Finite Group Databasebeta

← #24988168

Subgroups — #24988168

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148460C211yesmaximal, characteristic
2#19135532C211yesmaximal, characteristic, complemented
3#19133286C211yesmaximal, characteristic, complemented
4#19133273C211yesmaximal, characteristic
5#19133049C211yesmaximal, characteristic, complemented
6#19133045C211yesmaximal, characteristic
7C43×#1801C211yesmaximal, characteristic, complemented
8#14583634—21no—
9#14583627—21no—
10#14583622—21no—
11#14583621—22no—
12#14583609—21no—
13#14583590—22no—
14#14583496C414yes—
15#14583473—21no—
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583433—22no—
19#14583380—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582654—22no—
23#14582647—21no—
24#14582646—21no—
25#14582644—21no—
26#14582642—21no—
27#14582629—22no—
28#14582626—22no—
29C2×C4×Q8×C43C2211yescharacteristic
30C43×#423C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×#101×C43—21no—
33C43×#343—21no—
34C2×#10621898—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37#13063325D411yescharacteristic
38#13063325D411yescharacteristic
39#13063325D411yescharacteristic
40#13063323—22no—
41#13063322D411yescharacteristic
42#13063320—24no—
43#13063319—24no—
44#13063317—22no—
45#13063317—21no—
46#13063315—24no—
47#13063314—22no—
48#13063313—22no—
49#13063313—21no—
50#13063310—24no—
51#13063308—24no—
52#13063304—21no—
53#13063304C2×C412yes—
54#13063303—24no—
55#13063301—22no—
56#13063301—22no—
57#13063299—21no—
58#13063299C2×C412yes—
59C4×Dic86—22no—
60C4×Dic86—21no—
61C4×Dic86D412yes—
62#13063290—22no—
63C4×D172—22no—
64C4×D172—21no—
65C4×D172D412yes—
66#13063287—22no—
67C4×C22⋊D43—24no—
68#13063284—21no—
69#13063283—22no—
70#13063282—24no—
71C4⋊C4×D43—22no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4×C43⋊C8—21no—
75C4×C43⋊C8—21no—
76C22×Q8×C43D411yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C4×Q8×C43—21no—
80C4×Q8×C43—21no—
81C4×Q8×C43—21no—
82C4×Q8×C43—21no—
83C2×C4⋊C4×C43C2×C412yes—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C42×C43D412yes—
86C2×C42×C43C2311yescharacteristic
87C4⋊C8×C43—21no—
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43—21no—
91#101×C43—42no—
92C2×Q8×C43—21no—
93C2×Q8×C43—21no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43—21no—
97C2×Q8×C43—21no—
98C22×C4×C43C22⋊C412yes—
99C22×C4×C43C22⋊C412yes—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C2×C22⋊D43—22no—
104#10621898—41no—
105#10621898—41no—
106#10621898—41no—
107#10621898—41no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172C22⋊C412yes—
111C2×C4×D43—22no—
112C2×C4×D43—24no—
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86C22⋊C412yes—
116M16×C43—41no—
117M16×C43—41no—
118M16×C43—41no—
119M16×C43—41no—
120C2×C8×C43—41no—
121C2×C8×C43—41no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C42×C43—22no—
127C42×C43—22no—
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C22⋊Dic43—22no—
133(C2×D43)⋊C4—24no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—24no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43C22⋊C412yes—
143C4⋊Dic43C22⋊C412yes—
144Dic43⋊C4—24no—
145Dic43⋊C4—24no—
146Dic43⋊C4—24no—
147Dic43⋊C4—22no—
148Dic43⋊C4—22no—
