Finite Group Databasebeta

← #34047949

Subgroups — #34047949

Order 19072.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011871C211yesmaximal, characteristic
2C2×#18011867C211yesmaximal, characteristic, complemented
3#23749566C211yesmaximal, characteristic, complemented
4#23749560C211yesmaximal, characteristic, complemented
5#23749559C211yesmaximal, characteristic, complemented
6#23749554C211yesmaximal, characteristic, complemented
7#23749553C211yesmaximal, characteristic, complemented
8#23749541C211yesmaximal, characteristic
9#23749540C211yesmaximal, characteristic
10C4⋊C4×Dic149C211yesmaximal, characteristic, complemented
11#23749476C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
13#23749472C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic, complemented
15#397×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C23×Dic149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011871—24no—
20#18011867—24no—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
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
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53C23×D149C2311yescharacteristic
54C2×C22⋊D149—22no—
55C2×C22⋊D149—22no—
56C2×C22⋊D149—22no—
57C22×Dic149—22no—
58C22×Dic149—22no—
59C22×Dic149D414yes—
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C2×C4×D149—22no—
68C2×C4×D149—22no—
69C2×C4×D149—22no—
70C4⋊Dic149—22no—
71#14558715—22no—
72#14558715—22no—
73#14558715—22no—
74#14558715—22no—
75#14558715—22no—
76C22⋊Dic149—22no—
77C22⋊Dic149—22no—
78#14558713—22no—
79#14558713—22no—
80#14558713—22no—
81#14558713—22no—
82#14558713—22no—
83C4×Dic149—22no—
84C4×Dic149—22no—
85C4×Dic149—22no—
86C4×Dic149—22no—
87C4×Dic149—22no—
88C24×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C4⋊C4×C149—22no—
96C22⋊C4×C149—22no—
97C22⋊C4×C149—22no—
98C22⋊C4×C149—22no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
104C22×D149—21no—
105C22×D149#4112yes—
106C22⋊D149—28no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—28no—
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×Dic149C2×D412yes—
124C2×Dic149C2×D412yes—
125C2×Dic149#4112yes—
126C2×Dic149#4112yes—
127C2×Dic149#4112yes—
128C2×Dic149#4112yes—
129C4×D149—44no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149—21no—
135C23×C149—21no—
136C23×C149C2×D412yes—
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—21no—
154C2×C4×C149—21no—
155C2×C4×C149#4112yes—
156C22×C149—22no—
157C22×C149—22no—
158C22×C149—22no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149C22×D411yescharacteristic
164C22×C149C2×#4111yescharacteristic
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—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C4×C149—22no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149—41no—
183Dic149—22no—
184Dic149—22no—
185Dic149—22no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189Dic149#12314yes—
190C2×C149—42no—
191C2×C149C2×#12311yescharacteristic
192C2×C149#52511yescharacteristic
193C2×C149#52911yescharacteristic
194C2×C149#52911yescharacteristic
195C2×C149#52911yescharacteristic
196C2×C149#52911yescharacteristic
197C2×C149#53211yescharacteristic
198D149—42no—
199C149#239511yescharacteristic, complemented, Sylow
200#2395—1491nomaximal, Sylow
201C2×C4×D4—1491no—
202C2×#117—1491no—
203#400—1491no—
204#399—1491no—
205#398—1491no—
206#397—1491no—
207#397—1491no—
208#397D14911yescharacteristic, complemented
209#394—1491no—
210#394—1491no—
211C4×C4⋊C4—1491no—
212C4×C4⋊C4—1491no—
213C4×C22⋊C4—1491no—
214C4×C22⋊C4—1491no—
215C4×C22⋊C4—1491no—
216C22×D4—1491no—
217C23×C4—1491no—
218C23×C4—1491no—
219C4×D4—2984no—
220#117—2984no—
221C2×C4⋊C4—1491no—
