Finite Group Databasebeta

← #34056350

Subgroups — #34056350

Order 19072.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic, complemented
2C2×#18011941C211yesmaximal, characteristic, complemented
3#23750294C211yesmaximal, characteristic
4#23750288C211yesmaximal, characteristic, complemented
5#23749996C211yesmaximal, characteristic, complemented
6#23749873C211yesmaximal, characteristic, complemented
7#23749870C211yesmaximal, characteristic, complemented
8#23749833C211yesmaximal, characteristic, complemented
9#23749824C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749766C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13#23749717C211yesmaximal, characteristic, complemented
14#23749700C211yesmaximal, characteristic, complemented
15#452×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19#18011943—24no—
20#18011941—24no—
21C2×#14558726C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558725C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558723C2211yescharacteristic
28C2×#14558720C2211yescharacteristic
29C2×#14558719C2211yescharacteristic
30#18011910—21no—
31#18011909C2211yescharacteristic
32#18011907—21no—
33#18011907C2211yescharacteristic
34#18011891C2211yescharacteristic
35#18011889—21no—
36#18011888—21no—
37#18011885—21no—
38#18011885C2211yescharacteristic
39#18011882—21no—
40#18011882C2211yescharacteristic
41Q8×Dic149C2211yescharacteristic
42#18011876C2211yescharacteristic
43C4×C22⋊D149—21no—
44C4×C22⋊D149C2211yescharacteristic
45#18011871—21no—
46#18011844C2211yescharacteristic
47#18011840C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011835C2211yescharacteristic
51#18011831C2211yescharacteristic
52#18011823C2211yescharacteristic
53C8×Dic149C2211yescharacteristic
54C2×#41×C149C2211yescharacteristic
55C2×Q16×C149C2211yescharacteristic
56C2×SD16×C149C2211yescharacteristic
57C22⋊Q8×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#102×C149C2211yescharacteristic
60C22⋊C8×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—41no—
63C2×Dic298—21no—
64C2×Dic298—22no—
65C2×Dic298—21no—
66C2×Dic298—41no—
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69Q8×D149—22no—
70Q8×D149—41no—
71C2×D596—21no—
72C2×D596C2311yescharacteristic
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149D411yescharacteristic
78C22×Dic149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82#14558726—22no—
83#14558726D414yescomplemented
84#14558725—22no—
85#14558725—41no—
86#14558724—22no—
87#14558724—22no—
88#14558723—22no—
89#14558720—22no—
90#14558719—22no—
91C2×#11924746C2311yescharacteristic
92C2×#11924746C2311yescharacteristic
93C4⋊Dic149—21no—
94C4⋊Dic149—21no—
95C4⋊Dic149C2311yescharacteristic
96#14558715—21no—
97#14558715—21no—
98#14558715—21no—
99#14558715D411yescharacteristic
100C22⋊Dic149—21no—
101C22⋊Dic149D411yescharacteristic
102#14558713—21no—
103#14558713—21no—
104#14558713D411yescharacteristic
105C4×Dic149—21no—
106C4×Dic149—21no—
107C4×Dic149C2311yescharacteristic
108#41×C149—22no—
109#41×C149—41no—
110C2×Q8×C149C2311yescharacteristic
111C2×Q8×C149C2311yescharacteristic
112C2×D4×C149—21no—
113C2×D4×C149C2311yescharacteristic
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116Q16×C149—22no—
117SD16×C149—41no—
118C2×C8×C149C2311yescharacteristic
119C2×C8×C149C2311yescharacteristic
120C4⋊C4×C149—21no—
121C4⋊C4×C149C2311yescharacteristic
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—42no—
129Dic298—42no—
130Dic298C2×D412yes—
131D596—21no—
132D596—21no—
133D596—42no—
134C22⋊D149—22no—
135C22⋊D149—42no—
136C22⋊D149—81no—
137C22⋊D149—81no—
138C22⋊D149—81no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—42no—
143C2×Dic149C2×D411yescharacteristic
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—42no—
149C4×D149—42no—
150#11924746—21no—
151#11924746C2×D412yes—
152C23×C149—21no—
153C23×C149C2×D411yescharacteristic
154Q8×C149—21no—
155Q8×C149—21no—
156Q8×C149—21no—
157Q8×C149C2×D412yes—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149—42no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—42no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C8×C149—21no—
170C8×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149C22×D411yescharacteristic
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C4×C149—21no—
185C4×C149—22no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149C22×D411yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—22no—
192Dic149—21no—
193Dic149—41no—
194Dic149—41no—
195Dic149#13712yescomplemented