149C4×Dic43—24no—
150C4×Dic43—22no—
151C2×C43⋊C8—22no—
152C2×C43⋊C8—41no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—42no—
155C2×C43⋊C8—41no—
156C23×C43C2×C22⋊C411yescharacteristic
157C22×D43—22no—
158Q8×C43—41no—
159Q8×C43—41no—
160Q8×C43—41no—
161Q8×C43—41no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—22no—
167C2×C4×C43—22no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43C2×C22⋊C411yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12011yescharacteristic
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#13511yescharacteristic
177C2×C4×C43#13511yescharacteristic
178C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C43#13711yescharacteristic
180C22⋊D43—42no—
181C22⋊D43—42no—
182C2×Dic43—22no—
183C2×Dic43—22no—
184C2×Dic43—22no—
185D172—42no—
186D172—41no—
187D172—41no—
188D172—41no—
189D172—41no—
190C4×D43—42no—
191C4×D43—42no—
192C4×D43—84no—
193Dic86—41no—
194Dic86—41no—
195Dic86—41no—
196Dic86—41no—
197Dic86—42no—
198C8×C43—81no—
199C8×C43—81no—
200C43⋊C8—42no—
201C43⋊C8—81no—
202#8357—431nomaximal, Sylow
203C22×C43—21no—
204C22×C43—21no—
205C22×C43#37911yescharacteristic
206C22×C43#41611yescharacteristic
207C22×C43#41711yescharacteristic
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—42no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—42no—
215C4×C43—42no—
216C4×C43#44911yescharacteristic
217C4×C43#44911yescharacteristic
218C4×C43#45211yescharacteristic
219C4×C43#45211yescharacteristic
220C4×C43#45411yescharacteristic
221C4×C43#45611yescharacteristic
222Dic43—42no—
223Dic43—42no—
224Dic43—42no—
225#3507—431no—
226#1984—431no—
227#1801D4311yescharacteristic, complemented
228#1550—431no—
229#1547—431no—
230#1493—431no—
231#1492—431no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#178811yescharacteristic
235C2×C43#179111yescharacteristic
236C2×C43#179311yescharacteristic
237D43—82no—
238#559—861no—
239#557—861no—
240#556—862no—
241#556—861no—
242#554—861no—
243#552—862no—
244#539—434no—
245#536—861no—
246#533—431no—
247#532—431no—
248#529—862no—
249#520—861no—
250C2×C4×Q8C2×D4311yescharacteristic
251#423C2×D4311yescharacteristic
252#423C2×D4311yescharacteristic
253C2×C4⋊C8—431no—
254C2×#101—21no—
255C2×C4×C8—431no—
256#343—21no—
257#336—862no—
258#333—861no—
259#332—861no—
260#332—861no—
261#331—861no—
262Q8⋊C8—862no—
263D4⋊C8—862no—
264C43#835711yescharacteristic, complemented, Sylow
265C2×#41—861no—
266C22×Q8C22⋊D4311yescharacteristic
267C2×M16—21no—
268C2×M16—21no—
269C22×C8—861no—
270C22×C8—861no—
271C4⋊Q8—431no—
272C4⋊Q8—431no—
273C4⋊Q8—431no—
274C4⋊Q8—862no—
275#127—431no—
276#126—864no—
277#126—864no—
278#125—862no—
279#125—864no—
280#125—861no—
281#124—862no—
282#124—862no—
283#124—861no—
284#123—864no—
285#123—864no—
286C22⋊Q8—432no—
287C22⋊Q8—864no—
288C22⋊Q8—862no—
289C22⋊Q8—862no—
290C22⋊Q8—861no—
291#121—432no—
292#121—861no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—432no—
298C4×Q8—862no—
299C4×Q8—862no—
300C4×Q8—861no—
301C4×D4—432no—
302C4×D4—862no—
303C4×D4—862no—
304C4×D4—864no—
305C4×D4—861no—
306#117—864no—
307#117—862no—
308#117—861no—
309C2×C4⋊C4—862no—
310C2×C4⋊C4C4×D4312yes—
311C2×C4⋊C4C22⋊D4311yescharacteristic
312C2×C42D17212yes—
313C2×C42C22×D4311yescharacteristic
