Finite Group Databasebeta

← #34047697

Subgroups — #34047697

Order 19072.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011888C211yesmaximal, characteristic
2C2×C4×Dic298C211yesmaximal, characteristic, complemented
3C22×#14558715C211yesmaximal, characteristic
4#23749529C211yesmaximal, characteristic, complemented
5#23749523C211yesmaximal, characteristic, complemented
6#23749522C211yesmaximal, characteristic, complemented
7#23749522C211yesmaximal, characteristic, complemented
8#23749509C211yesmaximal, characteristic, complemented
9#23749508C211yesmaximal, characteristic, complemented
10#23749500C211yesmaximal, characteristic
11#23749498C211yesmaximal, characteristic
12C4×#14558715C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic149C211yesmaximal, characteristic
14C22⋊C4×Dic149C211yesmaximal, characteristic
15C4×C22⋊C4×C149C211yesmaximal, characteristic
16C22×Dic298C2211yescharacteristic
17C23×Dic149C2211yescharacteristic
18C23×Dic149C2211yescharacteristic
19#18011888C418yescomplemented
20C4×Dic298—24no—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×C4⋊Dic149C2211yescharacteristic
23C2×C4⋊Dic149C2211yescharacteristic
24C2×#14558715—24no—
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558715C2211yescharacteristic
29C2×#14558715C2211yescharacteristic
30C2×#14558715C2211yescharacteristic
31C2×#14558715C2211yescharacteristic
32C2×#14558715C2211yescharacteristic
33C2×C22⋊Dic149C2211yescharacteristic
34C2×C22⋊Dic149C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37C2×C4×Dic149C2211yescharacteristic
38C2×C4×Dic149C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46#18011818C2211yescharacteristic
47C23×C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50C2×C42×C149C2211yescharacteristic
51C2×C42×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C2×Dic298—22no—
55C2×Dic298—22no—
56C2×Dic298C2×C414yescomplemented
57C22×Dic149—22no—
58C22×Dic149—22no—
59C22×Dic149—22no—
60C22×Dic149—22no—
61C22×Dic149—41no—
62C22×Dic149C2×C414yes—
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C22×Dic149C2311yescharacteristic
70C22×Dic149C2311yescharacteristic
71C4⋊Dic149—22no—
72C4⋊Dic149—41no—
73C4⋊Dic149C2×C414yescomplemented
74#14558715—22no—
75#14558715—22no—
76#14558715—22no—
77#14558715—22no—
78#14558715—41no—
79#14558715C2×C414yescomplemented
80#14558715C2×C414yescomplemented
81#14558715D414yes—
82C22⋊Dic149—22no—
83C22⋊Dic149C2×C414yes—
84C4×Dic149—22no—
85C4×Dic149—22no—
86C4×Dic149—22no—
87C4×Dic149—41no—
88C24×C149C2311yescharacteristic
89C22×C4×C149—22no—
90C22×C4×C149—22no—
91C22×C4×C149—41no—
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22⋊C4×C149C2×C414yes—
99C22⋊C4×C149Q814yescomplemented
100C42×C149—22no—
101C42×C149—41no—
102Dic298—28no—
103C2×Dic149—21no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—28no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—44no—
122C2×Dic149C22×C412yes—
123C2×Dic149C22×C412yes—
124C2×Dic149C22×C412yes—
125C2×Dic149C22×C412yes—
126C2×Dic149C2×D412yes—
127C2×Dic149C2×D412yes—
128C2×Dic149#4112yes—
129C23×C149—21no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149C22×C412yes—
134C23×C149C2×Q812yes—
135C23×C149#4112yes—
136C23×C149C2411yescharacteristic
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—44no—
151C2×C4×C149C22×C412yes—
152C2×C4×C149C22×C412yes—
153C2×C4×C149C2×D412yes—
154C2×C4×C149C2×Q812yes—
155C2×C4×C149C2×Q812yes—
156C22×C149—22no—
157C22×C149—22no—
158C22×C149—22no—
159C22×C149—22no—
160C22×C149—22no—
161C22×C149—22no—
162C22×C149C4×Q814yescomplemented
163C22×C149C23×C411yescharacteristic
164C22×C149C22×D411yescharacteristic
165C22×C149C22×Q811yescharacteristic
166C22×C149C2×#4111yescharacteristic
167C22×C149C2×#4111yescharacteristic
168C22×C149H(5,𝔽2)11yescharacteristic
169C22×C1492−1+411yescharacteristic
170C4×C149—22no—
171C4×C149—22no—
172C4×C149—22no—
173C4×C149—22no—
174C4×C149—22no—
175C4×C149—41no—
176Dic149—22no—
177Dic149—22no—
178Dic149—22no—
179Dic149—22no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183Dic149C4×D414yes—
184C2×C149—24no—
185C2×C149C2×C4×D411yescharacteristic
186C2×C149C2×C4×Q811yescharacteristic
187C2×C149#52011yescharacteristic
188C2×C149#54611yescharacteristic
189C2×C149D4×Q811yescharacteristic
190C2×C149#55211yescharacteristic
