Finite Group Databasebeta

← #24992420

Subgroups — #24992420

Order 11008.

508 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#19144686C211yesmaximal, characteristic
2#19134420C211yesmaximal, characteristic, complemented
3#19133207C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic, complemented
5#19132495C211yesmaximal, characteristic, complemented
6#19132450C211yesmaximal, characteristic, complemented
7C43×#2974C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583217—21no—
10#14583189C411yescharacteristic, complemented
11#14583189C411yescharacteristic, complemented
12#14583094C411yescharacteristic, complemented
13#14583094C411yescharacteristic, complemented
14#14583033—21no—
15#14583009—21no—
16#14583009—21no—
17#14582956C2211yescharacteristic
18C2×#13063246—21no—
19C2×#13063236C2211yescharacteristic
20C4×C4⋊Dic43C2211yescharacteristic
21#14582661—21no—
22#14582638—22no—
23#14582634—21no—
24#14582634—21no—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#436—21no—
27C43×#435—22no—
28C8×D4×C43—21no—
29C43×#432C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#407—21no—
32C2×C22⋊C8×C43—21no—
33C2×#10621898—21no—
34C2×#10621882—21no—
35C2×#10621882—21no—
36C22×C43⋊C8—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—
46#13063256—21no—
47#13063256—21no—
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50#13063246—24no—
51#13063246—21no—
52#13063246—21no—
53#13063245—21no—
54#13063245—21no—
55C22⋊(C43⋊C8)—21no—
56#13063236—21no—
57#13063236—21no—
58#13063236—21no—
59C43⋊#95—21no—
60C22×D4×C43D411yescharacteristic
61C23×C4×C43—21no—
62C2×M16×C43—22no—
63C22×C8×C43—22no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43C2×C411yescharacteristic
67C4×D4×C43C2×C411yescharacteristic
68C4×D4×C43D411yescharacteristic
69C4×D4×C43D411yescharacteristic
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C22⋊C8×C43—22no—
76C22⋊C8×C43—22no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D411yescharacteristic
79C22⋊C8×C43D411yescharacteristic
80#97×C43D412yes—
81C4×C8×C43—21no—
82C24×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—41no—
86C2×D4×C43C22⋊C411yescharacteristic
87C2×D4×C43C22⋊C411yescharacteristic
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—82no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—41no—
98C22×Dic43—41no—
99#10621898—81no—
100#10621898—81no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×C4×D43—41no—
105C2×Dic86—21no—
106M16×C43—82no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C2×C8×C43—82no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C22⋊C4×C43—21no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122#10621882—42no—
123#10621882—42no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—22no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—41no—
130C4×Dic43—81no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—42no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—81no—
142C23×C43#12111yescharacteristic
143C22×D43—41no—
144D4×C43—21no—
145D4×C43—21no—
146D4×C43—21no—
147D4×C43—42no—
148D4×C43#10412yes—
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—41no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
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—81no—
168C22⋊D43—81no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173D172—41no—
174D172—41no—
175D172—81no—
176D172—81no—
177C4×D43—82no—
178Dic86—81no—
179C8×C43—41no—
180C8×C43—42no—
181C8×C43—41no—
182C43⋊C8—42no—
183C43⋊C8—41no—
184C43⋊C8—41no—
185#9163—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—22no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43#38611yescharacteristic
197C22×C43#47111yescharacteristic
198C22×C43#47211yescharacteristic
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43C2×#10411yescharacteristic
210C4×C43#42111yescharacteristic
211Dic43—82no—
212Dic43—81no—
213#3109—431no—
214#2974D4311yescharacteristic, complemented
215#1762—431no—
216#1530—431no—
217#1502—431no—
218#1302—431no—
219#1285—431no—
220C2×C43—21no—
221C2×C43—21no—
222C2×C43—42no—
223C2×C43—81no—
224C2×C43#187111yescharacteristic
225C2×C43#190411yescharacteristic
226C2×C43#190711yescharacteristic
227D43—161no—
228#532—431no—
229C2×C4×D4C2×D4311yescharacteristic
230#481—861no—
231#476—431no—
