Finite Group Databasebeta

← #24992491

Subgroups — #24992491

Order 11008.

562 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#19144076C211yesmaximal, characteristic
2#19143164C211yesmaximal, characteristic, complemented
3#19133264C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5#19132980C211yesmaximal, characteristic, complemented
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063353—21no—
9C2×#13063333—21no—
10C2×#13063322C2211yescharacteristic
11C4×#10621898C2211yescharacteristic
12#14583100—21no—
13#14583100C412yes—
14#14583095—21no—
15#14583095C412yes—
16#14582952C2211yescharacteristic
17#14582927—21no—
18#14582924—22no—
19#14582921—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22#14582905—21no—
23#14582642—21no—
24#14582642—21no—
25#14582642—22no—
26#14582629—21no—
27#14582626—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×D172—21no—
33C22×D172—21no—
34C22×D172—21no—
35#13063353—42no—
36#13063353—42no—
37C2×#10621873—22no—
38C2×D344—22no—
39#13063333—42no—
40#13063333—42no—
41C2×#10621872—22no—
42C22×C43⋊C8—21no—
43C2×C8×D43—22no—
44#13063322—21no—
45#13063322—21no—
46#13063322—21no—
47#13063322C2×C412yes—
48C4×Dic86C2×C411yescharacteristic
49C4×Dic86D411yescharacteristic
50C4×D172C2×C411yescharacteristic
51C4×D172D411yescharacteristic
52C4×C22⋊D43—21no—
53C4×C22⋊D43—21no—
54#13063284D411yescharacteristic
55#13063282—21no—
56C42×D43—21no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)D411yescharacteristic
60C4⋊(C43⋊C8)D411yescharacteristic
61Dic43⋊C8—22no—
62Dic43⋊C8—22no—
63#13063247—22no—
64#13063247—22no—
65C22⋊(C43⋊C8)—21no—
66C4×C43⋊C8—21no—
67C2×M16×C43—21no—
68C2×M16×C43—21no—
69C22×C8×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43C2×C412yes—
76C4⋊C8×C43D412yes—
77C23×D43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C2×C22⋊D43—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898D812yes—
85#10621898SD1612yes—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—81no—
97C2×D172—81no—
98C2×D172—82no—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×Dic86C22⋊C411yescharacteristic
104M16×C43—41no—
105M16×C43—41no—
106M16×C43—41no—
107M16×C43—41no—
108C2×C8×C43—22no—
109C2×C8×C43—22no—
110C2×C8×C43—41no—
111C2×C8×C43—81no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C22⋊Dic43—21no—
117(C2×D43)⋊C4—21no—
118(C2×D43)⋊C4—21no—
119C4⋊Dic43C22⋊C411yescharacteristic
120C4⋊Dic43C22⋊C411yescharacteristic
121Dic43⋊C4—21no—
122Dic43⋊C4—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131D344—44no—
132#10621873—44no—
133#10621872—44no—
134C8×D43—44no—
135C23×C43#12311yescharacteristic
136C22×D43—21no—
137C22×D43—42no—
138C22×D43—82no—
139C22×D43—82no—
140C22×D43—81no—
141C22×D43—81no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43C2×C22⋊C411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43C2×SD1611yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43#13711yescharacteristic
155C22⋊D43—22no—
156C22⋊D43—22no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160D172—21no—
161D172—42no—
162D172—42no—
163D172—82no—
164D172—82no—
165D172—82no—
166D172—81no—
167D172—81no—
168D172—81no—
169D172—81no—
170D172#10212yes—
171C4×D43—22no—
172C4×D43—22no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—81no—
176Dic86—21no—
177Dic86#10212yes—
178C8×C43—42no—
179C8×C43—42no—
180C8×C43—81no—
181C43⋊C8—41no—
182C43⋊C8—41no—
183C43⋊C8—81no—
184#9173—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43#38611yescharacteristic
188C22×C43#48011yescharacteristic
189C22×C43#48111yescharacteristic
190C2×D43—22no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—82no—
194C2×D43—82no—
195C2×D43—82no—
196C2×D43—162no—
197C2×D43—162no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43C2×#10211yescharacteristic
202C4×C43#41711yescharacteristic
203C4×C43#44711yescharacteristic
204C4×C43#44811yescharacteristic
205C4×C43#47111yescharacteristic
206C4×C43#47211yescharacteristic
207Dic43—22no—
208Dic43—41no—
209Dic43—41no—
210#3038—431no—
211#2906—431no—
212#1545—431no—
213C2×#331—431no—
214#1477—431no—
215#1301—431no—
216#1292D4311yescharacteristic, complemented
217C2×C43—21no—
218C2×C43—21no—
219C2×C43#187411yescharacteristic
220C2×C43#190311yescharacteristic
221C2×C43#190711yescharacteristic
222D43—42no—
223D43—162no—
224C2×AGL(1,ℤ/8)—861no—
