Finite Group Databasebeta

← #24992488

Subgroups — #24992488

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#19144075C211yesmaximal, characteristic
2#19143163C211yesmaximal, characteristic, complemented
3#19133262C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132470C211yesmaximal, characteristic, complemented
7C43×#1477C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C2×#13063332—21no—
10C2×#13063322C2211yescharacteristic
11#14583099—21no—
12#14583099C412yes—
13#14583094—21no—
14#14583094C412yes—
15#14582926—22no—
16#14582926—21no—
17#14582923—21no—
18#14582923C2211yescharacteristic
19#14582923C2211yescharacteristic
20C2×C4⋊(C43⋊C8)—21no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582903—21no—
23#14582642—21no—
24#14582642—21no—
25#14582642—22no—
26C4×#41×C43C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×Q8⋊C8—21no—
30C43×D4⋊C8—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34#13063350—42no—
35#13063350—42no—
36C2×#10621884—22no—
37C2×#10621882—22no—
38#13063332—42no—
39#13063332—42no—
40C2×#10621877—22no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C22×C43⋊C8—22no—
44C22×C43⋊C8—21no—
45#13063322—21no—
46#13063322—21no—
47#13063322—21no—
48#13063322C2×C412yes—
49C4⋊(C43⋊C8)—22no—
50C4⋊(C43⋊C8)—22no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2×C412yes—
55C4⋊(C43⋊C8)D411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57C4⋊(C43⋊C8)D412yes—
58#13063245—22no—
59#13063245—22no—
60C2×#41×C43D411yescharacteristic
61C22×C8×C43—21no—
62C4×Q8×C43C2×C411yescharacteristic
63C4×Q8×C43D411yescharacteristic
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43C2×C411yescharacteristic
67C4×D4×C43D411yescharacteristic
68#117×C43—21no—
69#117×C43D411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77C23×D43—41no—
78#41×C43—21no—
79#41×C43—21no—
80#41×C43D812yes—
81#41×C43SD1612yes—
82C2×Q8×C43C22⋊C411yescharacteristic
83C2×D4×C43—21no—
84C2×D4×C43C22⋊C411yescharacteristic
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—81no—
102C2×D172—81no—
103C2×D172—82no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—81no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43C22⋊C411yescharacteristic
110C4⋊C4×C43C22⋊C411yescharacteristic
111C22⋊C4×C43—21no—
112C22⋊C4×C43—21no—
113C22⋊C4×C43—21no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43C22×C411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121#10621884—44no—
122#10621882—44no—
123#10621877—44no—
124#10621877—41no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—44no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C23×C43—21no—
136C23×C43#12311yescharacteristic
137C22×D43—42no—
138C22×D43—82no—
139C22×D43—82no—
140C22×D43—81no—
141C22×D43—81no—
142Q8×C43—21no—
143Q8×C43#10212yes—
144D4×C43—22no—
145D4×C43—22no—
146D4×C43—21no—
147D4×C43#10212yes—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—81no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43C2×SD1611yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C43#13711yescharacteristic
169D172—42no—
170D172—42no—
171D172—82no—
172D172—82no—
173D172—82no—
174D172—81no—
175D172—81no—
176D172—81no—
177D172—81no—
178C8×C43—81no—
179C8×C43—81no—
180C43⋊C8—42no—
181C43⋊C8—41no—
182C43⋊C8—42no—
183C43⋊C8—41no—
184#9173—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43#38611yescharacteristic
191C22×C43#48011yescharacteristic
192C22×C43#48111yescharacteristic
193C2×D43—82no—
194C2×D43—82no—
195C2×D43—82no—
196C2×D43—162no—
197C2×D43—162no—
198C4×C43—22no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43C2×#10211yescharacteristic
205C4×C43#41711yescharacteristic
206C4×C43#44711yescharacteristic
207C4×C43#44811yescharacteristic
208C4×C43#47111yescharacteristic
209C4×C43#47211yescharacteristic
210#3038—431no—
211#2906—431no—
212#1545—431no—
213C2×#331—431no—
214#1477D4311yescharacteristic, complemented
215#1301—431no—
216#1292—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—42no—
220C2×C43#187411yescharacteristic
221C2×C43#190311yescharacteristic
222C2×C43#190711yescharacteristic
223D43—162no—
224C2×AGL(1,ℤ/8)—861no—
225C2×#131—861no—
