Finite Group Databasebeta

← #34078638

Subgroups — #34078638

Order 19328.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012768C211yesmaximal, characteristic
2C2×Q16×D151C211yesmaximal, characteristic, complemented
3#23752782C211yesmaximal, characteristic
4#23752688C211yesmaximal, characteristic, complemented
5#23752433C211yesmaximal, characteristic, complemented
6#23752432C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752423C211yesmaximal, characteristic, complemented
9#23752422C211yesmaximal, characteristic, complemented
10#23752421C211yesmaximal, characteristic, complemented
11#23752420C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752219C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012768—24no—
20C2×Dic604C2211yescharacteristic
21C2×Dic604C2211yescharacteristic
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558994C2211yescharacteristic
25Q16×D151—24no—
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—
36Q8×Dic151C2211yescharacteristic
37C4×Dic302—21no—
38C4×Dic302C2211yescharacteristic
39#18012704—21no—
40#18012704C2211yescharacteristic
41#18012697—21no—
42#18012697C2211yescharacteristic
43#18012696—21no—
44#18012696C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic
46Dic151⋊C8C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
52#18012662C2211yescharacteristic
53#18012660C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559003—22no—
62#14559003—22no—
63C2×Dic302—21no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68Q8×D151—22no—
69Q8×D151—22no—
70Q8×D151—22no—
71Q8×D151D414yes—
72C2×C22⋊D151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77Dic604—22no—
78Dic604—22no—
79#14558994—22no—
80#14558994—22no—
81#14558994—22no—
82#14558992—22no—
83#14558987—22no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C8×D151—22no—
87C4⋊Dic151—21no—
88C4⋊Dic151—21no—
89C4⋊Dic151—21no—
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96Dic151⋊C4D411yescharacteristic
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101(C2×D151)⋊C4D411yescharacteristic
102C4×Dic151—21no—
103C4×Dic151—21no—
104C4×Dic151—21no—
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110Q16×C151—22no—
111SD16×C151—22no—
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C4⋊C4×C151—21no—
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C42×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—24no—
123Dic302—21no—
124Dic302—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—42no—
128Dic302C2×D412yes—
129C22⋊D151—42no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—42no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—24no—
139C4×D151—42no—
140C4×D151C2×D412yes—
141C4×D151#4112yes—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C23×C151—21no—
145Q8×C151—21no—
146Q8×C151—21no—
147Q8×C151—21no—
148Q8×C151C2×D412yes—
149D4×C151—21no—
150D4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2×D411yescharacteristic
156C2×C4×C151C2411yescharacteristic
157C8×C151—21no—
158C8×C151—21no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151C22×D411yescharacteristic
163C2×D151—21no—
164C2×D151—21no—
165C2×D151#12112yes—
166C4×C151—22no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151C22×D411yescharacteristic
172C4×C151C2×#4111yescharacteristic
173Dic151—22no—
174Dic151—21no—
175Dic151—21no—
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179Dic151#12112yes—
180C2×C151—81no—
181C2×C151C2×#12111yescharacteristic
182C2×C151#57811yescharacteristic
183C2×C151#57811yescharacteristic
184D151—22no—
185C151#304411yescharacteristic, complemented, Sylow
186#3044—1511nomaximal, Sylow
187C2×#137—1511no—
188C22×Q16—1511no—
189#536—1511no—
190#519—1511no—
191#464—1511no—
192#464—1511no—
193#464—1511no—
