Finite Group Databasebeta

← #24991302

Subgroups — #24991302

Order 11008.

516 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144655C211yesmaximal, characteristic
2#19135422C211yesmaximal, characteristic, complemented
3C4×#13063252C211yesmaximal, characteristic, complemented
4#19133011C211yesmaximal, characteristic, complemented
5#19132484C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#2990C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583223—21no—
10#14583194C411yescharacteristic, complemented
11#14583189C411yescharacteristic, complemented
12#14583099C411yescharacteristic, complemented
13#14583094C411yescharacteristic, complemented
14#14583044—21no—
15C4×#10621884—21no—
16C4×#10621882—21no—
17#14582952C2211yescharacteristic
18C2×#13063252—21no—
19C2×#13063251—22no—
20C4×#10621877C2211yescharacteristic
21C42×Dic43C2211yescharacteristic
22#14582658—21no—
23#14582626—21no—
24#14582626—21no—
25C4×#41×C43C2211yescharacteristic
26C43×#446—21no—
27C43×#435—22no—
28C8×D4×C43—21no—
29C43×#432—21no—
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×C4⋊C8×C43—21no—
33C2×#10621898—21no—
34C2×#10621884—21no—
35C2×#10621882—21no—
36C2×#10621877—21no—
37#13063325C2×C411yescharacteristic
38#13063322C2×C411yescharacteristic
39#13063313—21no—
40#13063299—21no—
41#13063299—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47#13063258—21no—
48#13063256—21no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51#13063252—24no—
52#13063251—44no—
53#13063249—21no—
54#13063246—21no—
55#13063245—21no—
56#13063245—21no—
57C22⋊(C43⋊C8)—21no—
58#13063236—21no—
59C4×C43⋊C8—21no—
60C4×C43⋊C8—21no—
61C2×#41×C43D411yescharacteristic
62C2×M16×C43D412yes—
63C22×C8×C43—22no—
64C4×Q8×C43C2×C411yescharacteristic
65C4×Q8×C43D411yescharacteristic
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43C2×C411yescharacteristic
69C4×D4×C43D411yescharacteristic
70#117×C43—21no—
71#117×C43D411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—22no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43D411yescharacteristic
78C4⋊C8×C43D411yescharacteristic
79C22⋊C8×C43—22no—
80C22⋊C8×C43—21no—
81#97×C43—22no—
82C4×C8×C43—21no—
83#41×C43—22no—
84#41×C43—41no—
85C2×Q8×C43C22⋊C411yescharacteristic
86C2×D4×C43—21no—
87C2×D4×C43C22⋊C411yescharacteristic
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—41no—
95C22×Dic43—41no—
96#10621898—42no—
97#10621898—42no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—21no—
101C2×C4×D43—41no—
102C2×Dic86—21no—
103M16×C43—42no—
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—22no—
107C2×C8×C43—82no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43C22⋊C411yescharacteristic
111C4⋊C4×C43C22⋊C411yescharacteristic
112C22⋊C4×C43—21no—
113C22⋊C4×C43—21no—
114C22⋊C4×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43—21no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122#10621884—42no—
123#10621882—42no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4×Dic43—22no—
129C4×Dic43—22no—
130C4×Dic43—22no—
131C4×Dic43—41no—
132C4×Dic43—41no—
133C4×Dic43—41no—
134#10621877—22no—
135#10621877—41no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—41no—
139C23×C43—21no—
140C23×C43#12111yescharacteristic
141C22×D43—41no—
142Q8×C43—21no—
143Q8×C43—21no—
144D4×C43—21no—
145D4×C43—42no—
146D4×C43#10412yescomplemented
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C22⋊D43—82no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172D172—42no—
173D172—41no—
174D172—41no—
175D172—41no—
176D172—41no—
177C4×D43—81no—
178C4×D43—81no—
179Dic86—42no—
180C8×C43—41no—
181C8×C43—42no—
182C8×C43—41no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—41no—
186#8969—431nomaximal, Sylow
187C22×C43—22no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43#38611yescharacteristic
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—41no—
203C4×C43C2×#10411yescharacteristic
204C4×C43#42111yescharacteristic
205C4×C43#44311yescharacteristic
206C4×C43#44411yescharacteristic
207C4×C43#45311yescharacteristic
208C4×C43#45411yescharacteristic
209Dic43—44no—
210Dic43—81no—
211#3106—431no—
212#2990D4311yescharacteristic, complemented
213#1962—431no—
214C4×#104—431no—
215#1484—431no—
216#1299—431no—
217#1276—431no—
218C2×C43—41no—
219C2×C43—42no—
220C2×C43#187111yescharacteristic
221C2×C43#187611yescharacteristic
222C2×C43#188311yescharacteristic
