Finite Group Databasebeta

← #35308287

Subgroups — #35308287

Order 21248.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127982C211yesmaximal, characteristic
2#24908265C211yesmaximal, characteristic, complemented
3#24908257C211yesmaximal, characteristic
4#24907464C211yesmaximal, characteristic
5C2×#19127446C211yesmaximal, characteristic, complemented
6#24905347C211yesmaximal, characteristic, complemented
7C2×#335×C83C211yesmaximal, characteristic, complemented
8C2×#14581792C2211yescharacteristic
9C2×C4×D332C2211yescharacteristic
10#19127982—22no—
11#19127982—22no—
12C2×#14581726—21no—
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×#14581717—21no—
15C2×#14581717—21no—
16C2×#14581714—21no—
17C2×#14581714—21no—
18C2×(C2×D83)⋊C8—21no—
19C2×(C2×D83)⋊C8—21no—
20#19127571C2211yescharacteristic
21#19127464—21no—
22#19127446—22no—
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4×C8×C83C2211yescharacteristic
26#335×C83—22no—
27C22×Dic166—21no—
28C22×D332D411yescharacteristic
29C22×C4×D83—21no—
30C22×C83⋊C8—21no—
31#14581792—21no—
32#14581792—21no—
33#14581792—21no—
34#14581792D412yes—
35C4×D332—21no—
36C4×D332—21no—
37C4×D332—21no—
38C4×D332—21no—
39C2×C4⋊Dic83—21no—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83D411yescharacteristic
45C2×(C2×D83)⋊C4—21no—
46#14581726—24no—
47C4⋊(C83⋊C8)—21no—
48C4⋊(C83⋊C8)—21no—
49#14581717—42no—
50#14581717—42no—
51#14581714—24no—
52#14581714—42no—
53(C2×D83)⋊C8—42no—
54(C2×D83)⋊C8—42no—
55C22×C8×C83—21no—
56C22×C8×C83—21no—
57C22×C8×C83D411yescharacteristic
58C22×C8×C83D411yescharacteristic
59C2×C42×C83C2311yescharacteristic
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83D412yes—
64C4×C8×C83—21no—
65C4×C8×C83—21no—
66C23×D83—21no—
67C2×Dic166—22no—
68C2×Dic166—41no—
69C2×Dic166—41no—
70C2×Dic166—41no—
71C2×Dic166—41no—
72C2×Dic166—41no—
73C2×D332—21no—
74C2×D332—21no—
75C2×D332—21no—
76C2×D332—21no—
77C2×D332—21no—
78C2×D332Q1612yes—
79C22×Dic83—21no—
80C22×Dic83—41no—
81C22×Dic83—41no—
82C2×C4×D83—41no—
83C2×C4×D83—41no—
84C2×C4×D83—41no—
85C2×C4×D83—41no—
86C2×C4×D83—41no—
87C2×C4×D83—41no—
88C2×C83⋊C8—41no—
89C2×C83⋊C8—41no—
90C2×C83⋊C8—41no—
91C4⋊Dic83—22no—
92C4⋊Dic83—21no—
93C4⋊Dic83—22no—
94C4⋊Dic83—21no—
95C4⋊Dic83—41no—
96C4⋊Dic83—41no—
97C4⋊Dic83—41no—
98C4⋊Dic83—41no—
99C4⋊Dic83—41no—
100C4⋊Dic83—41no—
101C4⋊Dic83—81no—
102(C2×D83)⋊C4—41no—
103(C2×D83)⋊C4—41no—
104C22×C4×C83C2×D411yescharacteristic
105C22×C4×C83C2×D411yescharacteristic
106C22×C4×C83#4111yescharacteristic
107C2×C8×C83—21no—
108C2×C8×C83—21no—
109C2×C8×C83—22no—
110C2×C8×C83—21no—
111C2×C8×C83—21no—
112C2×C8×C83—21no—
113C2×C8×C83—41no—
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C2×C8×C83—41no—
118C2×C8×C83D812yes—
119C42×C83C2×D411yescharacteristic
120C42×C83C2×D411yescharacteristic
121C42×C83#4111yescharacteristic
122C42×C83#4111yescharacteristic
123C23×C83#12111yescharacteristic
124C22×D83—22no—
125C22×D83—41no—
126C22×D83—41no—
127C22×D83—41no—
128C22×D83—41no—
129C22×D83—41no—
130C22×D83—41no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83#12011yescharacteristic
134C2×C4×C83#12111yescharacteristic
135C2×C4×C83#12111yescharacteristic
136C2×C4×C83#12311yescharacteristic
137C2×C4×C83#12311yescharacteristic
