Finite Group Databasebeta

← #34047853

Subgroups — #34047853

Order 19072.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011889C211yesmaximal, characteristic
2#23749530C211yesmaximal, characteristic, complemented
3#23749529C211yesmaximal, characteristic, complemented
4#23749522C211yesmaximal, characteristic, complemented
5#23749516C211yesmaximal, characteristic
6#23749515C211yesmaximal, characteristic
7#23749515C211yesmaximal, characteristic
8#23749514C211yesmaximal, characteristic
9#23749511C211yesmaximal, characteristic, complemented
10#23749509C211yesmaximal, characteristic, complemented
11#23749506C211yesmaximal, characteristic, complemented
12#23749506C211yesmaximal, characteristic, complemented
13#23749487C211yesmaximal, characteristic
14#23749482C211yesmaximal, characteristic
15#389×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18#18011889C418yescomplemented
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558713C2211yescharacteristic
25C2×#14558713C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31C2×C4×Dic149C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33#18011818C2211yescharacteristic
34#18011818C2211yescharacteristic
35#18011818C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C4⋊C4×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C23×D149C2311yescharacteristic
53C2×Dic298—41no—
54C2×Dic298—41no—
55C2×Dic298C2×C414yes—
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C2×C4×D149—41no—
64C2×C4×D149—41no—
65C2×C4×D149C2×C414yes—
66C4⋊Dic149—41no—
67#14558715—41no—
68#14558715—41no—
69#14558715C2×C414yes—
70#14558715C2×C414yes—
71#14558713—41no—
72#14558713—41no—
73#14558713—41no—
74#14558713—41no—
75#14558713C2×C414yes—
76#14558713C2×C414yes—
77C4×Dic149—41no—
78C4×Dic149—41no—
79C4×Dic149—41no—
80C22×C4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—41no—
88C4⋊C4×C149—41no—
89C4⋊C4×C149—41no—
90C4⋊C4×C149C2×C414yes—
91C42×C149—41no—
92C22×D149—21no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149—21no—
97C22×D149—21no—
98C22×D149C22×C412yes—
99Dic298—44no—
100C2×Dic149—21no—
101C2×Dic149—21no—
102C2×Dic149—21no—
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—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149C22×C412yes—
119C2×Dic149C22×C412yes—
120C2×Dic149C22×C412yes—
121C4×D149—44no—
122C23×C149C2411yescharacteristic
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
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×C149C22×C412yes—
142C2×C4×C149C22×C412yes—
143C2×C4×C149C22×C412yes—
144C22×C149C23×C411yescharacteristic
145C22×C149H(5,𝔽2)11yescharacteristic
146C22×C149H(5,𝔽2)11yescharacteristic
147C22×C149H(5,𝔽2)11yescharacteristic
148C22×C1492−1+411yescharacteristic
149C22×C1492−1+411yescharacteristic
150C22×C1492−1+411yescharacteristic
151C2×D149—22no—
152C2×D149—22no—
153C2×D149—22no—
154C2×D149—41no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C4×C149—22no—
159C4×C149—22no—
160C4×C149—22no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165Dic149—22no—
166Dic149—22no—
167Dic149—22no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149#51811yescharacteristic
173C2×C149#51911yescharacteristic
174C2×C149#52011yescharacteristic
175C2×C149#56211yescharacteristic
176C2×C149#56211yescharacteristic
177C2×C149#56311yescharacteristic
178C2×C149#56311yescharacteristic
179D149—42no—
180C149#237811yescharacteristic, complemented, Sylow
181#2378—1491nomaximal, Sylow
182C2×C22⋊Q8—1491no—
183#391—1491no—
184#391—1491no—
185#389—1491no—
186#389D14911yescharacteristic, complemented
187#388—1491no—
