Finite Group Databasebeta

← #49098566

Subgroups — #49098566

Order 35968.

560 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
1C2×C4×D1124C211yesmaximal, characteristic
2C2×#22582836C211yesmaximal, characteristic, complemented
3#31823405C211yesmaximal, characteristic, complemented
4#31823398C211yesmaximal, characteristic, complemented
5#31823396C211yesmaximal, characteristic, complemented
6#31823392C211yesmaximal, characteristic, complemented
7#31823392C211yesmaximal, characteristic, complemented
8#31823389C211yesmaximal, characteristic, complemented
9#31823381C211yesmaximal, characteristic
10#31823380C211yesmaximal, characteristic
11C4×#17985117C211yesmaximal, characteristic, complemented
12C4×#17985115C211yesmaximal, characteristic, complemented
13C4×#17985115C211yesmaximal, characteristic, complemented
14C4×#17985115C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C281C211yesmaximal, characteristic, complemented
16C22×D1124C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18C22×C4×D281C2211yescharacteristic
19C4×D1124—24no—
20#22582836—24no—
21C2×C4⋊Dic281C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985115C2211yescharacteristic
27C2×#17985115C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×C4×Dic281C2211yescharacteristic
37C2×C4×Dic281C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C42×C281C2211yescharacteristic
49C2×C42×C281C2211yescharacteristic
50C2×C42×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53C23×D281C2311yescharacteristic
54C23×D281C2311yescharacteristic
55C2×D1124—22no—
56C2×D1124—22no—
57C2×D1124—22no—
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C2×C4×D281—22no—
65C2×C4×D281—22no—
66C2×C4×D281—22no—
67C2×C4×D281—22no—
68C2×C4×D281—22no—
69C2×C4×D281D414yes—
70C4⋊Dic281—22no—
71#17985117—22no—
72#17985117—22no—
73#17985117—22no—
74#17985117—22no—
75#17985115—22no—
76#17985115—22no—
77#17985115—22no—
78#17985115—22no—
79#17985115—22no—
80#17985115—22no—
81#17985115—22no—
82#17985115—22no—
83#17985115—22no—
84#17985115—22no—
85C4×Dic281—22no—
86C4×Dic281—22no—
87C22×C4×C281C2311yescharacteristic
88C22×C4×C281C2311yescharacteristic
89C22×C4×C281C2311yescharacteristic
90C22×C4×C281C2311yescharacteristic
91C22×C4×C281C2311yescharacteristic
92C22×C4×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C4⋊C4×C281—22no—
95C4⋊C4×C281—22no—
96C42×C281—22no—
97C42×C281—22no—
98C42×C281—22no—
99C22×D281—21no—
100C22×D281—21no—
101C22×D281—21no—
102C22×D281—21no—
103C22×D281—21no—
104C22×D281—21no—
105C22×D281—21no—
106C22×D281—21no—
107C22×D281—21no—
108C22×D281—21no—
109C22×D281—21no—
110C22×D281—21no—
111C22×D281C2×D412yes—
112C22×D281#4112yes—
113D1124—28no—
114C2×Dic281—21no—
115C2×Dic281—21no—
116C2×Dic281—21no—
117C2×Dic281—21no—
118C2×Dic281—21no—
119C2×Dic281—21no—
120C2×Dic281—21no—
121C2×Dic281—21no—
122C2×Dic281—21no—
123C2×Dic281—21no—
124C2×Dic281—21no—
125C2×Dic281—21no—
126C2×Dic281—21no—
127C2×Dic281—21no—
128C2×Dic281—21no—
129C2×Dic281—21no—
130C2×Dic281C2×D412yes—
131C2×Dic281#4112yes—
