Finite Group Databasebeta

← #24991625

Subgroups — #24991625

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582836C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic
3#19134686C211yesmaximal, characteristic, complemented
4#19134683C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic
6#19132474C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43—21no—
9C22×C4⋊Dic43C2211yescharacteristic
10C22×(C2×D43)⋊C4—21no—
11C22×(C2×D43)⋊C4C2211yescharacteristic
12C2×C22⋊C4×D43—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582836—22no—
15#14582836C414yescomplemented
16#14582773—22no—
17#14582770—22no—
18#14582759C2211yescharacteristic
19#14582757—21no—
20#14582662—22no—
21#14582661—22no—
22#14582622—22no—
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#380C2211yescharacteristic
25C2×#95×C43C2211yescharacteristic
26C24×D43D411yescharacteristic
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29C22×C4×D43—22no—
30C22×C43⋊C8—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—24no—
37C2×C4⋊Dic43—44no—
38C2×C4⋊Dic43C2×C412yescomplemented
39C2×C4⋊Dic43D412yes—
40C2×Dic43⋊C4—22no—
41C2×C22⋊Dic43—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—44no—
49C2×(C2×D43)⋊C4C2×C412yes—
50C2×(C2×D43)⋊C4D412yes—
51C22⋊C4×D43—42no—
52C22⋊C4×D43—42no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C2×C4⋊C4×C43D412yes—
61C2×C22⋊C4×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43C2×C412yescomplemented
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—21no—
72C23×D43—42no—
73C23×D43—42no—
74C23×D43C22⋊C412yes—
75C23×D43SD1612yes—
76C23×D43Q1612yes—
77C22×C4×C43—24no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—42no—
95C22×Dic43—42no—
96C22×Dic43—42no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99C22×Dic43C22⋊C412yes—
100C2×C4×D43—44no—
101C2×C4×D43—82no—
102C2×C4×D43—82no—
103C2×C8×C43—42no—
104C2×C8×C43—41no—
105C4⋊C4×C43—42no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊Dic43—41no—
109C22⋊Dic43—41no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—44no—
115(C2×D43)⋊C4—48no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—48no—
119C4⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4⋊Dic43—42no—
122Dic43⋊C4—82no—
123C2×C43⋊C8—42no—
124C2×C43⋊C8—41no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43C2×C22⋊C411yescharacteristic
128C23×C43#12011yescharacteristic
129C23×C43#12311yescharacteristic
130C23×C43C2×SD1611yescharacteristic
131C23×C43C2×Q1611yescharacteristic
132C23×C43AGL(1,ℤ/8)11yescharacteristic
133C23×C43#13711yescharacteristic
134C22×D43—22no—
135C22×D43—22no—
136C22×D43—22no—
137C22×D43—22no—
138C22×D43—22no—
139C22×D43—22no—
140C22×D43—42no—
141C22×D43—42no—
142C22×D43—42no—
143C22×D43—42no—
144C22×D43—44no—
145C22×D43—44no—
146C22×D43—82no—
147C22×D43—82no—
148C22×D43—81no—
149C22×D43—81no—
150C22×D43#10314yes—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—24no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—44no—
159C2×C4×C43—44no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×Dic43—22no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—81no—
179C2×Dic43—82no—
180C2×Dic43—82no—
181C4×D43—88no—
182C8×C43—81no—
183C43⋊C8—81no—
184#9021—431nomaximal, Sylow
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—22no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43#38611yescharacteristic
194C22×C43C2×#10311yescharacteristic
195C22×C43#41711yescharacteristic
196C22×C43#45011yescharacteristic
197C22×C43#45111yescharacteristic
198C22×C43#45312yes—
199C22×C43#45812yes—
200C22×C43#48311yescharacteristic
201C22×C43#48411yescharacteristic
202C2×D43—24no—
203C2×D43—44no—
204C2×D43—44no—
205C2×D43—42no—
206C2×D43—42no—
207C2×D43—44no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—82no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—44no—
216C4×C43—82no—
217Dic43—42no—
218Dic43—82no—
219Dic43—82no—
220C2×#399—431no—
221#2315—431no—
222#1824—431no—
223#1824—431no—
224C2×#323—431no—
225#1294—431no—
226#1294D4311yescharacteristic, complemented
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43#161312yes—
232C2×C43#161412yes—
233C2×C43#187211yescharacteristic
234C2×C43#188711yescharacteristic
235C2×C43#189011yescharacteristic
236D43—44no—
237C22×C4⋊C4—431no—
238C22×C4⋊C4—861no—
239C22×C22⋊C4—431no—
240C22×C22⋊C4—861no—
