Finite Group Databasebeta

← #24993072

Subgroups — #24993072

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145372C211yesmaximal, characteristic
2#19133099C211yesmaximal, characteristic
3C2×#14582637C211yesmaximal, characteristic, complemented
4#19132958C211yesmaximal, characteristic, complemented
5#19132483C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C43×#2977C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583240—21no—
10#14583227C411yescharacteristic, complemented
11#14583210C411yescharacteristic, complemented
12#14583138—21no—
13#14583126—21no—
14#14583061—21no—
15#14583054C411yescharacteristic, complemented
16#14583037C411yescharacteristic, complemented
17#14582863C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19C2×C43⋊#95C2211yescharacteristic
20#14582637—21no—
21#14582637—21no—
22#14582636—21no—
23#14582633—21no—
24#14582624—21no—
25#14582624—21no—
26C43×#525C2211yescharacteristic
27C43×#435—21no—
28C43×#435—21no—
29C8×D4×C43—21no—
30C8×D4×C43—21no—
31C43×#433—21no—
32C43×#408—21no—
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C22×Dic86C2×C411yescharacteristic
36C23×Dic43—21no—
37C2×#10621885—21no—
38C2×#10621883—21no—
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41#13063304—21no—
42#13063304—21no—
43#13063304—21no—
44#13063304—21no—
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48#13063258—21no—
49#13063256—21no—
50#13063249—21no—
51#13063248—21no—
52#13063248—21no—
53#13063246—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)C2×C411yescharacteristic
58C22⋊(C43⋊C8)C2×C411yescharacteristic
59C43⋊#95—21no—
60C43⋊#95—21no—
61C2×#41×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C2×M16×C43—21no—
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C22×C8×C43—21no—
67#123×C43—21no—
68C22⋊Q8×C43C2×C411yescharacteristic
69C22⋊Q8×C43D411yescharacteristic
70#121×C43C2×C411yescharacteristic
71#121×C43D411yescharacteristic
72#120×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75#117×C43D411yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43D411yescharacteristic
83C22⋊C8×C43D411yescharacteristic
84C22⋊C8×C43D411yescharacteristic
85C22⋊C8×C43D411yescharacteristic
86#97×C43—21no—
87C4×C8×C43—21no—
88C24×C43#4111yescharacteristic
89#41×C43—81no—
90C2×Q8×C43C22⋊C411yescharacteristic
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43C22⋊C411yescharacteristic
95C22×C4×C43—21no—
96C22×C4×C43—81no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—41no—
107C22×Dic43—41no—
108C22×Dic43—81no—
109C22×Dic43—81no—
110C2×Dic86—21no—
111C2×Dic86—21no—
112C2×Dic86—81no—
113M16×C43—81no—
114C2×C8×C43—21no—
115C2×C8×C43—21no—
116C2×C8×C43—21no—
117C2×C8×C43—21no—
118C2×C8×C43—81no—
119C2×C8×C43—81no—
120C2×C8×C43—81no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43C22⋊C411yescharacteristic
124C4⋊C4×C43C22⋊C411yescharacteristic
125C22⋊C4×C43—21no—
126C22⋊C4×C43—21no—
127C22⋊C4×C43—21no—
128C22⋊C4×C43—21no—
129C22⋊C4×C43—21no—
130C42×C43—21no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133#10621885—81no—
134#10621883—81no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137Dic43⋊C4—41no—
138Dic43⋊C4—41no—
139#10621877—81no—
140C2×C43⋊C8—21no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—81no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43C4×D411yescharacteristic
151C23×C43#12111yescharacteristic
152C23×C43#12311yescharacteristic
153Q8×C43—41no—
154D4×C43—41no—
155D4×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—41no—
159D4×C43—81no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43C2×C22⋊C411yescharacteristic
172C2×C4×C43C4×D411yescharacteristic
173C2×C4×C43#12011yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—81no—
181C2×Dic43—82no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—82no—
185Dic86—41no—
186Dic86—41no—
187Dic86—81no—
188C8×C43—41no—
189C8×C43—41no—
190C8×C43—41no—
191C8×C43—41no—
192C43⋊C8—41no—
193C43⋊C8—41no—
194C43⋊C8—81no—
195#9263—431nomaximal, Sylow
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43#38611yescharacteristic
211C22×C43#44311yescharacteristic
212C22×C43#44411yescharacteristic
213C22×C43#47111yescharacteristic
214C22×C43#47311yescharacteristic
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—41no—
220C4×C43—41no—
221C4×C43—41no—
222Dic43—82no—
223Dic43—81no—
224Dic43—81no—
225#3190—431no—
226#2977D4311yescharacteristic
227#1504—431no—
228C2×#328—431no—
229#1472—431no—
230#1298—431no—
231#1280—431no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43—41no—