132C4×D281—28no—
133C4×D281—44no—
134C23×C281C2411yescharacteristic
135C2×C4×C281—21no—
136C2×C4×C281—21no—
137C2×C4×C281—21no—
138C2×C4×C281—21no—
139C2×C4×C281—21no—
140C2×C4×C281—21no—
141C2×C4×C281—21no—
142C2×C4×C281—21no—
143C2×C4×C281—21no—
144C2×C4×C281—21no—
145C2×C4×C281—21no—
146C2×C4×C281—21no—
147C2×C4×C281—21no—
148C2×C4×C281—21no—
149C2×C4×C281—21no—
150C2×C4×C281—21no—
151C2×C4×C281C2×D412yes—
152C2×C4×C281#4112yes—
153C2×C4×C281#4112yes—
154C2×C4×C281#4112yes—
155C2×C4×C281#4112yes—
156C22×C281C22×D411yescharacteristic
157C22×C281C2×#4111yescharacteristic
158C22×C281C2×#4111yescharacteristic
159C22×C281C2×#4111yescharacteristic
160C22×C281C2×#4111yescharacteristic
161C22×C281C2×#4111yescharacteristic
162C22×C281C2×#4111yescharacteristic
163C2×D281—22no—
164C2×D281—22no—
165C2×D281—22no—
166C2×D281—22no—
167C2×D281—22no—
168C2×D281—22no—
169C2×D281—41no—
170C2×D281—41no—
171C2×D281—41no—
172C2×D281—41no—
173C2×D281—41no—
174C2×D281—41no—
175C2×D281—41no—
176C2×D281—41no—
177C4×C281—22no—
178C4×C281—22no—
179C4×C281—41no—
180C4×C281—41no—
181C4×C281—41no—
182C4×C281—41no—
183C4×C281#12314yes—
184Dic281—22no—
185Dic281—22no—
186Dic281—41no—
187Dic281—41no—
188Dic281—41no—
189Dic281—41no—
190C2×C281C2×#12311yescharacteristic
191C2×C281#52511yescharacteristic
192C2×C281#52911yescharacteristic
193C2×C281#52911yescharacteristic
194C2×C281#52911yescharacteristic
195C2×C281#52911yescharacteristic
196C2×C281#53211yescharacteristic
197D281—42no—
198D281—42no—
199C281#239511yescharacteristic, complemented, Sylow
200#2395—2811nomaximal, Sylow
201C2×C4×D4—2811no—
202C2×#117—2811no—
203#400—2811no—
204#399—2811no—
205#398—2811no—
206#397—2811no—
207#397—2811no—
208#397—2811no—
209#394—2811no—
210#394—2811no—
211C4×C4⋊C4—2811no—
212C4×C4⋊C4D28111yescharacteristic, complemented
213C4×C22⋊C4—2811no—
214C4×C22⋊C4—2811no—
215C4×C22⋊C4—2811no—
216C22×D4—2811no—
217C23×C4—2811no—
218C23×C4—2811no—
219C4×D4—5624no—
220#117—5624no—
221C2×C4⋊C4—2811no—
222C2×C4⋊C4—2811no—
223C2×C4⋊C4—2811no—
224C2×C4⋊C4—2811no—
225C2×C4⋊C4—2811no—
226C2×C4⋊C4C2×D28111yescharacteristic
227C2×C4⋊C4C2×D28111yescharacteristic
228C2×C22⋊C4—2811no—
229C2×C22⋊C4—2811no—
230C2×C22⋊C4—2811no—
231C2×C22⋊C4—2811no—
232C2×C22⋊C4—2811no—
233C2×C22⋊C4—2811no—
234C2×C22⋊C4—2811no—
235C2×C22⋊C4—2811no—
236C2×C22⋊C4—2811no—
237C2×C22⋊C4—2811no—
238C2×C42—2811no—
239C2×C42—2811no—
240C2×C42C2×D28111yescharacteristic
241C2×C42C2×D28111yescharacteristic
242C2×C42C2×D28111yescharacteristic
243#95—2811no—
244#95—2811no—
245#95—2811no—
246#95—2811no—
247#95—2811no—
248#95—2811no—
249#95—2811no—
250#95—2811no—
251#95C2×D28111yescharacteristic
252#95C2×D28111yescharacteristic
253C24—2811no—
254C24—2811no—
255C2×D4—5622no—
256C2×D4—5622no—
257C2×D4—5622no—
258C22×C4—2811no—
259C22×C4—2811no—
260C22×C4—2814no—
261C22×C4—2811no—
262C22×C4—2811no—
263C22×C4—2811no—
264C22×C4—2811no—
265C22×C4—5622no—
266C22×C4—5622no—
267C22×C4—5622no—
268C22×C4—5622no—
269C22×C4—5622no—
270C22×C4C22×D28111yescharacteristic
