Finite Group Databasebeta

← #49119513

Subgroups — #49119513

Order 36224.

564 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic283C211yesmaximal, characteristic
2C22×Dic283⋊C4C211yesmaximal, characteristic
3C2×C283⋊#95C211yesmaximal, characteristic
4C2×C283⋊#95C211yesmaximal, characteristic
5C2×C283⋊#95C211yesmaximal, characteristic
6C2×C283⋊#95C211yesmaximal, characteristic
7C2×#95×C283C211yesmaximal, characteristic
8C23×Dic283C2211yescharacteristic
9C23×Dic283C2211yescharacteristic
10C23×Dic283C2211yescharacteristic
11C23×Dic283C2211yescharacteristic
12C2×C4⋊Dic283—22no—
13C2×C4⋊Dic283—22no—
14C2×C4⋊Dic283C414yescomplemented
15C2×Dic283⋊C4—22no—
16C2×Dic283⋊C4—22no—
17C2×Dic283⋊C4—22no—
18C283⋊#95—22no—
19C283⋊#95—22no—
20C283⋊#95—22no—
21C283⋊#95—22no—
22C23×C4×C283C2211yescharacteristic
23C23×C4×C283C2211yescharacteristic
24C23×C4×C283C2211yescharacteristic
25#95×C283—22no—
26C22×Dic283—21no—
27C22×Dic283—21no—
28C22×Dic283—21no—
29C22×Dic283—21no—
30C22×Dic283—21no—
31C22×Dic283—21no—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C22×Dic283—21no—
35C22×Dic283—21no—
36C22×Dic283—21no—
37C22×Dic283—21no—
38C22×Dic283—21no—
39C22×Dic283—21no—
40C22×Dic283—21no—
41C22×Dic283—21no—
42C22×Dic283—21no—
43C22×Dic283—21no—
44C22×Dic283—21no—
45C22×Dic283—21no—
46C22×Dic283—21no—
47C22×Dic283—21no—
48C22×Dic283C2×C412yes—
49C22×Dic283C2×C412yes—
50C22×Dic283D412yes—
51C22×Dic283D412yes—
52C22×Dic283D412yes—
53C22×Dic283Q812yes—
54C4⋊Dic283—28no—
55Dic283⋊C4—28no—
56C24×C283C2311yescharacteristic
57C22×C4×C283—21no—
58C22×C4×C283—21no—
59C22×C4×C283—21no—
60C22×C4×C283—21no—
61C22×C4×C283—21no—
62C22×C4×C283—21no—
63C22×C4×C283—21no—
64C22×C4×C283—21no—
65C22×C4×C283—21no—
66C22×C4×C283—21no—
67C22×C4×C283—21no—
68C22×C4×C283—21no—
69C22×C4×C283—21no—
70C22×C4×C283—21no—
71C22×C4×C283—21no—
72C22×C4×C283—21no—
73C22×C4×C283C2×C412yes—
74C22×C4×C283D412yes—
75C22×C4×C283D412yes—
76C22×C4×C283Q812yes—
77C22×C4×C283Q812yes—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—22no—
81C2×Dic283—22no—
82C2×Dic283—22no—
83C2×Dic283—22no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—41no—
94C2×Dic283—41no—
95C2×Dic283—41no—
96C2×Dic283—41no—
97C2×Dic283—41no—
98C2×Dic283—41no—
99C2×Dic283—41no—
100C2×Dic283—41no—
101C2×Dic283—41no—
102C2×Dic283—41no—
103C2×Dic283—41no—
104C2×Dic283—41no—
105C2×Dic283C22⋊C414yes—
106C23×C283C22×C411yescharacteristic
107C23×C283C2×D411yescharacteristic
108C23×C283C2×D411yescharacteristic
109C23×C283C2×D411yescharacteristic
110C23×C283C2×D411yescharacteristic
111C23×C283C2×D411yescharacteristic
112C23×C283C2×Q811yescharacteristic
113C23×C283C2×Q811yescharacteristic
114C23×C283C2×Q811yescharacteristic
115C23×C283#4111yescharacteristic
116C23×C283#4111yescharacteristic
117C23×C283#4111yescharacteristic
118C23×C283#4111yescharacteristic
119C23×C283#4111yescharacteristic
120C23×C283#4111yescharacteristic
121C2×C4×C283—22no—
122C2×C4×C283—22no—
123C2×C4×C283—22no—
124C2×C4×C283—22no—
125C2×C4×C283—22no—
126C2×C4×C283—22no—
127C2×C4×C283—22no—
128C2×C4×C283—22no—
129C2×C4×C283—22no—
130C2×C4×C283—22no—
131C2×C4×C283—22no—
132C2×C4×C283—22no—
133C2×C4×C283—41no—
134C2×C4×C283—41no—
