Finite Group Databasebeta

← #24991482

Subgroups — #24991482

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144050C211yesmaximal, characteristic
2#19143163C211yesmaximal, characteristic, complemented
3#19133047C211yesmaximal, characteristic, complemented
4#19132995C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1476C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C2×#13063332—21no—
10#14583449C2211yescharacteristic
11#14583121—21no—
12#14583114—21no—
13#14583109C411yescharacteristic
14#14583104C411yescharacteristic
15#14583099C411yescharacteristic
16#14583094C411yescharacteristic
17#14582926—22no—
18#14582926—21no—
19#14582923—21no—
20#14582923C2211yescharacteristic
21C2×C4⋊(C43⋊C8)—21no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24#14582893—21no—
25#14582628—21no—
26#14582628—21no—
27#14582628—22no—
28C4×#41×C43C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×Q8⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898—21no—
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40#13063332—42no—
41#13063332—42no—
42C2×#10621877—22no—
43C2×#10621877—21no—
44C22×C43⋊C8—22no—
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47#13063325C2×C411yescharacteristic
48#13063322C2×C411yescharacteristic
49#13063313—21no—
50#13063299—21no—
51#13063299—21no—
52C4×D172—21no—
53C4×D172—21no—
54C4⋊(C43⋊C8)—22no—
55C4⋊(C43⋊C8)—22no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)C2×C411yescharacteristic
60C4⋊(C43⋊C8)C2×C411yescharacteristic
61C4⋊(C43⋊C8)D411yescharacteristic
62C4⋊(C43⋊C8)D411yescharacteristic
63C4⋊(C43⋊C8)D412yes—
64#13063248—21no—
65#13063248—21no—
66#13063245—21no—
67#13063245—21no—
68C2×#41×C43D411yescharacteristic
69C22×C8×C43—21no—
70C4×Q8×C43C2×C411yescharacteristic
71C4×Q8×C43D411yescharacteristic
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43C2×C411yescharacteristic
75C4×D4×C43D411yescharacteristic
76#117×C43—21no—
77#117×C43D411yescharacteristic
78C2×C42×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C4×C8×C43—21no—
85#41×C43—21no—
86#41×C43—21no—
87#41×C43D812yes—
88#41×C43SD1612yes—
89C2×Q8×C43C22⋊C411yescharacteristic
90C2×D4×C43—21no—
91C2×D4×C43C22⋊C411yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C2×C22⋊D43—41no—
99#10621898—41no—
100#10621898—41no—
101#10621898—41no—
102#10621898—41no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—21no—
106C2×C4×D43—41no—
107C2×Dic86—21no—
108C2×C8×C43—22no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43C22⋊C411yescharacteristic
115C4⋊C4×C43C22⋊C411yescharacteristic
116C22⋊C4×C43—21no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C42×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43C22×C411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126#10621885—42no—
127#10621884—42no—
128#10621883—42no—
129#10621882—42no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134#10621877—44no—
135#10621877—41no—
136#10621877—41no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—44no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C23×C43—21no—
148C23×C43#12311yescharacteristic
149C22×D43—41no—
150Q8×C43—21no—
151Q8×C43#10212yes—
152D4×C43—22no—
153D4×C43—22no—
154D4×C43—21no—
155D4×C43#10212yes—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—81no—
167C2×C4×C43C2×C22⋊C411yescharacteristic
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43C4×D411yescharacteristic
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43C2×D811yescharacteristic
174C2×C4×C43C2×SD1611yescharacteristic
175C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C43#13711yescharacteristic
177C22⋊D43—81no—
178C22⋊D43—81no—
179C2×Dic43—41no—
180D172—42no—
181D172—41no—
182D172—41no—
183D172—41no—
184D172—41no—
185C4×D43—81no—
186C4×D43—81no—
187Dic86—41no—
188Dic86—41no—
189C8×C43—42no—
190C8×C43—81no—
191C43⋊C8—41no—
192C43⋊C8—41no—
193C43⋊C8—41no—
194C43⋊C8—42no—
195C43⋊C8—41no—
196#8995—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—22no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43#38611yescharacteristic
203C22×C43#48011yescharacteristic
204C22×C43#48111yescharacteristic
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—81no—
208C4×C43—22no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43C2×#10211yescharacteristic
215C4×C43#41711yescharacteristic
216C4×C43#44311yescharacteristic
217C4×C43#44411yescharacteristic
218C4×C43#44711yescharacteristic
219C4×C43#44811yescharacteristic
220Dic43—81no—
221#3035—431no—
222#2906—431no—
223#1492—431no—
224#1480—431no—
225#1476D4311yescharacteristic, complemented
226#1301—431no—
227#1277—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—42no—
