Finite Group Databasebeta

← #35307789

Subgroups — #35307789

Order 21248.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912637C211yesmaximal, characteristic
2#24908266C211yesmaximal, characteristic, complemented
3#24908227C211yesmaximal, characteristic, complemented
4#24907464C211yesmaximal, characteristic
5C2×#19127428C211yesmaximal, characteristic
6#24905302C211yesmaximal, characteristic, complemented
7C2×#333×C83C211yesmaximal, characteristic, complemented
8C2×C4×D332C2211yescharacteristic
9C2×#14581724—21no—
10C2×#14581716—22no—
11C2×#14581714—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127612—22no—
14#19127602—21no—
15#19127571C2211yescharacteristic
16#19127566—21no—
17#19127558—21no—
18#19127558—21no—
19C4×C4⋊Dic83C2211yescharacteristic
20#19127464—21no—
21#19127464—21no—
22#19127428—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4⋊C8×C83C2211yescharacteristic
26#333×C83—22no—
27C22×D332D411yescharacteristic
28C22×C4×D83—21no—
29C22×C83⋊C8—21no—
30C4×D332—21no—
31C4×D332—21no—
32C4×D332—21no—
33C4×D332—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83—21no—
36C2×C4⋊Dic83—21no—
37C2×C4⋊Dic83D411yescharacteristic
38C2×C4⋊Dic83D411yescharacteristic
39C2×C4⋊Dic83D411yescharacteristic
40C2×(C2×D83)⋊C4—22no—
41C2×(C2×D83)⋊C4—22no—
42C2×(C2×D83)⋊C4—21no—
43C2×C4×Dic83—21no—
44#14581724—42no—
45#14581716—44no—
46#14581714—42no—
47C4×C83⋊C8—21no—
48C4×C83⋊C8—21no—
49C83⋊#95—22no—
50C83⋊#95—22no—
51C83⋊#95—21no—
52C22×Q8×C83D412yes—
53C22×C8×C83—21no—
54C22×C8×C83—21no—
55C4⋊Q8×C83—21no—
56C4⋊Q8×C83—21no—
57C4⋊Q8×C83—21no—
58C4⋊Q8×C83—21no—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C42×C83C2311yescharacteristic
62C4⋊C8×C83—21no—
63C4⋊C8×C83—21no—
64C4⋊C8×C83—21no—
65C4⋊C8×C83D412yes—
66C23×D83—21no—
67C2×D332—21no—
68C2×D332—21no—
69C2×D332—21no—
70C2×D332—21no—
71C2×D332—21no—
72C2×D332SD1612yes—
73C22×Dic83—21no—
74C22×Dic83—21no—
75C22×Dic83—21no—
76C22×Dic83—41no—
77C2×C4×D83—41no—
78C2×C4×D83—41no—
79C2×C4×D83—41no—
80C2×C4×D83—41no—
81C2×C4×D83—41no—
82C2×C4×D83—41no—
83C2×C83⋊C8—22no—
84C2×C83⋊C8—41no—
85C2×C83⋊C8—41no—
86C4⋊Dic83—21no—
87C4⋊Dic83—21no—
88C4⋊Dic83—21no—
89C4⋊Dic83—21no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83—42no—
93C4⋊Dic83—41no—
94C4⋊Dic83—41no—
95C4⋊Dic83—41no—
96C4⋊Dic83—41no—
97(C2×D83)⋊C4—41no—
98(C2×D83)⋊C4—41no—
99(C2×D83)⋊C4—82no—
100(C2×D83)⋊C4—82no—
101C4×Dic83—41no—
102C4×Dic83—41no—
103C2×Q8×C83—22no—
104C2×Q8×C83—22no—
105C2×Q8×C83—42no—
106C2×Q8×C83—42no—
107C22×C4×C83—22no—
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110C22×C4×C83C2×D411yescharacteristic
111C2×C8×C83—22no—
112C2×C8×C83—41no—
113C2×C8×C83—41no—
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C4⋊C4×C83—41no—
118C4⋊C4×C83—41no—
119C4⋊C4×C83—41no—
120C4⋊C4×C83—41no—
121C42×C83C2×D411yescharacteristic
122C42×C83#4111yescharacteristic
123C42×C83#4111yescharacteristic
124C42×C83#4111yescharacteristic
125C23×C83#12011yescharacteristic
126C22×D83—22no—
127C22×D83—41no—
128C22×D83—41no—
129C22×D83—41no—
130C22×D83—41no—
131C22×D83—41no—
132C22×D83—41no—
133Q8×C83—44no—
134Q8×C83—82no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—42no—
138C2×C4×C83—42no—
139C2×C4×C83—42no—
140C2×C4×C83#12111yescharacteristic
141C2×C4×C83#12111yescharacteristic
142C2×C4×C83#12111yescharacteristic
143C2×C4×C83#12311yescharacteristic
