Finite Group Databasebeta

← #34078794

Subgroups — #34078794

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012768C211yesmaximal, characteristic, complemented
2C2×#18012745C211yesmaximal, characteristic, complemented
3#23752791C211yesmaximal, characteristic
4#23752785C211yesmaximal, characteristic, complemented
5#23752471C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752456C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752453C211yesmaximal, characteristic, complemented
10#23752452C211yesmaximal, characteristic, complemented
11#23752440C211yesmaximal, characteristic, complemented
12#23752251C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012768—24no—
20C2×Dic604C2211yescharacteristic
21C2×#14558994C2211yescharacteristic
22C2×#14558992C2211yescharacteristic
23#18012745—24no—
24C2×#14558988C2211yescharacteristic
25C2×#14558987C2211yescharacteristic
26C2×#14558987C2211yescharacteristic
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012738—21no—
30#18012725—21no—
31#18012724—21no—
32#18012721—21no—
33#18012719C2211yescharacteristic
34#18012719C2211yescharacteristic
35#18012718C2211yescharacteristic
36#18012718C2211yescharacteristic
37#18012716—21no—
38#18012715C2211yescharacteristic
39#18012712—21no—
40#18012711—21no—
41#18012710—21no—
42#18012710C2211yescharacteristic
43#18012697C2211yescharacteristic
44C4⋊C4×D151C2211yescharacteristic
45#18012673C2211yescharacteristic
46#18012672C2211yescharacteristic
47#18012670C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
52#18012662C2211yescharacteristic
53#18012660C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—22no—
63#14559003—22no—
64#14559003—22no—
65C2×Dic302—21no—
66C2×Dic302D411yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69Q8×D151—22no—
70Q8×D151—22no—
71C2×D604D411yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151D411yescharacteristic
75C2×C22⋊D151D411yescharacteristic
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80C2×C4×D151C2311yescharacteristic
81Dic604—22no—
82#14558994—22no—
83#14558992—22no—
84#14558988—22no—
85#14558987—22no—
86#14558987D414yescomplemented
87C2×C151⋊C8C2311yescharacteristic
88C2×C151⋊C8C2311yescharacteristic
89C8×D151—22no—
90C8×D151—22no—
91C4⋊Dic151—21no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106C4×Dic151—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111SD16×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151C2×D411yescharacteristic
121C22×D151C2×D411yescharacteristic
122Dic302—22no—
123Dic302—21no—
124Dic302—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—42no—
128D604—22no—
129C22⋊D151—22no—
130C22⋊D151—22no—
131C22⋊D151—42no—
132C22⋊D151—81no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—42no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—42no—
143C4×D151—81no—
144C4×D151C2×D412yes—
145C4×D151#4112yes—
146C151⋊C8—21no—
147C151⋊C8C2×D412yes—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—81no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151C2×D412yes—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151#12112yes—
177C4×C151—21no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151C22×D411yescharacteristic
182C4×C151C2×#4111yescharacteristic
183Dic151—21no—
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151#12112yes—
189C2×C151—41no—
190C2×C151—81no—
191C2×C151C2×#12111yescharacteristic
192C2×C151#57711yescharacteristic
193C2×C151#57811yescharacteristic
194D151—22no—
195D151—41no—
196C151#306311yescharacteristic, complemented, Sylow
197#3063—1511nomaximal, Sylow
198C2×#137—1511no—
199C2×#131—1511no—
200#537—1511no—
201#536—1511no—
202#470—1511no—
203#470—1511no—
204#468—1511no—
205#468—1511no—
