Finite Group Databasebeta

← #34047557

Subgroups — #34047557

Order 19072.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011869C211yesmaximal, characteristic
2C2×#18011868C211yesmaximal, characteristic
3C2×C4⋊C4×D149C211yesmaximal, characteristic
4#23749522C211yesmaximal, characteristic, complemented
5#23749520C211yesmaximal, characteristic, complemented
6#23749511C211yesmaximal, characteristic, complemented
7#23749510C211yesmaximal, characteristic, complemented
8#23749508C211yesmaximal, characteristic, complemented
9#23749487C211yesmaximal, characteristic
10#23749487C211yesmaximal, characteristic
11#23749484C211yesmaximal, characteristic
12C4×#14558715C211yesmaximal, characteristic, complemented
13#23749476C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic
15#387×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011869—24no—
20#18011868—24no—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×#14558715C2211yescharacteristic
29C4⋊C4×D149C418yescomplemented
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
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C2×C4×D149—22no—
63C2×C4×D149—22no—
64C2×C4×D149—22no—
65C2×C4×D149—22no—
66C2×C4×D149—22no—
67C2×C4×D149—22no—
68C2×C4×D149C2×C414yes—
69C2×C4×D149C2×C414yes—
70C2×C4×D149C2×C414yes—
71C4⋊Dic149—22no—
72C4⋊Dic149C2×C414yes—
73#14558715—22no—
74#14558715—22no—
75#14558715—22no—
76#14558715—22no—
77#14558715C2×C414yes—
78#14558715C2×C414yes—
79#14558713—22no—
80#14558713—22no—
81#14558713—22no—
82#14558713D414yes—
83C4×Dic149—22no—
84C4×Dic149—22no—
85C4×Dic149—22no—
86C4×Dic149—22no—
87C4×Dic149—22no—
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C4⋊C4×C149—22no—
96C4⋊C4×C149C2×C414yes—
97C42×C149—22no—
98C22×D149—21no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149C22×C412yes—
103C22×D149C2×D412yes—
104C22×D149#4112yes—
105C2×Dic149—21no—
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×Dic149C22×C412yes—
121C2×Dic149C22×C412yes—
122C2×Dic149C22×C412yes—
123C2×Dic149C2×D412yes—
124C2×Dic149#4112yes—
125C2×Dic149#4112yes—
126C4×D149—28no—
127C4×D149—28no—
128C4×D149—28no—
129C23×C149C2411yescharacteristic
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×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149C22×C412yes—
148C2×C4×C149C22×C412yes—
149C2×C4×C149C22×C412yes—
150C2×C4×C149C2×D412yes—
151C22×C149C23×C411yescharacteristic
152C22×C149C22×D411yescharacteristic
153C22×C149C2×#4111yescharacteristic
154C22×C149C2×#4111yescharacteristic
155C22×C149C2×#4111yescharacteristic
156C22×C1492−1+411yescharacteristic
157C22×C1492−1+411yescharacteristic
158C2×D149—22no—
159C2×D149—22no—
160C2×D149—22no—
161C2×D149—22no—
162C2×D149—22no—
163C2×D149—22no—
164C2×D149C4×D414yes—
165C4×C149—22no—
166C4×C149—22no—
167C4×C149—22no—
168C4×C149—22no—
169C4×C149—41no—
170C4×C149—41no—
171C4×C149—41no—
172Dic149—22no—
173Dic149—22no—
174Dic149—22no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178Dic149#11714yescomplemented
179C2×C149C2×#11711yescharacteristic
180C2×C149C2×C4×D411yescharacteristic
181C2×C149#51911yescharacteristic
182C2×C149#54711yescharacteristic
183C2×C149#54711yescharacteristic
184C2×C149#55211yescharacteristic
185C2×C149#55211yescharacteristic
186D149—24no—
187C149#234411yescharacteristic, complemented, Sylow
188#2344—1491nomaximal, Sylow
189C2×#117—1491no—
190C2×#117—1491no—
191C22×C4⋊C4—1491no—
192#389—1491no—
193#389—1491no—
194#387—1491no—
195#387—1491no—
196#387—1491no—
197#387D14911yescharacteristic, complemented
198#381—1491no—
199#381—1491no—
200#380—1491no—
201C4×C4⋊C4—1491no—
202C4×C4⋊C4—1491no—
203C4×C22⋊C4—1491no—
204C23×C4—1491no—
