Finite Group Databasebeta

← #34056316

Subgroups — #34056316

Order 19072.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011938C211yesmaximal, characteristic, complemented
2#23750286C211yesmaximal, characteristic, complemented
3#23750263C211yesmaximal, characteristic, complemented
4#23750010C211yesmaximal, characteristic, complemented
5#23749880C211yesmaximal, characteristic, complemented
6#23749878C211yesmaximal, characteristic, complemented
7#23749849C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749786C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749764C211yesmaximal, characteristic, complemented
13SD16×Dic149C211yesmaximal, characteristic, complemented
14#23749701C211yesmaximal, characteristic, complemented
15C2×#137×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18#18011938—24no—
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558723C2211yescharacteristic, complemented
22C2×D1192C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558719C2211yescharacteristic
25#18011900—21no—
26#18011900C2211yescharacteristic
27#18011900C2211yescharacteristic, complemented
28#18011894—21no—
29#18011887—21no—
30#18011887C2211yescharacteristic
31#18011887C2211yescharacteristic
32#18011885—21no—
33#18011885C2211yescharacteristic
34#18011885C2211yescharacteristic, complemented
35#18011883—21no—
36#18011879—21no—
37Q8×Dic149C2211yescharacteristic, complemented
38D4×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40C4×C22⋊D149C2211yescharacteristic
41C2×#14558713—21no—
42#18011843C2211yescharacteristic, complemented
43#18011840C2211yescharacteristic, complemented
44#18011835C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic, complemented
49#18011832C2211yescharacteristic
50C22⋊#11924746C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic
52C8×Dic149C2211yescharacteristic, complemented
53C2×#41×C149C2211yescharacteristic
54C22×Q8×C149C2211yescharacteristic, complemented
55#137×C149—24no—
56C2×Q16×C149C2211yescharacteristic, complemented
57C2×Q16×C149C2211yescharacteristic, complemented
58C2×SD16×C149C2211yescharacteristic
59C2×SD16×C149C2211yescharacteristic
60C2×M16×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558737—22no—
63#14558737—41no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149D411yescharacteristic
71D4×D149—22no—
72D4×D149—41no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149C2311yescharacteristic
76#14558723—22no—
77#14558723—41no—
78#14558723—41no—
79D1192—22no—
80#14558721—22no—
81#14558719—22no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149D411yescharacteristic
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713D411yescharacteristic
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×C149—22no—
118SD16×C149—22no—
119SD16×C149D414yescomplemented
120M16×C149—22no—
121C2×C8×C149C2311yescharacteristic
122C2×C8×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129D596—21no—
130D596—21no—
131D596—21no—
132D596—21no—
133D596—42no—
134C22⋊D149—41no—
135C22⋊D149—42no—
136C22⋊D149—42no—
137C22⋊D149—81no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—81no—
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C2×Dic149C2×D411yescharacteristic
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—42no—
147#11924746—21no—
148#11924746—21no—
149C23×C149—21no—
150C23×C149C2×D411yescharacteristic
151Q8×C149—21no—
152Q8×C149—21no—
153Q8×C149—21no—
154Q8×C149—21no—
155Q8×C149—21no—
156Q8×C149—42no—
157Q8×C149C2×D412yes—
158D4×C149—21no—
159D4×C149—42no—
160D4×C149C2×D412yes—
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×C149—42no—
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—21no—
173C22×C149—22no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—21no—
190C4×C149—22no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149C22×D411yescharacteristic
194C4×C149H(5,𝔽2)11yescharacteristic
195Dic149—21no—
196Dic149—21no—
197Dic149—21no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—42no—
201C2×C149—41no—
202C2×C149D4211yescharacteristic
203C2×C149#57511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—41no—
206D149—81no—
207D149—81no—
208C149#327511yescharacteristic, complemented, Sylow
209#3275—1491nomaximal, Sylow
210C2×#137D14911yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—1491no—
212#548—1491no—
213#546—1491no—
214#495—1491no—
215#470—1491no—