206#467—1511no—
207#467—1511no—
208#465—1511no—
209#465D15111yescharacteristic, complemented
210#428—1511no—
211#416—1511no—
212C2×#103—1511no—
213C2×#41—1511no—
214C2×#41—1511no—
215C22×Q8—1511no—
216#137—3024no—
217C2×Q16—1511no—
218C2×Q16—1511no—
219C2×SD16—1511no—
220C2×SD16C2×D15111yescharacteristic
221#131—3024no—
222C2×M16—1511no—
223C2×M16—1511no—
224C2×M16—1511no—
225C22×C8—1511no—
226C22×C8—1511no—
227C22×C8C2×D15111yescharacteristic
228C4⋊Q8—3021no—
229#124—3021no—
230#123—3021no—
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—1511no—
234C22⋊Q8—1511no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237C22⋊Q8—1511no—
238C22⋊Q8C2×D15111yescharacteristic
239#121—3021no—
240#121—3021no—
241#121—3021no—
242#121—1511no—
243#121C2×D15111yescharacteristic
244#117—1511no—
245C2×C4⋊C4—1511no—
246#107—1511no—
247#107—1511no—
248#106—1511no—
249#106C2×D15111yescharacteristic
250#103—1511no—
251#103—1511no—
252#103—1511no—
253#103—1511no—
254#103—1511no—
255#103C2×D15111yescharacteristic
256#102—1511no—
257#102C2×D15111yescharacteristic
258#41—3022no—
259#41—3022no—
260#41—3022no—
261#41—3022no—
262C2×Q8—3021no—
263C2×Q8—3022no—
264C2×Q8—3022no—
265C2×Q8—1511no—
266C2×Q8—1511no—
267C2×Q8—1511no—
268C2×Q8C22×D15111yescharacteristic
269C2×D4—21no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4C22×D15111yescharacteristic
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282Q16—3022no—
283Q16—3022no—
284SD16—22no—
285SD16—3022no—
286M16—3022no—
287M16—3022no—
288M16—1514no—
289C2×C8—22no—
290C2×C8—3022no—
291C2×C8—3022no—
292C2×C8—1511no—
293C2×C8—1511no—
294C2×C8C22×D15111yescharacteristic
295C2×C8C22×D15111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—1511no—
304C4⋊C4—1511no—
305C4⋊C4C22×D15111yescharacteristic
306C4⋊C4C22×D15111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C42—3021no—
317C23—21no—
318C23—1511no—
319C23—1511no—
320C23D4×D15111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—3022no—
324Q8—3021no—
325Q8—3021no—
326Q8—3021no—
327Q8—3021no—
328Q8—6042no—
329D4—21no—
330D4—21no—
331D4—81no—
332D4—3022no—
333D4—3022no—
334D4—3022no—
335D4—6042no—
336D4—12081no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—6042no—
349C2×C4—6042no—
350C2×C4—1511no—
351C2×C4—1511no—
352C2×C4—1512no—
353C2×C4—1512no—
354C2×C4—12081no—
355C2×C4D4×D15111yescharacteristic
356C2×C4C23×D15111yescharacteristic
357C8—21no—
358C8—3021no—
359C8—1512no—
360C8D4×D15112yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—3021no—
368C22—3021no—
369C22—3021no—
370C22—3021no—
371C22—3021no—
372C22—1512no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3021no—
379C4—6041no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4—1512no—
384C4C2×D4×D15111yescharacteristic
385C4#41×D15111yescharacteristic
386C2—41no—
387C2—81no—
388C2—3022no—
389C2—6041no—
390C2#121×D15111yescharacteristic
391C2#2375301811yescharacteristic
392C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752791C2
hypercenter#465D151
hypocenterC151#3063
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18012768C2semidirect
2. C2×#18012745C2semidirect
4. #23752785C2semidirect
5. #23752471C2semidirect
6. #23752468C2semidirect
7. #23752456C2semidirect
8. #23752455C2semidirect
9. #23752453C2semidirect
10. #23752452C2semidirect
11. #23752440C2semidirect
12. #23752251C2semidirect
13. #23752205C2semidirect
14. #103×D151C2semidirect
15. #465×C151C2semidirect
86. #14558987D4semidirect
196. C151#3063semidirect
209. #465D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C2×#180127452
#237527912
#237527852
#237524712
#237524682
#237524562
#237524552
#237524532
#237524522
#237524402
#237522512
#237522052
#103×D1512
#465×C1512
#3063151