Finite Group Databasebeta

← #49098590

Subgroups — #49098590

Order 35968.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic562C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D281C211yesmaximal, characteristic
3#31823405C211yesmaximal, characteristic, complemented
4#31823404C211yesmaximal, characteristic, complemented
5#31823392C211yesmaximal, characteristic, complemented
6#31823391C211yesmaximal, characteristic, complemented
7#31823379C211yesmaximal, characteristic
8#31823378C211yesmaximal, characteristic
9#31823376C211yesmaximal, characteristic, complemented
10#31823375C211yesmaximal, characteristic, complemented
11C4×#17985115C211yesmaximal, characteristic, complemented
12C4×#17985115C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic281C211yesmaximal, characteristic, complemented
14#31823309C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C281C211yesmaximal, characteristic, complemented
16C22×Dic562C2211yescharacteristic
17C22×C22⋊D281C2211yescharacteristic
18C22×C4×D281C2211yescharacteristic
19C4×Dic562—24no—
20C4×C22⋊D281—24no—
21C2×C4⋊Dic281C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×C22⋊Dic281C2211yescharacteristic
26C2×C22⋊Dic281C2211yescharacteristic
27C2×C22⋊Dic281C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35C2×C4×Dic281C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46C23×C4×C281C2211yescharacteristic
47C2×C22⋊C4×C281C2211yescharacteristic
48C2×C22⋊C4×C281C2211yescharacteristic
49C2×C42×C281C2211yescharacteristic
50C2×C42×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53C23×D281C2311yescharacteristic
54C2×Dic562—22no—
55C2×Dic562—22no—
56C2×Dic562—22no—
57C2×C22⋊D281—22no—
58C2×C22⋊D281—22no—
59C2×C22⋊D281—22no—
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C2×C4×D281—22no—
68C2×C4×D281—22no—
69C2×C4×D281—22no—
70C4⋊Dic281—22no—
71#17985117—22no—
72#17985117—22no—
73#17985117—22no—
74C22⋊Dic281—22no—
75C22⋊Dic281—22no—
76C22⋊Dic281—22no—
77#17985115—22no—
78#17985115—22no—
79#17985115—22no—
80#17985115—22no—
81#17985115—22no—
82C4×Dic281—22no—
83C4×Dic281—22no—
84C4×Dic281D414yes—
85C24×C281C2311yescharacteristic
86C22×C4×C281—22no—
87C22×C4×C281—22no—
88C22×C4×C281—22no—
89C22×C4×C281C2311yescharacteristic
90C22×C4×C281C2311yescharacteristic
91C22×C4×C281C2311yescharacteristic
92C22×C4×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C22×C4×C281C2311yescharacteristic
95C22⋊C4×C281—22no—
96C22⋊C4×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#4112yes—
106Dic562—28no—
107C22⋊D281—28no—
108C2×Dic281—21no—
109C2×Dic281—21no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281—21no—
113C2×Dic281—21no—
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×Dic281C2×D412yes—
127C2×Dic281C2×D412yes—
128C2×Dic281#4112yes—
129C4×D281—44no—
130C23×C281—21no—
131C23×C281—21no—
132C23×C281—21no—
133C23×C281—21no—
134C23×C281—21no—
135C23×C281—21no—
136C23×C281#4112yes—
137C23×C281C2411yescharacteristic
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×C281—21no—
152C2×C4×C281—44no—
153C2×C4×C281C2×D412yes—
154C2×C4×C281#4112yes—
155C2×C4×C281#4112yes—
156C2×C4×C281#4112yes—
157C22×C281—22no—
158C22×C281—22no—
159C22×C281—22no—
160C22×C281—41no—
161C22×C281—41no—
162C22×C281—41no—
163C22×C281—41no—
164C22×C281C22×D411yescharacteristic
165C22×C281C2×#4111yescharacteristic
166C22×C281C2×#4111yescharacteristic
167C22×C281C2×#4111yescharacteristic
168C22×C281C2×#4111yescharacteristic
169C22×C281C2×#4111yescharacteristic
170C22×C281C2×#4111yescharacteristic
171C2×D281—22no—
172C2×D281—22no—
173C2×D281—22no—
174C2×D281—41no—
175C2×D281—41no—
176C2×D281—41no—
177C2×D281—41no—
178C4×C281—22no—
179C4×C281—41no—
180C4×C281—41no—
181C4×C281—41no—
182C4×C281—41no—
183C4×C281#12414yes—
184Dic281—22no—
185Dic281—22no—
186Dic281—22no—
187Dic281—41no—
188Dic281—41no—
189Dic281—41no—
190Dic281—41no—
191C2×C281—42no—
192C2×C281#52511yescharacteristic
193C2×C281#52511yescharacteristic
194C2×C281C2×#12411yescharacteristic
195C2×C281#52911yescharacteristic
196C2×C281#52911yescharacteristic
197C2×C281#52911yescharacteristic
198C2×C281#52911yescharacteristic
199D281—42no—
200C281#239811yescharacteristic, complemented, Sylow
