Finite Group Databasebeta

← #34047625

Subgroups — #34047625

Order 19072.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011871C211yesmaximal, characteristic
2#23749516C211yesmaximal, characteristic, complemented
3#23749514C211yesmaximal, characteristic, complemented
4#23749509C211yesmaximal, characteristic, complemented
5#23749507C211yesmaximal, characteristic, complemented
6#23749504C211yesmaximal, characteristic
7#23749502C211yesmaximal, characteristic
8#23749492C211yesmaximal, characteristic, complemented
9#23749487C211yesmaximal, characteristic, complemented
10#23749483C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
12C4×#14558713C211yesmaximal, characteristic, complemented
13#23749471C211yesmaximal, characteristic, complemented
14C2×#18011818C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C23×Dic149C2211yescharacteristic
18C23×Dic149C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20#18011871C418yescomplemented
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×C22⋊Dic149C2211yescharacteristic
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
45C23×C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C42×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C23×D149C2311yescharacteristic
53C2×C22⋊D149—22no—
54C2×C22⋊D149—22no—
55C2×C22⋊D149C2×C414yes—
56C22×Dic149—22no—
57C22×Dic149—22no—
58C22×Dic149—41no—
59C22×Dic149—41no—
60C22×Dic149—41no—
61C22×Dic149C2×C414yes—
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C2×C4×D149—41no—
70C2×C4×D149—41no—
71C2×C4×D149C2×C414yescomplemented
72#14558715—41no—
73#14558715—41no—
74#14558715C2×C414yescomplemented
75C22⋊Dic149—22no—
76#14558713—22no—
77#14558713—22no—
78#14558713—41no—
79#14558713—41no—
80#14558713C2×C414yescomplemented
81C4×Dic149—22no—
82C4×Dic149—41no—
83C4×Dic149C2×C414yescomplemented
84C24×C149C2311yescharacteristic
85C22×C4×C149—22no—
86C22×C4×C149—22no—
87C22×C4×C149—41no—
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22⋊C4×C149—22no—
95C22⋊C4×C149C2×C414yes—
96C42×C149—22no—
97C42×C149—41no—
98C22×D149—21no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
104C22×D149C22×C412yes—
105C22⋊D149—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×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—44no—
124C2×Dic149—44no—
125C2×Dic149C22×C412yes—
126C2×Dic149C22×C412yes—
127C2×Dic149C22×C412yes—
128C2×Dic149#4112yes—
129C4×D149—44no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149C22×C412yes—
135C23×C149#4112yes—
136C23×C149#4112yes—
137C23×C149C2411yescharacteristic
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—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—44no—
154C2×C4×C149C22×C412yes—
155C2×C4×C149C22×C412yes—
156C2×C4×C149#4112yes—
157C22×C149—22no—
158C22×C149—22no—
159C22×C149—22no—
160C22×C149—22no—
161C22×C149—22no—
162C22×C149—22no—
163C22×C149#11714yes—
164C22×C149C23×C411yescharacteristic
165C22×C149C2×#4111yescharacteristic
166C22×C149C2×#4111yescharacteristic
167C22×C149C2×#4111yescharacteristic
168C22×C149C2×#4111yescharacteristic
169C22×C149H(5,𝔽2)11yescharacteristic
170C22×C149H(5,𝔽2)11yescharacteristic
171C2×D149—22no—
172C2×D149—22no—
173C2×D149—22no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C4×C149—22no—
179C4×C149—22no—
180C4×C149—22no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149—41no—
184Dic149—22no—
185Dic149—22no—
186Dic149—22no—
187Dic149—22no—
188Dic149—41no—
189Dic149—41no—
190Dic149—41no—
191C2×C149—24no—
192C2×C149C2×#11711yescharacteristic
193C2×C149C4×#4111yescharacteristic
194C2×C149#51811yescharacteristic
195C2×C149#55111yescharacteristic
196C2×C149#55111yescharacteristic
197C2×C149#55311yescharacteristic
198C2×C149#55311yescharacteristic
199D149—42no—
200C149#235311yescharacteristic, complemented, Sylow
201#2353—1491nomaximal, Sylow
202C2×C4×D4—1491no—
203#388—1491no—
204#388—1491no—
205#387—1491no—
206#387—1491no—
207#386—1491no—
208#386—1491no—
209#383—1491no—
210#381—1491no—
211#380—1491no—