135C2×C4×C283—41no—
136C2×C4×C283—41no—
137C2×C4×C283—41no—
138C2×C4×C283—41no—
139C2×C4×C283—41no—
140C2×C4×C283—41no—
141C2×C4×C283C4⋊C414yescomplemented
142C22×C283C2×C22⋊C411yescharacteristic
143C22×C283C2×C4⋊C411yescharacteristic
144C22×C283#11711yescharacteristic
145C22×C283C4×D411yescharacteristic
146C22×C283C4×D411yescharacteristic
147C22×C283C4×Q811yescharacteristic
148C22×C283C4×Q811yescharacteristic
149C22×C283#12011yescharacteristic
150C22×C283#12111yescharacteristic
151C22×C283#12111yescharacteristic
152C22×C283#12111yescharacteristic
153C22×C283#12111yescharacteristic
154C22×C283#12111yescharacteristic
155C22×C283#12111yescharacteristic
156C22×C283C22⋊Q811yescharacteristic
157C22×C283C22⋊Q811yescharacteristic
158C22×C283C22⋊Q811yescharacteristic
159C22×C283C22⋊Q811yescharacteristic
160C22×C283C22⋊Q811yescharacteristic
161C22×C283C22⋊Q811yescharacteristic
162C22×C283C22⋊Q811yescharacteristic
163C22×C283C22⋊Q811yescharacteristic
164C22×C283#12311yescharacteristic
165C22×C283#12311yescharacteristic
166C22×C283#12311yescharacteristic
167C22×C283#12411yescharacteristic
168C22×C283#12511yescharacteristic
169C22×C283#12511yescharacteristic
170C22×C283#12511yescharacteristic
171C22×C283#12511yescharacteristic
172C22×C283#12611yescharacteristic
173C22×C283#12611yescharacteristic
174C22×C283C4⋊Q811yescharacteristic
175C22×C283C4⋊Q811yescharacteristic
176C22×C283C4⋊Q811yescharacteristic
177C4×C283—24no—
178C4×C283—42no—
179C4×C283—42no—
180Dic283—24no—
181Dic283—42no—
182Dic283—42no—
183Dic283—42no—
184C2×C283#38011yescharacteristic
185C2×C283#38611yescharacteristic
186C2×C283#38711yescharacteristic
187C2×C283#38711yescharacteristic
188C2×C283#38911yescharacteristic
189C2×C283#38911yescharacteristic
190C2×C283#39111yescharacteristic
191C2×C283#39411yescharacteristic
192C2×C283#39511yescharacteristic
193C2×C283#39611yescharacteristic
194C2×C283#39611yescharacteristic
195C2×C283#39811yescharacteristic
196C2×C283#39811yescharacteristic
197C2×C283#39811yescharacteristic
198C2×C283#40011yescharacteristic
199C283#144111yescharacteristic, complemented, Sylow
200#1441—2831nomaximal, Sylow
201C22×C4⋊C4—2831no—
202C22×C4⋊C4—2831no—
203C2×#95—2831no—
204C2×#95—2831no—
205C2×#95—2831no—
206C2×#95—2831no—
207C2×#95D28311yescharacteristic
208C23×C4—2831no—
209C23×C4—2831no—
210C23×C4—2831no—
211C23×C4—2831no—
212C23×C4C2×D28311yescharacteristic
213C23×C4C2×D28311yescharacteristic
214C23×C4C2×D28311yescharacteristic
215C2×C4⋊C4—2834no—
216C2×C4⋊C4—5662no—
217C2×C4⋊C4—5662no—
218C2×C4⋊C4—5662no—
219C2×C4⋊C4—5662no—
220C2×C4⋊C4—5662no—
221#95—22no—
222#95—5662no—
223#95—5662no—
224#95—5662no—
225#95—5662no—
226C24C22×D28311yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—2832no—
244C22×C4—2832no—
245C22×C4—2832no—
246C22×C4—2832no—
247C22×C4—2832no—
248C22×C4—2832no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4C4×D28312yes—
272C22×C4C22⋊D28312yes—
273C22×C4D113212yes—
274C22×C4Dic56612yes—
275C22×C4Dic56612yes—
276C4⋊C4—5668no—
277C4⋊C4—5668no—
278C23C2×C4×D28311yescharacteristic
279C23D4×D28311yescharacteristic
280C23D4×D28311yescharacteristic
281C23D4×D28311yescharacteristic
282C23C2×C22⋊D28311yescharacteristic
