Finite Group Databasebeta

← #34054142

Subgroups — #34054142

Order 19072.

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×#18011931C211yesmaximal, characteristic, complemented
2#23750171C211yesmaximal, characteristic, complemented
3#41×Dic149C211yesmaximal, characteristic, complemented
4#23749849C211yesmaximal, characteristic, complemented
5#23749845C211yesmaximal, characteristic, complemented
6#23749842C211yesmaximal, characteristic, complemented
7#23749838C211yesmaximal, characteristic, complemented
8#23749833C211yesmaximal, characteristic, complemented
9#23749828C211yesmaximal, characteristic, complemented
10#23749823C211yesmaximal, characteristic, complemented
11#23749818C211yesmaximal, characteristic, complemented
12C2×#18011840C211yesmaximal, characteristic, complemented
13#23749622C211yesmaximal, characteristic, complemented
14#23749621C211yesmaximal, characteristic, complemented
15C2×#135×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17#18011931—24no—
18C2×#14558726C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011907C2211yescharacteristic
25#18011900C2211yescharacteristic
26#18011898C2211yescharacteristic
27#18011883—21no—
28#18011883—21no—
29Q8×Dic149C2211yescharacteristic
30Q8×Dic149C2211yescharacteristic
31D4×Dic149—21no—
32D4×Dic149—21no—
33D4×Dic149C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35C4×C22⋊D149—21no—
36C4×C22⋊D149—21no—
37#18011870—21no—
38#18011870C2211yescharacteristic
39C2×C4×Dic149—21no—
40C2×C4×Dic149C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011835C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011832C2211yescharacteristic
52#18011832C2211yescharacteristic
53C2×#41×C149C2211yescharacteristic
54C2×#41×C149C2211yescharacteristic
55#135×C149—24no—
56C2×Q16×C149C2211yescharacteristic
57C2×SD16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic
59C2×D8×C149C2211yescharacteristic
60C22×C8×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—22no—
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C22×Dic149—21no—
70C22×Dic149D411yescharacteristic
71C22×Dic149D411yescharacteristic
72C2×C4×D149—21no—
73#14558726—22no—
74#14558724—22no—
75#14558723—22no—
76#14558721—22no—
77C2×#11924746—22no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C4⋊Dic149—21no—
81C4⋊Dic149—21no—
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149D411yescharacteristic
97C4×Dic149D411yescharacteristic
98C4×Dic149C2311yescharacteristic
99C4×Dic149C2311yescharacteristic
100#41×C149—22no—
101#41×C149—22no—
102#41×C149—22no—
103#41×C149D414yescomplemented
104C2×Q8×C149C2311yescharacteristic
105C2×Q8×C149C2311yescharacteristic
106C2×D4×C149—21no—
107C2×D4×C149—21no—
108C2×D4×C149C2311yescharacteristic
109C2×D4×C149C2311yescharacteristic
110C22×C4×C149—21no—
111C22×C4×C149—21no—
112C22×C4×C149C2311yescharacteristic
113Q16×C149—22no—
114SD16×C149—22no—
115SD16×C149—22no—
116D8×C149—22no—
117C2×C8×C149—22no—
118C2×C8×C149C2311yescharacteristic
119C2×C8×C149C2311yescharacteristic
120C22×D149—21no—
121Dic298—21no—
122Dic298—21no—
123D596—21no—
124D596—21no—
125C22⋊D149—42no—
126C22⋊D149—42no—
127C22⋊D149—42no—
128C2×Dic149—22no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—41no—
133C2×Dic149—42no—
134C2×Dic149—42no—
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—42no—
140#11924746—21no—
141#11924746—21no—
142C23×C149—21no—
143C23×C149—21no—
144C23×C149C2×D411yescharacteristic
145Q8×C149—21no—
146Q8×C149—21no—
147Q8×C149—21no—
148Q8×C149C2×D412yes—
149D4×C149—24no—
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—42no—
154D4×C149C2×D412yes—
155C2×C4×C149—21no—
156C2×C4×C149—24no—
157C2×C4×C149—21no—
158C2×C4×C149—42no—
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2×D412yes—
161C2×C4×C149#4112yes—
162C2×C4×C149C2411yescharacteristic
163C8×C149—21no—
164C8×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—22no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149#12112yes—
174C22×C149C22×D411yescharacteristic
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C4×C149—22no—
179C4×C149—41no—
180C4×C149#12112yes—
181C4×C149C22×D411yescharacteristic
182C4×C149C2×#4111yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189Dic149#13512yescomplemented
190C2×C149—22no—
191C2×C149—42no—
192C2×C149—81no—
193C2×C149C2×#12111yescharacteristic
