Finite Group Databasebeta

← #49130714

Subgroups — #49130714

Order 36224.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583632C211yesmaximal, characteristic, complemented
2C2×#22583630C211yesmaximal, characteristic, complemented
3#31827011C211yesmaximal, characteristic, complemented
4#31826933C211yesmaximal, characteristic, complemented
5#31826690C211yesmaximal, characteristic, complemented
6#31826686C211yesmaximal, characteristic, complemented
7#31826683C211yesmaximal, characteristic, complemented
8#31826679C211yesmaximal, characteristic, complemented
9#31826674C211yesmaximal, characteristic, complemented
10#31826669C211yesmaximal, characteristic, complemented
11#31826664C211yesmaximal, characteristic, complemented
12#31826659C211yesmaximal, characteristic, complemented
13C2×Dic283⋊C8C211yesmaximal, characteristic, complemented
14#31826459C211yesmaximal, characteristic, complemented
15#416×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18#22583632—24no—
19#22583630—24no—
20C2×Dic1132C2211yescharacteristic
21C2×#17985382C2211yescharacteristic
22C2×#17985381C2211yescharacteristic
23C2×#17985381C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985379C2211yescharacteristic
26C2×D2264C2211yescharacteristic
27C2×#17985377C2211yescharacteristic
28C22×C283⋊C8C2211yescharacteristic
29#22583608C2211yescharacteristic
30#22583606C2211yescharacteristic
31#22583599C2211yescharacteristic
32#22583597C2211yescharacteristic
33#22583582—21no—
34#22583582—21no—
35#22583575C2211yescharacteristic
36#22583575C2211yescharacteristic
37#22583572C2211yescharacteristic
38#22583572C2211yescharacteristic
39C4×C22⋊D283—21no—
40C4×C22⋊D283—21no—
41(C22⋊D283)⋊C4—21no—
42(C22⋊D283)⋊C4—21no—
43#22583567—21no—
44C2×C4×Dic283C2211yescharacteristic
45C42×D283—21no—
46Dic283⋊C8C2211yescharacteristic
47Dic283⋊C8C2211yescharacteristic
48Dic283⋊C8C2211yescharacteristic
49Dic283⋊C8C2211yescharacteristic
50#22583533C2211yescharacteristic
51#22583533C2211yescharacteristic
52#22583530C2211yescharacteristic
53#22583530C2211yescharacteristic
54C2×#41×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic
56#117×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#102×C283C2211yescharacteristic
60#102×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—22no—
63#17985392—22no—
64#17985392D414yescomplemented
65C2×Dic566C2311yescharacteristic
66C2×Dic566C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C22×Dic283D411yescharacteristic
74C22×Dic283D411yescharacteristic
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283—21no—
79Dic1132—22no—
80#17985382—22no—
81#17985381—22no—
82#17985381—22no—
83#17985380—22no—
84#17985379—22no—
85D2264—22no—
86#17985377—22no—
87C2×C283⋊C8—22no—
88C2×C283⋊C8C2311yescharacteristic
89C2×C283⋊C8C2311yescharacteristic
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92Dic283⋊C4—21no—
93Dic283⋊C4—21no—
94C22⋊Dic283—21no—
95C22⋊Dic283—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100C4×Dic283—21no—
101C4×Dic283—21no—
102C4×Dic283D411yescharacteristic
103C4×Dic283D411yescharacteristic
104C4×Dic283C2311yescharacteristic
105C4×Dic283C2311yescharacteristic
106#41×C283—22no—
107#41×C283—22no—