138C2×C4×C83#12411yescharacteristic
139C2×C4×C83C2×D811yescharacteristic
140C2×C4×C83C2×Q1611yescharacteristic
141C2×C4×C83#13511yescharacteristic
142C2×C4×C83#13511yescharacteristic
143C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C83#13711yescharacteristic
147C2×Dic83—41no—
148C2×Dic83—42no—
149C2×Dic83—41no—
150C2×Dic83—41no—
151C2×Dic83—81no—
152C2×Dic83—81no—
153C2×Dic83—81no—
154C2×Dic83—81no—
155C2×Dic83—81no—
156D332—22no—
157D332—22no—
158D332—41no—
159D332—41no—
160C4×D83—81no—
161C4×D83—81no—
162C4×D83—81no—
163C4×D83—81no—
164Dic166—42no—
165Dic166—42no—
166Dic166—81no—
167Dic166—81no—
168C8×C83—22no—
169C8×C83—42no—
170C8×C83—41no—
171C8×C83—81no—
172C83⋊C8—81no—
173C22×C83#39411yescharacteristic
174C22×C83#45911yescharacteristic
175C22×C83#46311yescharacteristic
176C22×C83#46711yescharacteristic
177C22×C83#46811yescharacteristic
178C22×C83#47111yescharacteristic
179C22×C83#47311yescharacteristic
180C2×D83—42no—
181C2×D83—42no—
182C2×D83—42no—
183C2×D83—81no—
184C2×D83—81no—
185C2×D83—81no—
186C2×D83—81no—
187C4×C83—21no—
188C4×C83—21no—
189C4×C83#44911yescharacteristic
190C4×C83#45111yescharacteristic
191C4×C83#45911yescharacteristic
192C4×C83#46311yescharacteristic
193C4×C83#46611yescharacteristic
194C4×C83#46911yescharacteristic
195C4×C83#48411yescharacteristic
196C4×C83#48511yescharacteristic
197Dic83—82no—
198Dic83—81no—
199Dic83—161no—
200#10485—831nomaximal, Sylow
201C2×C83#166911yescharacteristic
202C2×C83#168311yescharacteristic
203C2×C83#168511yescharacteristic
204C2×C83#169911yescharacteristic
205C2×C83#203611yescharacteristic
206C2×C83#205211yescharacteristic
207C2×C83#205411yescharacteristic
208D83—82no—
209C2×#474—831no—
210#1956—831no—
211#1954—831no—
212#1802—831no—
213C2×#335D8311yescharacteristic, complemented
214C2×#332—831no—
215#1296—831no—
216C83#1048511yescharacteristic, complemented, Sylow
217C2×C4⋊Q8—831no—
218C2×C4×D4—831no—
219#474—1662no—
220#474—1662no—
221C2×#107—1661no—
222C2×C4⋊C8—831no—
223C2×C4⋊C8C2×D8311yescharacteristic
224C2×C4⋊C8C2×D8311yescharacteristic
225C2×#103—1661no—
226C2×#103—1661no—
227C2×#102—1661no—
228C2×#102—1661no—
229C2×C22⋊C8—1661no—
230C2×C22⋊C8—1661no—
231C2×C4×C8C2×D8311yescharacteristic
232#384—831no—
233#340—1661no—
234#335—22no—
235#332—1662no—
236C22×Q8—1661no—
237C22×D4—831no—
238C23×C4—1661no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—1661no—
242C22×C8D33211yescharacteristic
243C22×C8D33211yescharacteristic
244C4⋊Q8—832no—
245C4⋊Q8—1661no—
246C4⋊Q8—1661no—
247C4⋊Q8—1661no—
248C4×D4—1661no—
249C4×D4—1661no—
250C4×D4—1661no—
251C4×D4—1661no—
252C2×C4⋊C4—831no—
253C2×C4⋊C4—1661no—
254C2×C4⋊C4—1661no—
255C2×C4⋊C4—1661no—
256C2×C4⋊C4—1661no—
257C2×C4⋊C4—1661no—
258C2×C22⋊C4—1661no—
259C2×C42C22×D8311yescharacteristic
260#107—1664no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—1661no—
265C4⋊C8—1661no—
266C4⋊C8C22⋊D8312yes—
267#103—3322no—
268#103—3322no—
269#102—3322no—
270#102—1664no—
271C22⋊C8—3322no—
272C22⋊C8—3322no—
273C4×C8—21no—
274C4×C8—21no—
275C24—1661no—
276C2×Q8—3321no—
277C2×Q8—3321no—
278C2×Q8—3321no—
279C2×Q8—3321no—
280C2×Q8—3321no—
281C2×Q8—1662no—
282C2×D4—832no—
283C2×D4—1661no—
284C2×D4—1661no—
285C2×D4—1661no—
286C2×D4—1661no—
287C2×D4—1661no—
288C22×C4—3321no—
289C22×C4—3321no—
