Finite Group Databasebeta

← #34058341

Subgroups — #34058341

Order 19072.

1492 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×#18011959C211yesmaximal, characteristic, complemented
2C22×Q8×D149C211yesmaximal, characteristic, complemented
3#23750290C213yesmaximal, complemented
4Q8×C22⋊D149C211yesmaximal, characteristic, complemented
5#23750288C213yesmaximal, complemented
6#23750287C211yesmaximal, characteristic, complemented
7#23750286C211yesmaximal, characteristic, complemented
8#23750285C213yesmaximal, complemented
9#23750284C213yesmaximal, complemented
10#23750200C213yesmaximal, complemented
11#23750198C213yesmaximal, complemented
12#23750138C213yesmaximal, complemented
13#23750134C213yesmaximal, complemented
14#23750101C211yesmaximal, characteristic, complemented
15D4×Q8×C149C211yesmaximal, characteristic, complemented
16#18011959—28no—
17C2×#14558737C2213yes—
18C2×#14558737C2211yescharacteristic, complemented
19C2×#14558736C2213yes—
20C2×#14558736C2213yescomplemented
21C22×Dic298C2213yes—
22C2×Q8×D149—28no—
23C2×Q8×D149C2213yes—
24C2×Q8×D149C2213yes—
25C2×Q8×D149C2211yescharacteristic
26C2×Q8×D149C2211yescharacteristic
27C2×Q8×D149C2213yescomplemented
28C22×C4×D149C2213yes—
29#18011910C2216yescomplemented
30#18011909C2213yescomplemented
31#18011900C2213yescomplemented
32#18011899C2213yescomplemented
33#18011897C2216yescomplemented
34#18011896C2216yes—
35#18011896C2213yes—
36#18011893C2213yes—
37#18011891C2213yescomplemented
38#18011890C2213yescomplemented
39#18011889C2213yes—
40#18011889C2216yescomplemented
41#18011889C2216yescomplemented
42#18011888C2213yes—
43#18011887C2213yes—
44#18011887C2213yescomplemented
45#18011886C2213yes—
46#18011885C2213yes—
47#18011884C2213yes—
48#18011883C2213yes—
49#18011881C2213yes—
50#18011879C2211yescharacteristic
51Q8×Dic149C2211yescharacteristic, complemented
52C4×Dic298C2213yescomplemented
53#18011876C2213yescomplemented
54C4×D596C2213yes—
55#18011873C2216yes—
56C4×C22⋊D149C2213yes—
57C4×C22⋊D149C2213yes—
58#18011871C2216yes—
59#18011869C2213yes—
60#18011868C2213yes—
61C22×Q8×C149C2211yescharacteristic
62C22×Q8×C149C2211yescharacteristic, complemented
63C4⋊Q8×C149C2213yescomplemented
64C22⋊Q8×C149C2213yes—
65C22⋊Q8×C149C2213yescomplemented
66C4×Q8×C149C2211yescharacteristic, complemented
67C4×D4×C149C2213yes—
68C23×D149C2311yescharacteristic
69#14558737—212no—
70#14558737—24no—
71#14558736—212no—
72#14558736—212no—
73C2×Dic298—212no—
74C2×Dic298C2313yes—
75C2×Dic298C2313yes—
76C2×Dic298C2316yes—
77C2×Dic298C2313yes—
78Q8×D149—212no—
79Q8×D149—212no—
80Q8×D149—212no—
81Q8×D149—24no—
82Q8×D149D418yescomplemented
83C2×D596C2313yes—
84C2×D596C2313yes—
85C2×D596C2313yes—
86C2×C22⋊D149C2311yescharacteristic