232#476—431no—
233#459—431no—
234#459—431no—
235#447—861no—
236#442—861no—
237#442—861no—
238#436—21no—
239#435—22no—
240C8×D4—21no—
241#432—431no—
242#432C2×D4311yescharacteristic
243#431C2×D4311yescharacteristic
244C2×#102—861no—
245#407—21no—
246C2×C22⋊C8—21no—
247C2×#97—431no—
248C4×C4⋊C4—431no—
249#340—861no—
250#329—862no—
251#327—861no—
252#327—861no—
253C43#916311yescharacteristic, complemented, Sylow
254C2×#41—861no—
255C22×D4D17211yescharacteristic
256C23×C4—21no—
257C2×D8—861no—
258C2×D8—861no—
259C2×M16—22no—
260C22×C8—22no—
261C22×C8—861no—
262C4⋊Q8—431no—
263#127—431no—
264#124—861no—
265#121—861no—
266#121—861no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4C4×D4311yescharacteristic
272C4×D4C4×D4311yescharacteristic
273C4×D4C22⋊D4311yescharacteristic
274C4×D4C22⋊D4311yescharacteristic
275C2×C4⋊C4—861no—
276C2×C4⋊C4D17211yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42—861no—
279C2×C42C22×D4311yescharacteristic
280#106—861no—
281#106—861no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—431no—
285C4⋊C8—431no—
286#102—864no—
287#102—861no—
288#102—861no—
289#102—861no—
290#102—861no—
291C22⋊C8—22no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294C22⋊C8—861no—
295C22⋊C8C22⋊D4311yescharacteristic
296C22⋊C8C22⋊D4311yescharacteristic
297#97—861no—
298#97—861no—
299#97—861no—
300#97C22⋊D4312yes—
301C4×C8—21no—
302#95—861no—
303C24—21no—
304#41—3441no—
305#41—3441no—
306C2×Q8—861no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—41no—
310C2×D4—861no—
311C2×D4—861no—
312C2×D4—861no—
313C2×D4—1721no—
314C2×D4(C2×D43)⋊C411yescharacteristic
315C2×D4(C2×D43)⋊C411yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—82no—
322C22×C4—1721no—
323C22×C4—1721no—
324C22×C4C2×D17211yescharacteristic
325C22×C4#1062189811yescharacteristic
326C22×C4C2×C22⋊D4311yescharacteristic
327D8—1722no—
328D8—1722no—
329M16—82no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—82no—
334C2×C8—862no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—1721no—
338C2×C8—1721no—
339C4⋊C4—21no—
340C4⋊C4—862no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—1721no—
344C4⋊C4(C2×D43)⋊C411yescharacteristic
345C4⋊C4(C2×D43)⋊C411yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C42—3441no—
353C42C2×C4×D4311yescharacteristic
354C42#1062189811yescharacteristic
355C42C2×C22⋊D4311yescharacteristic
356C42C2×C22⋊D4311yescharacteristic
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—81no—
363C23—1721no—
364C23#1306329911yescharacteristic
365Q8—3441no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—3441no—
371D4—3441no—
372D4—3441no—
373D4—3441no—
374D4—1721no—
375D4—1721no—
376D4#1306325112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—3442no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—1722no—
393C2×C4—1721no—
394C2×C4C2×(C2×D43)⋊C411yescharacteristic
395C2×C4C4×C22⋊D4311yescharacteristic
396C2×C4C4×C22⋊D4311yescharacteristic
397C2×C4#1306329411yescharacteristic
398C2×C4#1306329911yescharacteristic
399C2×C4#1306330811yescharacteristic
400C8—41no—
401C8—42no—
402C8—41no—
403C8—1722no—
404C8—1721no—
405C8—1721no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—3441no—
417C22—3441no—
418C22—3441no—
419C22#1458277811yescharacteristic
420C22#1458316211yescharacteristic
421C22#1458316911yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—3442no—
430C4—3441no—
431C4C2×#1306325111yescharacteristic
432C4#1458291511yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—6881no—
438C2#1913489711yescharacteristic
439C2#1913508211yescharacteristic
440C2#1913510311yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2974C2
socleC22×C43#386
prime radical#19144686C2
cosocleC2×C42×C43C23
hypercenter#2974D43
hypocenterC43#9163
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19134420C2semidirect
3. #19133207C2semidirect
4. #19133091C2semidirect
5. #19132495C2semidirect
6. #19132450C2semidirect
7. C43×#2974C2semidirect
10. #14583189C4semidirect
11. #14583189C4semidirect
12. #14583094C4semidirect
13. #14583094C4semidirect
214. #2974D43semidirect
253. C43#9163semidirect

Maximal subgroups

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

subgroupindex
#191446862
#191344202
#191332072
#191330912
#191324952
#191324502
C43×#29742
#916343