C211yesmaximal, characteristic, complemented
5#19133045C211yesmaximal, characteristic
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583218—21no—
11#14583185C411yescharacteristic, complemented
12#14583185C411yescharacteristic, complemented
13#14583100C411yescharacteristic, complemented
14#14583100C411yescharacteristic, complemented
15#14583040—21no—
16#14583028—22no—
17#14583026—21no—
18#14583023—21no—
19C4×#10621873—21no—
20C4×#10621873—21no—
21#14582922—21no—
22C2×#13063253—21no—
23C2×#13063253—21no—
24C2×#13063248—21no—
25C4×#10621877C2211yescharacteristic
26M16×Dic43—21no—
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582661—21no—
29#14582626—22no—
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C2×#10621898—21no—
34C22×Dic86D411yescharacteristic
35C2×#10621873—21no—
36C2×#10621873—21no—
37C2×#10621877D411yescharacteristic
38C2×#10621877D411yescharacteristic
39C22×C43⋊C8—21no—
40#13063325C2×C411yescharacteristic
41#13063322C2×C411yescharacteristic
42#13063313—21no—
43#13063299—21no—
44#13063299—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86C2×C411yescharacteristic
48C4×Dic86C2×C411yescharacteristic
49C4×Dic86D411yescharacteristic
50C4×Dic86D411yescharacteristic
51C4×D172—21no—
52C4×D172—21no—
53C2×C4⋊Dic43D411yescharacteristic
54C2×Dic43⋊C4—21no—
55C2×C4×Dic43—21no—
56#13063257—21no—
57#13063257—21no—
58Dic43⋊C8—22no—
59Dic43⋊C8—22no—
60#13063253—42no—
61#13063253—42no—
62#13063250—21no—
63#13063250—21no—
64#13063248—24no—
65#13063247—21no—
66#13063247—21no—
67#13063236—21no—
68#13063235—22no—
69C4×C43⋊C8—21no—
70C4×C43⋊C8—21no—
71C4×C43⋊C8—21no—
72C8×Dic43—22no—
73C2×M16×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C42×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43C2×C411yescharacteristic
79C4⋊C8×C43C2×C411yescharacteristic
80C4⋊C8×C43D412yes—
81C22⋊C8×C43—21no—
82C4×C8×C43—21no—
83#95×C43—21no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C2×C22⋊D43—41no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91#10621898—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×C4×D43—41no—
99C2×Dic86—22no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86—41no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×Dic86C22⋊C411yescharacteristic
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—41no—
112C42×C43—41no—
113C42×C43—41no—
114C42×C43C22×C411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43C22⋊C411yescharacteristic
124C4⋊Dic43C22⋊C411yescharacteristic
125Dic43⋊C4—21no—
126Dic43⋊C4—21no—
127Dic43⋊C4—21no—
128Dic43⋊C4—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133#10621877—21no—
134#10621877—21no—
135#10621877—21no—
136#10621877SD1612yescomplemented
137C2×C43⋊C8—21no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—41no—
142#10621873—42no—
143#10621873—42no—
144C23×C43#12111yescharacteristic
145C22×D43—41no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43C2×SD1611yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43#13711yescharacteristic
162C22⋊D43—81no—
163C22⋊D43—81no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171D172—42no—
172D172—41no—
173D172—41no—
174D172—41no—
175D172—41no—
176C4×D43—81no—
177C4×D43—81no—
178Dic86—21no—
179Dic86—21no—
180Dic86—21no—
181Dic86—42no—
182Dic86—41no—
183Dic86—41no—
184Dic86#10412yescomplemented
185C8×C43—41no—
186C8×C43—41no—
187C8×C43—42no—
188C43⋊C8—22no—
189C43⋊C8—42no—
190C43⋊C8—41no—
191#8992—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43#38611yescharacteristic
195C22×C43#46011yescharacteristic
196C22×C43#46411yescharacteristic
197C2×D43—81no—
198C2×D43—81no—
199C2×D43—81no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—82no—
204C4×C43C2×#10411yescharacteristic
205C4×C43#42111yescharacteristic
206C4×C43C4×SD1611yescharacteristic
207C4×C43#44011yescharacteristic
208C4×C43#44811yescharacteristic
209C4×C43#44911yescharacteristic
210Dic43—22no—
211Dic43—41no—
212Dic43—41no—
213Dic43—41no—
214Dic43—81no—
215#3103—431no—
216Q8×M16—431no—
217#1980—431no—
218C4×#103—431no—
219#1492—431no—
220#1303D4311yescharacteristic, complemented
221#1278—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43#187111yescharacteristic
225C2×C43#188011yescharacteristic
226C2×C43#188111yescharacteristic
227D43—161no—
228#532—431no—
229C2×C4×Q8—431no—
230#481—861no—