201#2398—2811nomaximal, Sylow
202C2×C4×Q8—2811no—
203C2×C4×D4—2811no—
204#400—2811no—
205#400—2811no—
206#397—2811no—
207#397—2811no—
208#394—2811no—
209#394—2811no—
210#393—2811no—
211#393—2811no—
212C4×C22⋊C4—2811no—
213C4×C22⋊C4—2811no—
214C4×C22⋊C4—2811no—
215C4×C22⋊C4D28111yescharacteristic, complemented
216#376—2811no—
217C22×Q8—2811no—
218C22×D4—2811no—
219C23×C4—2811no—
220C23×C4C2×D28111yescharacteristic
221C4×Q8—5624no—
222C4×D4—5624no—
223C2×C4⋊C4—2811no—
224C2×C4⋊C4—2811no—
225C2×C4⋊C4—2811no—
226C2×C4⋊C4—2811no—
227C2×C22⋊C4—2811no—
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⋊C4C2×D28111yescharacteristic
236C2×C22⋊C4C2×D28111yescharacteristic
237C2×C42—2811no—
238C2×C42—2811no—
239C2×C42—2811no—
240C2×C42C2×D28111yescharacteristic
241C2×C42C2×D28111yescharacteristic
242#95—2811no—
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#95—2811no—
252#95C2×D28111yescharacteristic
253#95C2×D28111yescharacteristic
254C24—2811no—
255C24C22×D28111yescharacteristic
256C2×Q8—5622no—
257C2×Q8—5622no—
258C2×Q8—5622no—
259C2×D4—5622no—
260C2×D4—5622no—
261C2×D4—5622no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—2811no—
266C22×C4—2811no—
267C22×C4—2811no—
268C22×C4—2811no—
269C22×C4—2811no—
270C22×C4—2811no—
271C22×C4—2811no—
272C22×C4—5622no—
273C22×C4—5622no—
274C22×C4—5622no—
275C22×C4C22×D28111yescharacteristic
276C22×C4C22×D28111yescharacteristic
277C22×C4C22×D28111yescharacteristic
278C22×C4C22×D28111yescharacteristic
279C22×C4C22×D28111yescharacteristic
280C22×C4C22×D28111yescharacteristic
281C4⋊C4—5622no—
282C4⋊C4—5622no—
283C4⋊C4—5622no—
284C4⋊C4—5622no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—5622no—
288C22⋊C4—5622no—
289C22⋊C4—5622no—
290C22⋊C4—5622no—
291C22⋊C4—5622no—
292C22⋊C4—5622no—
293C22⋊C4—5622no—
294C22⋊C4—5622no—
295C42—22no—
296C42—22no—
297C42—2814no—
298C42—5622no—
299C42—5622no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—2812no—
307C23—5621no—
308C23—5621no—
309C23—5621no—
310C23—5621no—
311C23—5621no—
312C23—5621no—
313C23#1798513812yes—
314C23C23×D28111yescharacteristic
315Q8—5628no—
316D4—5628no—
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—44no—
332C2×C4—2812no—
333C2×C4—2812no—
334C2×C4—2812no—
335C2×C4—5621no—
336C2×C4—5621no—
337C2×C4—5621no—
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—5621no—
351C2×C4—5621no—
352C2×C4—5621no—
353C2×C4—11244no—
354C2×C4D4×D28112yes—
355C2×C4#1798513712yes—
356C2×C4#1798513812yes—
357C2×C4#1798513812yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—5622no—
366C22—5622no—
367C22—5622no—
368C22—11241no—
369C22—11241no—
370C22—11241no—
371C22—11241no—
372C22C2×D4×D28111yescharacteristic
373C22#41×D28111yescharacteristic
374C22#41×D28111yescharacteristic
375C22C2×#1798513711yescharacteristic
376C22C2×#1798513811yescharacteristic
377C22C2×#1798513811yescharacteristic
378C22C2×#1798513811yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—5622no—
385C4—5622no—
386C4—5622no—
387C4—11241no—
388C4—11241no—
389C4—11241no—
390C4—11241no—
391C4#2258286514yes—
392C2—42no—
393C2—11242no—
394C2#3182397211yescharacteristic
395C2#3182397211yescharacteristic
396C2C2×#2258286511yescharacteristic
397C2#3182399111yescharacteristic
398C2#3182399311yescharacteristic
399C2#3182399511yescharacteristic
400C2#3182399711yescharacteristic
subgroupG/H
centerC22×C4C22×D281
commutator, socle, cosocleC23×C281C24
FrattiniC23C23×D281
FittingC4×C22⋊C4×C281C2
prime radicalC22×C22⋊D281C22
hypercenterC4×C22⋊C4D281
hypocenterC281#2398
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic562C2semidirect
3. #31823405C2semidirect
4. #31823404C2semidirect
5. #31823392C2semidirect
6. #31823391C2semidirect
9. #31823376C2semidirect
10. #31823375C2semidirect
11. C4×#17985115C2semidirect
12. C4×#17985115C2semidirect
13. C4×C22⋊Dic281C2semidirect
14. #31823309C2semidirect
15. C4×C22⋊C4×C281C2semidirect
200. C281#2398semidirect
215. C4×C22⋊C4D281semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic5622
C2×C4×C22⋊D2812
#318234052
#318234042
#318233922
#318233912
#318233792
#318233782
#318233762
#318233752
C4×#179851152
C4×C22⋊Dic2812
#318233092
C4×C22⋊C4×C2812
#2398281