Finite Group Databasebeta

← #35307824

Subgroups — #35307824

Order 21248.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912459C211yesmaximal, characteristic
2#24908425C211yesmaximal, characteristic, complemented
3#24908227C211yesmaximal, characteristic, complemented
4#24907464C211yesmaximal, characteristic
5C2×#19127428C211yesmaximal, characteristic
6#24905302C211yesmaximal, characteristic, complemented
7C2×#332×C83C211yesmaximal, characteristic, complemented
8C2×#14581781—21no—
9C2×C4×D332C2211yescharacteristic
10C2×#14581724—21no—
11C2×#14581714—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127627—22no—
14#19127608—21no—
15#19127571C2211yescharacteristic
16#19127558—21no—
17#19127558—21no—
18C4×C4⋊Dic83C2211yescharacteristic
19#19127464—21no—
20#19127464—21no—
21#19127463—22no—
22#19127428—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4⋊C8×C83C2211yescharacteristic
26#332×C83—22no—
27C22×D332D411yescharacteristic
28C22×C4×D83—21no—
29C22×C83⋊C8—21no—
30#14581781—42no—
31#14581781—42no—
32C4×D332—21no—
33C4×D332—21no—
34C4×D332—21no—
35C4×D332—21no—
36C2×C4⋊Dic83—21no—
37C2×C4⋊Dic83—21no—
38C2×C4⋊Dic83—21no—
39C2×C4⋊Dic83D411yescharacteristic
40C2×C4⋊Dic83D411yescharacteristic
41C2×C4⋊Dic83D411yescharacteristic
42C2×(C2×D83)⋊C4—22no—
43C2×(C2×D83)⋊C4—22no—
44C2×(C2×D83)⋊C4—21no—
45C2×C4×Dic83—21no—
46#14581724—42no—
47#14581714—42no—
48C4×C83⋊C8—21no—
49C4×C83⋊C8—21no—
50C83⋊#95—22no—
51C83⋊#95—22no—
52C83⋊#95—21no—
53C22×Q8×C83—21no—
54C22×C8×C83—21no—
55C22×C8×C83—21no—
56C4⋊Q8×C83—21no—
57C4⋊Q8×C83—21no—
58C4⋊Q8×C83—21no—
59C4⋊Q8×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C4⋊C4×C83D412yes—
62C2×C42×C83C2311yescharacteristic
63C4⋊C8×C83—21no—
64C4⋊C8×C83—21no—
65C4⋊C8×C83—21no—
66C4⋊C8×C83D412yes—
67C23×D83—21no—
68C2×D332—21no—
69C2×D332—21no—
70C2×D332—21no—
71C2×D332—21no—
72C2×D332—21no—
73C2×D332SD1612yes—
74C22×Dic83—21no—
75C22×Dic83—21no—
76C22×Dic83—21no—
77C22×Dic83—41no—
78C2×C4×D83—41no—
79C2×C4×D83—41no—
80C2×C4×D83—41no—
81C2×C4×D83—41no—
82C2×C4×D83—41no—
83C2×C4×D83—41no—
84C2×C83⋊C8—22no—
85C2×C83⋊C8—41no—
86C2×C83⋊C8—41no—
87C4⋊Dic83—21no—
88C4⋊Dic83—21no—
89C4⋊Dic83—21no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83—21no—
93C4⋊Dic83—42no—
94C4⋊Dic83—41no—
95C4⋊Dic83—41no—
96C4⋊Dic83—41no—
97C4⋊Dic83—41no—
98(C2×D83)⋊C4—44no—
99(C2×D83)⋊C4—44no—
100(C2×D83)⋊C4—41no—
101(C2×D83)⋊C4—41no—
102C4×Dic83—41no—
103C4×Dic83—41no—
104C2×Q8×C83—41no—
105C2×Q8×C83—41no—
106C2×Q8×C83—41no—
107C2×Q8×C83—41no—
108C2×Q8×C83—41no—
109C2×Q8×C83—41no—
110C22×C4×C83—22no—
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83C2×D411yescharacteristic
113C22×C4×C83C2×D411yescharacteristic
114C2×C8×C83—22no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C2×C8×C83—41no—
118C2×C8×C83—41no—
119C2×C8×C83—41no—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—22no—
122C4⋊C4×C83—41no—
123C4⋊C4×C83—41no—
124C42×C83C2×D411yescharacteristic
125C42×C83#4111yescharacteristic
126C42×C83#4111yescharacteristic
127C42×C83#4111yescharacteristic
128C23×C83#12011yescharacteristic
129C22×D83—22no—
130C22×D83—41no—
131C22×D83—41no—
132C22×D83—41no—
133C22×D83—41no—
134C22×D83—41no—
135C22×D83—41no—
136Q8×C83—81no—
137Q8×C83—81no—
138Q8×C83—81no—
139Q8×C83—81no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—42no—
143C2×C4×C83—42no—
144C2×C4×C83—42no—
