Finite Group Databasebeta

← #34078561

Subgroups — #34078561

Order 19328.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012759C211yesmaximal, characteristic, complemented
2#23752758C211yesmaximal, characteristic, complemented
3#41×Dic151C211yesmaximal, characteristic, complemented
4#23752436C211yesmaximal, characteristic, complemented
5#23752432C211yesmaximal, characteristic, complemented
6#23752429C211yesmaximal, characteristic, complemented
7#23752425C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752415C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752405C211yesmaximal, characteristic, complemented
12C2×Dic151⋊C8C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14#23752208C211yesmaximal, characteristic, complemented
15C2×#135×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17#18012759—24no—
18C2×#14558994C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012737C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012728C2211yescharacteristic
26#18012726C2211yescharacteristic
27#18012711—21no—
28#18012711—21no—
29Q8×Dic151C2211yescharacteristic
30Q8×Dic151C2211yescharacteristic
31D4×Dic151—21no—
32D4×Dic151—21no—
33D4×Dic151C2211yescharacteristic
34D4×Dic151C2211yescharacteristic
35C4×C22⋊D151—21no—
36C4×C22⋊D151—21no—
37#18012698—21no—
38#18012698C2211yescharacteristic
39C2×C4×Dic151—21no—
40C2×C4×Dic151C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012660C2211yescharacteristic
52#18012660C2211yescharacteristic
53C2×#41×C151C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic
55#135×C151—24no—
56C2×Q16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic
59C2×D8×C151C2211yescharacteristic
60C22×C8×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—22no—
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C22×Dic151—21no—
69C22×Dic151—21no—
70C22×Dic151D411yescharacteristic
71C22×Dic151D411yescharacteristic
72C2×C4×D151—21no—
73#14558994—22no—
74#14558992—22no—
75#14558991—22no—
76#14558989—22no—
77C2×C151⋊C8—22no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151—21no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151D411yescharacteristic
97C4×Dic151D411yescharacteristic
98C4×Dic151C2311yescharacteristic
99C4×Dic151C2311yescharacteristic
100#41×C151—22no—
101#41×C151—22no—
102#41×C151—22no—
103#41×C151D414yescomplemented
104C2×Q8×C151C2311yescharacteristic
105C2×Q8×C151C2311yescharacteristic
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151C2311yescharacteristic
113Q16×C151—22no—
114SD16×C151—22no—
115SD16×C151—22no—
116D8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C22×D151—21no—
121Dic302—21no—
122Dic302—21no—
123D604—21no—
124D604—21no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C2×Dic151—22no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—41no—
133C2×Dic151—42no—
134C2×Dic151—42no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C4×D151—42no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151C2×D411yescharacteristic
145Q8×C151—21no—
146Q8×C151—21no—
147Q8×C151—21no—
148Q8×C151C2×D412yes—
149D4×C151—24no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—42no—
154D4×C151C2×D412yes—
155C2×C4×C151—21no—
156C2×C4×C151—24no—
157C2×C4×C151—21no—
158C2×C4×C151—42no—
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2×D412yes—
161C2×C4×C151#4112yes—
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—22no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151#12112yes—
174C22×C151C22×D411yescharacteristic
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C4×C151—22no—
179C4×C151—41no—
180C4×C151#12112yes—
181C4×C151C22×D411yescharacteristic
182C4×C151C2×#4111yescharacteristic
183Dic151—21no—
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189Dic151#13512yescomplemented
190C2×C151—22no—
191C2×C151—42no—
192C2×C151—81no—
193C2×C151C2×#12111yescharacteristic
194C2×C151C2×#13511yescharacteristic
195C2×C151#57511yescharacteristic
196D151—81no—
197C151#303511yescharacteristic, complemented, Sylow
198#3035—1511nomaximal, Sylow
199C2×#135—1511no—
