Finite Group Databasebeta

← #24984797

Subgroups — #24984797

Order 11008.

630 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#19137159C211yesmaximal, characteristic
2#19134737C211yesmaximal, characteristic, complemented
3#19134447C211yesmaximal, characteristic, complemented
4#19132416C211yesmaximal, characteristic, complemented
5#19132415C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic, complemented
7C43×#1270C211yesmaximal, characteristic, complemented
8C2×#13063321C411yescharacteristic
9C2×D4×Dic43C411yescharacteristic
10C2×#13063287C411yescharacteristic
11C2×(C22⋊D43)⋊C4—21no—
12C2×(C22⋊D43)⋊C4—21no—
13C2×Dic43⋊C8—21no—
14C2×#13063235—21no—
15#14582801C2211yescharacteristic
16#14582799—21no—
17#14582799—21no—
18#14582768C411yescharacteristic
19C42×Dic43C2211yescharacteristic
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#390C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C22⋊D43—21no—
30C23×Dic43—21no—
31C22×C4×D43—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063321—22no—
35#13063321—22no—
36D4×Dic43—42no—
37#13063287—42no—
38(C22⋊D43)⋊C4—42no—
39(C22⋊D43)⋊C4—42no—
40(C22⋊D43)⋊C4—42no—
41(C22⋊D43)⋊C4—42no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55Dic43⋊C8—24no—
56#13063235—42no—
57C22×D4×C43C2×C411yescharacteristic
58C22×C8×C43—21no—
59C22×C8×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C24×C43—21no—
65C23×D43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43M1612yes—
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—24no—
75C2×C22⋊D43—24no—
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—42no—
80C22×Dic43—21no—
81C22×Dic43—42no—
82C22×Dic43—42no—
83C22×Dic43—42no—
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×D172—21no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172M1612yes—
92C2×C4×D43—42no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C42×C43—41no—
107C22⋊Dic43—42no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—42no—
113C4⋊Dic43—41no—
114Dic43⋊C4—42no—
115Dic43⋊C4—42no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120C4×Dic43—22no—
121C4×Dic43—22no—
122C4×Dic43—41no—
123C4×Dic43D812yes—
124C4×Dic43SD1612yes—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C23×C43—22no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43C2×C22⋊C411yescharacteristic
139C22×D43—22no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—41no—
145C22×D43—41no—
146D4×C43—42no—
147D4×C43—42no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43C2×M1611yescharacteristic
158C2×C4×C43C2×M1611yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43C2×SD1611yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C22⋊D43—48no—
164C22⋊D43—48no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—84no—
177C2×Dic43#10012yes—
178C2×Dic43#10212yes—
179C2×Dic43#10212yes—
180C2×Dic43#10412yes—
181D172—42no—
182D172—42no—
183C4×D43—84no—
184C8×C43—42no—
185C8×C43—81no—
186C43⋊C8—42no—
187C43⋊C8—81no—
188#7621—431nomaximal, Sylow
189C22×C43—42no—
190C22×C43—42no—
191C22×C43—42no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43#40711yescharacteristic
197C22×C43#41011yescharacteristic
198C22×C43C2×#10011yescharacteristic
199C22×C43C2×#10211yescharacteristic
200C22×C43#41811yescharacteristic
201C22×C43C2×#10411yescharacteristic
202C22×C43#42111yescharacteristic
203C2×D43—42no—
204C2×D43—42no—
205C2×D43—42no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—81no—
217Dic43—22no—
218Dic43—22no—
219Dic43—22no—
220Dic43—22no—
221Dic43—81no—
222C4×#127—431no—
223#1839—431no—
224#1767—431no—
225#1270—431no—
226#1270—431no—
227#1270—431no—
228#1270D4311yescharacteristic, complemented
229C2×C43—82no—
230C2×C43#146611yescharacteristic
231C2×C43#148611yescharacteristic
232C2×C43#149011yescharacteristic
233C2×C43#150211yescharacteristic
234C2×C43#151411yescharacteristic
235C2×C43#153011yescharacteristic
236C2×C43#154511yescharacteristic
237D43—82no—
238C2×#127—431no—
239C2×C4×D4—431no—
240C2×C4×D4—431no—