145C2×C4×C83#12111yescharacteristic
146C2×C4×C83#12111yescharacteristic
147C2×C4×C83#12111yescharacteristic
148C2×C4×C83#12311yescharacteristic
149C2×C4×C83#12311yescharacteristic
150C2×C4×C83#12411yescharacteristic
151C2×C4×C83C2×SD1611yescharacteristic
152C2×C4×C83#13511yescharacteristic
153C2×C4×C83#13511yescharacteristic
154C2×C4×C83#13511yescharacteristic
155C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C83#13711yescharacteristic
159C2×Dic83—41no—
160C2×Dic83—41no—
161C2×Dic83—41no—
162C2×Dic83—41no—
163C2×Dic83—41no—
164C2×Dic83—41no—
165C2×Dic83—41no—
166C2×Dic83—41no—
167C2×Dic83—41no—
168C2×Dic83—81no—
169C2×Dic83—81no—
170C2×Dic83—81no—
171D332—22no—
172D332—22no—
173D332—41no—
174D332—41no—
175C4×D83—81no—
176C4×D83—81no—
177C4×D83—81no—
178C4×D83—81no—
179C8×C83—42no—
180C8×C83—81no—
181C83⋊C8—42no—
182C22×C83#39411yescharacteristic
183C22×C83#44911yescharacteristic
184C22×C83#44911yescharacteristic
185C22×C83#45011yescharacteristic
186C22×C83#45211yescharacteristic
187C22×C83#45411yescharacteristic
188C22×C83#45611yescharacteristic
189C2×D83—42no—
190C2×D83—42no—
191C2×D83—42no—
192C2×D83—81no—
193C2×D83—81no—
194C2×D83—81no—
195C2×D83—81no—
196C4×C83—21no—
197C4×C83—21no—
198C4×C83—82no—
199C4×C83#46311yescharacteristic
200C4×C83#46411yescharacteristic
201C4×C83#46511yescharacteristic
202C4×C83#46911yescharacteristic
203C4×C83#48111yescharacteristic
204C4×C83#48211yescharacteristic
205C4×C83#48811yescharacteristic
206C4×C83#48911yescharacteristic
207Dic83—81no—
208Dic83—81no—
209Dic83—81no—
210Dic83—161no—
211#10417—831nomaximal, Sylow
212C2×C83#162811yescharacteristic
213C2×C83#163511yescharacteristic
214C2×C83#165011yescharacteristic
215C2×C83#165411yescharacteristic
216C2×C83#203411yescharacteristic
217C2×C83#203811yescharacteristic
218C2×C83#204211yescharacteristic
219D83—82no—
220#2547—831no—
221#1990—831no—
222#1948—831no—
223#1802—831no—
224C2×#332D8311yescharacteristic, complemented
225C2×D4⋊C8—831no—
226#1279—831no—
227C83#1041711yescharacteristic, complemented, Sylow
228C2×C4⋊Q8C2×D8311yescharacteristic
229C2×#124—1661no—
230C2×C4×D4—831no—
231C2×#106—1661no—
232C2×C4⋊C8C2×D8311yescharacteristic
233C2×C4⋊C8C2×D8311yescharacteristic
234C2×#102—1661no—
235C2×C4×C8—831no—
236#397—1662no—
237#391—1661no—
238#384—831no—
239#380—1661no—
240#380—1661no—
241C4×C4⋊C4—831no—
242#340—1661no—
243#340—1661no—
244#340—1662no—
245#332—22no—
246D4⋊C8—1662no—
247C22×Q8—21no—
248C22×D4—831no—
249C23×C4—1661no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—1661no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257#124—3322no—
258#124—3322no—
259C4×D4—1661no—
260C4×D4—1661no—
261C4×D4—1661no—
262C4×D4—1661no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—831no—
265C2×C4⋊C4—831no—
266C2×C4⋊C4—831no—
267C2×C4⋊C4—1661no—
268C2×C4⋊C4—1661no—
269C2×C4⋊C4—1661no—
270C2×C4⋊C4D33212yes—
271C2×C22⋊C4—1662no—
272C2×C22⋊C4—1662no—
273C2×C22⋊C4—1661no—
274C2×C42—1661no—
275C2×C42C22×D8311yescharacteristic
276#106—3322no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8C22⋊D8312yes—
281#102—3322no—
282C4×C8—1661no—
283C4×C8—1661no—
284#95—1662no—
285#95—1662no—
286#95—1661no—
287C24—1661no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—832no—
295C2×D4—1661no—
296C2×D4—1661no—
297C2×D4—1661no—
298C2×D4—1661no—
299C2×D4—1661no—
300C22×C4—22no—
301C22×C4—3321no—
302C22×C4—3321no—
303C22×C4—3321no—
