Finite Group Databasebeta

← #35323095

Subgroups — #35323095

Order 21248.

396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912656C211yesmaximal, characteristic
2#24907457C211yesmaximal, characteristic
3#101×Dic83C211yesmaximal, characteristic
4#24905590C211yesmaximal, characteristic
5#24905589C211yesmaximal, characteristic
6#24905589C211yesmaximal, characteristic
7C83×#1394C211yesmaximal, characteristic
8C2×#14581783C411yescharacteristic
9C2×Q8×Dic83C2211yescharacteristic
10#19127724—21no—
11C2×#14581711C2211yescharacteristic
12C2×#14581711C2211yescharacteristic
13M16×Dic83—21no—
14#19127633—21no—
15#19127633—21no—
16#19127608C2211yescharacteristic
17#19127584—21no—
18#19127584—21no—
19#19127571C411yescharacteristic
20#19127566C411yescharacteristic
21C4×Dic83⋊C4C411yescharacteristic
22#19127469—21no—
23#19127469—21no—
24C2×#101×C83C2211yescharacteristic
25C2×#101×C83C2211yescharacteristic
26#391×C83C2211yescharacteristic
27C2×#13050574—21no—
28C2×#13050574—21no—
29#14581783—41no—
30#14581783—41no—
31Q8×Dic83—41no—
32Q8×Dic83—41no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83—21no—
36C2×C4⋊Dic83C2×C411yescharacteristic
37C2×C4⋊Dic83C2×C411yescharacteristic
38C2×C4⋊Dic83D411yescharacteristic
39C2×C4⋊Dic83D411yescharacteristic
40C2×Dic83⋊C4—21no—
41C2×Dic83⋊C4—21no—
42C2×C4×Dic83C2×C411yescharacteristic
43C2×C4×Dic83C2×C411yescharacteristic
44C2×C4×Dic83D411yescharacteristic
45C2×C4×Dic83D411yescharacteristic
46Dic83⋊C8—41no—
47Dic83⋊C8—41no—
48#14581711—21no—
49#14581711—21no—
50#14581711—21no—
51#14581711Q812yes—
52#14581702—41no—
53C8×Dic83—41no—
54C83⋊#95—21no—
55C83⋊#95—21no—
56C83⋊#95—21no—
57C83⋊#95—21no—
58C83⋊#95—21no—
59C22×Q8×C83C2311yescharacteristic
60C2×M16×C83—21no—
61C2×M16×C83—21no—
62C2×C4⋊C4×C83C2×C411yescharacteristic
63C2×C42×C83C2×C411yescharacteristic
64#101×C83—21no—
65#101×C83—21no—
66#101×C83—21no—
67#101×C83Q812yes—
68#95×C83—21no—
69#95×C83—21no—
70C22×Dic83—21no—
71C22×Dic83—21no—
72C22×Dic83C22⋊C411yescharacteristic
73C22×Dic83C22⋊C411yescharacteristic
74C22×Dic83C22⋊C411yescharacteristic
75C22×Dic83C22⋊C411yescharacteristic
76#13050574—22no—
77#13050574—41no—
78#13050574—41no—
79#13050574—41no—
80C2×C83⋊C8—41no—
81C2×C83⋊C8—41no—
82C4⋊Dic83—41no—
83C4⋊Dic83—41no—
84C4⋊Dic83—41no—
85C4⋊Dic83—42no—
86C4⋊Dic83—42no—
87C4⋊Dic83—42no—
88C4⋊Dic83—41no—
89Dic83⋊C4—42no—
90Dic83⋊C4—41no—
91Dic83⋊C4—41no—
92C4×Dic83—21no—
93C4×Dic83—21no—
94C4×Dic83—21no—
95C4×Dic83—21no—
96C4×Dic83—21no—
97C4×Dic83—21no—
98C4×Dic83—41no—
99C2×Q8×C83—41no—
100C2×Q8×C83—41no—
101C2×Q8×C83C2×Q811yescharacteristic
102C2×Q8×C83C2×Q811yescharacteristic
103C2×Q8×C83#4111yescharacteristic
104C2×Q8×C83#4111yescharacteristic
105C22×C4×C83—21no—
106C22×C4×C83—21no—
107C22×C4×C83C22×C411yescharacteristic
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110M16×C83—22no—
111M16×C83—41no—
112M16×C83—41no—
113M16×C83—41no—
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C4⋊C4×C83—41no—
117C42×C83—41no—
118C23×C83C2×C22⋊C411yescharacteristic
119Q8×C83—41no—
120Q8×C83—41no—
121Q8×C83—41no—
122Q8×C83—41no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—22no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—42no—
133C2×C4×C83—41no—
134C2×C4×C83C4×Q811yescharacteristic
135C2×C4×C83C4×Q811yescharacteristic
136C2×C4×C83C22⋊Q811yescharacteristic
137C2×C4×C83C22⋊Q811yescharacteristic
138C2×C4×C83#12411yescharacteristic
139C2×C4×C83C4⋊Q811yescharacteristic
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—41no—
144C2×Dic83—41no—
145C2×Dic83—41no—
146C2×Dic83—41no—
147C2×Dic83—41no—
148C2×Dic83—41no—
149C2×Dic83—41no—
150C2×Dic83—41no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83#9911yescharacteristic
154C2×Dic83#9911yescharacteristic
155C8×C83—42no—
156C8×C83—81no—
157C83⋊C8—42no—
158C83⋊C8—81no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83#39111yescharacteristic
162C22×C83C2×#9911yescharacteristic
163C22×C83#41011yescharacteristic
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—21no—
170C4×C83—42no—
