Finite Group Databasebeta

← #24992890

Subgroups — #24992890

Order 11008.

588 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#19144595C211yesmaximal, characteristic
2#19135423C211yesmaximal, characteristic, complemented
3#19133089C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132428C211yesmaximal, characteristic, complemented
7C43×#2293C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583212—21no—
10#14583179C412yescomplemented
11#14583094C412yescomplemented
12#14583033—21no—
13C4×#10621882—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16#14582923C2211yescharacteristic
17C2×#13063253—21no—
18C2×#13063253—21no—
19#14582632—22no—
20D4⋊(C43⋊C8)—22no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#117×C43—21no—
23C43×#390—21no—
24C43×#389—21no—
25C43×#388—22no—
26C4×C4⋊C4×C43C2211yescharacteristic
27C4×C22⋊C4×C43—21no—
28C43×C43C2211yescharacteristic
29C2×#10621898—21no—
30C2×#10621882—22no—
31C2×#10621877—21no—
32#13063325C2×C411yescharacteristic
33#13063322C2×C411yescharacteristic
34#13063313—21no—
35#13063299—21no—
36#13063299—21no—
37C4×D172—21no—
38C4×D172—21no—
39#13063258—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yes—
44#13063253—42no—
45#13063253—42no—
46#13063246—22no—
47#13063245—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C22×D4×C43D411yescharacteristic
53C23×C4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43C2×C412yes—
57C4×D4×C43D412yes—
58#117×C43—42no—
59#117×C43—42no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—22no—
66C2×C42×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43—21no—
69C2×C42×C43D411yescharacteristic
70C2×C42×C43D411yescharacteristic
71C2×C42×C43C2311yescharacteristic
72#95×C43—22no—
73#95×C43D412yes—
74C24×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—42no—
77C2×D4×C43C22⋊C412yes—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—44no—
104C4⋊C4×C43C22⋊C412yes—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—44no—
108C22⋊C4×C43—44no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43—21no—
112C42×C43—42no—
113C42×C43—42no—
114C42×C43—41no—
115C42×C43—41no—
116C42×C43D812yescomplemented
117C42×C43C22×C411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43#4111yescharacteristic
121#10621882—44no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C23×C43—22no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43#12011yescharacteristic
137C22×D43—41no—
138D4×C43—22no—
139D4×C43—22no—
140D4×C43—42no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43#13511yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
169C22⋊D43—81no—
170C22⋊D43—81no—
171C2×Dic43—41no—
172D172—42no—
173D172—41no—
174D172—41no—
175D172—81no—
176C4×D43—81no—
177C4×D43—81no—
178Dic86—41no—
179Dic86—41no—
180C43⋊C8—42no—
181C43⋊C8—81no—
182C43⋊C8—81no—
183#9237—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—82no—
190C22×C43—82no—
191C22×C43#38611yescharacteristic
192C22×C43#44711yescharacteristic
193C22×C43#44911yescharacteristic
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—42no—
202C4×C43—42no—
203C4×C43—82no—
204C4×C43#42112yes—
205C4×C43C4×D811yescharacteristic
206C4×C43#44211yescharacteristic
207C4×C43#45911yescharacteristic
208C4×C43#46311yescharacteristic
209Dic43—81no—
210#3100—431no—
211#2293D4311yescharacteristic, complemented
212#1962—431no—
213#1502—431no—
214#1486—431no—
215#1303—431no—
216#1276—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—82no—
220C2×C43#187911yescharacteristic
221C2×C43#189711yescharacteristic
222C2×C43#190611yescharacteristic
223D43—161no—
224#532—431no—
225C2×C4×D4C2×D4311yescharacteristic
226C2×#117—21no—
227#480—861no—
228#474—432no—
229#459—432no—
230#447—861no—
231C4×D8—862no—
232#431—431no—
233#431—431no—
234#423—431no—
235C2×#104—861no—
236C2×#104—861no—
237#390—21no—