144C2×C4×C83#12311yescharacteristic
145C2×C4×C83#12411yescharacteristic
146C2×C4×C83C2×SD1611yescharacteristic
147C2×C4×C83#13511yescharacteristic
148C2×C4×C83#13511yescharacteristic
149C2×C4×C83#13511yescharacteristic
150C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C83#13711yescharacteristic
152C2×C4×C83#13711yescharacteristic
153C2×C4×C83#13711yescharacteristic
154C2×Dic83—41no—
155C2×Dic83—41no—
156C2×Dic83—41no—
157C2×Dic83—41no—
158C2×Dic83—41no—
159C2×Dic83—41no—
160C2×Dic83—41no—
161C2×Dic83—41no—
162C2×Dic83—41no—
163C2×Dic83—81no—
164C2×Dic83—81no—
165C2×Dic83—81no—
166D332—22no—
167D332—22no—
168D332—41no—
169D332—41no—
170C4×D83—81no—
171C4×D83—81no—
172C4×D83—81no—
173C4×D83—81no—
174C8×C83—42no—
175C8×C83—81no—
176C83⋊C8—42no—
177C22×C83#39411yescharacteristic
178C22×C83#44811yescharacteristic
179C22×C83#44911yescharacteristic
180C22×C83#45211yescharacteristic
181C22×C83#45211yescharacteristic
182C22×C83#45311yescharacteristic
183C22×C83#45511yescharacteristic
184C2×D83—42no—
185C2×D83—42no—
186C2×D83—42no—
187C2×D83—81no—
188C2×D83—81no—
189C2×D83—81no—
190C2×D83—81no—
191C4×C83—21no—
192C4×C83—21no—
193C4×C83—82no—
194C4×C83#46311yescharacteristic
195C4×C83#46411yescharacteristic
196C4×C83#46511yescharacteristic
197C4×C83#47011yescharacteristic
198C4×C83#48311yescharacteristic
199C4×C83#48511yescharacteristic
200C4×C83#48811yescharacteristic
201C4×C83#48911yescharacteristic
202Dic83—81no—
203Dic83—81no—
204Dic83—81no—
205Dic83—161no—
206#10412—831nomaximal, Sylow
207C2×C83#162211yescharacteristic
208C2×C83#163411yescharacteristic
209C2×C83#164311yescharacteristic
210C2×C83#164611yescharacteristic
211C2×C83#203511yescharacteristic
212C2×C83#203711yescharacteristic
213C2×C83#204211yescharacteristic
214D83—82no—
215#2563—831no—
216#1956—831no—
217#1948—831no—
218#1802—831no—
219C2×#333D8311yescharacteristic, complemented
220C2×D4⋊C8—831no—
221#1279—831no—
222C83#1041211yescharacteristic, complemented, Sylow
223C2×C4⋊Q8C2×D8311yescharacteristic
224C2×C4×D4—831no—
225C2×#106—1661no—
226C2×C4⋊C8C2×D8311yescharacteristic
227C2×C4⋊C8C2×D8311yescharacteristic
228C2×#103—1662no—
229C2×#102—1661no—
230C2×C4×C8—831no—
231#393—1662no—
232#390—1661no—
233#384—831no—
234#382—1661no—
235#380—1661no—
236#380—1661no—
237C4×C4⋊C4—831no—
238#340—1661no—
239#340—1661no—
240#333—22no—
241D4⋊C8—1662no—
242C22×Q8D33212yes—
243C22×D4—831no—
244C23×C4—1661no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—1661no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4×D4—1661no—
253C4×D4—1661no—
254C4×D4—1661no—
255C4×D4—1661no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—831no—
259C2×C4⋊C4—831no—
260C2×C4⋊C4—831no—
261C2×C4⋊C4—1661no—
262C2×C4⋊C4—1661no—
263C2×C4⋊C4—1661no—
264C2×C22⋊C4—1661no—
265C2×C22⋊C4—1662no—
266C2×C22⋊C4—1662no—
267C2×C42—1661no—
268C2×C42C22×D8311yescharacteristic
269#106—3322no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8C22⋊D8312yes—
274#103—3324no—
275#102—3322no—
276C4×C8—1661no—
277C4×C8—1661no—
278#95—1662no—
279#95—1662no—
280#95—1661no—
281C24—1661no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—832no—
287C2×D4—1661no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4—1661no—
291C2×D4—1661no—
292C22×C4—22no—
293C22×C4—3321no—
294C22×C4—3321no—
295C22×C4—3321no—
296C22×C4—3321no—
297C22×C4—3321no—