283C23C2×D113211yescharacteristic
284C23Q8×D28311yescharacteristic
285C23C2×Dic56611yescharacteristic
286C23C2×Dic56611yescharacteristic
287C23#1798539111yescharacteristic
288C23#1798539111yescharacteristic
289C23#1798539111yescharacteristic
290C23#1798539211yescharacteristic
291C23#1798539211yescharacteristic
292C23#1798539311yescharacteristic
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—2834no—
314C2×C4—5662no—
315C2×C4—5662no—
316C2×C4—5662no—
317C2×C4—5662no—
318C2×C4—5662no—
319C2×C4—5662no—
320C2×C4—5662no—
321C2×C4—5662no—
322C2×C4—5662no—
323C2×C4—5662no—
324C2×C4—5662no—
325C2×C4—5662no—
326C2×C4—5662no—
327C2×C4—5662no—
328C2×C4—5662no—
329C2×C4—11321no—
330C2×C4—11321no—
331C2×C4—11321no—
332C2×C4—11321no—
333C2×C4—11321no—
334C2×C4—11321no—
335C2×C4—11321no—
336C2×C4—11321no—
337C2×C4—11321no—
338C2×C4—11321no—
339C2×C4—11321no—
340C2×C4—11321no—
341C2×C4Dic283⋊C414yescomplemented
342C22C22⋊C4×D28311yescharacteristic
343C22C2×Dic283⋊C411yescharacteristic
344C22#2258356611yescharacteristic
345C22#2258357211yescharacteristic
346C22C4×D113211yescharacteristic
347C22#2258357511yescharacteristic
348C22C4×Dic56611yescharacteristic
349C22#2258358011yescharacteristic
350C22#2258358111yescharacteristic
351C22#2258358211yescharacteristic
352C22#2258358211yescharacteristic
353C22#2258358311yescharacteristic
354C22#2258358411yescharacteristic
355C22#2258358511yescharacteristic
356C22#2258358611yescharacteristic
357C22#2258358711yescharacteristic
358C22#2258358711yescharacteristic
359C22#2258358711yescharacteristic
360C22#2258358711yescharacteristic
361C22#2258358811yescharacteristic
362C22#2258358911yescharacteristic
363C22#2258359011yescharacteristic
364C22#2258359211yescharacteristic
365C22#2258359411yescharacteristic
366C22#2258359511yescharacteristic
367C22#2258359611yescharacteristic
368C22#2258360011yescharacteristic
369C22#2258360111yescharacteristic
370C22#2258360111yescharacteristic
371C22#2258360211yescharacteristic
372C22#2258360311yescharacteristic
373C22#2258360511yescharacteristic
374C22#2258360911yescharacteristic
375C22#2258360911yescharacteristic
376C22#2258361011yescharacteristic
377C4—24no—
378C4—42no—
379C4—42no—
380C4—5664no—
381C4—11322no—
382C4—11322no—
383C4—11322no—
384C2#3182632311yescharacteristic
385C2#3182634311yescharacteristic
386C2#3182634811yescharacteristic
387C2#3182635011yescharacteristic
388C2#3182636111yescharacteristic
389C2#3182636311yescharacteristic
390C2#3182636911yescharacteristic
391C2#3182638111yescharacteristic
392C2#3182638611yescharacteristic
393C2#3182638711yescharacteristic
394C2#3182638811yescharacteristic
395C2#3182639711yescharacteristic
396C2#3182639811yescharacteristic
397C2#3182639911yescharacteristic
398C2#3182640711yescharacteristic
subgroupG/H
center, FrattiniC24C22×D283
commutatorC23×C283C22×C4
FittingC2×#95×C283C2
socle, prime radical, cosocleC24×C283C23
hypercenterC2×#95D283
hypocenterC283#1441
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
14. C2×C4⋊Dic283C4semidirect
141. C2×C4×C283C4⋊C4semidirect
199. C283#1441semidirect
341. C2×C4Dic283⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic2832
C22×Dic283⋊C42
C2×C283⋊#952
C2×#95×C2832
#1441283