Finite Group Databasebeta

← #35297735

Subgroups — #35297735

Order 21248.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127552C211yesmaximal, characteristic
2#24907529C212yesmaximal
3#24905306C211yesmaximal, characteristic
4#24905305C212yesmaximal
5C83×#1280C211yesmaximal, characteristic
6C22×Dic83⋊C4C411yescharacteristic
7C22×Dic83⋊C4C411yescharacteristic
8C22×C4×Dic83C411yescharacteristic
9C22×C4×Dic83C411yescharacteristic
10C22×C4×Dic83C2211yescharacteristic
11C2×C22⋊(C83⋊C8)C2212yes—
12#19127552—22no—
13#19127552—22no—
14C2×C83⋊#95C2211yescharacteristic
15#19127455—22no—
16#19127455—22no—
17C2×C22⋊C8×C83C2212yes—
18C2×#95×C83C2211yescharacteristic
19C23×Dic83C2×C411yescharacteristic
20C23×Dic83C2×C411yescharacteristic
21C23×Dic83C2×C411yescharacteristic
22C23×Dic83C2×C411yescharacteristic
23C22×C83⋊C8—22no—
24C2×Dic83⋊C4—22no—
25C2×Dic83⋊C4—22no—
26C2×Dic83⋊C4—22no—
27C2×Dic83⋊C4—22no—
28C2×Dic83⋊C4—22no—
29C2×Dic83⋊C4C814yescomplemented
30C2×C4×Dic83—21no—
31C2×C4×Dic83—21no—
32C2×C4×Dic83—21no—
33C2×C4×Dic83—21no—
34C2×C4×Dic83—21no—
35C2×C4×Dic83—22no—
36C2×C4×Dic83—21no—
37C2×C4×Dic83—42no—
38C2×C4×Dic83—42no—
39C2×C4×Dic83D412yes—
40C2×C4×Dic83D412yes—
41C22⋊(C83⋊C8)—22no—
42C22⋊(C83⋊C8)—22no—
43C83⋊#95—22no—
44C23×C4×C83C2×C411yescharacteristic
45C23×C4×C83C2×C411yescharacteristic
46C23×C4×C83C2311yescharacteristic
47C22×C8×C83—22no—
48C22⋊C8×C83—22no—
49C22⋊C8×C83—22no—
50#95×C83—22no—
51C22×Dic83—21no—
52C22×Dic83—21no—
53C22×Dic83—21no—
54C22×Dic83—21no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C22×Dic83—22no—
58C22×Dic83—22no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83—21no—
63C22×Dic83—41no—
64C22×Dic83—41no—
65C22×Dic83—41no—
66C22×Dic83—41no—
67C22×Dic83C22⋊C412yes—
68C22×Dic83C22⋊C411yescharacteristic
69C22×Dic83C22⋊C411yescharacteristic
70C22×Dic83C2×C812yes—
71C22×Dic83C2×C812yes—
72C22×Dic83M1612yes—
73C22×Dic83M1612yes—
74C2×C83⋊C8—42no—
75C2×C83⋊C8—42no—
76C2×C83⋊C8—42no—
77Dic83⋊C4—28no—
78Dic83⋊C4—28no—
79C4×Dic83—22no—
80C4×Dic83—22no—
81C4×Dic83—22no—
82C4×Dic83—22no—
83C4×Dic83—42no—
84C4×Dic83—42no—
85C4×Dic83—42no—
86C4×Dic83—42no—
87C24×C83C22×C411yescharacteristic
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83—21no—
92C22×C4×C83—41no—
93C22×C4×C83—41no—
94C22×C4×C83—41no—
95C22×C4×C83—41no—
96C22×C4×C83—41no—
97C22×C4×C83—41no—
98C22×C4×C83C2×C812yes—
99C22×C4×C83M1612yes—
100C22×C4×C83C2×D412yes—
101C22×C4×C83#4111yescharacteristic
102C22×C4×C83#4112yes—
103C22×C4×C83#4111yescharacteristic
104C2×C8×C83—42no—
105C2×C8×C83—42no—
106C2×C8×C83—42no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83C2×C22⋊C411yescharacteristic
112C23×C83#11711yescharacteristic
113C23×C83#11711yescharacteristic
114C23×C83C22×C811yescharacteristic
115C23×C83C2×M1611yescharacteristic
116C23×C83C2×M1611yescharacteristic
117C23×C83C2×M1611yescharacteristic
118C2×C4×C83—22no—
119C2×C4×C83—22no—
120C2×C4×C83—22no—
121C2×C4×C83—22no—
