Finite Group Databasebeta

← #34047129

Subgroups — #34047129

Order 19072.

696 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011873C211yesmaximal, characteristic
2C2×#18011869C211yesmaximal, characteristic, complemented
3C2×C42×D149C211yesmaximal, characteristic, complemented
4#23749516C211yesmaximal, characteristic, complemented
5#23749514C211yesmaximal, characteristic, complemented
6#23749511C211yesmaximal, characteristic, complemented
7#23749503C211yesmaximal, characteristic
8#23749503C211yesmaximal, characteristic
9#23749499C211yesmaximal, characteristic, complemented
10#23749496C211yesmaximal, characteristic, complemented
11#23749476C211yesmaximal, characteristic, complemented
12#23749472C211yesmaximal, characteristic, complemented
13#23749472C211yesmaximal, characteristic, complemented
14#23749470C211yesmaximal, characteristic, complemented
15#387×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21#18011873C418yescomplemented
22#18011869—24no—
23C2×C4⋊Dic149C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
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
39C2×C4×Dic149C2211yescharacteristic
40C42×D149—24no—
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
55C23×D149C2311yescharacteristic
56C2×D596—22no—
57C2×D596—22no—
58C2×D596C2×C414yes—
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C2×C4×D149—22no—
66C2×C4×D149—22no—
67C2×C4×D149—22no—
68C2×C4×D149—22no—
69C2×C4×D149—22no—
70C2×C4×D149—22no—
71C2×C4×D149—22no—
72C2×C4×D149—22no—
73C2×C4×D149—22no—
74C2×C4×D149—22no—
75C2×C4×D149C2×C414yes—
76C2×C4×D149C2×C414yescomplemented
77C4⋊Dic149—22no—
78#14558715—22no—
79#14558715—22no—
80#14558713—22no—
81#14558713—22no—
82#14558713—22no—
83#14558713—22no—
84#14558713—22no—
85#14558713—22no—
86#14558713C2×C414yes—
87#14558713C2×C414yescomplemented
88C4×Dic149—22no—
89C4×Dic149—22no—
90C4×Dic149—22no—
91C4×Dic149—22no—
92C4×Dic149C2×C414yescomplemented
93C4×Dic149D414yescomplemented
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C4⋊C4×C149—22no—
102C4⋊C4×C149C2×C414yescomplemented
103C42×C149—22no—
104C22×D149—21no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149C22×C412yes—
115C22×D149C22×C412yes—
116C22×D149#4112yes—
117C22×D149#4112yes—
118D596—28no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149C22×C412yes—
132C2×Dic149C22×C412yes—
133C2×Dic149C2×D412yes—
134C2×Dic149C2×D412yes—
135C2×Dic149#4112yes—
136C2×Dic149#4112yes—
137C4×D149—28no—
138C4×D149—28no—
139C4×D149—28no—
140C4×D149—28no—
141C23×C149C2411yescharacteristic
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—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149C22×C412yes—
159C2×C4×C149C22×C412yes—
160C2×C4×C149C22×C412yes—
161C2×C4×C149C2×D412yes—
162C2×C4×C149#4112yes—
163C22×C149C23×C411yescharacteristic
164C22×C149C22×D411yescharacteristic
165C22×C149C2×#4111yescharacteristic
166C22×C149C2×#4111yescharacteristic
167C22×C149C2×#4111yescharacteristic
168C22×C149C2×#4111yescharacteristic
169C22×C149C2×#4111yescharacteristic
170C2×D149—22no—
171C2×D149—22no—
172C2×D149—22no—
173C2×D149—22no—
174C2×D149—22no—
175C2×D149—22no—
176C2×D149—22no—
177C2×D149—22no—
178C2×D149—22no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149#11714yescomplemented
184C4×C149—22no—
185C4×C149—22no—
186C4×C149—22no—
187C4×C149—22no—
188C4×C149—22no—
189C4×C149—41no—
190C4×C149—41no—
191Dic149—22no—
192Dic149—22no—
193Dic149—22no—
194Dic149—41no—
195Dic149—41no—
196Dic149C4×D414yes—
197C2×C149C2×#11711yescharacteristic
198C2×C149C2×C4×D411yescharacteristic
199C2×C149C4×#4111yescharacteristic
200C2×C149#52511yescharacteristic
201C2×C149#52511yescharacteristic
202C2×C149#52911yescharacteristic
203C2×C149#52911yescharacteristic
204D149—24no—
205D149—42no—
206C149#229011yescharacteristic, complemented, Sylow
207#2290—1491nomaximal, Sylow
208C2×C4×D4—1491no—
209C2×#117—1491no—
210C22×C42—1491no—
211#388—1491no—
212#388—1491no—
213#387—1491no—
214#387D14911yescharacteristic, complemented
215#386—1491no—
216#386—1491no—
217#385—1491no—
218#385—1491no—
219C4×C4⋊C4—1491no—
220C4×C22⋊C4—1491no—
221C4×C22⋊C4—1491no—
222#376—1491no—
223C22×D4—1491no—
224C23×C4—1491no—
225C23×C4—1491no—