304C22×C4—3321no—
305C22×C4—3321no—
306C22×C4—3321no—
307C22×C4—3321no—
308C22×C4—1661no—
309C22×C4—1661no—
310C22×C4—1661no—
311C22×C4D4×D8311yescharacteristic
312C22×C4D4×D8311yescharacteristic
313C22×C4C2×D33211yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—3321no—
321C2×C8—3321no—
322C2×C8—1662no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—3322no—
328C4⋊C4—3321no—
329C4⋊C4—3321no—
330C4⋊C4—3321no—
331C4⋊C4—3321no—
332C4⋊C4—1661no—
333C4⋊C4—1661no—
334C4⋊C4—1661no—
335C4⋊C4—1661no—
336C4⋊C4—1661no—
337C4⋊C4—1661no—
338C22⋊C4—3324no—
339C22⋊C4—3324no—
340C22⋊C4—3321no—
341C22⋊C4—3321no—
342C42—3321no—
343C42—3321no—
344C42C2×C22⋊D8311yescharacteristic
345C42#1305058911yescharacteristic
346C42#1305058911yescharacteristic
347C42#1305059011yescharacteristic
348C23—3321no—
349C23—3321no—
350C23—3321no—
351C23—3321no—
352C23—3321no—
353C23—3321no—
354C23—1662no—
355C23#1458176211yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—3321no—
361D4—3321no—
362D4—1662no—
363D4—1662no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—3321no—
370C2×C4—3321no—
371C2×C4—3321no—
372C2×C4—3321no—
373C2×C4—3321no—
374C2×C4—3321no—
375C2×C4—3321no—
376C2×C4—3321no—
377C2×C4—3321no—
378C2×C4—6641no—
379C2×C4—6641no—
380C2×C4—6641no—
381C2×C4—6641no—
382C2×C4—6641no—
383C2×C4—6641no—
384C2×C4—6641no—
385C2×C4#1458176311yescharacteristic
386C2×C4#1458176411yescharacteristic
387C2×C4#1458176611yescharacteristic
388C2×C4#1458177411yescharacteristic
389C2×C4#1458177611yescharacteristic
390C2×C4#1458177811yescharacteristic
391C2×C4SD16×D8311yescharacteristic
392C2×C4#1458181311yescharacteristic
393C2×C4#1458181311yescharacteristic
394C2×C4#1458181511yescharacteristic
395C2×C4#1458181611yescharacteristic
396C2×C4#1458181611yescharacteristic
397C2×C4#1458181911yescharacteristic
398C2×C4#1458182411yescharacteristic
399C8—42no—
400C8—81no—
401C8—3322no—
402C22—3322no—
403C22—3322no—
404C22—3322no—
405C22—6641no—
406C22—6641no—
407C22—6641no—
408C22—6641no—
409C22#1912761711yescharacteristic
410C22#1912784711yescharacteristic
411C22#1912784911yescharacteristic
412C22#1912785311yescharacteristic
413C22#1912786611yescharacteristic
414C22#1912787611yescharacteristic
415C22#1912788611yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—13281no—
420C4—6641no—
421C4—6641no—
422C4—6641no—
423C4#1912791811yescharacteristic
424C4#1912792511yescharacteristic
425C4#1912792711yescharacteristic
426C4#1912795111yescharacteristic
427C4#1912801811yescharacteristic
428C4#1912802411yescharacteristic
429C4#1912805711yescharacteristic
430C4#1912806211yescharacteristic
431C2—6642no—
432C2#2490657411yescharacteristic
433C2#2490661511yescharacteristic
434C2#2490672011yescharacteristic
435C2#2490674811yescharacteristic
436C2#2490865111yescharacteristic
437C2#2490868111yescharacteristic
438C2#2490870111yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#332×C83C2
socleC23×C83#120
prime radicalC22×D332D4
hypercenterC2×#332D83
hypocenterC83#10417
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #24908425C2semidirect
3. #24908227C2semidirect
6. #24905302C2semidirect
7. C2×#332×C83C2semidirect
224. C2×#332D83semidirect
227. C83#10417semidirect

Maximal subgroups

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

subgroupindex
#249124592
#249084252
#249082272
#249074642
C2×#191274282
#249053022
C2×#332×C832
#1041783