298C22×C4—3321no—
299C22×C4—3321no—
300C22×C4—1661no—
301C22×C4—1661no—
302C22×C4—1661no—
303C22×C4D4×D8311yescharacteristic
304C22×C4D4×D8311yescharacteristic
305C22×C4C2×D33211yescharacteristic
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—3321no—
313C2×C8—3321no—
314C2×C8—1662no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—3322no—
320C4⋊C4—3321no—
321C4⋊C4—3321no—
322C4⋊C4—3321no—
323C4⋊C4—3321no—
324C4⋊C4—1661no—
325C4⋊C4—1661no—
326C4⋊C4—1661no—
327C4⋊C4—1661no—
328C4⋊C4—1661no—
329C4⋊C4—1661no—
330C22⋊C4—3321no—
331C22⋊C4—3321no—
332C22⋊C4—6642no—
333C22⋊C4—6642no—
334C42—3321no—
335C42—3321no—
336C42C2×C22⋊D8311yescharacteristic
337C42#1305058911yescharacteristic
338C42#1305058911yescharacteristic
339C42#1305059011yescharacteristic
340C23—3321no—
341C23—3321no—
342C23—3321no—
343C23—3321no—
344C23—3321no—
345C23—3321no—
346C23—1662no—
347C23#1458176211yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—3321no—
351D4—3321no—
352D4—1662no—
353D4—1662no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—3321no—
360C2×C4—3321no—
361C2×C4—3321no—
362C2×C4—3321no—
363C2×C4—3321no—
364C2×C4—3321no—
365C2×C4—3321no—
366C2×C4—3321no—
367C2×C4—3321no—
368C2×C4—6641no—
369C2×C4—6641no—
370C2×C4—6641no—
371C2×C4—6641no—
372C2×C4—6641no—
373C2×C4—6641no—
374C2×C4—6641no—
375C2×C4#1458176311yescharacteristic
376C2×C4#1458176411yescharacteristic
377C2×C4#1458176611yescharacteristic
378C2×C4#1458177411yescharacteristic
379C2×C4#1458177611yescharacteristic
380C2×C4#1458177811yescharacteristic
381C2×C4SD16×D8311yescharacteristic
382C2×C4#1458181311yescharacteristic
383C2×C4#1458181311yescharacteristic
384C2×C4#1458181511yescharacteristic
385C2×C4#1458181911yescharacteristic
386C2×C4#1458182411yescharacteristic
387C2×C4#1458182411yescharacteristic
388C2×C4#1458182411yescharacteristic
389C8—42no—
390C8—81no—
391C8—3322no—
392C22—3322no—
393C22—3322no—
394C22—3322no—
395C22—6641no—
396C22—6641no—
397C22—6641no—
398C22—6641no—
399C22#1912761711yescharacteristic
400C22#1912784111yescharacteristic
401C22#1912784911yescharacteristic
402C22#1912786611yescharacteristic
403C22#1912786611yescharacteristic
404C22#1912787111yescharacteristic
405C22#1912788111yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—13281no—
410C4—6641no—
411C4—6641no—
412C4—6641no—
413C4#1912791811yescharacteristic
414C4#1912792511yescharacteristic
415C4#1912792711yescharacteristic
416C4#1912795611yescharacteristic
417C4#1912803011yescharacteristic
418C4#1912804011yescharacteristic
419C4#1912805711yescharacteristic
420C4#1912806211yescharacteristic
421C2—6642no—
422C2#2490653611yescharacteristic
423C2#2490660911yescharacteristic
424C2#2490667111yescharacteristic
425C2#2490669211yescharacteristic
426C2#2490865811yescharacteristic
427C2#2490867411yescharacteristic
428C2#2490870111yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#333×C83C2
socleC23×C83#120
prime radicalC22×D332D4
hypercenterC2×#333D83
hypocenterC83#10412
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. #24908266C2semidirect
3. #24908227C2semidirect
6. #24905302C2semidirect
7. C2×#333×C83C2semidirect
219. C2×#333D83semidirect
222. C83#10412semidirect

Maximal subgroups

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

subgroupindex
#249126372
#249082662
#249082272
#249074642
C2×#191274282
#249053022
C2×#333×C832
#1041283