Finite Group Databasebeta

← #34056344

Subgroups — #34056344

Order 19072.

476 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011942C211yesmaximal, characteristic, complemented
2C2×#18011941C211yesmaximal, characteristic, complemented
3#23750284C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749873C211yesmaximal, characteristic, complemented
6#23749869C211yesmaximal, characteristic, complemented
7#23749847C211yesmaximal, characteristic, complemented
8#23749844C211yesmaximal, characteristic, complemented
9#23749781C211yesmaximal, characteristic, complemented
10#23749780C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749768C211yesmaximal, characteristic, complemented
13C4×#14558726C211yesmaximal, characteristic, complemented
14#23749703C211yesmaximal, characteristic, complemented
15#548×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18#18011942—24no—
19#18011941—24no—
20C2×#14558726C2211yescharacteristic
21C2×#14558726C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558724C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27C2×#14558723C2211yescharacteristic
28C2×#14558721C2211yescharacteristic
29C2×#14558720C2211yescharacteristic
30C2×#14558720C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011897—21no—
33#18011890C2211yescharacteristic
34#18011889—21no—
35#18011885C2211yescharacteristic
36#18011883—21no—
37C4×Dic298C2211yescharacteristic
38#18011871—21no—
39#18011844C2211yescharacteristic
40C4⋊#11924746C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011835C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011831C2211yescharacteristic
47C22⋊#11924746C2211yescharacteristic
48C22⋊#11924746C2211yescharacteristic
49C4×#11924746C2211yescharacteristic
50C2×#41×C149C2211yescharacteristic
51C22×Q8×C149C2211yescharacteristic
52#124×C149—21no—
53#124×C149C2211yescharacteristic
54C22⋊Q8×C149—21no—
55C22⋊Q8×C149C2211yescharacteristic
56#121×C149—21no—
57#121×C149C2211yescharacteristic
58C4×Q8×C149C2211yescharacteristic
59C4×D4×C149—21no—
60C4×D4×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—41no—
63C2×Dic298—22no—
64C2×Dic298—21no—
65C2×Dic298—41no—
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C22×Dic149—21no—
72C2×C4×D149—21no—
73#14558726—22no—
74#14558726—22no—
75#14558726—41no—
76#14558726D414yescomplemented
77#14558724—22no—
78#14558724—22no—
79#14558723—22no—
80#14558723—22no—
81#14558721—41no—
82#14558720—22no—
83#14558720—22no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149C2311yescharacteristic
89#14558715—21no—
90#14558715—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95C4×Dic149—21no—
96#41×C149—22no—
97#41×C149—41no—
98C2×Q8×C149—21no—
99C2×Q8×C149—22no—
100C2×Q8×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149—21no—
104C2×D4×C149—21no—
105C2×D4×C149D411yescharacteristic
106C2×D4×C149C2311yescharacteristic
107C22×C4×C149—21no—
108C22×C4×C149—21no—
109C22×C4×C149C2311yescharacteristic
110C22×C4×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149—21no—
113C4⋊C4×C149D411yescharacteristic
114C4⋊C4×C149C2311yescharacteristic
115C22⋊C4×C149—21no—
116C22⋊C4×C149—21no—
117C22⋊C4×C149—21no—
118C22⋊C4×C149—21no—
119C22⋊C4×C149D411yescharacteristic
120C22⋊C4×C149D411yescharacteristic
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—42no—
128Dic298C2×D412yes—
129D596—21no—
130D596—21no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—42no—
137C4×D149—42no—
138#11924746—21no—
139#11924746—21no—
140#11924746—21no—
141#11924746C2×D412yes—
142C23×C149—21no—
143C23×C149C2×D411yescharacteristic
144C23×C149C2×D411yescharacteristic
145Q8×C149—21no—
146Q8×C149—21no—
147Q8×C149—21no—
148Q8×C149—42no—
149Q8×C149C2×D412yes—
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—41no—
153D4×C149—42no—
154D4×C149—42no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—42no—
163C2×C4×C149—42no—
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2×D411yescharacteristic
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C4×C149—21no—
183C4×C149—21no—
184C4×C149—22no—
185C4×C149—21no—
186C4×C149—21no—
187C4×C149—41no—
188C4×C149—41no—
189C4×C149C22×D411yescharacteristic
190C4×C149H(5,𝔽2)11yescharacteristic
191Dic149—22no—
192Dic149—41no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—41no—
