Finite Group Databasebeta

← #34052830

Subgroups — #34052830

Order 19072.

450 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23749555C211yesmaximal, characteristic, complemented
2#23749554C211yesmaximal, characteristic, complemented
3#23749553C211yesmaximal, characteristic, complemented
4#23749549C211yesmaximal, characteristic, complemented
5#23749547C211yesmaximal, characteristic, complemented
6#23749542C211yesmaximal, characteristic, complemented
7#23749542C211yesmaximal, characteristic, complemented
8#23749541C211yesmaximal, characteristic, complemented
9#23749540C211yesmaximal, characteristic, complemented
10#23749540C211yesmaximal, characteristic, complemented
11#23749534C211yesmaximal, characteristic
12#23749525C211yesmaximal, characteristic, complemented
13#23749515C211yesmaximal, characteristic, complemented
14#23749506C211yesmaximal, characteristic, complemented
15#399×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×C22⋊Dic149C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44C2×C4⋊C4×C149C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51C23×D149C2311yescharacteristic
52C23×D149C2311yescharacteristic
53C2×D596—41no—
54C2×D596—41no—
55C2×D596—41no—
56C2×C22⋊D149—22no—
57C2×C22⋊D149—41no—
58C2×C22⋊D149—41no—
59C2×C22⋊D149—41no—
60C2×C22⋊D149—41no—
61C2×C22⋊D149—41no—
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C4⋊Dic149—41no—
69#14558715—22no—
70#14558715—41no—
71#14558715—41no—
72#14558715—41no—
73C22⋊Dic149—41no—
74C22⋊Dic149—41no—
75#14558713—22no—
76#14558713—41no—
77#14558713—41no—
78#14558713—41no—
79#14558713—41no—
80#14558713—41no—
81#14558713—41no—
82#14558713—41no—
83#14558713—41no—
84#14558713—41no—
85C4×Dic149—41no—
86C24×C149C2311yescharacteristic
87C22×C4×C149C2311yescharacteristic
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C4⋊C4×C149—41no—
94C4⋊C4×C149—41no—
95C4⋊C4×C149—41no—
96C22⋊C4×C149—41no—
97C22⋊C4×C149—41no—
98C22⋊C4×C149—41no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
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—
113D596—44no—
114C22⋊D149—44no—
115C22⋊D149—44no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
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×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149#4112yes—
134C23×C149—21no—
135C23×C149—21no—
136C23×C149—21no—
137C23×C149—21no—
138C23×C149—21no—
139C23×C149—21no—
140C23×C149—21no—
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×C149—21no—
159C2×C4×C149—21no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149C2×#4111yescharacteristic
168C22×C149H(5,𝔽2)11yescharacteristic
169C22×C149H(5,𝔽2)11yescharacteristic
170C22×C149H(5,𝔽2)11yescharacteristic
171C22×C149H(5,𝔽2)11yescharacteristic
172C22×C149H(5,𝔽2)11yescharacteristic
173C22×C1492−1+411yescharacteristic
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C4×C149—41no—
189C4×C149—41no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149—41no—
194Dic149—22no—
195Dic149—41no—
196Dic149—41no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—81no—
201C2×C149#53811yescharacteristic
202C2×C149#54011yescharacteristic
203C2×C149#54211yescharacteristic
204C2×C149#56011yescharacteristic
205C2×C149#56011yescharacteristic
206C2×C149#56211yescharacteristic
207C2×C149#56211yescharacteristic
208D149—81no—
209D149—81no—
210C149#282911yescharacteristic, complemented, Sylow
211#2829—1491nomaximal, Sylow
212#399D14911yescharacteristic, complemented
213#398—1491no—
214#397—1491no—
215#397—1491no—
216#396—1491no—
217#396—1491no—
218#394—1491no—
219#394—1491no—
220#394—1491no—
221#394—1491no—
222#394—1491no—
223#392—1491no—
224#390—1491no—
225#388—1491no—
226#387—1491no—
227C22×D4—1491no—
228C22×D4—1491no—
229C22×D4—1491no—
230C2×C4⋊C4—1491no—