87C2×C22⋊D149C2313yes—
88C2×C22⋊D149C2313yes—
89C2×C22⋊D149C2311yescharacteristic
90C22×Dic149C2313yes—
91C2×C4×D149—212no—
92C2×C4×D149C2313yes—
93C2×C4×D149C2313yes—
94C2×C4×D149C2313yes—
95C2×C4×D149C2313yes—
96C2×C4×D149C2316yes—
97C2×C4×D149C2313yes—
98C4⋊Dic149C2313yes—
99C4⋊Dic149C2313yes—
100#14558715C2313yes—
101#14558715C2316yes—
102#14558715C2313yes—
103#14558715C2313yes—
104#14558715C2313yes—
105C22⋊Dic149C2311yescharacteristic
106C22⋊Dic149C2313yes—
107#14558713C2311yescharacteristic
108#14558713C2313yes—
109#14558713C2316yes—
110#14558713C2313yes—
111#14558713C2313yes—
112#14558713C2316yes—
113#14558713C2311yescharacteristic
114#14558713C2313yes—
115C4×Dic149C2313yes—
116C4×Dic149C2316yes—
117C2×Q8×C149—24no—
118C2×Q8×C149—24no—
119C2×Q8×C149C2313yes—
120C2×Q8×C149C2313yes—
121C2×Q8×C149C2311yescharacteristic
122C2×D4×C149C2311yescharacteristic
123C22×C4×C149C2313yes—
124C22×C4×C149C2313yes—
125C4⋊C4×C149C2316yes—
126C4⋊C4×C149C2313yes—
127C4⋊C4×C149C2313yes—
128C22⋊C4×C149C2313yes—
129C22⋊C4×C149C2313yes—
130C42×C149C2313yes—
131C22×D149—22no—
132C22×D149—22no—
133C22×D149—22no—
134C22×D149C2413yes—
135C22×D149C2411yescharacteristic
136C22×D149C2411yescharacteristic
137Dic298—26no—
138Dic298—212no—
139Dic298—26no—
140Dic298C2×D4112yes—
141D596—26no—
142D596—26no—
143D596—26no—
144C22⋊D149—26no—
145C22⋊D149—22no—
146C22⋊D149—22no—
147C22⋊D149—26no—
148C2×Dic149—26no—
149C2×Dic149C2411yescharacteristic
150C2×Dic149C2413yes—
151C2×Dic149C2411yescharacteristic
152C2×Dic149C2413yes—
153C2×Dic149C2413yes—
154C4×D149—26no—
155C4×D149—26no—
156C4×D149—26no—
157C4×D149—26no—
158C4×D149—212no—
159C4×D149C2×D4112yes—
160C23×C149C2411yescharacteristic
161C23×C149C2411yescharacteristic
162Q8×C149—26no—
163Q8×C149—26no—
164Q8×C149C2×D414yes—
165D4×C149—22no—
166C2×C4×C149—26no—
167C2×C4×C149—26no—
168C2×C4×C149C2413yes—
169C2×C4×C149C2413yes—
170C2×C4×C149C2413yes—
171C2×C4×C149C2411yescharacteristic
172C2×C4×C149C2413yes—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—21no—
178C22×C1492−1+412yescomplemented
179C22×C149C2511yescharacteristic
180C2×D149—28no—
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—23no—
186C2×D149—23no—
187C2×D149—23no—
188C2×D149C22×D412yes—
189C2×D1492−1+412yescomplemented
190C4×C149—23no—
191C4×C149—23no—
192C4×C149—21no—
193C4×C149—23no—
194C4×C149C22×D416yes—
195Dic149—21no—
196Dic149—23no—
197Dic149—21no—
198Dic149—23no—
199Dic149C22×D416yes—
200C2×C149—22no—
201C2×C149—41no—
202C2×C149C23×D411yescharacteristic
203C2×C149C2×2−1+411yescharacteristic
204C2×C149C2×2−1+411yescharacteristic
205D149—22no—
206D149—22no—
207D149—43no—
208C149#348611yescharacteristic, complemented, Sylow
209#3486—1491nomaximal, Sylow
210C2×2−1+4—1491no—