226C2×#127—431no—
227C4×#41C2×D4311yescharacteristic
228#460—432no—
229#460—861no—
230#459—432no—
231#459—861no—
232#431C2×D4311yescharacteristic
233#424—862no—
234#424—861no—
235#423—431no—
236#423—431no—
237#423—861no—
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—21no—
246D4⋊C8—21no—
247C43#917311yescharacteristic, complemented, Sylow
248C2×#41D17211yescharacteristic
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—862no—
259C2×M16—861no—
260C2×M16—861no—
261C22×C8—21no—
262C22×C8—862no—
263C22×C8—861no—
264#127—432no—
265#127—861no—
266#127—861no—
267#127—861no—
268C4×Q8C4×D4311yescharacteristic
269C4×Q8C22⋊D4311yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C4×D4311yescharacteristic
273C4×D4C22⋊D4311yescharacteristic
274#117—21no—
275#117D17211yescharacteristic
276C2×C42—21no—
277C2×C42C22×D4311yescharacteristic
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—432no—
282C4⋊C8—431no—
283C4⋊C8—431no—
284C4⋊C8—432no—
285C4⋊C8—862no—
286C4⋊C8—862no—
287C4⋊C8—861no—
288C4⋊C8—861no—
289C4⋊C8—861no—
290#102—862no—
291#102—862no—
292C22⋊C8—21no—
293C4×C8—21no—
294C24—1721no—
295#41—21no—
296#41—21no—
297#41#1062187312yes—
298#41D34412yes—
299C2×Q8(C2×D43)⋊C411yescharacteristic
300C2×D4—21no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—3441no—
305C2×D4—3441no—
306C2×D4—3442no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4(C2×D43)⋊C411yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4C2×D17211yescharacteristic
319C22×C4#1062190011yescharacteristic
320C22×C4#1062190011yescharacteristic
321SD16—1724no—
322D8—1724no—
323M16—1724no—
324M16—1721no—
325M16—1721no—
326M16—1721no—
327M16—1721no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—81no—
331C2×C8—862no—
332C2×C8—861no—
333C2×C8—861no—
334C2×C8—862no—
335C2×C8—1724no—
336C2×C8—1721no—
337C2×C8—1721no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4(C2×D43)⋊C411yescharacteristic
341C4⋊C4(C2×D43)⋊C411yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42C2×C4×D4311yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C42C2×C22⋊D4311yescharacteristic
352C23—21no—
353C23—3442no—
354C23—3442no—
355C23—3441no—
356C23—3441no—
357C23—1722no—
358C23#1306330911yescharacteristic
359Q8—21no—
360Q8#1306324712yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—3442no—
365D4—3442no—
366D4—3442no—
367D4—3441no—
368D4—3441no—
369D4—3441no—
370D4—3441no—
371D4—1722no—
372D4—1722no—
373D4#1306324712yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×(C2×D43)⋊C411yescharacteristic
386C2×C4(C22⋊D43)⋊C411yescharacteristic
387C2×C4(C22⋊D43)⋊C411yescharacteristic
388C2×C4#1306329511yescharacteristic
389C2×C4#1306329711yescharacteristic
390C2×C4#1306329711yescharacteristic
391C2×C4C2×D34411yescharacteristic
392C2×C4C2×#1062187311yescharacteristic
393C2×C4#1306335311yescharacteristic
394C2×C4#1306335811yescharacteristic
395C8—81no—
396C8—81no—
397C8—1722no—
398C8—1721no—
399C8—1722no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—3442no—
407C22—3442no—
408C22—3442no—
409C22—6882no—
410C22—6882no—
411C22#1458277611yescharacteristic
412C22#1458321311yescharacteristic
413C22#1458321811yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4C2×#1306324711yescharacteristic
421C4#1458290111yescharacteristic
422C4#1458303511yescharacteristic
423C4#1458304011yescharacteristic
424C4#1458316411yescharacteristic
425C4#1458316711yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—6882no—
430C2#1913491011yescharacteristic
431C2#1913507311yescharacteristic
432C2#1913510111yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1477C2
socleC22×C43#386
prime radical#19144075C2
cosocleC2×C42×C43C23
hypercenter#1477D43
hypocenterC43#9173
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143163C2semidirect
3. #19133262C2semidirect
4. C2×#14582642C2semidirect
5. #19132491C2semidirect
6. #19132470C2semidirect
7. C43×#1477C2semidirect
214. #1477D43semidirect
247. C43#9173semidirect

Maximal subgroups

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

subgroupindex
#191440752
#191431632
#191332622
C2×#145826422
#191324912
#191324702
C43×#14772
#917343