Finite Group Databasebeta

← #34078661

Subgroups — #34078661

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012768C211yesmaximal, characteristic, complemented
2C2×#18012758C211yesmaximal, characteristic
3#23752782C211yesmaximal, characteristic, complemented
4#23752691C211yesmaximal, characteristic, complemented
5#23752433C211yesmaximal, characteristic, complemented
6#23752431C211yesmaximal, characteristic, complemented
7#23752425C211yesmaximal, characteristic, complemented
8#23752423C211yesmaximal, characteristic, complemented
9#23752421C211yesmaximal, characteristic, complemented
10#23752417C211yesmaximal, characteristic, complemented
11#23752415C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752210C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012768—24no—
20#18012758—24no—
21C2×Dic604C2211yescharacteristic
22C2×Dic604C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic
26C2×#14558992C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012739C2211yescharacteristic
30#18012737C2211yescharacteristic
31#18012726C2211yescharacteristic
32#18012721—21no—
33#18012721—21no—
34#18012716—21no—
35#18012716—21no—
36C4×Dic302C2211yescharacteristic
37#18012704C2211yescharacteristic
38D4×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40(C22⋊D151)⋊C4—21no—
41#18012696C2211yescharacteristic
42#18012695—21no—
43C2×Dic151⋊C4—21no—
44C4⋊C4×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic
46Dic151⋊C8C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
52#18012662C2211yescharacteristic
53#18012660C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559003—22no—
62#14559003—22no—
63#14559003—22no—
64#14559003D414yes—
65C2×Dic302—21no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69Q8×D151—22no—
70Q8×D151—22no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151—21no—
74C22×Dic151—21no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79Dic604—22no—
80Dic604—22no—
81#14558994—22no—
82#14558992—22no—
83#14558992—22no—
84#14558992—22no—
85#14558987—22no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C8×D151—22no—
89C4⋊Dic151—21no—
90C4⋊Dic151—21no—
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4D411yescharacteristic
98Dic151⋊C4D411yescharacteristic
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102(C2×D151)⋊C4D411yescharacteristic
103(C2×D151)⋊C4D411yescharacteristic
104C4×Dic151—21no—
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151—21no—
111SD16×C151—22no—
112D8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—21no—
123Dic302—21no—
124Dic302—21no—
125Dic302—21no—
126Dic302—42no—
127Dic302C2×D412yes—
128C22⋊D151—24no—
129C22⋊D151—42no—
130C2×Dic151—21no—
131C2×Dic151—24no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—42no—
136C2×Dic151—81no—
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—42no—
141C4×D151—81no—
142C4×D151C2×D412yes—
143C4×D151#4112yes—
144C151⋊C8—21no—
145C151⋊C8—21no—
146C23×C151—21no—
147C23×C151—21no—
148Q8×C151—21no—
149Q8×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151C2×D412yes—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—81no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2411yescharacteristic
160C8×C151—21no—
161C8×C151—21no—
162C22×C151—22no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151C22×D411yescharacteristic
169C2×D151—21no—
170C2×D151—21no—
171C2×D151#12112yes—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151C22×D411yescharacteristic
177C4×C151C2×#4111yescharacteristic
178Dic151—22no—
179Dic151—21no—
180Dic151—21no—
181Dic151—41no—
182Dic151—41no—
183Dic151—41no—
184Dic151#12112yes—
185C2×C151—42no—
186C2×C151—81no—
187C2×C151C2×#12111yescharacteristic
188C2×C151#57711yescharacteristic
189C2×C151#57811yescharacteristic
190D151—22no—
191C151#304611yescharacteristic, complemented, Sylow
192#3046—1511nomaximal, Sylow
193C2×#137—1511no—
194C2×#135—1511no—
195#536—1511no—
196#520—1511no—