211C23×Q8—1491no—
212D4×Q8—1491no—
213D4×Q8—1493no—
214D4×Q8—1493no—
215D4×Q8D14911yescharacteristic, complemented
216#548—1491no—
217#548—1493no—
218#548—1491no—
219#548—1493no—
220#536—1493no—
221#536—1493no—
222#525—1493no—
223#525—1493no—
224#519—1491no—
2252−1+4—2988no—
226C2×#41—1493no—
227C2×#41—1491no—
228C2×#41—1493no—
229C2×#41—1493no—
230C22×Q8—2988no—
231C22×Q8—1493no—
232C22×Q8—1493no—
233C22×Q8—1491no—
234C22×Q8—1493no—
235C22×Q8—1491no—
236C22×Q8—1493no—
237C22×Q8C2×D14911yescharacteristic
238C22×Q8C2×D14911yescharacteristic, complemented
239C23×C4—1493no—
240C4⋊Q8—1493no—
241C4⋊Q8—1496no—
242C4⋊Q8C2×D14913yescomplemented
243#124—1493no—
244#124—1496no—
245#124—1493no—
246#123—1496no—
247#123—1493no—
248#123—1493no—
249C22⋊Q8—1493no—
250C22⋊Q8—1493no—
251C22⋊Q8—1493no—
252C22⋊Q8—1493no—
253C22⋊Q8—1496no—
254C22⋊Q8—1496no—
255C22⋊Q8—1493no—
256C22⋊Q8—1493no—
257C22⋊Q8C2×D14913yes—
258C22⋊Q8C2×D14913yescomplemented
259#121—1493no—
260#121—1493no—
261#121—1493no—
262#121—1493no—
263#120—1491no—
264#120—1493no—
265C4×Q8—1491no—
266C4×Q8—1493no—
267C4×Q8—1493no—
268C4×Q8C2×D14911yescharacteristic, complemented
269C4×D4—1493no—
270C4×D4—1493no—
271C4×D4—1496no—
272C4×D4—1496no—
273C4×D4—1493no—
274C4×D4C2×D14913yes—
275#117—1493no—
276#117—1493no—
277C24—1491no—
278#41—29812no—
279#41—29812no—
280#41—2984no—
281#41—29812no—
282C2×Q8—24no—
283C2×Q8—24no—
284C2×Q8—29812no—
285C2×Q8—29812no—
286C2×Q8—29812no—
287C2×Q8—2984no—
288C2×Q8—29812no—
289C2×Q8—1498no—
290C2×Q8—1493no—
291C2×Q8—1496no—
292C2×Q8—1493no—
293C2×Q8—1493no—
294C2×Q8C22×D14913yes—
295C2×Q8C22×D14913yes—
296C2×Q8C22×D14911yescharacteristic
297C2×D4—1491no—
298C2×D4—1493no—
299C2×D4—1491no—
300C2×D4—1493no—
301C2×D4—1493no—
302C2×D4—1493no—
303C2×D4—1493no—
304C2×D4C22×D14911yescharacteristic
305C22×C4—29812no—
306C22×C4—1493no—
307C22×C4—1493no—
308C22×C4—1493no—
309C22×C4—1496no—
310C22×C4—1493no—
311C22×C4—1493no—
312C22×C4—1493no—
313C22×C4C22×D14913yes—
314C22×C4C22×D14913yes—
315C4⋊C4—1493no—
316C4⋊C4—1493no—
317C4⋊C4—1493no—
318C4⋊C4—1493no—
319C4⋊C4—1496no—
320C4⋊C4—1493no—
321C4⋊C4—1493no—
322C4⋊C4C22×D14913yes—
323C4⋊C4C22×D14916yes—
324C4⋊C4C22×D14913yes—
325C22⋊C4—1491no—
326C22⋊C4—1493no—
327C22⋊C4—1493no—
328C22⋊C4—1491no—
329C22⋊C4—1493no—
330C22⋊C4—1491no—
331C22⋊C4—1493no—
332C22⋊C4—1496no—
333C22⋊C4—1496no—
334C22⋊C4—1493no—
335C22⋊C4C22×D14913yes—
336C22⋊C4C22×D14913yes—
337C42—1493no—
338C42—1496no—
339C42C22×D14913yes—
340C23—2982no—
341C23—2982no—
342C23—2982no—
343C23—1493no—
344C23—1491no—
345C23—1491no—
346C23C23×D14911yescharacteristic
347C23C23×D14911yescharacteristic
348Q8—26no—
349Q8—26no—
350Q8—29812no—
351Q8—2986no—
352Q8—2986no—
353Q8—14912no—