171C4×C83—81no—
172Dic83—21no—
173Dic83—21no—
174Dic83—41no—
175Dic83—41no—
176Dic83—41no—
177Dic83—81no—
178Dic83—81no—
179#13303—831nomaximal, Sylow
180C2×C83—21no—
181C2×C83—21no—
182C2×C83#199611yescharacteristic
183C2×C83#213211yescharacteristic
184C2×C83#213311yescharacteristic
185#2565—831no—
186#1801—831no—
187C4×#101—831no—
188#1394—831no—
189#1394—831no—
190#1394—831no—
191#1394D8311yescharacteristic
192C83#1330311yescharacteristic, complemented, Sylow
193C2×#125—831no—
194C2×C4×Q8—831no—
195#423—1661no—
196C2×#101—831no—
197C2×#101—831no—
198C2×#101C2×D8311yescharacteristic
199C2×#101C2×D8311yescharacteristic
200C4×M16—1661no—
201#398—1661no—
202#398—1661no—
203#391—831no—
204#391C2×D8311yescharacteristic
205#387—1661no—
206#387—1661no—
207#384—831no—
208#382—831no—
209C4×C4⋊C4—831no—
210#343—1661no—
211#343—1661no—
212C22×Q8C22×D8311yescharacteristic
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—1661no—
216C2×M16—1661no—
217#125—3321no—
218#125—3321no—
219C4×Q8—3321no—
220C4×Q8—3321no—
221C2×C4⋊C4—831no—
222C2×C4⋊C4—831no—
223C2×C4⋊C4—831no—
224C2×C4⋊C4—831no—
225C2×C4⋊C4—1661no—
226C2×C4⋊C4—1661no—
227C2×C4⋊C4—1661no—
228C2×C4⋊C4—1661no—
229C2×C4⋊C4—1661no—
230C2×C4⋊C4C4×D8311yescharacteristic
231C2×C42—831no—
232C2×C42—831no—
233C2×C42—831no—
234C2×C42—831no—
235C2×C42C4×D8311yescharacteristic
236C4⋊C8—3321no—
237C4⋊C8—3321no—
238#101—21no—
239#101—21no—
240#101—21no—
241#101—832no—
242#101—1661no—
243#101—1661no—
244#101—1661no—
245#101Dic16612yes—
246#97—3321no—
247C4×C8—3321no—
248#95—21no—
249#95—21no—
250#95—1661no—
251#95—1661no—
252#95—1661no—
253#95—1661no—
254#95—1661no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8Q8×D8311yescharacteristic
258C2×Q8C2×Dic16611yescharacteristic
259C2×Q8#1305058911yescharacteristic
260C2×Q8#1305059011yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—831no—
264C22×C4—831no—
265C22×C4—831no—
266C22×C4—831no—
267C22×C4—1661no—
268C22×C4—1661no—
269C22×C4C2×C4×D8311yescharacteristic
270C22×C4D4×D8311yescharacteristic
271C22×C4D4×D8311yescharacteristic
272M16—22no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—3321no—
277M16—3321no—
278M16—3321no—
279M16—1662no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—3321no—
283C2×C8—3321no—
284C4⋊C4—41no—
285C4⋊C4—3321no—
286C4⋊C4—3322no—
287C4⋊C4—3322no—
288C4⋊C4—3322no—
289C4⋊C4—3321no—
290C4⋊C4—3321no—
291C4⋊C4—3321no—
292C4⋊C4—3321no—
293C4⋊C4—3321no—
294C4⋊C4—3322no—
295C42—41no—
296C42—3321no—
297C42—1661no—
298C42—1661no—
299C42—1661no—
300C42—1661no—
301C42—1661no—
302C42—1661no—
303C23C22⋊C4×D8311yescharacteristic
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—3321no—
320C2×C4—3321no—
321C2×C4—3321no—
322C2×C4—3321no—
323C2×C4—3321no—
324C2×C4—3321no—
325C2×C4—3321no—
326C2×C4—3321no—
327C2×C4—3321no—
328C2×C4—3321no—
329C2×C4—831no—
330C2×C4—831no—
331C2×C4—1661no—
332C2×C4—1661no—
333C2×C4—1661no—
334C2×C4#1458175711yescharacteristic
335C2×C4C4×Dic16611yescharacteristic
336C2×C4#1458176911yescharacteristic
337C2×C4#1458177011yescharacteristic
338C2×C4#1458177811yescharacteristic
339C2×C4#1458179111yescharacteristic
340C8—42no—
341C8—81no—
342C8—3322no—
343C8—6641no—
344C22—21no—
345C22—21no—
346C22#1912760511yescharacteristic
347C22#99×D8311yescharacteristic
348C22#1912767311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—81no—
357C4—3321no—
358C4—3321no—
359C4—3321no—
360C4—6641no—
361C4—6641no—
362C4—1661no—
363C4—1661no—
364C2—21no—
365C2—21no—
366C2#2490844611yescharacteristic
367C2#2490914711yescharacteristic
368C2#2490914911yescharacteristic
subgroupG/H
centerC22#99×D83
commutatorC22×C4×C83C22×C4
FrattiniC22×Q8C22×D83
FittingC83×#1394C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC22×Q8×C83C23
hypercenter#1394D83
hypocenterC83#13303
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
192. C83#13303semidirect

Maximal subgroups

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

subgroupindex
#249126562
#249074572
#101×Dic832
#249055902
#249055892
C83×#13942
#1330383