223D43—161no—
224#532—431no—
225C4×#41C2×D4311yescharacteristic
226#482—861no—
227#477—431no—
228#476—431no—
229#460—431no—
230#459—431no—
231#449—861no—
232#446—21no—
233C4×SD16—861no—
234C4×D8—861no—
235#435—22no—
236C8×D4—21no—
237#432—21no—
238#431—431no—
239#431C2×D4311yescharacteristic
240#423C2×D4311yescharacteristic
241C2×C4⋊C8—21no—
242C2×#104—861no—
243C2×#104—862no—
244C4×M16—431no—
245C43—431no—
246#339—861no—
247D4⋊C8—861no—
248D4⋊C8—861no—
249C43#896911yescharacteristic, complemented, Sylow
250C2×#41—861no—
251C2×#41D17211yescharacteristic
252C2×SD16—861no—
253C2×D8—861no—
254C2×M16—861no—
255C2×M16C22⋊D4312yes—
256C22×C8—22no—
257C4⋊Q8—431no—
258#127—431no—
259#124—861no—
260#121—861no—
261#121—861no—
262C4×Q8C4×D4311yescharacteristic
263C4×Q8C22⋊D4311yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—861no—
267C4×D4—861no—
268C4×D4C4×D4311yescharacteristic
269C4×D4C22⋊D4311yescharacteristic
270#117—21no—
271#117D17211yescharacteristic
272C2×C42—21no—
273C2×C42—861no—
274C2×C42—861no—
275C2×C42—861no—
276C2×C42C22×D4311yescharacteristic
277#107—861no—
278#106—861no—
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—431no—
283C4⋊C8—431no—
284C4⋊C8C22⋊D4311yescharacteristic
285C4⋊C8C22⋊D4311yescharacteristic
286#104—864no—
287#104—1724no—
288#103—861no—
289#102—861no—
290#102—861no—
291#102—861no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294C22⋊C8—861no—
295#97—22no—
296#97—861no—
297C4×C8—21no—
298C4×C8—861no—
299C4×C8—861no—
300#41—22no—
301#41—41no—
302#41—1722no—
303#41—1722no—
304C2×Q8—861no—
305C2×Q8(C2×D43)⋊C411yescharacteristic
306C2×D4—21no—
307C2×D4—861no—
308C2×D4—861no—
309C2×D4—861no—
310C2×D4—1721no—
311C2×D4(C2×D43)⋊C411yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4C2×D17211yescharacteristic
318C22×C4#1062189811yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320SD16—1722no—
321D8—1722no—
322M16—42no—
323M16—862no—
324M16—1721no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—82no—
329C2×C8—861no—
330C2×C8—861no—
331C2×C8—1721no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4(C2×D43)⋊C411yescharacteristic
337C4⋊C4(C2×D43)⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—862no—
347C42—862no—
348C42—862no—
349C42—1721no—
350C42—1721no—
351C42—1721no—
352C42C2×C4×D4311yescharacteristic
353C42#1062189811yescharacteristic
354C42C2×C22⋊D4311yescharacteristic
355C42C2×C22⋊D4311yescharacteristic
356C23—21no—
357C23—1721no—
358C23#1306329911yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—1722no—
362D4—21no—
363D4—42no—
364D4—3442no—
365D4—1722no—
366D4—1721no—
367D4—1721no—
368D4—1721no—
369D4—1721no—
370D4#1306325112yescomplemented
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—3441no—
386C2×C4—3441no—
387C2×C4—1721no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4C2×(C2×D43)⋊C411yescharacteristic
392C2×C4C4×C22⋊D4311yescharacteristic
393C2×C4C4×C22⋊D4311yescharacteristic
394C2×C4#1306329411yescharacteristic
395C2×C4#1306329911yescharacteristic
396C2×C4#1306330811yescharacteristic
397C8—41no—
398C8—42no—
399C8—41no—
400C8—1722no—
401C8—1721no—
402C8—1721no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—3441no—
410C22—3441no—
411C22—3441no—
412C22#1458277811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—3441no—
420C4—1724no—
421C4C2×#1306325111yescharacteristic
422C4#1458291511yescharacteristic
423C4#1458301411yescharacteristic
424C4#1458301911yescharacteristic
425C4#1458306711yescharacteristic
426C4#1458307211yescharacteristic
427C2—41no—
428C2—42no—
429C2—6881no—
430C2#1913489711yescharacteristic
431C2#1913492211yescharacteristic
432C2#1913497111yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2990C2
socleC22×C43#386
prime radical#19144655C2
cosocleC2×C42×C43C23
hypercenter#2990D43
hypocenterC43#8969
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #19135422C2semidirect
3. C4×#13063252C2semidirect
4. #19133011C2semidirect
5. #19132484C2semidirect
6. #19132427C2semidirect
7. C43×#2990C2semidirect
10. #14583194C4semidirect
11. #14583189C4semidirect
12. #14583099C4semidirect
13. #14583094C4semidirect
146. D4×C43#104semidirect
212. #2990D43semidirect
249. C43#8969semidirect
370. D4#13063251semidirect

Maximal subgroups

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

subgroupindex
#191446552
#191354222
C4×#130632522
#191330112
#191324842
#191324272
C43×#29902
#896943