354Q8D4×D14914yes—
355D4—22no—
356D4—2986no—
357D4—2986no—
358D4—2982no—
359D4—2982no—
360D4—2986no—
361D4—2986no—
362D4—2986no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—2986no—
366C2×C4—2986no—
367C2×C4—29812no—
368C2×C4—2986no—
369C2×C4—2986no—
370C2×C4—2986no—
371C2×C4—1491no—
372C2×C4—1493no—
373C2×C4—1493no—
374C2×C4—1491no—
375C2×C4—1493no—
376C2×C4—14912no—
377C2×C4C23×D14913yes—
378C2×C4C23×D14911yescharacteristic
379C2×C4C23×D14913yes—
380C2×C4C23×D14913yes—
381C2×C4C23×D14913yes—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—2988no—
388C22—2981no—
389C22—2981no—
390C22—2981no—
391C22—2981no—
392C22—2983no—
393C22—2983no—
394C22—2983no—
395C22—1492no—
396C22—1492no—
397C22#1801195912yescomplemented
398C22C24×D14911yescharacteristic
399C4—23no—
400C4—23no—
401C4—23no—
402C4—21no—
403C4—2981no—
404C4—2983no—
405C4—2981no—
406C4—2983no—
407C4—1496no—
408C4C2×D4×D14916yes—
409C2—22no—
410C2—41no—
411C2—2982no—
412C2—2982no—
413C2—5963no—
414C2C22×D4×D14911yescharacteristic
415C22−1+4×D14911yescharacteristic
416C2C2×#1801195911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
FittingD4×Q8×C149C2
hypercenterD4×Q8D149
hypocenterC149#3486
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#18011959C2semidirect
2. C22×Q8×D149C2semidirect
3. #23750290C2semidirect
4. Q8×C22⋊D149C2semidirect
5. #23750288C2semidirect
6. #23750287C2semidirect
7. #23750286C2semidirect
8. #23750285C2semidirect
9. #23750284C2semidirect
10. #23750200C2semidirect
11. #23750198C2semidirect
12. #23750138C2semidirect
13. #23750134C2semidirect
14. #23750101C2semidirect
15. D4×Q8×C149C2semidirect
18. C2×#14558737C22semidirect
20. C2×#14558736C22semidirect
27. C2×Q8×D149C22semidirect
29. #18011910C22semidirect
30. #18011909C22semidirect
31. #18011900C22semidirect
32. #18011899C22semidirect
33. #18011897C22semidirect
37. #18011891C22semidirect
38. #18011890C22semidirect
40. #18011889C22semidirect
41. #18011889C22semidirect
44. #18011887C22semidirect
51. Q8×Dic149C22semidirect
52. C4×Dic298C22semidirect
53. #18011876C22semidirect
62. C22×Q8×C149C22semidirect
63. C4⋊Q8×C149C22semidirect
65. C22⋊Q8×C149C22semidirect
66. C4×Q8×C149C22semidirect
82. Q8×D149D4semidirect
178. C22×C1492−1+4semidirect
189. C2×D1492−1+4semidirect
208. C149#3486semidirect
215. D4×Q8D149semidirect
238. C22×Q8C2×D149semidirect
242. C4⋊Q8C2×D149semidirect
258. C22⋊Q8C2×D149semidirect
268. C4×Q8C2×D149semidirect
397. C22#18011959semidirect

Maximal subgroups

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

subgroupindex
C2×#180119592
C22×Q8×D1492
#237502902
Q8×C22⋊D1492
#237502882
#237502872
#237502862
#237502852
#237502842
#237502002
#237501982
#237501382
#237501342
#237501012
D4×Q8×C1492
#3486149