241C22×C22⋊C4—861no—
242C2×C22⋊C8—431no—
243C2×C22⋊C8C2×D4311yescharacteristic
244#399—434no—
245#399—862no—
246#385—862no—
247#385—862no—
248#380—431no—
249#380—861no—
250#380C2×D4311yescharacteristic
251C2×#95C2×D4311yescharacteristic
252#340—862no—
253#340—862no—
254#323—862no—
255C43#902111yescharacteristic, complemented, Sylow
256C25—431no—
257C23×C4—21no—
258C23×C4—431no—
259C23×C4—862no—
260C23×C4—861no—
261C23×C4C22×D4311yescharacteristic
262C22×C8—21no—
263C22×C8—861no—
264C2×C4⋊C4—432no—
265C2×C4⋊C4—432no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—864no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—1724no—
274C2×C4⋊C4D17212yes—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—432no—
277C2×C22⋊C4—432no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—864no—
283C2×C22⋊C4—862no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—1722no—
286C2×C22⋊C4—1722no—
287C2×C22⋊C4—1724no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292#95—21no—
293#95—21no—
294#95—862no—
295#95—861no—
296#95C4×D4312yescomplemented
297C24—432no—
298C24—432no—
299C24—432no—
300C24—861no—
301C24—861no—
302C24—861no—
303C24—861no—
304C24—1722no—
305C24—1722no—
306C24D4×D4311yescharacteristic
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—432no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—862no—
318C22×C4—862no—
319C22×C4—3442no—
320C22×C4—3442no—
321C22×C4—1724no—
322C22×C4—1722no—
323C22×C4—1722no—
324C22×C4—1721no—
325C22×C4—1721no—
326C22×C4—1722no—
327C22×C4C2×C4×D4311yescharacteristic
328C22×C4C2×D17211yescharacteristic
329C22×C4#1062189811yescharacteristic
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190211yescharacteristic
333C2×C8—42no—
334C2×C8—41no—
335C2×C8—1722no—
336C2×C8—1721no—
337C4⋊C4—42no—
338C4⋊C4—862no—
339C4⋊C4—862no—
340C4⋊C4—3442no—
341C4⋊C4—1722no—
342C4⋊C4—1728no—
343C4⋊C4—1721no—
344C4⋊C4—1721no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—862no—
348C22⋊C4—862no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C22⋊C4—1728no—
352C22⋊C4—1724no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C23—22no—
356C23—22no—
357C23—434no—
358C23—862no—
359C23—862no—
360C23—862no—
361C23—862no—
362C23—862no—
363C23—862no—
364C23—3441no—
365C23—3441no—
366C23—3442no—
367C23—3442no—
368C23—1722no—
369C23—1722no—
370C23—1724no—
371C23—1724no—
372C23—1722no—
373C23—1722no—
374C23C22⋊C4×D4311yescharacteristic
375C23#1306329511yescharacteristic
376C23#1306331011yescharacteristic
377C23SD16×D4311yescharacteristic
378C23Q16×D4311yescharacteristic
379C23#1306334911yescharacteristic
380C23#1306335411yescharacteristic
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—862no—
396C2×C4—3448no—
397C2×C4—3442no—
398C2×C4—3442no—
399C2×C4—3441no—
400C2×C4—1722no—
401C2×C4—1722no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4—1722no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4#1306328711yescharacteristic
409C2×C4C4×D17211yescharacteristic
410C2×C4#1306329811yescharacteristic
411C2×C4#1306330011yescharacteristic
412C8—81no—
413C8—3441no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—864no—
423C22—3442no—
424C22—3442no—
425C22—3442no—
426C22—1724no—
427C22—1722no—
428C22—1722no—
429C22—1724no—
430C22—1724no—
431C22#1458277711yescharacteristic
432C22#103×D4311yescharacteristic
433C22#1458289711yescharacteristic
434C22#1458305111yescharacteristic
435C22#1458305611yescharacteristic
436C22#1458306812yes—
437C22#1458309012yes—
438C22#1458323111yescharacteristic
439C22#1458323611yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—44no—
445C4—82no—
446C4—3442no—
447C4—3442no—
448C4—1722no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—1724no—
454C2#1913361612yes—
455C2#1913362112yes—
456C2#1913490111yescharacteristic
457C2#1913499211yescharacteristic
458C2#1913500711yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#9021
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
3. #19134686C2semidirect
4. #19134683C2semidirect
6. #19132474C2semidirect
7. C43×#1294C2semidirect
15. #14582836C4semidirect
38. C2×C4⋊Dic43C2×C4semidirect
66. #95×C43C2×C4semidirect
226. #1294D43semidirect
255. C43#9021semidirect
296. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828362
#191372082
#191346862
#191346832
C2×#145826222
#191324742
C43×#12942
#902143