Finite Group Databasebeta

← #24992687

Subgroups — #24992687

Order 11008.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144050C211yesmaximal, characteristic
2#19134615C211yesmaximal, characteristic, complemented
3#19133091C211yesmaximal, characteristic, complemented
4#19133047C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132435C211yesmaximal, characteristic, complemented
7C8×#41×C43C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9#14583449C2211yescharacteristic
10#14583121—21no—
11#14583114—21no—
12#14583109C411yescharacteristic, complemented
13#14583104C411yescharacteristic, complemented
14#14583099C411yescharacteristic, complemented
15#14583094C411yescharacteristic, complemented
16#14582923C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×#13063252—21no—
19#14582893—21no—
20C4×C4⋊Dic43C2211yescharacteristic
21#14582658—21no—
22#14582634—22no—
23#14582628—21no—
24#14582628—21no—
25C4×#41×C43C2211yescharacteristic
26C8×Q8×C43—21no—
27C8×D4×C43—21no—
28C8×D4×C43—22no—
29C43×#431—21no—
30C43×#431C2211yescharacteristic
31C2×C4×C8×C43—21no—
32C2×C4×C8×C43C2211yescharacteristic
33C2×#10621898—21no—
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40C2×#10621877—21no—
41C22×C43⋊C8—21no—
42#13063325C2×C411yescharacteristic
43#13063322C2×C411yescharacteristic
44#13063313—21no—
45#13063299—21no—
46#13063299—21no—
47C4×D172—21no—
48C4×D172—21no—
49C2×C4⋊Dic43—21no—
50C2×C4×Dic43—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56#13063252—42no—
57#13063248—21no—
58#13063248—21no—
59#13063245—21no—
60#13063245—21no—
61C43⋊#95—21no—
62C2×#41×C43D411yescharacteristic
63C22×C8×C43—22no—
64C22×C8×C43—21no—
65C4×Q8×C43C2×C411yescharacteristic
66C4×Q8×C43D411yescharacteristic
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43C2×C411yescharacteristic
70C4×D4×C43D411yescharacteristic
71#117×C43—21no—
72#117×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—22no—
76C4⋊C8×C43—21no—
77C22⋊C8×C43—22no—
78C22⋊C8×C43D412yes—
79C4×C8×C43—22no—
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43D411yescharacteristic
83C4×C8×C43D411yescharacteristic
84#41×C43—21no—
85#41×C43—21no—
86#41×C43D812yes—
87#41×C43SD1612yes—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×D4×C43—21no—
90C2×D4×C43C22⋊C411yescharacteristic
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—41no—
98C22×Dic43—41no—
99#10621898—41no—
100#10621898—41no—
101#10621898—41no—
102#10621898—41no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—21no—
106C2×C4×D43—41no—
107C2×Dic86—21no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C2×C8×C43—21no—
111C2×C8×C43—42no—
112C2×C8×C43—44no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43C22⋊C411yescharacteristic
116C4⋊C4×C43C22⋊C411yescharacteristic
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C22⋊C4×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43C22×C411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C42×C43#4111yescharacteristic
127#10621885—42no—
128#10621884—42no—
129#10621883—42no—
130#10621882—42no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—41no—
133C4⋊Dic43—22no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—41no—
137C4×Dic43—41no—
138C4×Dic43—41no—
139#10621877—41no—
140#10621877—41no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—21no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C23×C43—21no—
147C23×C43#12111yescharacteristic
148C22×D43—41no—
149Q8×C43—21no—
150Q8×C43#10212yes—
151D4×C43—22no—
152D4×C43—22no—
153D4×C43—21no—
154D4×C43#10212yes—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43C2×C22⋊C411yescharacteristic
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43#12011yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12311yescharacteristic
172C2×C4×C43C2×D811yescharacteristic
173C2×C4×C43C2×SD1611yescharacteristic
174C2×C4×C43#13511yescharacteristic
175C2×C4×C43#13511yescharacteristic
176C22⋊D43—81no—
177C22⋊D43—81no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182D172—41no—
183D172—41no—
184D172—41no—
185D172—41no—
186D172—81no—
187C4×D43—81no—
188C4×D43—81no—
189Dic86—41no—
190Dic86—41no—
191C8×C43—22no—
192C8×C43—42no—
193C8×C43—41no—
194C43⋊C8—41no—
195C43⋊C8—41no—
196C43⋊C8—81no—
197#9208—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—22no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43#38611yescharacteristic
204C22×C43#46511yescharacteristic
205C22×C43#46611yescharacteristic
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—22no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—41no—
214C4×C43—41no—
215C4×C43C2×#10211yescharacteristic
216C4×C43#41611yescharacteristic
217C4×C43#44311yescharacteristic
218C4×C43#44411yescharacteristic
219C4×C43#46511yescharacteristic
220C4×C43#46611yescharacteristic
221Dic43—82no—
222Dic43—81no—
223#3035—431no—
224C8×#41D4311yescharacteristic, complemented
225#1806—431no—
226#1502—431no—
227#1492—431no—
228#1301—431no—
229#1279—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—42no—