241C2×C4×D4—861no—
242C2×C4×D4—861no—
243C2×C4⋊C8—861no—
244C2×#97—861no—
245#390—431no—
246#390—861no—
247#390—861no—
248#390C2×D4311yescharacteristic
249#384—431no—
250C43—431no—
251#336—431no—
252#336—431no—
253#336—861no—
254#336—861no—
255#336C2×D4311yescharacteristic
256#336C2×D4311yescharacteristic
257C43#762111yescharacteristic, complemented, Sylow
258C22×D4—431no—
259C22×D4—861no—
260C22×D4—861no—
261C22×D4C4×D4311yescharacteristic
262C23×C4—861no—
263C23×C4—861no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—861no—
267C22×C8—861no—
268#127—862no—
269#127—862no—
270C4×D4—1722no—
271C4×D4—1722no—
272C4×D4—1722no—
273C4×D4—1722no—
274C4×D4—1722no—
275C4×D4—1722no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4C4×D4311yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C42—431no—
287C2×C42—431no—
288C2×C42—431no—
289C2×C42—431no—
290C2×C42—431no—
291C2×C42—431no—
292C2×C42C22×D4311yescharacteristic
293C4⋊C8—864no—
294#97—1722no—
295C24—21no—
296C24—861no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—432no—
301C2×D4—864no—
302C2×D4—864no—
303C2×D4—861no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1722no—
307C2×D4—1722no—
308C2×D4—1722no—
309C2×D4—1722no—
310C2×D4#1062187212yes—
311C22×C4—21no—
312C22×C4—431no—
313C22×C4—431no—
314C22×C4—431no—
315C22×C4—431no—
316C22×C4—861no—
317C22×C4—1722no—
318C22×C4—1722no—
319C22×C4—1722no—
320C22×C4—1722no—
321C22×C4—1722no—
322C22×C4—1722no—
323C22×C4C2×C4×D4311yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—862no—
333C2×C8—1721no—
334C2×C8—1721no—
335C2×C8—1721no—
336C2×C8—1721no—
337C2×C8—1721no—
338C4⋊C4—41no—
339C4⋊C4—1721no—
340C4⋊C4—1722no—
341C4⋊C4—1722no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—1722no—
347C22⋊C4—1722no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C42—41no—
353C42—432no—
354C42—432no—
355C42—862no—
356C42—862no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—861no—
361C42—1721no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—862no—
370C23—1721no—
371C23—1721no—
372C23—1721no—
373C23—1721no—
374C23—1721no—
375C23—1721no—
376C23C22⋊C4×D4311yescharacteristic
377D4—42no—
378D4—42no—
379D4—1722no—
380D4—1722no—
381D4—1728no—
382D4—1728no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—432no—
393C2×C4—432no—
394C2×C4—432no—
395C2×C4—432no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—3444no—
405C2×C4—3444no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4M16×D4311yescharacteristic
410C2×C4C2×#1062187211yescharacteristic
411C2×C4D8×D4311yescharacteristic
412C2×C4SD16×D4311yescharacteristic
413C2×C4#1306334911yescharacteristic
414C2×C4#1306335211yescharacteristic
415C8—42no—
416C8—81no—
417C8—3441no—
418C8—1722no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—3441no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22—1722no—
431C22—1722no—
432C22—1722no—
433C22#1458286111yescharacteristic
434C22#1458287111yescharacteristic
435C22#100×D4311yescharacteristic
436C22#102×D4311yescharacteristic
437C22#1458290211yescharacteristic
438C22#104×D4311yescharacteristic
439C22#1458291411yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—862no—
448C4—862no—
449C4—862no—
450C4—862no—
451C4—3441no—
452C2—82no—
453C2—3442no—
454C2#1913293411yescharacteristic
455C2#1913301811yescharacteristic
456C2#1913303611yescharacteristic
457C2#1913308811yescharacteristic
458C2#1913314011yescharacteristic
459C2#1913320411yescharacteristic
460C2#1913326111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#1270D43
hypocenterC43#7621
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19134737C2semidirect
3. #19134447C2semidirect
4. #19132416C2semidirect
5. #19132415C2semidirect
6. #19132415C2semidirect
7. C43×#1270C2semidirect
228. #1270D43semidirect
257. C43#7621semidirect

Maximal subgroups

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

subgroupindex
#191371592
#191347372
#191344472
#191324162
#191324152
C43×#12702
#762143