196C2×C149—81no—
197C2×C149D4211yescharacteristic
198C2×C149#57511yescharacteristic
199C2×C149#57811yescharacteristic
200D149—81no—
201C149#327711yescharacteristic, complemented, Sylow
202#3277—1491nomaximal, Sylow
203C2×#137—1491no—
204C2×#137—1491no—
205#548—1491no—
206#548D14911yescharacteristic, complemented
207#495—1491no—
208#468—1491no—
209#468—1491no—
210#464—1491no—
211#464—1491no—
212#451—1491no—
213#451—1491no—
214#449—1491no—
215#449—1491no—
216C4×Q16—1491no—
217#436—1491no—
218C2×#41—1491no—
219C2×#41C2×D14911yescharacteristic
220C22×Q8—1491no—
221C22×Q8C2×D14911yescharacteristic
222#137—2984no—
223#137—2984no—
224C2×Q16—1491no—
225C2×Q16—1491no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×D8—1491no—
233C2×M16—1491no—
234C2×M16—1491no—
235#124—21no—
236#124—2981no—
237#124—1491no—
238#124C2×D14911yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—2981no—
241C22⋊Q8—1491no—
242C22⋊Q8C2×D14911yescharacteristic
243#121—21no—
244#121—2981no—
245#121—1491no—
246#121C2×D14911yescharacteristic
247C4×Q8—1491no—
248C4×Q8C2×D14911yescharacteristic
249C4×D4—21no—
250C4×D4—2981no—
251C4×D4C2×D14911yescharacteristic
252#107—1491no—
253C4⋊C8—1491no—
254#103—1491no—
255#103—1491no—
256#103—1491no—
257#103—1491no—
258#102—1491no—
259#102—1491no—
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262C4×C8—1491no—
263#41—22no—
264#41—41no—
265#41—2982no—
266#41—5961no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—2982no—
271C2×Q8—2981no—
272C2×Q8—5961no—
273C2×Q8—1491no—
274C2×Q8—1491no—
275C2×Q8C22×D14911yescharacteristic
276C2×Q8C22×D14911yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—1491no—
282C2×D4C22⋊D14911yescharacteristic
283C2×D4C22×D14911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4C22×D14911yescharacteristic
289C22×C4C22×D14911yescharacteristic
290Q16—2982no—
291Q16—2982no—
292Q16—5961no—
293Q16—1494no—
294SD16—2982no—
295SD16—2982no—
296SD16—2982no—
297SD16—2982no—
298D8—5961no—
299M16—2982no—
300M16—2982no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8—1491no—
304C2×C8—1491no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4C22⋊D14911yescharacteristic
311C4⋊C4C22×D14911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4C22⋊D14911yescharacteristic
321C22⋊C4C22⋊D14911yescharacteristic
322C42—21no—
323C42—2981no—
324C42C22×D14911yescharacteristic
325C23—21no—
326C23—2981no—
327C23C2×C22⋊D14911yescharacteristic
328C23C2×C22⋊D14911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—2981no—
334Q8—2981no—
335Q8—2981no—
336Q8—5962no—
337Q8—1492no—
338Q8D4×D14912yes—
339D4—21no—
340D4—21no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—2981no—
345D4—2981no—
346D4—5962no—
347D4—5962no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—5962no—
361C2×C4—5962no—
362C2×C4C2×C22⋊D14911yescharacteristic
363C2×C4C2×C22⋊D14911yescharacteristic
364C2×C4C2×C22⋊D14911yescharacteristic
365C2×C4C2×C22⋊D14911yescharacteristic
366C2×C4C23×D14911yescharacteristic
367C8—2981no—
368C8—2981no—
369C8—2981no—
370C8—1492no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22C22×C22⋊D14911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—2982no—
392C4—5961no—
393C4—5961no—
394C4C2×D4×D14911yescharacteristic
395C4#1801195611yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—11921no—
400C2D4×C22⋊D14911yescharacteristic
401C2#2375042311yescharacteristic
402C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#548×C149C2
socleC22×C149C22×D4
hypercenter#548D149
hypocenterC149#3277
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
2. C2×#18011941C2semidirect
3. #23750284C2semidirect
4. #23750007C2semidirect
5. #23749873C2semidirect
6. #23749869C2semidirect
7. #23749847C2semidirect
8. #23749844C2semidirect
9. #23749781C2semidirect
10. #23749780C2semidirect
11. #23749770C2semidirect
12. #23749768C2semidirect
13. C4×#14558726C2semidirect
14. #23749703C2semidirect
15. #548×C149C2semidirect
76. #14558726D4semidirect
201. C149#3277semidirect
206. #548D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C2×#180119412
#237502842
#237500072
#237498732
#237498692
#237498472
#237498442
#237497812
#237497802
#237497702
#237497682
C4×#145587262
#237497032
#548×C1492
#3277149