122C2×C4×C83—41no—
123C2×C4×C83—42no—
124C2×C4×C83—41no—
125C2×C4×C83—42no—
126C2×C4×C83—42no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—42no—
132C2×C4×C83—42no—
133C2×C4×C83#12312yes—
134C2×C4×C83#12312yes—
135C2×Dic83—24no—
136C2×Dic83—24no—
137C2×Dic83—22no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—22no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—22no—
144C2×Dic83—22no—
145C2×Dic83—22no—
146C2×Dic83—22no—
147C2×Dic83—22no—
148C2×Dic83—22no—
149C2×Dic83—42no—
150C2×Dic83—42no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83—41no—
154C2×Dic83—41no—
155C2×Dic83—42no—
156C2×Dic83—42no—
157C2×Dic83C22⋊C814yes—
158C2×Dic83#10012yes—
159C2×Dic83#10112yes—
160C8×C83—82no—
161C83⋊C8—82no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—21no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83—21no—
169C22×C83—21no—
170C22×C83—21no—
171C22×C83—21no—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83#38111yescharacteristic
175C22×C83C2×C22⋊C811yescharacteristic
176C22×C83#40711yescharacteristic
177C22×C83#41011yescharacteristic
178C22×C83#41011yescharacteristic
179C22×C83C2×#10011yescharacteristic
180C22×C83C2×#10111yescharacteristic
181C22×C83#43111yescharacteristic
182C22×C83#43111yescharacteristic
183C22×C83#43211yescharacteristic
184C22×C83#43211yescharacteristic
185C4×C83—22no—
186C4×C83—22no—
187C4×C83—42no—
188C4×C83—42no—
189Dic83—24no—
190Dic83—22no—
191Dic83—22no—
192Dic83—42no—
193Dic83—42no—
194#8701—831nomaximal, Sylow
195C2×C83—21no—
196C2×C83—21no—
197C2×C83—21no—
198C2×C83—21no—
199C2×C83#146011yescharacteristic
200C2×C83#146111yescharacteristic
201C2×C83#146611yescharacteristic
202C2×C83#146711yescharacteristic
203C2×C83#181711yescharacteristic
204C2×C83#182011yescharacteristic
205C2×C83#182111yescharacteristic
206C2×C4×C4⋊C4—831no—
207#1817—832no—
208#1280—832no—
209#1280—831no—
210#1280D8311yescharacteristic
211C83#870111yescharacteristic, complemented, Sylow
212C22×C4⋊C4—831no—
213C22×C4⋊C4—831no—
214C22×C42—831no—
215C22×C42—831no—
216C22×C42—831no—
217C2×C22⋊C8—832no—
218C2×C22⋊C8C2×D8312yes—
219C4×C4⋊C4—1662no—
220C4×C4⋊C4—1662no—
221C2×#95—831no—
222C2×#95C2×D8311yescharacteristic
223#336—1662no—
224#336—1662no—
225C23×C4—831no—
226C23×C4—831no—
227C23×C4—831no—
228C23×C4—831no—
229C23×C4C4×D8311yescharacteristic
230C23×C4C4×D8311yescharacteristic
231C23×C4C22×D8311yescharacteristic
232C22×C8—22no—
233C22×C8—1662no—
234C2×C4⋊C4—834no—
235C2×C4⋊C4—1662no—
236C2×C4⋊C4—1662no—
237C2×C4⋊C4—1662no—
238C2×C4⋊C4—1662no—
239C2×C4⋊C4—1662no—
240C2×C42—3322no—
241C2×C42—3322no—
242C2×C42—832no—
243C2×C42—832no—
244C2×C42—1661no—
245C2×C42—1661no—
246C2×C42—1661no—
247C2×C42—1661no—
248C2×C42—1661no—
249C2×C42—1662no—
250C2×C42—1661no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—1662no—
254C22⋊C8—1662no—
255#95—22no—
256#95—1662no—
257C24C2×C4×D8311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—3321no—
269C22×C4—3321no—