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—861no—
319C4⋊C8—861no—
320#101—42no—
321C4×C8—861no—
322C4×C8—861no—
323#41—1721no—
324#41—1721no—
325#41—1721no—
326#41—1721no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—432no—
334C2×Q8—861no—
335C2×Q8—861no—
336C2×D4—432no—
337C2×D4—862no—
338C2×D4—861no—
339C2×D4—861no—
340C22×C4—864no—
341C22×C4—862no—
342C22×C4(C2×D43)⋊C412yes—
343C22×C4(C2×D43)⋊C412yes—
344C22×C4C2×C4×D4311yescharacteristic
345C22×C4C2×D17211yescharacteristic
346C22×C4C2×C22⋊D4311yescharacteristic
347M16—41no—
348M16—41no—
349M16—41no—
350M16—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—862no—
354C2×C8—1722no—
355C2×C8—1721no—
356C2×C8—1721no—
357C2×C8—1721no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—432no—
363C4⋊C4—432no—
364C4⋊C4—864no—
365C4⋊C4—864no—
366C4⋊C4—864no—
367C4⋊C4—862no—
368C4⋊C4—861no—
369C4⋊C4—861no—
370C4⋊C4—862no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C22⋊C4—864no—
374C22⋊C4—864no—
375C22⋊C4—864no—
376C22⋊C4—862no—
377C22⋊C4—862no—
378C22⋊C4—862no—
379C42—22no—
380C42—22no—
381C42—864no—
382C42—862no—
383C42D4×D4311yescharacteristic
384C42D4×D4311yescharacteristic
385C42D4×D4311yescharacteristic
386C42D4×D4311yescharacteristic
387C23—862no—
388C23C2×(C2×D43)⋊C411yescharacteristic
389Q8—41no—
390Q8—41no—
391Q8—41no—
392Q8—41no—
393Q8—1722no—
394Q8—1721no—
395Q8—1721no—
396Q8—1721no—
397Q8—1721no—
398D4—1722no—
399D4—1722no—
400D4—1722no—
401D4—1721no—
402D4—1721no—
403D4—1721no—
404D4—1721no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—862no—
414C2×C4—862no—
415C2×C4—862no—
416C2×C4—3444no—
417C2×C4—1722no—
418C2×C4—1722no—
419C2×C4C22⋊C4×D4311yescharacteristic
420C2×C4C22⋊C4×D4311yescharacteristic
421C2×C4#1306329311yescharacteristic
422C2×C4#1306329311yescharacteristic
423C2×C4#1306329511yescharacteristic
424C2×C4#1306329511yescharacteristic
425C2×C4#1306334511yescharacteristic
426C2×C4#1306334511yescharacteristic
427C2×C4#1306335111yescharacteristic
428C2×C4#1306335611yescharacteristic
429C8—81no—
430C8—81no—
431C8—3441no—
432C8—1722no—
433C22—21no—
434C22—21no—
435C22—1722no—
436C22—1722no—
437C22—1722no—
438C22#1458275411yescharacteristic
439C22#1458289311yescharacteristic
440C22#1458289811yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—42no—
445C4—42no—
446C4—1722no—
447C4—1722no—
448C4—1722no—
449C4#1458304211yescharacteristic
450C4#1458304211yescharacteristic
451C4#1458305911yescharacteristic
452C4#1458305911yescharacteristic
453C4#1458307411yescharacteristic
454C4#1458308411yescharacteristic
455C2—21no—
456C2—21no—
457C2—3442no—
458C2#1913453311yescharacteristic
459C2#1913454411yescharacteristic
460C2#1913455611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1801C2
socleC22×C43#379
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1801D43
hypocenterC43#8357
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #19135532C2semidirect
3. #19133286C2semidirect
5. #19133049C2semidirect
7. C43×#1801C2semidirect
227. #1801D43semidirect
264. C43#8357semidirect

Maximal subgroups

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

subgroupindex
#191484602
#191355322
#191332862
#191332732
#191330492
#191330452
C43×#18012
#835743