Finite Group Databasebeta

← #34047719

Subgroups — #34047719

Order 19072.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011889C211yesmaximal, characteristic
2C2×C4×Dic298C211yesmaximal, characteristic, complemented
3C2×#18011868C211yesmaximal, characteristic
4#23749529C211yesmaximal, characteristic, complemented
5#23749520C211yesmaximal, characteristic, complemented
6#23749517C211yesmaximal, characteristic
7#23749516C211yesmaximal, characteristic
8#23749516C211yesmaximal, characteristic
9#23749515C211yesmaximal, characteristic
10#23749511C211yesmaximal, characteristic, complemented
11#23749509C211yesmaximal, characteristic, complemented
12C4×#14558715C211yesmaximal, characteristic, complemented
13#23749476C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic
15C4×C4⋊C4×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18#18011889C418yescomplemented
19C4×Dic298—24no—
20#18011868—24no—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×C4×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
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C4⋊C4×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic
50C2×C42×C149C2211yescharacteristic
51C2×C42×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C2×Dic298—22no—
56C2×Dic298—22no—
57C2×Dic298C2×C414yes—
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C2×C4×D149—22no—
66C2×C4×D149—22no—
67C2×C4×D149C2×C414yes—
68C4⋊Dic149—22no—
69#14558715—22no—
70#14558715—22no—
71#14558715—22no—
72#14558715C2×C414yes—
73#14558715C2×C414yes—
74#14558715D414yes—
75#14558713—22no—
76#14558713—22no—
77#14558713—22no—
78#14558713—22no—
79#14558713C2×C414yes—
80#14558713C2×C414yes—
81C4×Dic149—22no—
82C4×Dic149—22no—
83C4×Dic149—22no—
84C4×Dic149—22no—
85C4×Dic149—22no—
86C22×C4×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C4⋊C4×C149—22no—
94C4⋊C4×C149C2×C414yes—
95C42×C149—22no—
96C42×C149—22no—
97C42×C149—22no—
98C22×D149—21no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
104C22×D149C22×C412yes—
105Dic298—28no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
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×Dic149C22×C412yes—
122C2×Dic149C22×C412yes—
123C2×Dic149C22×C412yes—
124C2×Dic149C2×D412yes—
125C2×Dic149C2×D412yes—
126C2×Dic149#4112yes—
127C4×D149—28no—
128C23×C149C2411yescharacteristic
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
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×C149C22×C412yes—
145C2×C4×C149C22×C412yes—
146C2×C4×C149C22×C412yes—
147C2×C4×C149C2×D412yes—
148C2×C4×C149#4112yes—
149C2×C4×C149#4112yes—
150C22×C149C23×C411yescharacteristic
151C22×C149C22×D411yescharacteristic
152C22×C149C2×#4111yescharacteristic
153C22×C149C2×#4111yescharacteristic
154C22×C149C2×#4111yescharacteristic
155C22×C1492−1+411yescharacteristic
156C22×C1492−1+411yescharacteristic
157C2×D149—22no—
158C2×D149—22no—
159C2×D149—22no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—22no—
165C4×C149—22no—
166C4×C149—22no—
167C4×C149—22no—
168C4×C149—22no—
169C4×C149—22no—
170C4×C149—41no—
171Dic149—22no—
172Dic149—22no—
173Dic149—22no—
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149C4×D414yes—
178C2×C149C2×C4×D411yescharacteristic
179C2×C149C4×#4111yescharacteristic
180C2×C149#51911yescharacteristic
181C2×C149#54711yescharacteristic
182C2×C149#54811yescharacteristic
183C2×C149#55211yescharacteristic
184C2×C149#55611yescharacteristic
185D149—42no—
186C149#236211yescharacteristic, complemented, Sylow
187#2362—1491nomaximal, Sylow
188C2×C22⋊Q8—1491no—
189C2×C4×Q8—1491no—
190C2×#117—1491no—
191#391—1491no—
192#389—1491no—
193#388—1491no—
194#388—1491no—
195#388—1491no—
196#388—1491no—
197#387—1491no—
198#387—1491no—
199C4×C4⋊C4—1491no—
200C4×C4⋊C4—1491no—