270C22×C4—3321no—
271C22×C4—3321no—
272C22×C4—832no—
273C22×C4—832no—
274C22×C4—832no—
275C22×C4—832no—
276C22×C4—831no—
277C22×C4—831no—
278C22×C4—832no—
279C22×C4—1661no—
280C22×C4—1661no—
281C22×C4—1661no—
282C22×C4—1661no—
283C22×C4—1662no—
284C22×C4—1662no—
285C22×C4—1661no—
286C22×C4—1661no—
287C22×C4—1661no—
288C22×C4—1661no—
289C22×C4—1661no—
290C22×C4—1661no—
291C22×C4C8×D8312yes—
292C22×C4#1305057312yes—
293C22×C4D4×D8312yes—
294C22×C4#1305058911yescharacteristic
295C22×C4#1305059012yes—
296C22×C4#1305059111yescharacteristic
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—3322no—
301C2×C8—3322no—
302C2×C8—3322no—
303C4⋊C4—1668no—
304C4⋊C4—1668no—
305C42—3322no—
306C42—3322no—
307C42—3322no—
308C42—3322no—
309C42—1662no—
310C42—1662no—
311C42—1662no—
312C42—1662no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23C22⋊C4×D8311yescharacteristic
318C23#1458174911yescharacteristic
319C23#1458175011yescharacteristic
320C23C2×C8×D8311yescharacteristic
321C23M16×D8311yescharacteristic
322C23M16×D8311yescharacteristic
323C23C2×#1305057311yescharacteristic
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—3322no—
340C2×C4—3322no—
341C2×C4—3321no—
342C2×C4—3321no—
343C2×C4—3321no—
344C2×C4—3321no—
345C2×C4—3322no—
346C2×C4—3322no—
347C2×C4—834no—
348C2×C4—832no—
349C2×C4—832no—
350C2×C4—1662no—
351C2×C4—1662no—
352C2×C4—1664no—
353C2×C4—1664no—
354C2×C4—1662no—
355C2×C4—1661no—
356C2×C4—1661no—
357C2×C4—1662no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4—1662no—
361C2×C4—1662no—
362C2×C4—1662no—
363C2×C4—1662no—
364C2×C4#1458177412yes—
365C2×C4#1458177712yes—
366C8—82no—
367C8—6642no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22#1912756311yescharacteristic
381C22C22⋊C8×D8311yescharacteristic
382C22#1912766311yescharacteristic
383C22#1912767311yescharacteristic
384C22#1912767311yescharacteristic
385C22#100×D8311yescharacteristic
386C22#101×D8311yescharacteristic
387C22#1912775211yescharacteristic
388C22#1912775311yescharacteristic
389C22#1912775611yescharacteristic
390C22#1912775711yescharacteristic
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—3322no—
396C4—3322no—
397C4—1664no—
398C4—1662no—
399C4—1662no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2490578211yescharacteristic
405C2#2490578511yescharacteristic
406C2#2490580211yescharacteristic
407C2#2490580511yescharacteristic
408C2#2490753011yescharacteristic
409C2#2490753911yescharacteristic
410C2#2490754211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC23×C83C22×C8
FrattiniC23×C4C22×D83
FittingC83×#1280C2
socleC23×C83C2×C22⋊C4
prime radicalC24×C83C22×C4
cosocleC23×C4×C83C23
hypercenter#1280D83
hypocenterC83#8701
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
29. C2×Dic83⋊C4C8semidirect
211. C83#8701semidirect

Maximal subgroups

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

subgroupindex
C2×#191275522
#249075292
#249053062
#249053052
C83×#12802
#870183