233C2×C43#187611yescharacteristic
234C2×C43#189311yescharacteristic
235C2×C43#190611yescharacteristic
236D43—161no—
237C2×#135—861no—
238#532—431no—
239C4×#41C2×D4311yescharacteristic
240#464—861no—
241#463—861no—
242#462—431no—
243#461—431no—
244#460—431no—
245#459—431no—
246C8×Q8—21no—
247C8×D4—21no—
248C8×D4—22no—
249#431—21no—
250#431C2×D4311yescharacteristic
251#423—431no—
252C2×C4⋊C8—431no—
253C2×#104—861no—
254#416—861no—
255C2×C4×C8—21no—
256C2×C4×C8C2×D4311yescharacteristic
257C4×C4⋊C4—431no—
258#339—861no—
259#327—862no—
260D4⋊C8—861no—
261D4⋊C8—861no—
262C43#920811yescharacteristic, complemented, Sylow
263C2×#41—861no—
264C2×#41D17211yescharacteristic
265#135—1722no—
266#135—1722no—
267C2×Q16—861no—
268C2×SD16—861no—
269C2×SD16—861no—
270C2×D8—861no—
271C2×M16—861no—
272C22×C8—22no—
273C22×C8—21no—
274C22×C8—861no—
275C4⋊Q8—431no—
276#127—431no—
277#124—861no—
278#121—861no—
279#121—861no—
280C4×Q8C4×D4311yescharacteristic
281C4×Q8C22⋊D4311yescharacteristic
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—861no—
285C4×D4—861no—
286C4×D4C4×D4311yescharacteristic
287C4×D4C22⋊D4311yescharacteristic
288#117—21no—
289#117D17211yescharacteristic
290C2×C4⋊C4—861no—
291C2×C42—21no—
292C2×C42—861no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—22no—
295C4⋊C8—21no—
296C4⋊C8—431no—
297C4⋊C8—431no—
298C4⋊C8—861no—
299C4⋊C8—861no—
300C4⋊C8—861no—
301#104—1722no—
302#103—861no—
303#103—861no—
304#102—861no—
305#102—861no—
306C22⋊C8—22no—
307C22⋊C8C22⋊D4312yes—
308C4×C8—22no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8C22⋊D4311yescharacteristic
312C4×C8C22⋊D4311yescharacteristic
313#95—861no—
314#41—21no—
315#41—21no—
316#41—1721no—
317#41—1721no—
318#41—1721no—
319#41—1721no—
320#41#1062187312yes—
321#41D34412yes—
322C2×Q8—861no—
323C2×Q8(C2×D43)⋊C411yescharacteristic
324C2×D4—21no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—1721no—
329C2×D4(C2×D43)⋊C411yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—1721no—
334C22×C4—1721no—
335C22×C4C2×D17211yescharacteristic
336C22×C4#1062189811yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338Q16—1722no—
339SD16—1722no—
340SD16—1722no—
341D8—1722no—
342M16—1721no—
343M16—1721no—
344C2×C8—21no—
345C2×C8—22no—
346C2×C8—21no—
347C2×C8—42no—
348C2×C8—44no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—862no—
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4—1721no—
360C4⋊C4(C2×D43)⋊C411yescharacteristic
361C4⋊C4(C2×D43)⋊C411yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—1721no—
366C22⋊C4—1721no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—1721no—
371C42—1721no—
372C42C2×C4×D4311yescharacteristic
373C42#1062189811yescharacteristic
374C42C2×C22⋊D4311yescharacteristic
375C42C2×C22⋊D4311yescharacteristic
376C23—21no—
377C23—1721no—
378C23#1306329911yescharacteristic
379Q8—21no—
380Q8—1721no—
381Q8—1721no—
382Q8#1306324712yes—
383D4—22no—
384D4—22no—
385D4—21no—
386D4—3441no—
387D4—3441no—
388D4—3441no—
389D4—1721no—
390D4—1721no—
391D4—1721no—
392D4—1721no—
393D4#1306324712yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—3441no—
406C2×C4—3441no—
407C2×C4—3441no—
408C2×C4—3441no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4C2×(C2×D43)⋊C411yescharacteristic
412C2×C4C4×C22⋊D4311yescharacteristic
413C2×C4C4×C22⋊D4311yescharacteristic
414C2×C4#1306329411yescharacteristic
415C2×C4#1306329911yescharacteristic
416C2×C4#1306330811yescharacteristic
417C2×C4C2×D34411yescharacteristic
418C2×C4C2×#1062187311yescharacteristic
419C2×C4#1306334711yescharacteristic
420C2×C4#1306334711yescharacteristic
421C8—22no—
422C8—42no—
423C8—41no—
424C8—3441no—
425C8—1721no—
426C8—1721no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—3441no—
433C22—3441no—
434C22—3441no—
435C22#1458277811yescharacteristic
436C22#1458312811yescharacteristic
437C22#1458313511yescharacteristic
438C4—22no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—3442no—
445C4—3441no—
446C4C2×#1306324711yescharacteristic
447C4#1458289611yescharacteristic
448C4#1458301411yescharacteristic
449C4#1458301911yescharacteristic
450C4#1458312811yescharacteristic
451C4#1458313511yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—6881no—
456C2#1913492211yescharacteristic
457C2#1913502311yescharacteristic
458C2#1913509611yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC8×#41×C43C2
socleC22×C43#386
prime radical#19144050C2
cosocleC2×C42×C43C23
hypercenterC8×#41D43
hypocenterC43#9208
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #19134615C2semidirect
3. #19133091C2semidirect
4. #19133047C2semidirect
5. #19132491C2semidirect
6. #19132435C2semidirect
7. C8×#41×C43C2semidirect
12. #14583109C4semidirect
13. #14583104C4semidirect
14. #14583099C4semidirect
15. #14583094C4semidirect
224. C8×#41D43semidirect
262. C43#9208semidirect

Maximal subgroups

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

subgroupindex
#191440502
#191346152
#191330912
#191330472
#191324912
#191324352
C8×#41×C432
#920843