226C23×C4—1491no—
227C23×C4—1491no—
228C4×D4—1498no—
229#117—2984no—
230C2×C4⋊C4—1491no—
231C2×C4⋊C4—1491no—
232C2×C4⋊C4—1491no—
233C2×C4⋊C4C2×D14911yescharacteristic
234C2×C4⋊C4C2×D14911yescharacteristic
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⋊C4—1491no—
242C2×C22⋊C4—1491no—
243C2×C42—2984no—
244C2×C42—1491no—
245C2×C42—1491no—
246C2×C42—1491no—
247C2×C42—1491no—
248C2×C42—1491no—
249C2×C42—1491no—
250C2×C42C2×D14911yescharacteristic
251#95—1491no—
252#95—1491no—
253#95—1491no—
254#95—1491no—
255#95—1491no—
256#95—1491no—
257#95C2×D14911yescharacteristic
258#95C2×D14911yescharacteristic
259#95C2×D14911yescharacteristic
260#95C2×D14911yescharacteristic
261C24—1491no—
262C24—1491no—
263C2×D4—2982no—
264C2×D4—2982no—
265C2×D4—1494no—
266C22×C4—2982no—
267C22×C4—2982no—
268C22×C4—2982no—
269C22×C4—2982no—
270C22×C4—2982no—
271C22×C4—2982no—
272C22×C4—2982no—
273C22×C4—2982no—
274C22×C4—2982no—
275C22×C4—2982no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4—1494no—
282C22×C4—1494no—
283C22×C4—1491no—
284C22×C4C22×D14911yescharacteristic
285C22×C4C22×D14911yescharacteristic
286C22×C4C22×D14911yescharacteristic
287C22×C4C22×D14911yescharacteristic
288C22×C4C22×D14911yescharacteristic
289C22×C4C22×D14911yescharacteristic
290C22×C4C22×D14911yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—2982no—
293C4⋊C4—2982no—
294C4⋊C4—2982no—
295C4⋊C4C4×D14914yescomplemented
296C22⋊C4—2982no—
297C22⋊C4—2982no—
298C22⋊C4—2982no—
299C22⋊C4—2982no—
300C22⋊C4—2982no—
301C22⋊C4—2982no—
302C22⋊C4—1494no—
303C22⋊C4—1494no—
304C42—22no—
305C42—2982no—
306C42—2982no—
307C42—2982no—
308C42—2982no—
309C42—1494no—
310C42—1494no—
311C23—2981no—
312C23—2981no—
313C23—2981no—
314C23—2981no—
315C23—2981no—
316C23—2981no—
317C23—2981no—
318C23—2981no—
319C23—2981no—
320C23—2981no—
321C23—1492no—
322C23—1492no—
323C23—1492no—
324C23—1492no—
325C23C23×D14911yescharacteristic
326D4—2988no—
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—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—2988no—
344C2×C4—2988no—
345C2×C4—2988no—
346C2×C4—2988no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—1492no—
360C2×C4—1492no—
361C2×C4—1492no—
362C2×C4—1492no—
363C2×C4—1492no—
364C2×C4—1492no—
365C2×C4C2×C4×D14912yes—
366C2×C4C2×C4×D14912yes—
367C2×C4C2×C4×D14912yes—
368C2×C4D4×D14912yes—
369C2×C4#1455873712yes—
370C22—2982no—
371C22—2982no—
372C22—2982no—
373C22—2982no—
374C22—2982no—
375C22—2982no—
376C22—2982no—
377C22—2982no—
378C22—2982no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—1494no—
384C22C22×C4×D14911yescharacteristic
385C22C2×D4×D14911yescharacteristic
386C22#41×D14911yescharacteristic
387C22#41×D14911yescharacteristic
388C22#41×D14911yescharacteristic
389C22#41×D14911yescharacteristic
390C22C2×#1455873711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—41no—
397C4—41no—
398C4—2982no—
399C4—2982no—
400C4—2982no—
401C4—5961no—
402C4—5961no—
403C4—1494no—
404C2—2984no—
405C2—5962no—
406C2#117×D14911yescharacteristic
407C2C4×D4×D14911yescharacteristic
408C2C4×#1455873711yescharacteristic
409C2#2375013311yescharacteristic
410C2#2375013811yescharacteristic
411C2#2375015811yescharacteristic
412C2#2375016011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#387×C149C2
socle, cosocleC23×C149C24
prime radicalC22×D596C22
hypercenter#387D149
hypocenterC149#2290
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×#18011869C2semidirect
3. C2×C42×D149C2semidirect
4. #23749516C2semidirect
5. #23749514C2semidirect
6. #23749511C2semidirect
9. #23749499C2semidirect
10. #23749496C2semidirect
11. #23749476C2semidirect
12. #23749472C2semidirect
13. #23749472C2semidirect
14. #23749470C2semidirect
15. #387×C149C2semidirect
21. #18011873C4semidirect
76. C2×C4×D149C2×C4semidirect
87. #14558713C2×C4semidirect
92. C4×Dic149C2×C4semidirect
93. C4×Dic149D4semidirect
102. C4⋊C4×C149C2×C4semidirect
183. C2×D149#117semidirect
206. C149#2290semidirect
214. #387D149semidirect
295. C4⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118732
C2×#180118692
C2×C42×D1492
#237495162
#237495142
#237495112
#237495032
#237494992
#237494962
#237494762
#237494722
#237494702
#387×C1492
#2290149