212C4×C22⋊C4—1491no—
213C4×C22⋊C4—1491no—
214C4×C22⋊C4D14911yescharacteristic, complemented
215#376—1491no—
216C2×#95—1491no—
217C22×D4—1491no—
218C23×C4—1491no—
219C23×C4—1491no—
220C23×C4—1491no—
221C23×C4C2×D14911yescharacteristic
222C4×D4—1498no—
223C2×C4⋊C4—1491no—
224C2×C4⋊C4—1491no—
225C2×C4⋊C4—1491no—
226C2×C22⋊C4—1491no—
227C2×C22⋊C4—1491no—
228C2×C22⋊C4—1491no—
229C2×C22⋊C4—1491no—
230C2×C22⋊C4—1491no—
231C2×C22⋊C4—1491no—
232C2×C22⋊C4C2×D14911yescharacteristic
233C2×C22⋊C4C2×D14911yescharacteristic
234C2×C42—1491no—
235C2×C42—1491no—
236C2×C42—1491no—
237C2×C42C2×D14911yescharacteristic
238C2×C42C2×D14911yescharacteristic
239#95—1491no—
240#95—1491no—
241#95—1491no—
242#95—1491no—
243#95—1491no—
244#95—1491no—
245#95—1491no—
246#95—1491no—
247#95—1491no—
248#95—1491no—
249#95—1491no—
250#95—1491no—
251#95C2×D14911yescharacteristic
252#95C2×D14911yescharacteristic
253C24—1491no—
254C24C22×D14911yescharacteristic
255C2×D4—2982no—
256C2×D4—2982no—
257C2×D4—1494no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—2982no—
262C22×C4—2982no—
263C22×C4—5961no—
264C22×C4—5961no—
265C22×C4—5961no—
266C22×C4—5961no—
267C22×C4—5961no—
268C22×C4—1491no—
269C22×C4—1491no—
270C22×C4—1491no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1494no—
276C22×C4—1494no—
277C22×C4C22×D14911yescharacteristic
278C22×C4C22×D14911yescharacteristic
279C22×C4C22×D14911yescharacteristic
280C22×C4C22×D14911yescharacteristic
281C22×C4C22×D14911yescharacteristic
282C22×C4C22×D14911yescharacteristic
283C4⋊C4—5961no—
284C4⋊C4—5961no—
285C4⋊C4—1494no—
286C22⋊C4—22no—
287C22⋊C4—2982no—
288C22⋊C4—2982no—
289C22⋊C4—2982no—
290C22⋊C4—5961no—
291C22⋊C4—5961no—
292C22⋊C4—1494no—
293C22⋊C4C4×D14914yes—
294C42—22no—
295C42—41no—
296C42—2982no—
297C42—5961no—
298C42—1494no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—2981no—
304C23—2981no—
305C23—2981no—
306C23—2981no—
307C23—2981no—
308C23—2981no—
309C23—1492no—
310C23C2×C4×D14912yes—
311C23#1455873612yes—
312C23#1455873612yes—
313C23C23×D14911yescharacteristic
314D4—2988no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—5964no—
349C2×C4—5964no—
350C2×C4—5964no—
351C2×C4—1492no—
352C2×C4—1492no—
353C2×C4—1492no—
354C2×C4—1492no—
355C2×C4C2×C4×D14912yes—
356C2×C4C2×C4×D14912yes—
357C2×C4#1455873512yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—2982no—
365C22—2982no—
366C22—2982no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22#1801186814yes—
372C22C22×C4×D14911yescharacteristic
373C22#41×D14911yescharacteristic
374C22C2×#1455873511yescharacteristic
375C22C2×#1455873611yescharacteristic
376C22C2×#1455873611yescharacteristic
377C22#1801195611yescharacteristic
378C22#1801195711yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—2982no—
386C4—2982no—
387C4—2982no—
388C4—2982no—
389C4—5961no—
390C4—5961no—
391C4—5961no—
392C2—24no—
393C2—5962no—
394C2C2×#1801186811yescharacteristic
395C2C4×#1455873511yescharacteristic
396C2#2375009711yescharacteristic
397C2#2375029911yescharacteristic
398C2#2375030111yescharacteristic
399C2#2375032111yescharacteristic
400C2#2375032411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenterC4×C22⋊C4D149
hypocenterC149#2353
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23749516C2semidirect
3. #23749514C2semidirect
4. #23749509C2semidirect
5. #23749507C2semidirect
8. #23749492C2semidirect
9. #23749487C2semidirect
10. #23749483C2semidirect
11. C22⋊C4×Dic149C2semidirect
12. C4×#14558713C2semidirect
13. #23749471C2semidirect
14. C2×#18011818C2semidirect
15. C4×C22⋊C4×C149C2semidirect
20. #18011871C4semidirect
71. C2×C4×D149C2×C4semidirect
74. #14558715C2×C4semidirect
80. #14558713C2×C4semidirect
83. C4×Dic149C2×C4semidirect
200. C149#2353semidirect
214. C4×C22⋊C4D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118712
#237495162
#237495142
#237495092
#237495072
#237495042
#237495022
#237494922
#237494872
#237494832
C22⋊C4×Dic1492
C4×#145587132
#237494712
C2×#180118182
C4×C22⋊C4×C1492
#2353149