216#469—1491no—
217#464—1491no—
218#463—1491no—
219#452—1491no—
220#450—1491no—
221#449—1491no—
222#448—1491no—
223C4×SD16—1491no—
224#436—1491no—
225C2×#41—1491no—
226C2×#41C2×D14911yescharacteristic
227C22×Q8C2×D14911yescharacteristic, complemented
228C22×D4—1491no—
229#137—24no—
230AGL(1,ℤ/8)—2984no—
231C2×Q16C2×D14911yescharacteristic, complemented
232C2×Q16C2×D14911yescharacteristic, complemented
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16C2×D14911yescharacteristic
237C2×SD16C2×D14911yescharacteristic
238C2×D8—1491no—
239C2×D8—1491no—
240C2×M16—1491no—
241C2×M16C2×D14911yescharacteristic, complemented
242#124—2981no—
243#124—1491no—
244#124—1491no—
245#123—2981no—
246C22⋊Q8—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8—1491no—
249#121—2981no—
250#121—2981no—
251#121—1491no—
252#121—1491no—
253#120—2981no—
254C4×Q8—1491no—
255C4×D4—2981no—
256C4×D4—1491no—
257C4×D4—1491no—
258C2×C22⋊C4—2981no—
259#106—1491no—
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103—1491no—
264#102—1491no—
265#102—1491no—
266#102—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C4×C8—1491no—
270C24—2981no—
271#41—22no—
272#41—41no—
273#41—2982no—
274#41—5961no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D14911yescharacteristic
279C2×Q8C22×D14911yescharacteristic
280C2×Q8C22×D14911yescharacteristic
281C2×D4—21no—
282C2×D4—2981no—
283C2×D4—2982no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4C22×D14911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4C22×D14911yescharacteristic
298Q16—22no—
299Q16—22no—
300SD16—22no—
301SD16—2982no—
302SD16—5961no—
303SD16—5961no—
304SD16C22⋊D14914yescomplemented
305D8—2982no—
306D8—2982no—
307M16—22no—
308M16—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4—1491no—
318C4⋊C4—1491no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—1491no—
329C22⋊C4—1491no—
330C42—2981no—
331C42—1491no—
332C23—21no—
333C23—2981no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—11921no—
339C23D4×D14911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D14912yes—
347D4—21no—
348D4—42no—
349D4—2981no—
350D4—2981no—
351D4—2981no—
352D4—2981no—
353D4—5962no—
354D4—5961no—
355D4—5962no—
356D4—5962no—
357D4—11921no—
358D4C2×C22⋊D14912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—5962no—
371C2×C4—1491no—
372C2×C4—1491no—
373C2×C4—1491no—
374C2×C4—11921no—
375C2×C4D4×D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—21no—
378C8—2981no—
379C8—2981no—
380C8C2×C22⋊D14912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—2981no—
388C22—2981no—
389C22—2981no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—2981no—
403C4—2981no—
404C4—2981no—
405C4—5961no—
406C4—5961no—
407C4C22×C22⋊D14911yescharacteristic
408C4#1801195611yescharacteristic
409C2—41no—
410C2—42no—
411C2—5961no—
412C2—11921no—
413C2—11921no—
414C2D4×C22⋊D14911yescharacteristic
415C2#2375042411yescharacteristic
416C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#137×C149C2
socleC22×C149C22×D4
hypercenterC2×#137D149
hypocenterC149#3275
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×#18011938C2semidirect
2. #23750286C2semidirect
3. #23750263C2semidirect
4. #23750010C2semidirect
5. #23749880C2semidirect
6. #23749878C2semidirect
7. #23749849C2semidirect
8. #23749842C2semidirect
9. #23749786C2semidirect
10. #23749774C2semidirect
11. #23749770C2semidirect
12. #23749764C2semidirect
13. SD16×Dic149C2semidirect
14. #23749701C2semidirect
15. C2×#137×C149C2semidirect
21. C2×#14558723C22semidirect
27. #18011900C22semidirect
34. #18011885C22semidirect
37. Q8×Dic149C22semidirect
42. #18011843C22semidirect
43. #18011840C22semidirect
44. #18011835C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
48. #18011833C22semidirect
50. C22⋊#11924746C22semidirect
52. C8×Dic149C22semidirect
54. C22×Q8×C149C22semidirect
56. C2×Q16×C149C22semidirect
57. C2×Q16×C149C22semidirect
60. C2×M16×C149C22semidirect
119. SD16×C149D4semidirect
208. C149#3275semidirect
210. C2×#137D149semidirect
227. C22×Q8C2×D149semidirect
231. C2×Q16C2×D149semidirect
232. C2×Q16C2×D149semidirect
241. C2×M16C2×D149semidirect
304. SD16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
#237502862
#237502632
#237500102
#237498802
#237498782
#237498492
#237498422
#237497862
#237497742
#237497702
#237497642
SD16×Dic1492
#237497012
C2×#137×C1492
#3275149