290C22×C4—3321no—
291C22×C4—3321no—
292C22×C4—3321no—
293C22×C4—3321no—
294C22×C4—3321no—
295C22×C4—3321no—
296C22×C4—1661no—
297C22×C4D4×D8311yescharacteristic
298C22×C4C2×D33211yescharacteristic
299C22×C4#1305059111yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—3321no—
312C2×C8—3321no—
313C2×C8—3321no—
314C2×C8D66412yes—
315C4⋊C4—3321no—
316C4⋊C4—3321no—
317C4⋊C4—3321no—
318C4⋊C4—3321no—
319C4⋊C4—3321no—
320C4⋊C4—3321no—
321C4⋊C4—6641no—
322C4⋊C4—1662no—
323C4⋊C4—1661no—
324C4⋊C4—1661no—
325C4⋊C4—1662no—
326C22⋊C4—3321no—
327C22⋊C4—3321no—
328C42D4×D8311yescharacteristic
329C42C2×C22⋊D8311yescharacteristic
330C42#1305059011yescharacteristic
331C42#1305059111yescharacteristic
332C23—3321no—
333C23—3321no—
334C23—3321no—
335C23—3321no—
336C23—3321no—
337C23—3321no—
338C23—1662no—
339C23#1458176711yescharacteristic
340Q8—3322no—
341Q8—3322no—
342Q8—6641no—
343Q8—6641no—
344D4—3321no—
345D4—3321no—
346D4—1662no—
347D4—1662no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—3321no—
351C2×C4—3322no—
352C2×C4—3321no—
353C2×C4—3321no—
354C2×C4—6641no—
355C2×C4—6641no—
356C2×C4—6641no—
357C2×C4—6641no—
358C2×C4—6641no—
359C2×C4—6641no—
360C2×C4—6641no—
361C2×C4—6641no—
362C2×C4—6641no—
363C2×C4#1458176011yescharacteristic
364C2×C4#1458176611yescharacteristic
365C2×C4#1458176711yescharacteristic
366C2×C4#1458177711yescharacteristic
367C2×C4#1458177711yescharacteristic
368C2×C4#1458178111yescharacteristic
369C2×C4C2×D66411yescharacteristic
370C2×C4Q16×D8311yescharacteristic
371C2×C4#1458181111yescharacteristic
372C2×C4#1458181411yescharacteristic
373C2×C4#1458181611yescharacteristic
374C2×C4#1458182011yescharacteristic
375C2×C4#1458182011yescharacteristic
376C2×C4#1458182411yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—81no—
381C8—6641no—
382C22—3322no—
383C22—3322no—
384C22—3322no—
385C22—6641no—
386C22—6641no—
387C22—6641no—
388C22—6641no—
389C22#1912761811yescharacteristic
390C22#1912789711yescharacteristic
391C22#1912791711yescharacteristic
392C22#1912794311yescharacteristic
393C22#1912794811yescharacteristic
394C22#1912796511yescharacteristic
395C22#1912797711yescharacteristic
396C4—21no—
397C4—21no—
398C4—13281no—
399C4—6641no—
400C4—6642no—
401C4#1912784311yescharacteristic
402C4#1912785511yescharacteristic
403C4#1912789711yescharacteristic
404C4#1912791711yescharacteristic
405C4#1912793711yescharacteristic
406C4#1912795411yescharacteristic
407C4#1912803811yescharacteristic
408C4#1912804411yescharacteristic
409C2—6642no—
410C2#2490682911yescharacteristic
411C2#2490691511yescharacteristic
412C2#2490692911yescharacteristic
413C2#2490701111yescharacteristic
414C2#2490866811yescharacteristic
415C2#2490876411yescharacteristic
416C2#2490877411yescharacteristic
subgroupG/H
centerC23#14581767
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#335×C83C2
socleC23×C83#121
prime radicalC22×D332D4
hypercenterC2×#335D83
hypocenterC83#10485
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #24908265C2semidirect
5. C2×#19127446C2semidirect
6. #24905347C2semidirect
7. C2×#335×C83C2semidirect
213. C2×#335D83semidirect
216. C83#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#191279822
#249082652
#249082572
#249074642
C2×#191274462
#249053472
C2×#335×C832
#1048583