205C23×C4—1491no—
206C23×C4—1491no—
207#117—2984no—
208#117—2984no—
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⋊C4—1491no—
216C2×C4⋊C4—1491no—
217C2×C4⋊C4—1498no—
218C2×C4⋊C4C2×D14911yescharacteristic
219C2×C4⋊C4C2×D14911yescharacteristic
220C2×C22⋊C4—1491no—
221C2×C22⋊C4—1491no—
222C2×C22⋊C4—1491no—
223C2×C22⋊C4—1491no—
224C2×C42—1491no—
225C2×C42—1491no—
226C2×C42—1491no—
227C2×C42—1491no—
228C2×C42—1491no—
229C2×C42C2×D14911yescharacteristic
230#95—1491no—
231#95—1491no—
232#95—1491no—
233#95—1491no—
234#95—1491no—
235#95—1491no—
236#95—1491no—
237#95—1491no—
238#95C2×D14911yescharacteristic
239#95C2×D14911yescharacteristic
240#95C2×D14911yescharacteristic
241#95C2×D14911yescharacteristic
242C24—1491no—
243C22×C4—2982no—
244C22×C4—2982no—
245C22×C4—2982no—
246C22×C4—2982no—
247C22×C4—2982no—
248C22×C4—2982no—
249C22×C4—1491no—
250C22×C4—1491no—
251C22×C4—1491no—
252C22×C4—1491no—
253C22×C4—1491no—
254C22×C4—1491no—
255C22×C4—1494no—
256C22×C4—1494no—
257C22×C4—1494no—
258C22×C4—1491no—
259C22×C4C22×D14911yescharacteristic
260C22×C4C22×D14911yescharacteristic
261C22×C4C22×D14911yescharacteristic
262C22×C4C22×D14911yescharacteristic
263C22×C4C22×D14911yescharacteristic
264C22×C4C22×D14911yescharacteristic
265C22×C4C22×D14911yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—2982no—
268C4⋊C4—2982no—
269C4⋊C4—2982no—
270C4⋊C4—2982no—
271C4⋊C4—2982no—
272C4⋊C4—1494no—
273C4⋊C4—1494no—
274C4⋊C4—1494no—
275C4⋊C4C4×D14914yes—
276C22⋊C4—2982no—
277C22⋊C4—2982no—
278C22⋊C4—2982no—
279C22⋊C4—1494no—
280C42—22no—
281C42—2982no—
282C42—2982no—
283C42—2982no—
284C42—2982no—
285C42—2982no—
286C23—2981no—
287C23—2981no—
288C23—2981no—
289C23—2981no—
290C23—1492no—
291C23—1492no—
292C23—1492no—
293C23C23×D14911yescharacteristic
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—21no—
310C2×C4—21no—
311C2×C4—2988no—
312C2×C4—2988no—
313C2×C4—2988no—
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—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—2981no—
329C2×C4—1492no—
330C2×C4—1492no—
331C2×C4—1492no—
332C2×C4—1492no—
333C2×C4—1492no—
334C2×C4—1492no—
335C2×C4C2×C4×D14912yes—
336C2×C4C2×C4×D14912yes—
337C2×C4C2×C4×D14912yes—
338C2×C4D4×D14912yes—
339C22—2982no—
340C22—2982no—
341C22—2982no—
342C22—2982no—
343C22—2982no—
344C22—2982no—
345C22—1494no—
346C22C22×C4×D14911yescharacteristic
347C22C2×D4×D14911yescharacteristic
348C22#41×D14911yescharacteristic
349C22#41×D14911yescharacteristic
350C22#41×D14911yescharacteristic
351C22#1801195811yescharacteristic
352C22#1801195911yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2982no—
361C4—2982no—
362C4—2982no—
363C4—5961no—
364C4—5961no—
365C4—5961no—
366C4—1494no—
367C2—2984no—
368C2#117×D14911yescharacteristic
369C2C4×D4×D14911yescharacteristic
370C2#2375010111yescharacteristic
371C2#2375027311yescharacteristic
372C2#2375027711yescharacteristic
373C2#2375030711yescharacteristic
374C2#2375031111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#387×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenter#387D149
hypocenterC149#2344
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #23749522C2semidirect
5. #23749520C2semidirect
6. #23749511C2semidirect
7. #23749510C2semidirect
8. #23749508C2semidirect
12. C4×#14558715C2semidirect
13. #23749476C2semidirect
15. #387×C149C2semidirect
29. C4⋊C4×D149C4semidirect
178. Dic149#117semidirect
187. C149#2344semidirect
197. #387D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118692
C2×#180118682
C2×C4⋊C4×D1492
#237495222
#237495202
#237495112
#237495102
#237495082
#237494872
#237494842
C4×#145587152
#237494762
#237494722
#387×C1492
#2344149