238#389—21no—
239#388—22no—
240C4×C4⋊C4C2×D4311yescharacteristic
241C4×C22⋊C4—21no—
242C43C2×D4311yescharacteristic
243#327—862no—
244D4⋊C8—862no—
245C43#923711yescharacteristic, complemented, Sylow
246C2×#41—861no—
247C22×D4C22⋊D4311yescharacteristic
248C23×C4—21no—
249C2×D8—862no—
250C2×M16—861no—
251C4⋊Q8—431no—
252#127—431no—
253#124—861no—
254#121—861no—
255#121—861no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—861no—
259C4×D4—861no—
260C4×D4C4×D4312yes—
261C4×D4D17212yes—
262#117—42no—
263#117—42no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C22⋊D4311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C22⋊D4311yescharacteristic
274C2×C42C22⋊D4311yescharacteristic
275C2×C42C22×D4311yescharacteristic
276#107—862no—
277C4⋊C8—432no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280C4⋊C8—861no—
281#104—1722no—
282#104—1722no—
283#102—862no—
284#102—862no—
285C22⋊C8—861no—
286C22⋊C8—861no—
287C4×C8—861no—
288C4×C8—861no—
289#95—22no—
290#95C22⋊D4312yes—
291C24—21no—
292#41—1721no—
293#41—1721no—
294#41—1721no—
295#41—1721no—
296C2×Q8—861no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—861no—
302C2×D4—1721no—
303C2×D4(C2×D43)⋊C412yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—1721no—
315C22×C4C2×C22⋊D4311yescharacteristic
316C22×C4C2×C22⋊D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—1724no—
319M16—1721no—
320M16—1721no—
321C2×C8—862no—
322C2×C8—1721no—
323C2×C8—1721no—
324C4⋊C4—21no—
325C4⋊C4—44no—
326C4⋊C4—42no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4(C2×D43)⋊C412yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—42no—
340C42—42no—
341C42—41no—
342C42—41no—
343C42#1062188212yescomplemented
344C42C2×C4×D4311yescharacteristic
345C42C2×D17211yescharacteristic
346C42#1062189811yescharacteristic
347C42#1062189811yescharacteristic
348C23—22no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—1721no—
354C23#1306329411yescharacteristic
355Q8—1721no—
356Q8—1721no—
357D4—22no—
358D4—22no—
359D4—42no—
360D4—3441no—
361D4—3441no—
362D4—3441no—
363D4—1722no—
364D4—1721no—
365D4—1721no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—3441no—
385C2×C4—3441no—
386C2×C4—1721no—
387C2×C4C2×(C2×D43)⋊C411yescharacteristic
388C2×C4C4×C22⋊D4311yescharacteristic
389C2×C4C4×C22⋊D4311yescharacteristic
390C2×C4#1306329911yescharacteristic
391C2×C4#1306329911yescharacteristic
392C2×C4#1306330811yescharacteristic
393C2×C4C2×#1062188211yescharacteristic
394C2×C4#1306334511yescharacteristic
395C2×C4#1306335011yescharacteristic
396C2×C4#1306335111yescharacteristic
397C8—3441no—
398C8—3441no—
399C8—1722no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—82no—
407C22—3441no—
408C22—3441no—
409C22—3441no—
410C22#1458277811yescharacteristic
411C22#1458303311yescharacteristic
412C22#1458304411yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—42no—
419C4—82no—
420C4—3441no—
421C4#1458291712yes—
422C4C4×#1062188211yescharacteristic
423C4#1458300911yescharacteristic
424C4#1458309411yescharacteristic
425C4#1458311411yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—6881no—
430C2#1913494311yescharacteristic
431C2#1913504311yescharacteristic
432C2#1913509611yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2293C2
socleC22×C43#386
prime radical#19144595C2
cosocleC2×C42×C43C23
hypercenter#2293D43
hypocenterC43#9237
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #19135423C2semidirect
3. #19133089C2semidirect
4. #19133020C2semidirect
5. #19132498C2semidirect
6. #19132428C2semidirect
7. C43×#2293C2semidirect
10. #14583179C4semidirect
11. #14583094C4semidirect
116. C42×C43D8semidirect
211. #2293D43semidirect
245. C43#9237semidirect
343. C42#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445952
#191354232
#191330892
#191330202
#191324982
#191324282
C43×#22932
#923743