194#464D15111yescharacteristic, complemented
195#462—1511no—
196#462—1511no—
197#462—1511no—
198#462—1511no—
199#424—1511no—
200#419—1511no—
201#416—1511no—
202C2×#41—1511no—
203C22×Q8—1511no—
204C22×Q8—1511no—
205#137—3024no—
206C2×Q16—3024no—
207C2×Q16—1511no—
208C2×Q16—1511no—
209C2×Q16—1511no—
210C2×Q16—1511no—
211C2×Q16—1511no—
212C2×Q16C2×D15111yescharacteristic
213C2×SD16—1511no—
214C2×SD16C2×D15111yescharacteristic
215C2×M16—1511no—
216C22×C8—1511no—
217C4⋊Q8—1511no—
218C4⋊Q8—1511no—
219#124—1511no—
220#124C2×D15111yescharacteristic
221#123—3021no—
222#123—3021no—
223C22⋊Q8—3021no—
224C22⋊Q8—3021no—
225C4×Q8—3021no—
226C4×Q8—3021no—
227C4×Q8—1511no—
228C4×Q8—1511no—
229C4×Q8—1511no—
230C4×Q8C2×D15111yescharacteristic
231#117—3021no—
232#117—3021no—
233#117—1511no—
234#117—1511no—
235C4⋊C8—1511no—
236C4⋊C8—1511no—
237C4⋊C8—1511no—
238C4⋊C8C2×D15111yescharacteristic
239#103—1511no—
240#103—1511no—
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#103C2×D15111yescharacteristic
245#102—1511no—
246#102C2×D15111yescharacteristic
247#41—3022no—
248#41—3022no—
249C2×Q8—3021no—
250C2×Q8—3021no—
251C2×Q8—3022no—
252C2×Q8—3022no—
253C2×Q8—3022no—
254C2×Q8—1514no—
255C2×Q8—1511no—
256C2×Q8—1511no—
257C2×Q8—1511no—
258C2×Q8C22×D15111yescharacteristic
259C2×Q8C22×D15111yescharacteristic
260C2×D4—3021no—
261C2×D4C22×D15111yescharacteristic
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—1511no—
266Q16—22no—
267Q16—3022no—
268Q16—3022no—
269Q16—3022no—
270Q16—3022no—
271Q16—3022no—
272SD16—22no—
273SD16—3022no—
274M16—3022no—
275C2×C8—3022no—
276C2×C8—1511no—
277C2×C8—1511no—
278C2×C8C22×D15111yescharacteristic
279C2×C8C22×D15111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—1511no—
289C4⋊C4—1511no—
290C4⋊C4—1511no—
291C4⋊C4C22×D15111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—1511no—
298C22⋊C4—1511no—
299C42—21no—
300C42—3021no—
301C42—3021no—
302C42—3021no—
303C42—3021no—
304C42—1511no—
305C42C22×D15111yescharacteristic
306C23—21no—
307C23—1511no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—3024no—
312Q8—3021no—
313Q8—3021no—
314Q8—3021no—
315Q8—3021no—
316Q8—3021no—
317Q8—6042no—
318Q8—1512no—
319Q8D4×D15112yes—
320D4—21no—
321D4—21no—
322D4—6042no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—3024no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—6042no—
332C2×C4—6042no—
333C2×C4—1511no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4—1512no—
337C2×C4—1512no—
338C2×C4D4×D15111yescharacteristic
339C2×C4D4×D15111yescharacteristic
340C2×C4C23×D15111yescharacteristic
341C8—21no—
342C8—21no—
343C8—3021no—
344C8—3021no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—3021no—
349C22—3021no—
350C22—1512no—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—3021no—
358C4—3021no—
359C4—3022no—
360C4—6041no—
361C4—6041no—
362C4—6041no—
363C4—1512no—
364C4C2×D4×D15111yescharacteristic
365C4#41×D15111yescharacteristic
366C2—81no—
367C2—3022no—
368C2#121×D15111yescharacteristic
369C2#2375302611yescharacteristic
370C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559003C22
hypercenter#464D151
hypocenterC151#3044
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D151C2semidirect
4. #23752688C2semidirect
5. #23752433C2semidirect
6. #23752432C2semidirect
7. #23752431C2semidirect
8. #23752423C2semidirect
9. #23752422C2semidirect
10. #23752421C2semidirect
11. #23752420C2semidirect
12. #23752237C2semidirect
13. #23752219C2semidirect
15. #464×C151C2semidirect
185. C151#3044semidirect
194. #464D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C2×Q16×D1512
#237527822
#237526882
#237524332
#237524322
#237524312
#237524232
#237524222
#237524212
#237524202
#237522372
#237522192
#237522052
#464×C1512
#3044151