Finite Group Databasebeta

← #34056342

Subgroups — #34056342

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×#18011943C211yesmaximal, characteristic, complemented
2#23750286C211yesmaximal, characteristic, complemented
3#23750282C211yesmaximal, characteristic, complemented
4#23750006C211yesmaximal, characteristic, complemented
5#23749871C211yesmaximal, characteristic, complemented
6#23749868C211yesmaximal, characteristic, complemented
7#23749849C211yesmaximal, characteristic, complemented
8#23749845C211yesmaximal, characteristic, complemented
9#23749781C211yesmaximal, characteristic, complemented
10#23749779C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749769C211yesmaximal, characteristic, complemented
13Q16×Dic149C211yesmaximal, characteristic, complemented
14#23749701C211yesmaximal, characteristic, complemented
15C2×#137×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18#18011943—24no—
19C2×#14558726C2211yescharacteristic
20C2×#14558726C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558723C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558719C2211yescharacteristic
25#18011900—21no—
26#18011900C2211yescharacteristic
27#18011898—21no—
28#18011898C2211yescharacteristic
29#18011890—21no—
30#18011890C2211yescharacteristic
31#18011887—21no—
32#18011887C2211yescharacteristic
33#18011885—21no—
34#18011885C2211yescharacteristic
35#18011882—21no—
36#18011882C2211yescharacteristic
37Q8×Dic149C2211yescharacteristic
38Q8×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40C4×C22⋊D149—21no—
41C4×C22⋊D149C2211yescharacteristic
42#18011845C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011832C2211yescharacteristic
50C22⋊#11924746C2211yescharacteristic
51#18011823C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×#41×C149C2211yescharacteristic
54C22×Q8×C149C2211yescharacteristic
55#137×C149—24no—
56C2×Q16×C149C2211yescharacteristic
57C2×Q16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic
59C2×SD16×C149C2211yescharacteristic
60C2×M16×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—41no—
63C2×Dic298—21no—
64C2×Dic298C2311yescharacteristic
65Q8×D149—22no—
66Q8×D149—41no—
67C2×D596—21no—
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149D411yescharacteristic
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74C2×C4×D149C2311yescharacteristic
75#14558726—22no—
76#14558726—41no—
77#14558725—22no—
78#14558723—22no—
79#14558721—41no—
80#14558719—22no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C4⋊Dic149—21no—
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149D411yescharacteristic
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713D411yescharacteristic
100C4×Dic149—21no—
101C4×Dic149—21no—
102C4×Dic149C2311yescharacteristic
103#41×C149—22no—
104#41×C149—41no—
105C2×Q8×C149—21no—
106C2×Q8×C149—22no—
107C2×Q8×C149—41no—
108C2×Q8×C149C2311yescharacteristic
109C2×Q8×C149C2311yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114C22×C4×C149—21no—
115C22×C4×C149C2311yescharacteristic
116Q16×C149—22no—
117Q16×C149D414yescomplemented
118SD16×C149—22no—
119SD16×C149—22no—
120M16×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—42no—
128D596—21no—
129D596—21no—
130D596—42no—
131C22⋊D149—41no—
132C22⋊D149—42no—
133C22⋊D149—42no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C2×Dic149C2×D411yescharacteristic
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—42no—
143C4×D149—42no—
144#11924746—21no—
145#11924746—21no—
146C23×C149—21no—
147C23×C149C2×D411yescharacteristic
148Q8×C149—21no—
149Q8×C149—21no—
150Q8×C149—21no—
151Q8×C149—21no—
152Q8×C149—42no—
153Q8×C149C2×D412yes—
154Q8×C149C2×D412yes—
155D4×C149—21no—
156D4×C149—21no—
157D4×C149—42no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—42no—
164C2×C4×C149—42no—
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2411yescharacteristic
167C8×C149—21no—
168C8×C149C2×D412yes—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149C22×D411yescharacteristic
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C4×C149—21no—