237C2×C43—81no—
238C2×C43#187611yescharacteristic
239C2×C43#190811yescharacteristic
240C2×C43#191311yescharacteristic
241#525C2×D4311yescharacteristic
242C2×C22⋊Q8—431no—
243#485—861no—
244#483—431no—
245#480—431no—
246#467—861no—
247#465—861no—
248#452—861no—
249#451—431no—
250#448—431no—
251#435—21no—
252#435—21no—
253C8×D4—21no—
254C8×D4—21no—
255#433—21no—
256#408—21no—
257#407—431no—
258C2×C22⋊C8—431no—
259C2×C22⋊C8C2×D4311yescharacteristic
260C2×C22⋊C8C2×D4311yescharacteristic
261C2×#95—431no—
262#328—861no—
263#328—861no—
264#328—861no—
265#327—861no—
266#324—861no—
267#324—861no—
268C43#926311yescharacteristic, complemented, Sylow
269C2×#41C22⋊D4311yescharacteristic
270C22×Q8—431no—
271C23×C4—861no—
272C23×C4C22×D4311yescharacteristic
273C2×Q16—861no—
274C2×SD16—861no—
275C2×M16—21no—
276C2×M16—861no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—861no—
281#123—21no—
282C22⋊Q8—861no—
283C22⋊Q8—861no—
284C22⋊Q8—861no—
285C22⋊Q8—861no—
286C22⋊Q8C4×D4311yescharacteristic
287C22⋊Q8D17211yescharacteristic
288#121C4×D4311yescharacteristic
289#121D17211yescharacteristic
290#120—21no—
291C4×D4—21no—
292C4×D4—21no—
293#117C22⋊D4311yescharacteristic
294C2×C4⋊C4—431no—
295C2×C4⋊C4—861no—
296C2×C22⋊C4—861no—
297#107—861no—
298#106—861no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301#103—861no—
302#103—861no—
303#103—861no—
304#102—861no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—431no—
310C22⋊C8—431no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C22⋊C8—861no—
314C22⋊C8C22⋊D4311yescharacteristic
315C22⋊C8C22⋊D4311yescharacteristic
316C22⋊C8C22⋊D4311yescharacteristic
317C22⋊C8C22⋊D4311yescharacteristic
318#97—21no—
319C4×C8—21no—
320#95—861no—
321#95—861no—
322C24#1062189811yescharacteristic
323#41—81no—
324C2×Q8—861no—
325C2×Q8—861no—
326C2×Q8—3441no—
327C2×Q8(C2×D43)⋊C411yescharacteristic
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4(C2×D43)⋊C411yescharacteristic
332C22×C4—21no—
333C22×C4—81no—
334C22×C4—862no—
335C22×C4—861no—
336C22×C4—861no—
337C22×C4—3441no—
338C22×C4—3441no—
339C22×C4—1721no—
340C22×C4—1721no—
341C22×C4C2×C4×D4311yescharacteristic
342C22×C4C2×D17211yescharacteristic
343C22×C4#1062189811yescharacteristic
344C22×C4C2×C22⋊D4311yescharacteristic
345C22×C4C2×C22⋊D4311yescharacteristic
346C22×C4C2×C22⋊D4311yescharacteristic
347Q16—3441no—
348SD16—3441no—
349M16—81no—
350M16—3441no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—81no—
356C2×C8—81no—
357C2×C8—81no—
358C2×C8—861no—
359C2×C8—861no—
360C2×C8—3441no—
361C2×C8—1721no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—861no—
365C4⋊C4—861no—
366C4⋊C4—1721no—
367C4⋊C4—1721no—
368C4⋊C4(C2×D43)⋊C411yescharacteristic
369C4⋊C4(C2×D43)⋊C411yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—1721no—
376C22⋊C4—1721no—
377C42—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23C4×C22⋊D4311yescharacteristic
385C23#1306329911yescharacteristic
386C23#1306330811yescharacteristic
387Q8—41no—
388Q8—3441no—
389Q8—1721no—
390Q8—1721no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—3441no—
409C2×C4—3442no—
410C2×C4—3441no—
411C2×C4—3441no—
412C2×C4—3442no—
413C2×C4—1722no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4C2×(C2×D43)⋊C411yescharacteristic
419C2×C4C4×C22⋊D4311yescharacteristic
420C2×C4#1306329411yescharacteristic
421C2×C4#1306329911yescharacteristic
422C8—41no—
423C8—41no—
424C8—41no—
425C8—41no—
426C8—3441no—
427C8—1721no—
428C8—1721no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22#1458277811yescharacteristic
444C22#1458301411yescharacteristic
445C22#1458301911yescharacteristic
446C22#1458316211yescharacteristic
447C22#1458317411yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—3442no—
456C4—3441no—
457C4—3441no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—81no—
464C2#1913492211yescharacteristic
465C2#1913511011yescharacteristic
466C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2977C2
socleC22×C43#386
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#2977D43
hypocenterC43#9263
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
3. C2×#14582637C2semidirect
4. #19132958C2semidirect
5. #19132483C2semidirect
6. #19132437C2semidirect
10. #14583227C4semidirect
11. #14583210C4semidirect
15. #14583054C4semidirect
16. #14583037C4semidirect
268. C43#9263semidirect

Maximal subgroups

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

subgroupindex
#191453722
#191330992
C2×#145826372
#191329582
#191324832
#191324372
C43×#29772
#926343