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283—21no—
110C2×D4×C283C2311yescharacteristic
111C22×C4×C283—21no—
112C22×C4×C283C2311yescharacteristic
113C2×C8×C283—22no—
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283C2311yescharacteristic
117C4⋊C4×C283C2311yescharacteristic
118C22⋊C4×C283—21no—
119C42×C283—21no—
120C22×D283—21no—
121C22×D283—21no—
122Dic566—21no—
123Dic566—21no—
124Dic566—21no—
125Dic566C2×D412yes—
126D1132—21no—
127D1132—21no—
128D1132—21no—
129D1132C2×D412yes—
130C22⋊D283—24no—
131C22⋊D283—42no—
132C22⋊D283—42no—
133C22⋊D283—42no—
134C2×Dic283—21no—
135C2×Dic283—22no—
136C2×Dic283—21no—
137C2×Dic283—41no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C2×Dic283C2×D411yescharacteristic
142C4×D283—24no—
143C4×D283—42no—
144C4×D283—42no—
145C4×D283—42no—
146C283⋊C8—21no—
147C283⋊C8—21no—
148C23×C283—21no—
149C23×C283C2×D411yescharacteristic
150Q8×C283—21no—
151Q8×C283—21no—
152D4×C283—21no—
153D4×C283—21no—
154D4×C283—42no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—42no—
159C2×C4×C283C2×D412yes—
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283#4112yes—
162C2×C4×C283C2411yescharacteristic
163C8×C283—21no—
164C8×C283—21no—
165C22×C283—21no—
166C22×C283—21no—
167C22×C283—41no—
168C22×C283—41no—
169C22×C283—41no—
170C22×C283#12112yes—
171C22×C283C22×D411yescharacteristic
172C2×D283—22no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—41no—
178C4×C283—41no—
179C4×C283—41no—
180C4×C283—41no—
181C4×C283#12112yes—
182C4×C283C22×D411yescharacteristic
183C4×C283C2×#4111yescharacteristic
184Dic283—22no—
185Dic283—21no—
186Dic283—21no—
187Dic283—21no—
188Dic283—41no—
189Dic283#13512yescomplemented
190C2×C283—22no—
191C2×C283—81no—
192C2×C283C2×#12111yescharacteristic
193C2×C283C2×#13511yescharacteristic
194C2×C283#57511yescharacteristic
195D283—42no—
196D283—81no—
197C283#303511yescharacteristic, complemented, Sylow
198#3035—2831nomaximal, Sylow
199C2×#135—2831no—
200C2×#135—2831no—
201#532—2831no—
202C4×#41—2831no—
203#464—2831no—
204#464—2831no—
205#463—2831no—
206#463—2831no—
207#462—2831no—
208#461—2831no—
209#460—2831no—
210#459—2831no—
211C2×C4⋊C8—2831no—
212#416—2831no—
213#416D28311yescharacteristic, complemented
214C2×#41—2831no—
215C2×#41—2831no—
216C2×#41C2×D28311yescharacteristic
217#135—5664no—
218#135—5664no—
219C2×Q16—2831no—
220C2×Q16—2831no—
221C2×SD16—2831no—
222C2×SD16—2831no—
223C2×SD16—2831no—
224C2×SD16—2831no—
225C2×D8—2831no—
226C2×D8—2831no—
227C22×C8—2831no—
228C22×C8C2×D28311yescharacteristic
229C4⋊Q8—2831no—
230#127—2831no—
231#124—2831no—
232#124—2831no—
233#121—5661no—
234#121—5661no—
235C4×Q8—2831no—
236C4×Q8—2831no—
237C4×D4—2831no—
238C4×D4—2831no—
239C4×D4—5661no—
240C4×D4—5661no—
241C4×D4—5661no—
242C4×D4—5661no—
243#117—5661no—
244#117C2×D28311yescharacteristic
245C2×C42—2831no—
246C2×C42—5661no—
247C4⋊C8—2831no—
248C4⋊C8—2831no—
249C4⋊C8—2831no—
250C4⋊C8—2831no—
251#103—2831no—
252#103—2831no—
253#103C2×D28311yescharacteristic
254#103C2×D28311yescharacteristic
255#102—2831no—
256#102—2831no—
257#102C2×D28311yescharacteristic
258#102C2×D28311yescharacteristic
259#41—22no—
260#41—22no—
261#41—2834no—
262#41—5662no—
263#41—5662no—