183C4×C149—22no—
184C4×C149—22no—
185C4×C149—41no—
186C4×C149C22×D411yescharacteristic
187C4×C149H(5,𝔽2)11yescharacteristic
188Dic149—21no—
189Dic149—21no—
190Dic149—21no—
191Dic149—41no—
192Dic149—41no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—81no—
196C2×C149D4211yescharacteristic
197C2×C149#57511yescharacteristic
198C2×C149#57811yescharacteristic
199D149—41no—
200D149—81no—
201C149#327711yescharacteristic, complemented, Sylow
202#3277—1491nomaximal, Sylow
203C2×#137—1491no—
204C2×#137D14911yescharacteristic, complemented
205#548—1491no—
206#548—1491no—
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—24no—
223#137—2984no—
224C2×Q16—1491no—
225C2×Q16—1491no—
226C2×Q16C2×D14911yescharacteristic
227C2×Q16C2×D14911yescharacteristic
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16C2×D14911yescharacteristic
231C2×SD16C2×D14911yescharacteristic
232C2×D8—1491no—
233C2×M16—1491no—
234C2×M16C2×D14911yescharacteristic
235#124—2981no—
236#124—2981no—
237#124—1491no—
238#124—1491no—
239C22⋊Q8—2981no—
240C22⋊Q8—2981no—
241C22⋊Q8—1491no—
242C22⋊Q8—1491no—
243#121—2981no—
244#121—2981no—
245#121—1491no—
246#121—1491no—
247C4×Q8—1491no—
248C4×Q8—1491no—
249C4×D4—2981no—
250C4×D4—2981no—
251C4×D4—1491no—
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—2981no—
271C2×Q8—2982no—
272C2×Q8—5961no—
273C2×Q8—1491no—
274C2×Q8C22×D14911yescharacteristic
275C2×Q8C22×D14911yescharacteristic
276C2×Q8C22×D14911yescharacteristic
277C2×D4—21no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4C22×D14911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4C22×D14911yescharacteristic
290Q16—22no—
291Q16—2982no—
292Q16—5961no—
293Q16C22⋊D14914yescomplemented
294SD16—22no—
295SD16—22no—
296SD16—2982no—
297SD16—2982no—
298D8—5961no—
299M16—22no—
300M16—2982no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8C22×D14911yescharacteristic
304C2×C8C22×D14911yescharacteristic
305C4⋊C4—2981no—
306C4⋊C4—2981no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4—1491no—
311C4⋊C4—1491no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—1491no—
321C22⋊C4—1491no—
322C42—2981no—
323C42—2981no—
324C42—1491no—
325C23—21no—
326C23—2981no—
327C23—1491no—
328C23D4×D14911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—42no—
334Q8—2981no—
335Q8—2981no—
336Q8—5962no—
337Q8C2×C22⋊D14912yes—
338Q8C2×C22⋊D14912yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—2981no—
343D4—2981no—
344D4—5962no—
345D4—5961no—
346D4—5962no—
347D4—5962no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—5962no—
361C2×C4—5962no—
362C2×C4—1491no—
363C2×C4—1491no—
364C2×C4—1491no—
365C2×C4D4×D14911yescharacteristic
366C2×C4C23×D14911yescharacteristic
367C8—21no—
368C8—2981no—
369C8—2981no—
370C8C2×C22⋊D14912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2981no—
378C22—2981no—
379C22—2981no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—22no—
386C4—22no—
387C4—41no—
388C4—2981no—
389C4—2981no—
390C4—2981no—
391C4—5961no—
392C4—5961no—
393C4—5961no—
394C4C22×C22⋊D14911yescharacteristic
395C4#1801195611yescharacteristic
396C2—41no—
397C2—81no—
398C2—5961no—
399C2—11921no—
400C2D4×C22⋊D14911yescharacteristic
401C2#2375042411yescharacteristic
402C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#137×C149C2
socleC22×C149C22×D4
hypercenterC2×#137D149
hypocenterC149#3277
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. #23750286C2semidirect
3. #23750282C2semidirect
4. #23750006C2semidirect
5. #23749871C2semidirect
6. #23749868C2semidirect
7. #23749849C2semidirect
8. #23749845C2semidirect
9. #23749781C2semidirect
10. #23749779C2semidirect
11. #23749770C2semidirect
12. #23749769C2semidirect
13. Q16×Dic149C2semidirect
14. #23749701C2semidirect
15. C2×#137×C149C2semidirect
117. Q16×C149D4semidirect
201. C149#3277semidirect
204. C2×#137D149semidirect
293. Q16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
#237502862
#237502822
#237500062
#237498712
#237498682
#237498492
#237498452
#237497812
#237497792
#237497702
#237497692
Q16×Dic1492
#237497012
C2×#137×C1492
#3277149