231C2×C4⋊C4—1491no—
232C2×C4⋊C4—1491no—
233C2×C4⋊C4—1491no—
234C2×C4⋊C4—1491no—
235C2×C4⋊C4C2×D14911yescharacteristic
236C2×C4⋊C4C2×D14911yescharacteristic
237C2×C4⋊C4C2×D14911yescharacteristic
238C2×C22⋊C4—1491no—
239C2×C22⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4—1491no—
242C2×C22⋊C4—1491no—
243C2×C22⋊C4—1491no—
244C2×C22⋊C4—1491no—
245C2×C22⋊C4—1491no—
246C2×C22⋊C4—1491no—
247C2×C22⋊C4—1491no—
248C2×C22⋊C4—1491no—
249C2×C22⋊C4—1491no—
250C2×C22⋊C4C2×D14911yescharacteristic
251C2×C22⋊C4C2×D14911yescharacteristic
252C2×C22⋊C4C2×D14911yescharacteristic
253C2×C42—1491no—
254#95—1491no—
255#95—1491no—
256#95—1491no—
257#95—1491no—
258#95—1491no—
259#95—1491no—
260#95—1491no—
261#95C2×D14911yescharacteristic
262C24—1491no—
263C24—1491no—
264C24C22×D14911yescharacteristic
265C2×D4—2982no—
266C2×D4—5961no—
267C2×D4—5961no—
268C2×D4—5961no—
269C2×D4—5961no—
270C2×D4—5961no—
271C2×D4—5961no—
272C2×D4—5961no—
273C2×D4—5961no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4C22×D14911yescharacteristic
281C22×C4C22×D14911yescharacteristic
282C22×C4C22×D14911yescharacteristic
283C22×C4C22×D14911yescharacteristic
284C22×C4C22×D14911yescharacteristic
285C22×C4C22×D14911yescharacteristic
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—2982no—
290C4⋊C4—5961no—
291C4⋊C4—5961no—
292C4⋊C4—5961no—
293C4⋊C4—5961no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—2982no—
298C22⋊C4—5961no—
299C22⋊C4—5961no—
300C22⋊C4—5961no—
301C22⋊C4—5961no—
302C22⋊C4—5961no—
303C22⋊C4—5961no—
304C22⋊C4—5961no—
305C22⋊C4—5961no—
306C22⋊C4—5961no—
307C22⋊C4—5961no—
308C22⋊C4—5961no—
309C42—5961no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—2981no—
318C23—2981no—
319C23—2981no—
320C23—2981no—
321C23—2981no—
322C23—2981no—
323C23—2981no—
324C23—2981no—
325C23—2981no—
326C23—2981no—
327C23—2981no—
328C23—2981no—
329C23—2981no—
330C23—2981no—
331C23C23×D14911yescharacteristic
332D4—5964no—
333D4—5964no—
334D4—5964no—
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—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—1492no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—5961no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22—5961no—
388C22—5961no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22#41×D14911yescharacteristic
393C22#1801195611yescharacteristic
394C22#1801195611yescharacteristic
395C22#1801195611yescharacteristic
396C22#1801195711yescharacteristic
397C22#1801195711yescharacteristic
398C22#1801195911yescharacteristic
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—2982no—
406C4—5961no—
407C4—5961no—
408C4—5961no—
409C4—5961no—
410C4—5961no—
411C2—81no—
412C2—11921no—
413C2—11921no—
414C2#2375021111yescharacteristic
415C2#2375022711yescharacteristic
416C2#2375024511yescharacteristic
417C2#2375036211yescharacteristic
418C2#2375036511yescharacteristic
419C2#2375037111yescharacteristic
420C2#2375037111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#399×C149C2
prime radical#23749534C2
hypercenter#399D149
hypocenterC149#2829
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #23749555C2semidirect
2. #23749554C2semidirect
3. #23749553C2semidirect
4. #23749549C2semidirect
5. #23749547C2semidirect
6. #23749542C2semidirect
7. #23749542C2semidirect
8. #23749541C2semidirect
9. #23749540C2semidirect
10. #23749540C2semidirect
12. #23749525C2semidirect
13. #23749515C2semidirect
14. #23749506C2semidirect
15. #399×C149C2semidirect
210. C149#2829semidirect
212. #399D149semidirect

Maximal subgroups

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

subgroupindex
#237495552
#237495542
#237495532
#237495492
#237495472
#237495422
#237495412
#237495402
#237495342
#237495252
#237495152
#237495062
#399×C1492
#2829149