271C22×C4C22×D28111yescharacteristic
272C22×C4C22×D28111yescharacteristic
273C22×C4C22×D28111yescharacteristic
274C22×C4C22×D28111yescharacteristic
275C22×C4C22×D28111yescharacteristic
276C22×C4C22×D28111yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—5622no—
280C4⋊C4—5622no—
281C4⋊C4—5622no—
282C4⋊C4—5622no—
283C4⋊C4—5622no—
284C22⋊C4—5622no—
285C22⋊C4—5622no—
286C22⋊C4—5622no—
287C22⋊C4—5622no—
288C22⋊C4—5622no—
289C22⋊C4—5622no—
290C22⋊C4—5622no—
291C22⋊C4—5622no—
292C22⋊C4—5622no—
293C22⋊C4—5622no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—5622no—
298C42—5622no—
299C23—2812no—
300C23—2812no—
301C23—5621no—
302C23—5621no—
303C23—5621no—
304C23—5621no—
305C23—5621no—
306C23—5621no—
307C23—5621no—
308C23—5621no—
309C23—5621no—
310C23—5621no—
311C23—5621no—
312C23—5621no—
313C23C23×D28111yescharacteristic
314D4—5628no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—2812no—
332C2×C4—2812no—
333C2×C4—5621no—
334C2×C4—5621no—
335C2×C4—5621no—
336C2×C4—5621no—
337C2×C4—5628no—
338C2×C4—5621no—
339C2×C4—5621no—
340C2×C4—5621no—
341C2×C4—5621no—
342C2×C4—5621no—
343C2×C4—5621no—
344C2×C4—5621no—
345C2×C4—5621no—
346C2×C4—5621no—
347C2×C4—5621no—
348C2×C4—5621no—
349C2×C4—5621no—
350C2×C4—11244no—
351C2×C4D4×D28112yes—
352C2×C4#1798513812yes—
353C2×C4#1798513812yes—
354C2×C4#1798513812yes—
355C2×C4#1798513912yes—
356C22—5622no—
357C22—5622no—
358C22—5622no—
359C22—5622no—
360C22—5622no—
361C22—5622no—
362C22—11241no—
363C22—11241no—
364C22—11241no—
365C22—11241no—
366C22—11241no—
367C22—11241no—
368C22—11241no—
369C22—11241no—
370C22C2×D4×D28111yescharacteristic
371C22#41×D28111yescharacteristic
372C22#41×D28111yescharacteristic
373C22C2×#1798513811yescharacteristic
374C22C2×#1798513811yescharacteristic
375C22C2×#1798513811yescharacteristic
376C22C2×#1798513911yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—5622no—
384C4—5622no—
385C4—11241no—
386C4—11241no—
387C4—11241no—
388C4—11241no—
389C4#2258286414yes—
390C2—11242no—
391C2—11242no—
392C2C2×#2258286411yescharacteristic
393C2#3182397211yescharacteristic
394C2#3182399111yescharacteristic
395C2#3182399711yescharacteristic
396C2#3182400011yescharacteristic
397C2#3182400011yescharacteristic
398C2#3182401011yescharacteristic
subgroupG/H
centerC22×C4C22×D281
commutator, socle, cosocleC23×C281C24
FrattiniC23C23×D281
FittingC4×C4⋊C4×C281C2
prime radicalC22×D1124C22
hypercenterC4×C4⋊C4D281
hypocenterC281#2395
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#22582836C2semidirect
3. #31823405C2semidirect
4. #31823398C2semidirect
5. #31823396C2semidirect
6. #31823392C2semidirect
7. #31823392C2semidirect
8. #31823389C2semidirect
11. C4×#17985117C2semidirect
12. C4×#17985115C2semidirect
13. C4×#17985115C2semidirect
14. C4×#17985115C2semidirect
15. C4×C4⋊C4×C281C2semidirect
199. C281#2395semidirect
212. C4×C4⋊C4D281semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D11242
C2×#225828362
#318234052
#318233982
#318233962
#318233922
#318233892
#318233812
#318233802
C4×#179851172
C4×#179851152
C4×C4⋊C4×C2812
#2395281