231C2×C43#187411yescharacteristic
232C2×C43#187611yescharacteristic
233C2×C43#188111yescharacteristic
234D43—161no—
235C2×#135—861no—
236C2×#131—861no—
237#532—431no—
238C4×#41C2×D4311yescharacteristic
239#464—861no—
240#463—861no—
241#462—431no—
242#461—431no—
243#460—431no—
244#459—431no—
245#431C2×D4311yescharacteristic
246#424—862no—
247#424—861no—
248#423—431no—
249#423—861no—
250C2×C4⋊C8—431no—
251C2×C4⋊C8—431no—
252C2×C4⋊C8—861no—
253#416—861no—
254C2×C4×C8C2×D4311yescharacteristic
255Q8⋊C8—21no—
256D4⋊C8—21no—
257D4⋊C8—861no—
258D4⋊C8—861no—
259D4⋊C8—862no—
260C43#899511yescharacteristic, complemented, Sylow
261C2×#41—861no—
262C2×#41D17211yescharacteristic
263#135—1722no—
264#135—1722no—
265C2×Q16—861no—
266C2×SD16—861no—
267C2×SD16—861no—
268C2×D8—861no—
269#131—1722no—
270#131—1722no—
271C2×M16—862no—
272C2×M16—861no—
273C22×C8—21no—
274C22×C8—862no—
275C22×C8—861no—
276C22×C8—861no—
277C4⋊Q8—431no—
278#127—431no—
279#124—861no—
280#121—861no—
281#121—861no—
282C4×Q8C4×D4311yescharacteristic
283C4×Q8C22⋊D4311yescharacteristic
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4C4×D4311yescharacteristic
289C4×D4C22⋊D4311yescharacteristic
290#117—21no—
291#117D17211yescharacteristic
292C2×C42—21no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—431no—
296C4⋊C8—431no—
297C4⋊C8—431no—
298C4⋊C8—431no—
299C4⋊C8—432no—
300C4⋊C8—862no—
301C4⋊C8—862no—
302C4⋊C8—861no—
303C4⋊C8—861no—
304C4⋊C8—861no—
305#103—861no—
306#103—861no—
307#102—861no—
308#102—861no—
309C22⋊C8—21no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313#41—21no—
314#41—21no—
315#41—1721no—
316#41—1721no—
317#41—1721no—
318#41—1721no—
319#41#1062187312yes—
320#41D34412yes—
321C2×Q8—861no—
322C2×Q8(C2×D43)⋊C411yescharacteristic
323C2×D4—21no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—1721no—
328C2×D4(C2×D43)⋊C411yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—1721no—
333C22×C4C2×D17211yescharacteristic
334C22×C4#1062190011yescharacteristic
335C22×C4#1062190011yescharacteristic
336Q16—1722no—
337SD16—1722no—
338SD16—1722no—
339D8—1722no—
340M16—1724no—
341M16—1721no—
342M16—1721no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—862no—
352C2×C8—1724no—
353C2×C8—1721no—
354C2×C8—1721no—
355C2×C8—1721no—
356C2×C8—1721no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4(C2×D43)⋊C411yescharacteristic
362C4⋊C4(C2×D43)⋊C411yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—1721no—
367C22⋊C4—1721no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42C2×C4×D4311yescharacteristic
372C42D4×D4311yescharacteristic
373C42D4×D4311yescharacteristic
374C42C2×C22⋊D4311yescharacteristic
375C23—21no—
376C23—1721no—
377C23#1306330911yescharacteristic
378Q8—21no—
379Q8—1721no—
380Q8—1721no—
381Q8#1306324712yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—3441no—
386D4—3441no—
387D4—1722no—
388D4—1721no—
389D4—1721no—
390D4—1721no—
391D4—1721no—
392D4#1306324712yes—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1721no—
407C2×C4C2×(C2×D43)⋊C411yescharacteristic
408C2×C4(C22⋊D43)⋊C411yescharacteristic
409C2×C4(C22⋊D43)⋊C411yescharacteristic
410C2×C4#1306329511yescharacteristic
411C2×C4#1306329711yescharacteristic
412C2×C4#1306329711yescharacteristic
413C2×C4C2×D34411yescharacteristic
414C2×C4C2×#1062187311yescharacteristic
415C2×C4#1306335311yescharacteristic
416C2×C4#1306335811yescharacteristic
417C8—42no—
418C8—81no—
419C8—1721no—
420C8—1721no—
421C8—1721no—
422C8—1722no—
423C8—1721no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—3441no—
430C22—3441no—
431C22—3441no—
432C22#1458277611yescharacteristic
433C22#1458321311yescharacteristic
434C22#1458321811yescharacteristic
435C4—22no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—3441no—
442C4C2×#1306324711yescharacteristic
443C4#1458290111yescharacteristic
444C4#1458301311yescharacteristic
445C4#1458301811yescharacteristic
446C4#1458303511yescharacteristic
447C4#1458304011yescharacteristic
448C2—21no—
449C2—21no—
450C2—42no—
451C2—6881no—
452C2#1913491011yescharacteristic
453C2#1913492011yescharacteristic
454C2#1913495511yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1476C2
socleC22×C43#386
prime radical#19144050C2
cosocleC2×C42×C43C23
hypercenter#1476D43
hypocenterC43#8995
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #19143163C2semidirect
3. #19133047C2semidirect
4. #19132995C2semidirect
5. #19132491C2semidirect
6. #19132430C2semidirect
7. C43×#1476C2semidirect
225. #1476D43semidirect
260. C43#8995semidirect

Maximal subgroups

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

subgroupindex
#191440502
#191431632
#191330472
#191329952
#191324912
#191324302
C43×#14762
#899543