196C2×C149—41no—
197C2×C149—81no—
198C2×C149D4211yescharacteristic
199C2×C149C2×#13711yescharacteristic
200C2×C149#57711yescharacteristic
201D149—41no—
202D149—81no—
203C149#327811yescharacteristic, complemented, Sylow
204#3278—1491nomaximal, Sylow
205C2×#137—1491no—
206C2×#137—1491no—
207#550—1491no—
208D4×Q8—1491no—
209#492—1491no—
210#468—1491no—
211#468—1491no—
212#462—1491no—
213#460—1491no—
214#452—1491no—
215#452D14911yescharacteristic, complemented
216#448—1491no—
217#448—1491no—
218C4×Q16—1491no—
219#436—1491no—
220C2×#41—1491no—
221C2×#41C2×D14911yescharacteristic
222C22×Q8—1491no—
223C22×Q8—1491no—
224#137—2984no—
225#137—2984no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×Q16C2×D14911yescharacteristic
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16C2×D14911yescharacteristic
235C2×M16—1491no—
236C2×M16—1491no—
237C4⋊Q8—2981no—
238C4⋊Q8—1491no—
239#127—2981no—
240#127—1491no—
241C22⋊Q8—2981no—
242C22⋊Q8—2981no—
243C22⋊Q8—1491no—
244C22⋊Q8C2×D14911yescharacteristic
245#121—2981no—
246#121—2981no—
247#121—1491no—
248#121—1491no—
249C4×Q8—1491no—
250C4×Q8—1491no—
251C4×D4—2981no—
252C4×D4—2981no—
253C4×D4—1491no—
254#107—1491no—
255C4⋊C8—1491no—
256#103—1491no—
257#103—1491no—
258#103—1491no—
259#103C2×D14911yescharacteristic
260#102—1491no—
261#102C2×D14911yescharacteristic
262C22⋊C8—1491no—
263C22⋊C8C2×D14911yescharacteristic
264C4×C8—1491no—
265#41—22no—
266#41—41no—
267#41—2982no—
268#41—5961no—
269C2×Q8—2981no—
270C2×Q8—2982no—
271C2×Q8—2981no—
272C2×Q8—2982no—
273C2×Q8—5961no—
274C2×Q8—5961no—
275C2×Q8—1491no—
276C2×Q8—1491no—
277C2×Q8C22×D14911yescharacteristic
278C2×Q8C22×D14911yescharacteristic
279C2×D4—21no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—1491no—
286C2×D4—1491no—
287C2×D4C22×D14911yescharacteristic
288C22×C4—21no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—2981no—
292C22×C4—1491no—
293C22×C4C22×D14911yescharacteristic
294Q16—22no—
295Q16—2982no—
296Q16—1494no—
297SD16—41no—
298SD16—2982no—
299SD16—2982no—
300SD16—2982no—
301SD16—2982no—
302SD16—5961no—
303M16—2982no—
304M16—2982no—
305C2×C8—1491no—
306C2×C8—1491no—
307C2×C8C22×D14911yescharacteristic
308C2×C8C22×D14911yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—2981no—
311C4⋊C4—2981no—
312C4⋊C4—2981no—
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—1491no—
316C4⋊C4—1491no—
317C4⋊C4C22×D14911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—1491no—
323C22⋊C4—1491no—
324C42—2981no—
325C42—2981no—
326C42—1491no—
327C23—21no—
328C23—2981no—
329C23—1491no—
330C23D4×D14911yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—2981no—
335Q8—2981no—
336Q8—2981no—
337Q8—5962no—
338Q8—5962no—
339Q8—1492no—
340Q8D4×D14912yes—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—2982no—
345D4—2981no—
346D4—2981no—
347D4—5962no—
348D4—5962no—
349D4—11921no—
350D4—11921no—
351D4—11921no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—5962no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—1491no—
367C2×C4—1491no—
368C2×C4—1491no—
369C2×C4D4×D14911yescharacteristic
370C2×C4C23×D14911yescharacteristic
371C8—21no—
372C8—21no—
373C8—2981no—
374C8—1492no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—2981no—
382C22—2981no—
383C22—2981no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22C2×D4×D14911yescharacteristic
388C4—21no—
389C4—22no—
390C4—41no—
391C4—41no—
392C4—2981no—
393C4—2981no—
394C4—2982no—
395C4—5961no—
396C4—5961no—
397C4—1492no—
398C4C2×D4×D14911yescharacteristic
399C4#1801195611yescharacteristic
400C2—41no—
401C2—81no—
402C2—5961no—
403C2—11921no—
404C2#2375025711yescharacteristic
405C2#137×D14911yescharacteristic
406C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#452×C149C2
socleC22×C149C22×D4
prime radical#23750294C2
hypercenter#452D149
hypocenterC149#3278
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. C2×#18011941C2semidirect
4. #23750288C2semidirect
5. #23749996C2semidirect
6. #23749873C2semidirect
7. #23749870C2semidirect
8. #23749833C2semidirect
9. #23749824C2semidirect
10. #23749790C2semidirect
11. #23749766C2semidirect
12. #23749762C2semidirect
13. #23749717C2semidirect
14. #23749700C2semidirect
15. #452×C149C2semidirect
83. #14558726D4semidirect
195. Dic149#137semidirect
203. C149#3278semidirect
215. #452D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×#180119412
#237502942
#237502882
#237499962
#237498732
#237498702
#237498332
#237498242
#237497902
#237497662
#237497622
#237497172
#237497002
#452×C1492
#3278149