264#41—5662no—
265C2×Q8—2831no—
266C2×Q8—2831no—
267C2×Q8C22×D28311yescharacteristic
268C2×D4—21no—
269C2×D4—2831no—
270C2×D4—2831no—
271C2×D4—5661no—
272C2×D4—5661no—
273C2×D4—5661no—
274C2×D4—5661no—
275C2×D4C22×D28311yescharacteristic
276C22×C4—21no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—5661no—
280C22×C4—5661no—
281C22×C4—5661no—
282C22×C4—5661no—
283C22×C4C22×D28311yescharacteristic
284Q16—5662no—
285Q16—5662no—
286SD16—5662no—
287SD16—5662no—
288SD16—5662no—
289SD16—5662no—
290D8—5662no—
291D8—5662no—
292C2×C8—22no—
293C2×C8—2831no—
294C2×C8—2831no—
295C2×C8—5662no—
296C2×C8C22×D28311yescharacteristic
297C2×C8C22×D28311yescharacteristic
298C4⋊C4—5661no—
299C4⋊C4—5661no—
300C4⋊C4—5661no—
301C4⋊C4—5661no—
302C4⋊C4C22×D28311yescharacteristic
303C4⋊C4C22×D28311yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—5661no—
306C22⋊C4—5661no—
307C22⋊C4—5661no—
308C22⋊C4—5661no—
309C22⋊C4—5661no—
310C22⋊C4—5661no—
311C42—21no—
312C42—2831no—
313C42—2831no—
314C42—2831no—
315C42—2831no—
316C42—5661no—
317C42—5661no—
318C23—21no—
319C23—5661no—
320C23—5661no—
321C23D4×D28311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—2832no—
325Q8—5661no—
326Q8—5661no—
327Q8—5661no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—2832no—
332D4—5664no—
333D4—5661no—
334D4—5661no—
335D4—5661no—
336D4—11322no—
337D4—11322no—
338D4—11322no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2831no—
344C2×C4—2831no—
345C2×C4—2831no—
346C2×C4—2831no—
347C2×C4—5662no—
348C2×C4—5661no—
349C2×C4—5664no—
350C2×C4—5661no—
351C2×C4—11322no—
352C2×C4—11322no—
353C2×C4—11321no—
354C2×C4—11322no—
355C2×C4D4×D28312yes—
356C2×C4D4×D28311yescharacteristic
357C2×C4#1798539212yes—
358C2×C4C23×D28311yescharacteristic
359C8—21no—
360C8—21no—
361C8—5661no—
362C8—5661no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—5662no—
369C22—11321no—
370C22—11321no—
371C22—11321no—
372C22—11321no—
373C22—11321no—
374C22#2258358312yes—
375C22C2×D4×D28311yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—2832no—
380C4—5662no—
381C4—5661no—
382C4—5661no—
383C4—5661no—
384C4—11321no—
385C4#2258358312yes—
386C4C2×D4×D28311yescharacteristic
387C4C2×#1798539211yescharacteristic
388C2—22no—
389C2—81no—
390C2—11322no—
391C2—22641no—
392C2C2×#2258358311yescharacteristic
393C2#135×D28311yescharacteristic
394C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
hypercenter#416D283
hypocenterC283#3035
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#22583632C2semidirect
2. C2×#22583630C2semidirect
3. #31827011C2semidirect
4. #31826933C2semidirect
5. #31826690C2semidirect
6. #31826686C2semidirect
7. #31826683C2semidirect
8. #31826679C2semidirect
9. #31826674C2semidirect
10. #31826669C2semidirect
11. #31826664C2semidirect
12. #31826659C2semidirect
13. C2×Dic283⋊C8C2semidirect
14. #31826459C2semidirect
15. #416×C283C2semidirect
64. #17985392D4semidirect
189. Dic283#135semidirect
197. C283#3035semidirect
213. #416D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836322
C2×#225836302
#318270112
#318269332
#318266902
#318266862
#318266832
#318266792
#318266742
#318266692
#318266642
#318266592
C2×Dic283⋊C82
#318264592
#416×C2832
#3035283