191C2×C149#55411yescharacteristic
192C149#236011yescharacteristic, complemented, Sylow
193#2360—1491nomaximal, Sylow
194C2×C22⋊Q8—1491no—
195C2×C4×Q8—1491no—
196C22×C4⋊C4—1491no—
197#391—1491no—
198#389—1491no—
199#389—1491no—
200#389—1491no—
201#387—1491no—
202#387—1491no—
203#385—1491no—
204#385—1491no—
205C4×C4⋊C4—1491no—
206C4×C22⋊C4—1491no—
207C4×C22⋊C4—1491no—
208C4×C22⋊C4D14911yescharacteristic
209C22×Q8—1491no—
210C23×C4—1491no—
211C23×C4—1491no—
212C23×C4C2×D14911yescharacteristic
213C22⋊Q8—1498no—
214C4×Q8—2984no—
215C2×C4⋊C4—2984no—
216C2×C4⋊C4—1491no—
217C2×C4⋊C4—1491no—
218C2×C4⋊C4—1491no—
219C2×C4⋊C4—1491no—
220C2×C4⋊C4—1491no—
221C2×C4⋊C4—1491no—
222C2×C4⋊C4—1491no—
223C2×C4⋊C4—1491no—
224C2×C4⋊C4—1491no—
225C2×C4⋊C4—1491no—
226C2×C4⋊C4—1491no—
227C2×C22⋊C4—1491no—
228C2×C22⋊C4—1491no—
229C2×C22⋊C4C2×D14911yescharacteristic
230C2×C22⋊C4C2×D14911yescharacteristic
231C2×C42—1491no—
232C2×C42—1491no—
233C2×C42—1491no—
234C2×C42—1491no—
235C2×C42C2×D14911yescharacteristic
236C2×C42C2×D14911yescharacteristic
237#95—1491no—
238#95—1491no—
239#95—1491no—
240#95—1491no—
241#95—1491no—
242#95—1491no—
243#95—1491no—
244#95—1491no—
245#95C2×D14911yescharacteristic
246#95C2×D14911yescharacteristic
247C24C22×D14911yescharacteristic
248C2×Q8—2982no—
249C2×Q8—2982no—
250C2×Q8—1494no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—2982no—
255C22×C4—2982no—
256C22×C4—2982no—
257C22×C4—2982no—
258C22×C4—5961no—
259C22×C4—1491no—
260C22×C4—1491no—
261C22×C4—1491no—
262C22×C4—1494no—
263C22×C4—1491no—
264C22×C4—1491no—
265C22×C4—1491no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4C22×D14911yescharacteristic
269C22×C4C22×D14911yescharacteristic
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272C22×C4C22×D14911yescharacteristic
273C22×C4C22×D14911yescharacteristic
274C4⋊C4—2982no—
275C4⋊C4—2982no—
276C4⋊C4—2982no—
277C4⋊C4—2982no—
278C4⋊C4—2982no—
279C4⋊C4—5961no—
280C4⋊C4—5961no—
281C4⋊C4—1494no—
282C4⋊C4—1494no—
283C4⋊C4—1494no—
284C4⋊C4—1494no—
285C22⋊C4—2982no—
286C22⋊C4—1494no—
287C22⋊C4C4×D14914yes—
288C22⋊C4Dic29814yescomplemented
289C42—22no—
290C42—41no—
291C42—2982no—
292C42—2982no—
293C42—2982no—
294C42—5961no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D14912yes—
300C23C2×Dic29812yes—
301C23#1455873612yes—
302C23C23×D14911yescharacteristic
303Q8—2988no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2988no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—5964no—
337C2×C4—1492no—
338C2×C4—1492no—
339C2×C4—1492no—
340C2×C4—1492no—
341C2×C4—1492no—
342C2×C4—1492no—
343C2×C4—1492no—
344C2×C4C2×C4×D14912yes—
345C2×C4C2×C4×D14912yes—
346C2×C4D4×D14912yes—
347C2×C4C2×Dic29812yes—
348C2×C4C2×Dic29812yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22C4×Dic29814yescomplemented
356C22C22×C4×D14911yescharacteristic
357C22C2×D4×D14911yescharacteristic
358C22C22×Dic29811yescharacteristic
359C22#41×D14911yescharacteristic
360C22C2×#1455873611yescharacteristic
361C22#1801195611yescharacteristic
362C22#1801195811yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—2982no—
370C4—2982no—
371C4—2982no—
372C4—2982no—
373C4—5961no—
374C4—5961no—
375C4—5961no—
376C4—1494no—
377C2—24no—
378C2C4×D4×D14911yescharacteristic
379C2C2×C4×Dic29811yescharacteristic
380C2#2375010411yescharacteristic
381C2#2375026511yescharacteristic
382C2D4×Dic29811yescharacteristic
383C2#2375030811yescharacteristic
384C2#2375033411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenterC4×C22⋊C4D149
hypocenterC149#2360
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic298C2semidirect
4. #23749529C2semidirect
5. #23749523C2semidirect
6. #23749522C2semidirect
7. #23749522C2semidirect
8. #23749509C2semidirect
9. #23749508C2semidirect
12. C4×#14558715C2semidirect
19. #18011888C4semidirect
56. C2×Dic298C2×C4semidirect
73. C4⋊Dic149C2×C4semidirect
79. #14558715C2×C4semidirect
80. #14558715C2×C4semidirect
99. C22⋊C4×C149Q8semidirect
162. C22×C149C4×Q8semidirect
192. C149#2360semidirect
288. C22⋊C4Dic298semidirect
355. C22C4×Dic298semidirect

Maximal subgroups

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

subgroupindex
C2×#180118882
C2×C4×Dic2982
C22×#145587152
#237495292
#237495232
#237495222
#237495092
#237495082
#237495002
#237494982
C4×#145587152
C22⋊C4×Dic1492
C4×C22⋊C4×C1492
#2360149