Finite Group Databasebeta

← #24992418

Subgroups — #24992418

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#19143630C211yesmaximal, characteristic, complemented
3#19133205C211yesmaximal, characteristic, complemented
4#19133089C211yesmaximal, characteristic, complemented
5#19132494C211yesmaximal, characteristic, complemented
6#19132451C211yesmaximal, characteristic, complemented
7C43×#1762C211yesmaximal, 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#14582977—21no—
18#14582971—22no—
19D4×C43⋊C8—21no—
20#14582956C2211yescharacteristic
21#14582956C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582863—21no—
24C2×C22⋊(C43⋊C8)—21no—
25#14582638—22no—
26#14582632—21no—
27#14582632—21no—
28C2×C4×D4×C43C2211yescharacteristic
29C2×#102×C43—21no—
30C2×#97×C43C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#340—21no—
33C2×#10621898—21no—
34C2×#10621882—21no—
35C2×#10621882—21no—
36C2×#10621877—22no—
37C22×C43⋊C8—22no—
38#13063325C2×C411yescharacteristic
39#13063322C2×C411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299—21no—
43C4×D172—21no—
44C4×D172—21no—
45#13063256—21no—
46#13063256—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51#13063246—21no—
52#13063246—21no—
53#13063245—21no—
54#13063245—21no—
55C22⋊(C43⋊C8)—22no—
56C22⋊(C43⋊C8)—22no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D411yescharacteristic
60C22⋊(C43⋊C8)D411yescharacteristic
61#13063236—21no—
62#13063236D412yes—
63C4×C43⋊C8—21no—
64C22×D4×C43D411yescharacteristic
65C23×C4×C43—21no—
66C22×C8×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43C2×C411yescharacteristic
70C4×D4×C43C2×C411yescharacteristic
71C4×D4×C43D411yescharacteristic
72C4×D4×C43D411yescharacteristic
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78#102×C43—24no—
79#97×C43—21no—
80#97×C43—21no—
81#95×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—41no—
94C22×C4×C43—82no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C2×C22⋊D43—41no—
99#10621898—81no—
100#10621898—81no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×C4×D43—41no—
105C2×Dic86—21no—
106C2×C8×C43—22no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—41no—
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×C43—81no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123#10621882—42no—
124#10621882—42no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129#10621877—82no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—82no—
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—42no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12311yescharacteristic
170C22⋊D43—81no—
171C22⋊D43—81no—
172C2×Dic43—41no—
173D172—41no—
174D172—41no—
175D172—81no—
176D172—81no—
177C4×D43—82no—
178Dic86—81no—
179C8×C43—42no—
180C43⋊C8—41no—
181C43⋊C8—42no—
182C43⋊C8—41no—
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×C43—82no—
210C4×C43C2×#10411yescharacteristic
211C4×C43#42111yescharacteristic
212Dic43—81no—
213#3109—431no—
214#2974—431no—
215#1762D4311yescharacteristic, complemented
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—861no—
239#435—862no—
240C8×D4—861no—
241#432—431no—
242#432—431no—
243#431—431no—
244C2×#102—21no—
245#407—861no—
246C2×C22⋊C8—861no—
247C2×#97C2×D4311yescharacteristic
248C4×C4⋊C4C2×D4311yescharacteristic
249#340—21no—
250#329—862no—
251#327—861no—
252#327—861no—
253C43#916311yescharacteristic, complemented, Sylow
254C2×#41—861no—
255C22×D4C22⋊D4311yescharacteristic
256C23×C4—21no—
257C2×D8—861no—
258C2×D8—861no—
259C2×M16—862no—
260C22×C8—21no—
261C22×C8—862no—
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×D4D17211yescharacteristic
274C4×D4D17211yescharacteristic
275C2×C4⋊C4—21no—
276C2×C4⋊C4C22⋊D4311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42—21no—
279C2×C42C22×D4311yescharacteristic
280#106—861no—
281#106—861no—
282C4⋊C8—431no—
283C4⋊C8—431no—
284C4⋊C8—861no—
285C4⋊C8—861no—
286#102—24no—
287#102—861no—
288#102—861no—
289#102—861no—
290#102—861no—
291C22⋊C8—431no—
292C22⋊C8—431no—
293C22⋊C8—862no—
294C22⋊C8—862no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297#97—21no—
298#97—21no—
299#97—432no—
300#97—861no—
301C4×C8—861no—
302#95—21no—
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—41no—
322C22×C4—82no—
323C22×C4—1721no—
324C22×C4D4×D4311yescharacteristic
325C22×C4#1062190011yescharacteristic
326C22×C4C2×C22⋊D4311yescharacteristic
327D8—1722no—
328D8—1722no—
329M16—3442no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—861no—
334C2×C8—861no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—862no—
338C2×C8—3442no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—861no—
343C4⋊C4—861no—
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—81no—
353C42C2×C4×D4311yescharacteristic
354C42C2×D17211yescharacteristic
355C42D4×D4311yescharacteristic
356C42#1062190011yescharacteristic
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—81no—
363C23—1721no—
364C23#1306329711yescharacteristic
365Q8—3441no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—3441no—
371D4—3441no—
372D4—3441no—
373D4—3441no—
374D4—1721no—
375D4—1721no—
376D4#1306325312yes—
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—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—3442no—
393C2×C4—1721no—
394C2×C4C2×(C2×D43)⋊C411yescharacteristic
395C2×C4(C22⋊D43)⋊C411yescharacteristic
396C2×C4(C22⋊D43)⋊C411yescharacteristic
397C2×C4#1306329511yescharacteristic
398C2×C4#1306329711yescharacteristic
399C2×C4#1306330911yescharacteristic
400C8—42no—
401C8—1721no—
402C8—1722no—
403C8—1721no—
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#1458277611yescharacteristic
420C22#1458316411yescharacteristic
421C22#1458316711yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—82no—
430C4—3441no—
431C4C2×#1306325311yescharacteristic
432C4#1458291711yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—6881no—
438C2#1913489511yescharacteristic
439C2#1913508011yescharacteristic
440C2#1913510111yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1762C2
socleC22×C43#386
prime radical#19144686C2
cosocleC2×C42×C43C23
hypercenter#1762D43
hypocenterC43#9163
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19133205C2semidirect
4. #19133089C2semidirect
5. #19132494C2semidirect
6. #19132451C2semidirect
7. C43×#1762C2semidirect
10. #14583189C4semidirect
11. #14583189C4semidirect
12. #14583094C4semidirect
13. #14583094C4semidirect
215. #1762D43semidirect
253. C43#9163semidirect

Maximal subgroups

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

subgroupindex
#191446862
#191436302
#191332052
#191330892
#191324942
#191324512
C43×#17622
#916343