201C4×C4⋊C4D14911yescharacteristic, complemented
202C4×C22⋊C4—1491no—
203C22×Q8—1491no—
204C23×C4—1491no—
205C22⋊Q8—1498no—
206C4×Q8—2984no—
207#117—2984no—
208C2×C4⋊C4—1491no—
209C2×C4⋊C4—1491no—
210C2×C4⋊C4—1491no—
211C2×C4⋊C4—1491no—
212C2×C4⋊C4—1491no—
213C2×C4⋊C4—1491no—
214C2×C4⋊C4—1491no—
215C2×C4⋊C4C2×D14911yescharacteristic
216C2×C4⋊C4C2×D14911yescharacteristic
217C2×C22⋊C4—1491no—
218C2×C22⋊C4—1491no—
219C2×C22⋊C4—1491no—
220C2×C22⋊C4—1491no—
221C2×C22⋊C4—1491no—
222C2×C22⋊C4—1491no—
223C2×C42—1491no—
224C2×C42—1491no—
225C2×C42—1491no—
226C2×C42—1491no—
227C2×C42—1491no—
228C2×C42C2×D14911yescharacteristic
229C2×C42C2×D14911yescharacteristic
230C2×C42C2×D14911yescharacteristic
231#95—1491no—
232#95—1491no—
233#95—1491no—
234#95—1491no—
235#95—1491no—
236#95—1491no—
237#95—1491no—
238#95—1491no—
239#95C2×D14911yescharacteristic
240#95C2×D14911yescharacteristic
241C24—1491no—
242C2×Q8—2982no—
243C2×Q8—2982no—
244C2×Q8—1494no—
245C22×C4—2982no—
246C22×C4—2982no—
247C22×C4—1491no—
248C22×C4—1491no—
249C22×C4—1491no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253C22×C4—1494no—
254C22×C4—1491no—
255C22×C4C22×D14911yescharacteristic
256C22×C4C22×D14911yescharacteristic
257C22×C4C22×D14911yescharacteristic
258C22×C4C22×D14911yescharacteristic
259C22×C4C22×D14911yescharacteristic
260C22×C4C22×D14911yescharacteristic
261C22×C4C22×D14911yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—2982no—
264C4⋊C4—2982no—
265C4⋊C4—2982no—
266C4⋊C4—2982no—
267C4⋊C4—1494no—
268C4⋊C4—1494no—
269C4⋊C4—1494no—
270C4⋊C4C4×D14914yes—
271C22⋊C4—2982no—
272C22⋊C4—2982no—
273C22⋊C4—2982no—
274C22⋊C4—2982no—
275C22⋊C4—1494no—
276C22⋊C4—1494no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—2982no—
281C42—2982no—
282C42—2982no—
283C42—2982no—
284C42—2982no—
285C23—2981no—
286C23—2981no—
287C23—2981no—
288C23—2981no—
289C23—2981no—
290C23—2981no—
291C23—1492no—
292C23C23×D14911yescharacteristic
293Q8—2988no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2988no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—2981no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—1492no—
326C2×C4—1492no—
327C2×C4—1492no—
328C2×C4—1492no—
329C2×C4—1492no—
330C2×C4—1492no—
331C2×C4C2×C4×D14912yes—
332C2×C4C2×C4×D14912yes—
333C2×C4C2×C4×D14912yes—
334C2×C4D4×D14912yes—
335C2×C4#1455873612yes—
336C2×C4#1455873612yes—
337C22—2982no—
338C22—2982no—
339C22—2982no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22C22×C4×D14911yescharacteristic
345C22C2×D4×D14911yescharacteristic
346C22#41×D14911yescharacteristic
347C22C2×#1455873611yescharacteristic
348C22C2×#1455873611yescharacteristic
349C22#1801195811yescharacteristic
350C22#1801195911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—2982no—
359C4—2982no—
360C4—2982no—
361C4—5961no—
362C4—5961no—
363C4—5961no—
364C4—1494no—
365C2—5962no—
366C2C4×D4×D14911yescharacteristic
367C2C4×#1455873611yescharacteristic
368C2#2375010111yescharacteristic
369C2#2375027611yescharacteristic
370C2#2375028411yescharacteristic
371C2#2375030811yescharacteristic
372C2#2375034711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C4⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenterC4×C4⋊C4D149
hypocenterC149#2362
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic298C2semidirect
4. #23749529C2semidirect
5. #23749520C2semidirect
10. #23749511C2semidirect
11. #23749509C2semidirect
12. C4×#14558715C2semidirect
13. #23749476C2semidirect
15. C4×C4⋊C4×C149C2semidirect
18. #18011889C4semidirect
186. C149#2362semidirect
201. C4×C4⋊C4D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118892
C2×C4×Dic2982
C2×#180118682
#237495292
#237495202
#237495172
#237495162
#237495152
#237495112
#237495092
C4×#145587152
#237494762
#237494722
C4×C4⋊C4×C1492
#2362149