Finite Group Databasebeta

← #34047151

Subgroups — #34047151

Order 19072.

652 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011871C211yesmaximal, characteristic
2C2×#18011869C211yesmaximal, characteristic, complemented
3C2×#18011867C211yesmaximal, characteristic, complemented
4#23749525C211yesmaximal, characteristic
5#23749525C211yesmaximal, characteristic
6#23749522C211yesmaximal, characteristic, complemented
7#23749520C211yesmaximal, characteristic, complemented
8#23749518C211yesmaximal, characteristic, complemented
9#23749516C211yesmaximal, characteristic, complemented
10#23749514C211yesmaximal, characteristic, complemented
11#23749476C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
13#23749472C211yesmaximal, characteristic, complemented
14C42×Dic149C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C23×Dic149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011871C418yescomplemented
20#18011869—24no—
21#18011867—24no—
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37C2×C4×Dic149C2211yescharacteristic
38C2×C4×Dic149C2211yescharacteristic
39C2×C4×Dic149C2211yescharacteristic
40C2×C4×Dic149C2211yescharacteristic
41C2×C4×Dic149C2211yescharacteristic
42C2×C4×Dic149C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46#18011818C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C42×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C2×C22⋊D149—22no—
56C2×C22⋊D149—22no—
57C2×C22⋊D149C2×C414yes—
58C22×Dic149—22no—
59C22×Dic149—22no—
60C22×Dic149C2×C414yes—
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C2×C4×D149—22no—
69C2×C4×D149—22no—
70C2×C4×D149C2×C414yes—
71C4⋊Dic149—22no—
72#14558715—22no—
73#14558715—22no—
74#14558715—22no—
75#14558715—22no—
76#14558715C2×C414yes—
77C22⋊Dic149—22no—
78C22⋊Dic149—22no—
79#14558713—22no—
80#14558713—22no—
81#14558713—22no—
82#14558713—22no—
83#14558713C2×C414yes—
84C4×Dic149—22no—
85C4×Dic149—22no—
86C4×Dic149—22no—
87C4×Dic149—22no—
88C4×Dic149—22no—
89C4×Dic149—22no—
90C4×Dic149C2×C414yes—
91C4×Dic149D414yescomplemented
92C24×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C4⋊C4×C149—22no—
100C22⋊C4×C149—22no—
101C22⋊C4×C149—22no—
102C22⋊C4×C149C2×C414yes—
103C42×C149—22no—
104C22×D149—21no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149C22×C412yes—
111C22⋊D149—28no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—28no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C22×C412yes—
126C2×Dic149C22×C412yes—
127C2×Dic149C22×C412yes—
128C2×Dic149C2×D412yes—
129C2×Dic149C2×D412yes—
130C2×Dic149#4112yes—
131C2×Dic149#4112yes—
132C2×Dic149#4112yes—
133C2×Dic149#4112yes—
134C4×D149—28no—
135C23×C149—21no—
136C23×C149—21no—
137C23×C149—21no—
138C23×C149—21no—
139C23×C149—21no—
140C23×C149—21no—
141C23×C149C22×C412yes—
142C23×C149C2411yescharacteristic
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—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C22×C412yes—
158C2×C4×C149C22×C412yes—
159C2×C4×C149C2×D412yes—
160C2×C4×C149#4112yes—
161C22×C149—22no—
162C22×C149—22no—
163C22×C149—22no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149C23×C411yescharacteristic
169C22×C149C22×D411yescharacteristic
170C22×C149C2×#4111yescharacteristic
171C22×C149C2×#4111yescharacteristic
172C22×C149C2×#4111yescharacteristic
173C22×C149C2×#4111yescharacteristic
174C22×C149C2×#4111yescharacteristic
175C2×D149—22no—
176C2×D149—22no—
177C2×D149—22no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C4×C149—22no—
183C4×C149—22no—
184C4×C149—22no—
185C4×C149—22no—
186C4×C149—41no—
187C4×C149—41no—
188Dic149—22no—
189Dic149—22no—
190Dic149—22no—
191Dic149—41no—
192Dic149—41no—
193Dic149#11714yescomplemented
194Dic149C4×D414yes—
195C2×C149—42no—
196C2×C149C2×#11711yescharacteristic
197C2×C149C2×C4×D411yescharacteristic
198C2×C149C4×#4111yescharacteristic
199C2×C149#52911yescharacteristic
200C2×C149#52911yescharacteristic
201C2×C149#53211yescharacteristic
202C2×C149#53211yescharacteristic
203D149—42no—
204C149#229311yescharacteristic, complemented, Sylow
205#2293—1491nomaximal, Sylow
206C2×C4×D4—1491no—
207C2×#117—1491no—
208C2×#117—1491no—
209#390—1491no—
210#390—1491no—
211#389—1491no—
212#389—1491no—
213#388—1491no—
214#388—1491no—
215#388—1491no—