225C2×#131—861no—
226C2×#127—431no—
227C4×#41—431no—
228#460—432no—
229#460—861no—
230#459—432no—
231#459—861no—
232#431—431no—
233#424—861no—
234#424—862no—
235#423—861no—
236#423C2×D4311yescharacteristic
237#423C2×D4311yescharacteristic
238C2×C4⋊C8—431no—
239C2×C4⋊C8—861no—
240C2×C4⋊C8C2×D4311yescharacteristic
241#418—861no—
242#331—861no—
243#331—861no—
244#331—862no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#917311yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C22×D4—861no—
250C22×D4—861no—
251C22×D4—861no—
252AGL(1,ℤ/8)—1722no—
253AGL(1,ℤ/8)—1722no—
254C2×SD16—862no—
255C2×D8—862no—
256#131—1722no—
257#131—1722no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—862no—
261C22×C8—21no—
262C22×C8—862no—
263C22×C8—861no—
264#127—432no—
265#127—861no—
266#127—861no—
267#127—861no—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×D4—431no—
271C4×D4—431no—
272C4×D4—861no—
273C4×D4—861no—
274#117—431no—
275#117—861no—
276C2×C42—861no—
277C2×C42C22×D4311yescharacteristic
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—431no—
283C4⋊C8—431no—
284C4⋊C8—862no—
285C4⋊C8—862no—
286C4⋊C8—861no—
287C4⋊C8—861no—
288C4⋊C8C4×D4312yes—
289C4⋊C8D17212yes—
290#102—862no—
291#102—862no—
292C22⋊C8—861no—
293C4×C8—861no—
294C24—1721no—
295#41—432no—
296#41—432no—
297#41—861no—
298#41—861no—
299C2×Q8—431no—
300C2×D4—431no—
301C2×D4—861no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—862no—
305C2×D4—3441no—
306C2×D4—3441no—
307C2×D4—3442no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4#1062189811yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4#1062190211yescharacteristic
321SD16—1724no—
322D8—1724no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—1724no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—81no—
332C2×C8—861no—
333C2×C8—861no—
334C2×C8—1724no—
335C2×C8—1721no—
336C2×C8—1721no—
337C2×C8—1721no—
338C4⋊C4—431no—
339C4⋊C4—431no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C42—861no—
346C42—861no—
347C42—861no—
348C42C2×C4×D4311yescharacteristic
349C42C2×D17211yescharacteristic
350C42D4×D4311yescharacteristic
351C42D4×D4311yescharacteristic
352C23—861no—
353C23—3442no—
354C23—3442no—
355C23—3441no—
356C23—3441no—
357C23—1722no—
358C23#1306331011yescharacteristic
359Q8—432no—
360Q8—861no—
361D4—432no—
362D4—862no—
363D4—862no—
364D4—861no—
365D4—3442no—
366D4—3442no—
367D4—3442no—
368D4—3441no—
369D4—3441no—
370D4—3441no—
371D4—3441no—
372D4—1722no—
373D4—1722no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—861no—
378C2×C4—862no—
379C2×C4—862no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—3441no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4#1306328711yescharacteristic
387C2×C4C4×D17211yescharacteristic
388C2×C4#1306329511yescharacteristic
389C2×C4#1306329811yescharacteristic
390C2×C4#1306330011yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4SD16×D4311yescharacteristic
393C2×C4#1306335211yescharacteristic
394C2×C4#1306335711yescharacteristic
395C8—42no—
396C8—42no—
397C8—81no—
398C8—3441no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—862no—
404C22—3442no—
405C22—3442no—
406C22—3442no—
407C22—1721no—
408C22—1721no—
409C22—6882no—
410C22—6882no—
411C22#1458277711yescharacteristic
412C22#1458321411yescharacteristic
413C22#1458321911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—862no—
418C4—1721no—
419C4—1721no—
420C4#102×D4311yescharacteristic
421C4#1458289911yescharacteristic
422C4#1458303411yescharacteristic
423C4#1458303911yescharacteristic
424C4#1458316511yescharacteristic
425C4#1458316811yescharacteristic
426C2—21no—
427C2—21no—
428C2—1722no—
429C2—6882no—
430C2#1913491111yescharacteristic
431C2#1913507611yescharacteristic
432C2#1913510411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radical#19144076C2
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9173
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
2. #19143164C2semidirect
3. #19133264C2semidirect
4. C2×#14582642C2semidirect
5. #19132980C2semidirect
6. #19132490C2semidirect
7. C43×#1292C2semidirect
216. #1292D43semidirect
247. C43#9173semidirect

Maximal subgroups

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

subgroupindex
#191440762
#191431642
#191332642
C2×#145826422
#191329802
#191324902
C43×#12922
#917343