200C2×#135D15111yescharacteristic, complemented
201#532—1511no—
202C4×#41—1511no—
203#464—1511no—
204#464—1511no—
205#463—1511no—
206#463—1511no—
207#462—1511no—
208#461—1511no—
209#460—1511no—
210#459—1511no—
211C2×C4⋊C8—1511no—
212#416—1511no—
213#416—1511no—
214C2×#41—1511no—
215C2×#41C2×D15111yescharacteristic
216C2×#41C2×D15111yescharacteristic
217#135—24no—
218#135—3024no—
219C2×Q16—1511no—
220C2×Q16C2×D15111yescharacteristic
221C2×SD16—1511no—
222C2×SD16—1511no—
223C2×SD16C2×D15111yescharacteristic
224C2×SD16C2×D15111yescharacteristic
225C2×D8—1511no—
226C2×D8C2×D15111yescharacteristic
227C22×C8—1511no—
228C22×C8C2×D15111yescharacteristic
229C4⋊Q8—1511no—
230#127—1511no—
231#124—1511no—
232#124—1511no—
233#121—3021no—
234#121—3021no—
235C4×Q8—1511no—
236C4×Q8—1511no—
237C4×D4—3021no—
238C4×D4—3021no—
239C4×D4—3021no—
240C4×D4—3021no—
241C4×D4—1511no—
242C4×D4—1511no—
243#117—3021no—
244#117—1511no—
245C2×C42—3021no—
246C2×C42—1511no—
247C4⋊C8—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8—1511no—
251#103—1511no—
252#103—1511no—
253#103—1511no—
254#103—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102—1511no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—3022no—
263#41—3022no—
264#41C22⋊D15114yescomplemented
265C2×Q8—1511no—
266C2×Q8C22×D15111yescharacteristic
267C2×Q8C22×D15111yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—1511no—
274C2×D4C22×D15111yescharacteristic
275C2×D4C22×D15111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4C22×D15111yescharacteristic
284Q16—22no—
285Q16—3022no—
286SD16—22no—
287SD16—22no—
288SD16—3022no—
289SD16—3022no—
290D8—22no—
291D8—3022no—
292C2×C8—22no—
293C2×C8—3022no—
294C2×C8—1511no—
295C2×C8—1511no—
296C2×C8C22×D15111yescharacteristic
297C2×C8C22×D15111yescharacteristic
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—1511no—
303C4⋊C4—1511no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C42—3021no—
312C42—3021no—
313C42—3021no—
314C42—1511no—
315C42—1511no—
316C42—1511no—
317C42—1511no—
318C23—21no—
319C23—21no—
320C23—3021no—
321C23D4×D15111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3021no—
326Q8—3021no—
327Q8C2×C22⋊D15112yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—3021no—
334D4—3021no—
335D4—6042no—
336D4—6042no—
337D4—6042no—
338D4C2×C22⋊D15112yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3022no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—6041no—
348C2×C4—6042no—
349C2×C4—6042no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4D4×D15111yescharacteristic
356C2×C4C2×C22⋊D15112yes—
357C2×C4#1455900312yes—
358C2×C4C23×D15111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3021no—
362C8—3021no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22#1801271112yes—
375C22C2×D4×D15111yescharacteristic
376C4—22no—
377C4—41no—
378C4—3021no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4—6041no—
384C4—1512no—
385C4#1801271112yes—
386C4C22×C22⋊D15111yescharacteristic
387C4C2×#1455900311yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—12081no—
392C2C2×#1801271111yescharacteristic
393C2#135×D15111yescharacteristic
394C2#2375300911yescharacteristic
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#135×C151C2
socleC22×C151C22×D4
hypercenterC2×#135D151
hypocenterC151#3035
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18012759C2semidirect
2. #23752758C2semidirect
3. #41×Dic151C2semidirect
4. #23752436C2semidirect
5. #23752432C2semidirect
6. #23752429C2semidirect
7. #23752425C2semidirect
8. #23752420C2semidirect
9. #23752415C2semidirect
10. #23752410C2semidirect
11. #23752405C2semidirect
12. C2×Dic151⋊C8C2semidirect
13. #23752209C2semidirect
14. #23752208C2semidirect
15. C2×#135×C151C2semidirect
103. #41×C151D4semidirect
189. Dic151#135semidirect
197. C151#3035semidirect
200. C2×#135D151semidirect
264. #41C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
#237527582
#41×Dic1512
#237524362
#237524322
#237524292
#237524252
#237524202
#237524152
#237524102
#237524052
C2×Dic151⋊C82
#237522092
#237522082
C2×#135×C1512
#3035151