216#388D14911yescharacteristic, complemented
217C4×C4⋊C4—1491no—
218C4×C22⋊C4—1491no—
219C4×C22⋊C4—1491no—
220C43—1491no—
221C22×D4—1491no—
222C23×C4—1491no—
223C23×C4—1491no—
224C4×D4—1498no—
225#117—2984no—
226#117—2984no—
227C2×C4⋊C4—1491no—
228C2×C4⋊C4—1491no—
229C2×C4⋊C4—1491no—
230C2×C4⋊C4—1491no—
231C2×C4⋊C4—1491no—
232C2×C4⋊C4—1491no—
233C2×C4⋊C4C2×D14911yescharacteristic
234C2×C22⋊C4—1491no—
235C2×C22⋊C4—1491no—
236C2×C22⋊C4—1491no—
237C2×C22⋊C4—1491no—
238C2×C22⋊C4—1491no—
239C2×C22⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4C2×D14911yescharacteristic
242C2×C22⋊C4C2×D14911yescharacteristic
243C2×C22⋊C4C2×D14911yescharacteristic
244C2×C42—1491no—
245C2×C42—1491no—
246C2×C42—1491no—
247C2×C42—1491no—
248C2×C42—1491no—
249C2×C42—1491no—
250C2×C42—1491no—
251C2×C42—1491no—
252C2×C42C2×D14911yescharacteristic
253#95—1491no—
254#95—1491no—
255#95—1491no—
256#95—1491no—
257#95C2×D14911yescharacteristic
258#95C2×D14911yescharacteristic
259C24—1491no—
260C24C22×D14911yescharacteristic
261C2×D4—2982no—
262C2×D4—2982no—
263C2×D4—1494no—
264C22×C4—2982no—
265C22×C4—2982no—
266C22×C4—2982no—
267C22×C4—2982no—
268C22×C4—1491no—
269C22×C4—1491no—
270C22×C4—1494no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1494no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4C22×D14911yescharacteristic
278C22×C4C22×D14911yescharacteristic
279C22×C4C22×D14911yescharacteristic
280C22×C4C22×D14911yescharacteristic
281C22×C4C22×D14911yescharacteristic
282C22×C4C22×D14911yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—2982no—
285C4⋊C4—2982no—
286C4⋊C4—2982no—
287C4⋊C4—2982no—
288C4⋊C4—2982no—
289C4⋊C4—1494no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—2982no—
293C22⋊C4—2982no—
294C22⋊C4—2982no—
295C22⋊C4—2982no—
296C22⋊C4—2982no—
297C22⋊C4—2982no—
298C22⋊C4—1494no—
299C22⋊C4C4×D14914yes—
300C42—22no—
301C42—2982no—
302C42—2982no—
303C42—2982no—
304C42—2982no—
305C42—2982no—
306C42—2982no—
307C42—1494no—
308C42—1494no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—2981no—
316C23—2981no—
317C23—2981no—
318C23—2981no—
319C23—2981no—
320C23—2981no—
321C23—1492no—
322C23C2×C4×D14912yes—
323C23C23×D14911yescharacteristic
324D4—2988no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2988no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2988no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—1492no—
354C2×C4—1492no—
355C2×C4—1492no—
356C2×C4—1492no—
357C2×C4—1492no—
358C2×C4—1492no—
359C2×C4—1492no—
360C2×C4—1492no—
361C2×C4—1492no—
362C2×C4C2×C4×D14912yes—
363C2×C4C2×C4×D14912yes—
364C2×C4D4×D14912yes—
365C2×C4#1455873512yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—2982no—
374C22—2982no—
375C22—2982no—
376C22—5961no—
377C22—5961no—
378C22—5961no—
379C22—5961no—
380C22C22×C4×D14911yescharacteristic
381C22C2×D4×D14911yescharacteristic
382C22#41×D14911yescharacteristic
383C22#41×D14911yescharacteristic
384C22#41×D14911yescharacteristic
385C22#41×D14911yescharacteristic
386C22C2×#1455873511yescharacteristic
387C4—22no—
388C4—22no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—2982no—
394C4—2982no—
395C4—2982no—
396C4—5961no—
397C4—5961no—
398C4—1494no—
399C4—1494no—
400C2—42no—
401C2—5962no—
402C2#117×D14911yescharacteristic
403C2C4×D4×D14911yescharacteristic
404C2C4×#1455873511yescharacteristic
405C2#2375015211yescharacteristic
406C2#2375015811yescharacteristic
407C2#2375017011yescharacteristic
408C2#2375017411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenter#388D149
hypocenterC149#2293
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#18011869C2semidirect
3. C2×#18011867C2semidirect
6. #23749522C2semidirect
7. #23749520C2semidirect
8. #23749518C2semidirect
9. #23749516C2semidirect
10. #23749514C2semidirect
11. #23749476C2semidirect
12. C22⋊C4×Dic149C2semidirect
13. #23749472C2semidirect
14. C42×Dic149C2semidirect
15. #388×C149C2semidirect
19. #18011871C4semidirect
91. C4×Dic149D4semidirect
193. Dic149#117semidirect
204. C149#2293semidirect
216. #388D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118712
C2×#180118692
C2×#180118672
#237495252
#237495222
#237495202
#237495182
#237495162
#237495142
#237494762
C22⋊C4×Dic1492
#237494722
C42×Dic1492
#388×C1492
#2293149