188#388—1491no—
189#388—1491no—
190#388—1491no—
191#387—1491no—
192#387—1491no—
193#387—1491no—
194#387—1491no—
195#381—1491no—
196#380—1491no—
197C22×Q8—1491no—
198C23×C4—1491no—
199C22⋊Q8—1498no—
200C2×C4⋊C4—1491no—
201C2×C4⋊C4—1491no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4—1491no—
204C2×C4⋊C4—1491no—
205C2×C4⋊C4C2×D14911yescharacteristic
206C2×C4⋊C4C2×D14911yescharacteristic
207C2×C4⋊C4C2×D14911yescharacteristic
208C2×C4⋊C4C2×D14911yescharacteristic
209C2×C22⋊C4—1491no—
210C2×C22⋊C4—1491no—
211C2×C22⋊C4—1491no—
212C2×C22⋊C4—1491no—
213C2×C22⋊C4—1491no—
214C2×C22⋊C4—1491no—
215C2×C42—1491no—
216C2×C42—1491no—
217C2×C42—1491no—
218C2×C42C2×D14911yescharacteristic
219#95—1491no—
220#95—1491no—
221#95—1491no—
222#95—1491no—
223#95—1491no—
224#95—1491no—
225#95—1491no—
226#95—1491no—
227#95—1491no—
228#95—1491no—
229#95—1491no—
230#95—1491no—
231#95C2×D14911yescharacteristic
232#95C2×D14911yescharacteristic
233C24—1491no—
234C2×Q8—5961no—
235C2×Q8—5961no—
236C2×Q8—1494no—
237C22×C4—5961no—
238C22×C4—5961no—
239C22×C4—1491no—
240C22×C4—1491no—
241C22×C4—1491no—
242C22×C4—1491no—
243C22×C4—1491no—
244C22×C4—1491no—
245C22×C4—1491no—
246C22×C4—1494no—
247C22×C4C22×D14911yescharacteristic
248C22×C4C22×D14911yescharacteristic
249C22×C4C22×D14911yescharacteristic
250C22×C4C22×D14911yescharacteristic
251C22×C4C22×D14911yescharacteristic
252C22×C4C22×D14911yescharacteristic
253C22×C4C22×D14911yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—5961no—
258C4⋊C4—5961no—
259C4⋊C4—5961no—
260C4⋊C4—1494no—
261C4⋊C4—1494no—
262C4⋊C4C4×D14914yes—
263C22⋊C4—5961no—
264C22⋊C4—5961no—
265C22⋊C4—5961no—
266C22⋊C4—5961no—
267C22⋊C4—1494no—
268C22⋊C4—1494no—
269C42—41no—
270C42—5961no—
271C42—5961no—
272C42—5961no—
273C23—2981no—
274C23—2981no—
275C23—2981no—
276C23—2981no—
277C23—2981no—
278C23—2981no—
279C23—1492no—
280C23C23×D14911yescharacteristic
281Q8—5964no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—2981no—
309C2×C4—2981no—
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—5964no—
319C2×C4—1492no—
320C2×C4—1492no—
321C2×C4—1492no—
322C2×C4C2×C4×D14912yes—
323C2×C4C2×C4×D14912yes—
324C2×C4C2×C4×D14912yes—
325C22—2982no—
326C22—2982no—
327C22—2982no—
328C22—5961no—
329C22—5961no—
330C22—5961no—
331C22—5961no—
332C22C22×C4×D14911yescharacteristic
333C22#1801195611yescharacteristic
334C22#1801195611yescharacteristic
335C22#1801195711yescharacteristic
336C22#1801195811yescharacteristic
337C22#1801195911yescharacteristic
338C22#1801195911yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2982no—
347C4—2982no—
348C4—2982no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4—5961no—
353C2—5962no—
354C2#2375009711yescharacteristic
355C2#2375010111yescharacteristic
356C2#2375010611yescharacteristic
357C2#2375037011yescharacteristic
358C2#2375037111yescharacteristic
359C2#2375037411yescharacteristic
360C2#2375037911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#389×C149C2
socle, cosocleC23×C149C24
prime radicalC23×D149C23
hypercenter#389D149
hypocenterC149#2378
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #23749530C2semidirect
3. #23749529C2semidirect
4. #23749522C2semidirect
9. #23749511C2semidirect
10. #23749509C2semidirect
11. #23749506C2semidirect
12. #23749506C2semidirect
15. #389×C149C2semidirect
18. #18011889C4semidirect
180. C149#2378semidirect
186. #389D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118892
#237495302
#237495292
#237495222
#237495162
#237495152
#237495142
#237495112
#237495092
#237495062
#237494872
#237494822
#389×C1492
#2378149