231#475—431no—
232#475—431no—
233#460—431no—
234#460—431no—
235#448—861no—
236#446—861no—
237#446—862no—
238C8×Q8—861no—
239C4×SD16—861no—
240C4×SD16—861no—
241#431C2×D4311yescharacteristic
242#423—861no—
243#423C2×D4311yescharacteristic
244C2×#104—861no—
245C2×#104—861no—
246C2×#103—861no—
247C4×M16—431no—
248C4×M16—861no—
249C2×C4×C8—431no—
250C4×C4⋊C4C2×D4311yescharacteristic
251#340—861no—
252D4⋊C8—862no—
253C43#899211yescharacteristic, complemented, Sylow
254C2×#41—861no—
255C22×Q8—431no—
256C2×SD16—861no—
257C2×SD16—861no—
258C2×M16—21no—
259C2×M16—431no—
260C2×M16—431no—
261C22×C8—861no—
262C4⋊Q8—431no—
263#127—431no—
264#124—861no—
265#121—861no—
266#121—861no—
267C4×Q8—431no—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×Q8—431no—
271C4×Q8—861no—
272C4×Q8—861no—
273C4×D4—861no—
274C4×D4—861no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—861no—
278C2×C42—21no—
279C2×C42—861no—
280C2×C42C22×D4311yescharacteristic
281#106—861no—
282#106—861no—
283C4⋊C8—21no—
284C4⋊C8—862no—
285C4⋊C8—862no—
286C4⋊C8C4×D4311yescharacteristic
287C4⋊C8C4×D4311yescharacteristic
288C4⋊C8D17212yes—
289#104—1722no—
290#104—1722no—
291#103—864no—
292#103—861no—
293#103—861no—
294#102—861no—
295#102—861no—
296C22⋊C8—21no—
297#97—862no—
298#97—861no—
299C4×C8—21no—
300C4×C8—862no—
301C4×C8—861no—
302C4×C8—861no—
303C4×C8—861no—
304#95—21no—
305#41—1721no—
306#41—1721no—
307#41—1721no—
308#41—1721no—
309C2×Q8—431no—
310C2×Q8—431no—
311C2×Q8—862no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—1721no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—1721no—
319C22×C4—41no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—1721no—
323C22×C4#1062189811yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326SD16—1722no—
327SD16—1722no—
328M16—41no—
329M16—41no—
330M16—432no—
331M16—861no—
332M16—861no—
333M16—861no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—861no—
338C2×C8—862no—
339C2×C8—861no—
340C2×C8—1721no—
341C2×C8—1721no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—431no—
345C4⋊C4—431no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C42—41no—
356C42—41no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—861no—
361C42C2×C4×D4311yescharacteristic
362C42C2×D17211yescharacteristic
363C42D4×D4311yescharacteristic
364C42#1062190211yescharacteristic
365C23—1721no—
366C23#1306329811yescharacteristic
367Q8—432no—
368Q8—861no—
369Q8—861no—
370Q8—861no—
371Q8—1722no—
372Q8—1721no—
373Q8—1721no—
374D4—3441no—
375D4—3441no—
376D4—1722no—
377D4—1721no—
378D4—1721no—
379D4—1721no—
380D4—1721no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—1722no—
395C2×C4—1721no—
396C2×C4C22⋊C4×D4311yescharacteristic
397C2×C4#1306328711yescharacteristic
398C2×C4C4×D17211yescharacteristic
399C2×C4#1306329511yescharacteristic
400C2×C4#1306330011yescharacteristic
401C2×C4#1306331011yescharacteristic
402C2×C4SD16×D4311yescharacteristic
403C2×C4#1306334611yescharacteristic
404C2×C4#1306334911yescharacteristic
405C2×C4#1306335711yescharacteristic
406C8—42no—
407C8—41no—
408C8—41no—
409C8—862no—
410C8—1722no—
411C8—1721no—
412C22—21no—
413C22—21no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22#1458277711yescharacteristic
418C22#1458309811yescharacteristic
419C22#1458312411yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—82no—
424C4—862no—
425C4—3441no—
426C4—1721no—
427C4—1721no—
428C4—1721no—
429C4#104×D4311yescharacteristic
430C4#1458291411yescharacteristic
431C4#1458298611yescharacteristic
432C4#1458299811yescharacteristic
433C4#1458303911yescharacteristic
434C4#1458304511yescharacteristic
435C2—21no—
436C2—21no—
437C2—6881no—
438C2#1913489611yescharacteristic
439C2#1913495111yescharacteristic
440C2#1913495611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#8992
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
4. C4×#13063248C2semidirect
6. #19132431C2semidirect
7. C43×#1303C2semidirect
11. #14583185C4semidirect
12. #14583185C4semidirect
13. #14583100C4semidirect
14. #14583100C4semidirect
136. #10621877SD16semidirect
184. Dic86#104semidirect
220. #1303D43semidirect
253. C43#8992semidirect

Maximal subgroups

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

subgroupindex
#191446272
#191435462
#191355132
C4×#130632482
#191330452
#191324312
C43×#13032
#899243