197#464—1511no—
198#464—1511no—
199#463—1511no—
200#463D15111yescharacteristic, complemented
201#462—1511no—
202#462—1511no—
203#461—1511no—
204#461—1511no—
205#424—1511no—
206#417—1511no—
207C2×#103—1511no—
208C2×#41—1511no—
209C2×#41—1511no—
210C22×Q8—1511no—
211#137—3024no—
212#135—3024no—
213C2×Q16—1511no—
214C2×Q16—1511no—
215C2×Q16—1511no—
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic
220C2×D8C2×D15111yescharacteristic
221C2×M16—1511no—
222C22×C8—1511no—
223C4⋊Q8—1511no—
224C4⋊Q8—1511no—
225#124—1511no—
226#124C2×D15111yescharacteristic
227#123—3021no—
228#123—3021no—
229C22⋊Q8—3021no—
230C22⋊Q8—3021no—
231C4×Q8—1511no—
232C4×Q8—1511no—
233C4×D4—3021no—
234C4×D4—3021no—
235C4×D4—1511no—
236C4×D4C2×D15111yescharacteristic
237#117—3021no—
238#117—1511no—
239C2×C4⋊C4—3021no—
240C2×C4⋊C4—1511no—
241C4⋊C8—1511no—
242C4⋊C8—1511no—
243C4⋊C8—1511no—
244C4⋊C8C2×D15111yescharacteristic
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#103—1511no—
249#103—1511no—
250#103C2×D15111yescharacteristic
251#102—1511no—
252#102C2×D15111yescharacteristic
253#41—3022no—
254#41—3022no—
255#41—3022no—
256#41—1514no—
257C2×Q8—3021no—
258C2×Q8—3022no—
259C2×Q8—3022no—
260C2×Q8—1511no—
261C2×Q8—1511no—
262C2×Q8—1511no—
263C2×Q8C22×D15111yescharacteristic
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4C22×D15111yescharacteristic
267C2×D4C22×D15111yescharacteristic
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—3021no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—1511no—
275Q16—3022no—
276Q16—3022no—
277Q16—3022no—
278SD16—22no—
279SD16—3022no—
280SD16—3022no—
281SD16—3022no—
282D8—22no—
283M16—3022no—
284C2×C8—3022no—
285C2×C8—1511no—
286C2×C8—1511no—
287C2×C8C22×D15111yescharacteristic
288C2×C8C22×D15111yescharacteristic
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4—1511no—
299C4⋊C4C22×D15111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—1511no—
307C22⋊C4—1511no—
308C42—3021no—
309C42—3021no—
310C42—1511no—
311C42C22×D15111yescharacteristic
312C23—21no—
313C23—21no—
314C23—1511no—
315Q8—21no—
316Q8—21no—
317Q8—3021no—
318Q8—3021no—
319Q8—3021no—
320Q8—3021no—
321Q8—3021no—
322Q8—6042no—
323Q8—1512no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—3024no—
328D4—6042no—
329D4D4×D15112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—3021no—
334C2×C4—3024no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—6042no—
339C2×C4—6042no—
340C2×C4—1511no—
341C2×C4—1511no—
342C2×C4—1511no—
343C2×C4—1512no—
344C2×C4—1512no—
345C2×C4—12081no—
346C2×C4—12081no—
347C2×C4D4×D15111yescharacteristic
348C2×C4D4×D15111yescharacteristic
349C2×C4C23×D15111yescharacteristic
350C8—21no—
351C8—21no—
352C8—3021no—
353C8—3021no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3021no—
361C22—3021no—
362C22—1512no—
363C22C2×D4×D15111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3021no—
369C4—3021no—
370C4—3022no—
371C4—6041no—
372C4—6041no—
373C4—6041no—
374C4—1512no—
375C4C2×D4×D15111yescharacteristic
376C4#41×D15111yescharacteristic
377C2—42no—
378C2—81no—
379C2—3022no—
380C2#121×D15111yescharacteristic
381C2#2375302211yescharacteristic
382C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012758C2
hypercenter#463D151
hypocenterC151#3046
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18012768C2semidirect
3. #23752782C2semidirect
4. #23752691C2semidirect
5. #23752433C2semidirect
6. #23752431C2semidirect
7. #23752425C2semidirect
8. #23752423C2semidirect
9. #23752421C2semidirect
10. #23752417C2semidirect
11. #23752415C2semidirect
12. #23752237C2semidirect
13. #23752210C2semidirect
14. #103×D151C2semidirect
15. #463×C151C2semidirect
191. C151#3046semidirect
200. #463D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C2×#180127582
#237527822
#237526912
#237524332
#237524312
#237524252
#237524232
#237524212
#237524172
#237524152
#237522372
#237522102
#103×D1512
#463×C1512
#3046151