194C2×C149C2×#13511yescharacteristic
195C2×C149#57511yescharacteristic
196D149—81no—
197C149#303511yescharacteristic, complemented, Sylow
198#3035—1491nomaximal, Sylow
199C2×#135—1491no—
200C2×#135D14911yescharacteristic, complemented
201#532—1491no—
202C4×#41—1491no—
203#464—1491no—
204#464—1491no—
205#463—1491no—
206#463—1491no—
207#462—1491no—
208#461—1491no—
209#460—1491no—
210#459—1491no—
211C2×C4⋊C8—1491no—
212#416—1491no—
213#416—1491no—
214C2×#41—1491no—
215C2×#41C2×D14911yescharacteristic
216C2×#41C2×D14911yescharacteristic
217#135—24no—
218#135—2984no—
219C2×Q16—1491no—
220C2×Q16C2×D14911yescharacteristic
221C2×SD16—1491no—
222C2×SD16—1491no—
223C2×SD16C2×D14911yescharacteristic
224C2×SD16C2×D14911yescharacteristic
225C2×D8—1491no—
226C2×D8C2×D14911yescharacteristic
227C22×C8—1491no—
228C22×C8C2×D14911yescharacteristic
229C4⋊Q8—1491no—
230#127—1491no—
231#124—1491no—
232#124—1491no—
233#121—2981no—
234#121—2981no—
235C4×Q8—1491no—
236C4×Q8—1491no—
237C4×D4—2981no—
238C4×D4—2981no—
239C4×D4—2981no—
240C4×D4—2981no—
241C4×D4—1491no—
242C4×D4—1491no—
243#117—2981no—
244#117—1491no—
245C2×C42—2981no—
246C2×C42—1491no—
247C4⋊C8—1491no—
248C4⋊C8—1491no—
249C4⋊C8—1491no—
250C4⋊C8—1491no—
251#103—1491no—
252#103—1491no—
253#103—1491no—
254#103—1491no—
255#102—1491no—
256#102—1491no—
257#102—1491no—
258#102—1491no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—2982no—
263#41—2982no—
264#41C22⋊D14914yescomplemented
265C2×Q8—1491no—
266C2×Q8C22×D14911yescharacteristic
267C2×Q8C22×D14911yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—1491no—
274C2×D4C22×D14911yescharacteristic
275C2×D4C22×D14911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2981no—
279C22×C4—2981no—
280C22×C4—2981no—
281C22×C4—1491no—
282C22×C4—1491no—
283C22×C4C22×D14911yescharacteristic
284Q16—22no—
285Q16—2982no—
286SD16—22no—
287SD16—22no—
288SD16—2982no—
289SD16—2982no—
290D8—22no—
291D8—2982no—
292C2×C8—22no—
293C2×C8—2982no—
294C2×C8—1491no—
295C2×C8—1491no—
296C2×C8C22×D14911yescharacteristic
297C2×C8C22×D14911yescharacteristic
298C4⋊C4—2981no—
299C4⋊C4—2981no—
300C4⋊C4—2981no—
301C4⋊C4—2981no—
302C4⋊C4—1491no—
303C4⋊C4—1491no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C42—2981no—
312C42—2981no—
313C42—2981no—
314C42—1491no—
315C42—1491no—
316C42—1491no—
317C42—1491no—
318C23—21no—
319C23—21no—
320C23—2981no—
321C23D4×D14911yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—2981no—
326Q8—2981no—
327Q8C2×C22⋊D14912yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—2981no—
334D4—2981no—
335D4—5962no—
336D4—5962no—
337D4—5962no—
338D4C2×C22⋊D14912yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2982no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—5961no—
348C2×C4—5962no—
349C2×C4—5962no—
350C2×C4—5962no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4—1491no—
354C2×C4—1491no—
355C2×C4D4×D14911yescharacteristic
356C2×C4C2×C22⋊D14912yes—
357C2×C4#1455873512yes—
358C2×C4C23×D14911yescharacteristic
359C8—21no—
360C8—21no—
361C8—2981no—
362C8—2981no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22#1801188312yes—
375C22C2×D4×D14911yescharacteristic
376C4—22no—
377C4—41no—
378C4—2981no—
379C4—2981no—
380C4—2981no—
381C4—5961no—
382C4—5961no—
383C4—5961no—
384C4—1492no—
385C4#1801188312yes—
386C4C22×C22⋊D14911yescharacteristic
387C4C2×#1455873511yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—11921no—
392C2C2×#1801188311yescharacteristic
393C2#135×D14911yescharacteristic
394C2#2375042211yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3035
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18011931C2semidirect
2. #23750171C2semidirect
3. #41×Dic149C2semidirect
4. #23749849C2semidirect
5. #23749845C2semidirect
6. #23749842C2semidirect
7. #23749838C2semidirect
8. #23749833C2semidirect
9. #23749828C2semidirect
10. #23749823C2semidirect
11. #23749818C2semidirect
12. C2×#18011840C2semidirect
13. #23749622C2semidirect
14. #23749621C2semidirect
15. C2×#135×C149C2semidirect
103. #41×C149D4semidirect
189. Dic149#135semidirect
197. C149#3035semidirect
200. C2×#135D149semidirect
264. #41C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119312
#237501712
#41×Dic1492
#237498492
#237498452
#237498422
#237498382
#237498332
#237498282
#237498232
#237498182
C2×#180118402
#237496222
#237496212
C2×#135×C1492
#3035149