222C2×C4⋊C4—1491no—
223C2×C4⋊C4—1491no—
224C2×C4⋊C4—1491no—
225C2×C4⋊C4—1491no—
226C2×C4⋊C4—1491no—
227C2×C4⋊C4C2×D14911yescharacteristic
228C2×C22⋊C4—1491no—
229C2×C22⋊C4—1491no—
230C2×C22⋊C4—1491no—
231C2×C22⋊C4—1491no—
232C2×C22⋊C4—1491no—
233C2×C22⋊C4—1491no—
234C2×C22⋊C4—1491no—
235C2×C22⋊C4C2×D14911yescharacteristic
236C2×C22⋊C4C2×D14911yescharacteristic
237C2×C22⋊C4C2×D14911yescharacteristic
238C2×C42—1491no—
239C2×C42—1491no—
240C2×C42—1491no—
241C2×C42—1491no—
242C2×C42—1491no—
243#95—1491no—
244#95—1491no—
245#95—1491no—
246#95—1491no—
247#95—1491no—
248#95—1491no—
249#95—1491no—
250#95C2×D14911yescharacteristic
251#95C2×D14911yescharacteristic
252#95C2×D14911yescharacteristic
253C24—1491no—
254C24C22×D14911yescharacteristic
255C2×D4—2982no—
256C2×D4—2982no—
257C2×D4—2982no—
258C22×C4—2982no—
259C22×C4—2982no—
260C22×C4—2982no—
261C22×C4—2982no—
262C22×C4—2982no—
263C22×C4—1491no—
264C22×C4—1491no—
265C22×C4—1491no—
266C22×C4—1494no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4—1491no—
270C22×C4—1491no—
271C22×C4C22×D14911yescharacteristic
272C22×C4C22×D14911yescharacteristic
273C22×C4C22×D14911yescharacteristic
274C22×C4C22×D14911yescharacteristic
275C22×C4C22×D14911yescharacteristic
276C22×C4C22×D14911yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—2982no—
279C4⋊C4—2982no—
280C4⋊C4—2982no—
281C4⋊C4—2982no—
282C4⋊C4—2982no—
283C4⋊C4—2982no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—2982no—
288C22⋊C4—2982no—
289C22⋊C4—2982no—
290C22⋊C4—2982no—
291C22⋊C4—2982no—
292C22⋊C4—2982no—
293C22⋊C4—2982no—
294C42—2982no—
295C42—2982no—
296C42—2982no—
297C42—2982no—
298C42—2982no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—2981no—
306C23—2981no—
307C23—2981no—
308C23—2981no—
309C23—2981no—
310C23—2981no—
311C23—1492no—
312C23D4×D14912yes—
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—21no—
331C2×C4—21no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2988no—
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—1492no—
350C2×C4—1492no—
351C2×C4—1492no—
352C2×C4—1492no—
353C2×C4—1492no—
354C2×C4—1492no—
355C2×C4#1455873512yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2982no—
364C22—2982no—
365C22—2982no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22C2×D4×D14911yescharacteristic
371C22#41×D14911yescharacteristic
372C22#41×D14911yescharacteristic
373C22#41×D14911yescharacteristic
374C22#41×D14911yescharacteristic
375C22#41×D14911yescharacteristic
376C22C2×#1455873511yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—2982no—
384C4—2982no—
385C4—2982no—
386C4—5961no—
387C4—5961no—
388C4—5961no—
389C4—1494no—
390C2—42no—
391C2—5962no—
392C2#123×D14911yescharacteristic
393C2#2375013311yescharacteristic
394C2#2375015211yescharacteristic
395C2#2375015411yescharacteristic
396C2#2375015811yescharacteristic
397C2#2375015811yescharacteristic
398C2#2375017011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#397×C149C2
prime radicalC22×C22⋊D149C22
hypercenter#397D149
hypocenterC149#2395
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#18011867C2semidirect
3. #23749566C2semidirect
4. #23749560C2semidirect
5. #23749559C2semidirect
6. #23749554C2semidirect
7. #23749553C2semidirect
10. C4⋊C4×Dic149C2semidirect
11. #23749476C2semidirect
12. C22⋊C4×Dic149C2semidirect
13. #23749472C2semidirect
14. #23749472C2semidirect
15. #397×C149C2semidirect
199. C149#2395semidirect
208. #397D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118712
C2×#180118672
#237495662
#237495602
#237495592
#237495542
#237495532
#237495412
#237495402
C4⋊C4×Dic1492
#237494762
C22⋊C4×Dic1492
#237494722
#397×C1492
#2395149