Finite Group Databasebeta

← #34057775

Subgroups — #34057775

Order 19072.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750360C211yesmaximal, characteristic, complemented
2#23750015C211yesmaximal, characteristic, complemented
3#23750012C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749847C211yesmaximal, characteristic, complemented
6#23749844C211yesmaximal, characteristic, complemented
7#23749840C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749820C211yesmaximal, characteristic, complemented
10#23749817C211yesmaximal, characteristic, complemented
11#23749756C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14C4×#14558721C211yesmaximal, characteristic, complemented
15#559×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25#18011908C2211yescharacteristic
26#18011900—21no—
27#18011899C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011896—21no—
30#18011896—21no—
31C4×Dic298C2211yescharacteristic
32C4×D596C2211yescharacteristic
33C4×D596C2211yescharacteristic
34#18011873—21no—
35#18011844C2211yescharacteristic
36C4⋊#11924746C2211yescharacteristic
37C4⋊#11924746C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011834C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011831C2211yescharacteristic
44#18011831C2211yescharacteristic
45#18011822C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48#127×C149C2211yescharacteristic
49#124×C149—21no—
50#124×C149C2211yescharacteristic
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53#123×C149—21no—
54C4×Q8×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4×D4×C149—21no—
57C4×D4×C149C2211yescharacteristic
58C4×D4×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×D596—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66#14558726—41no—
67#14558724—22no—
68#14558724—41no—
69#14558723—22no—
70#14558723—41no—
71#14558721—22no—
72#14558721—41no—
73#14558721—41no—
74#14558721—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558713—21no—
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87C4×Dic149—21no—
88C2×Q8×C149D411yescharacteristic
89C2×Q8×C149C2311yescharacteristic
90C2×D4×C149—21no—
91C2×D4×C149—21no—
92C2×D4×C149C2311yescharacteristic
93C2×D4×C149C2311yescharacteristic
94C22×C4×C149—21no—
95C22×C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149D411yescharacteristic
98C4⋊C4×C149D411yescharacteristic
99C4⋊C4×C149D411yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C22⋊C4×C149—21no—
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C42×C149C2311yescharacteristic
109C42×C149C2311yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113Dic298—21no—
114Dic298—21no—
115D596—21no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—42no—
120D596—81no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C4×D149—81no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127#11924746—21no—
128#11924746#4112yes—
129C23×C149—21no—
130C23×C149—21no—
131Q8×C149—21no—
132Q8×C149—21no—
133Q8×C149—41no—
134D4×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—42no—
139D4×C149—81no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—81no—
143C2×C4×C149—81no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2411yescharacteristic
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149C22×D411yescharacteristic
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—21no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149C2×#4111yescharacteristic
173C4×C149H(5,𝔽2)11yescharacteristic
174Dic149—41no—
175Dic149—41no—
176C2×C149—81no—
177C2×C149—81no—
178C2×C149#55011yescharacteristic
179C2×C149#57511yescharacteristic
180C2×C149#57611yescharacteristic
181D149—81no—
182D149—81no—
183C149#340311yescharacteristic, complemented, Sylow
184#3403—1491nomaximal, Sylow
185#559—1491no—
186#559D14911yescharacteristic, complemented
187#496—1491no—
188#496—1491no—
189#495—1491no—
190#464—1491no—
191#464—1491no—
192#463—1491no—
193#463—1491no—
194#459—1491no—
195#459—1491no—
196#446—1491no—
197#440—1491no—
198#440—1491no—
199C4×D8—1491no—
200C2×Q16—1491no—
201C2×SD16—1491no—
202C2×SD16—1491no—
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C2×D8—1491no—
207C2×D8—1491no—
208C2×D8—1491no—
209#127—1491no—
210#127C2×D14911yescharacteristic
211#124—21no—
212#124—2981no—
213#124—1491no—
214#124—1491no—
215#124C2×D14911yescharacteristic
216#124C2×D14911yescharacteristic
217#123—21no—
218#123—21no—
219#123—2981no—
220#123—2981no—
221C4×Q8—1491no—
222C4×Q8C2×D14911yescharacteristic
223C4×Q8C2×D14911yescharacteristic
224C4×D4—21no—
225C4×D4—2981no—
226C4×D4—1491no—
227C4×D4—1491no—
228C4×D4C2×D14911yescharacteristic
229C4×D4C2×D14911yescharacteristic
230#107—1491no—
231C4⋊C8—1491no—
232C4⋊C8—1491no—
233C4⋊C8—1491no—
234#103—1491no—
235#103—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#97—1491no—
241#97—1491no—
242C4×C8—1491no—
243C2×Q8—1491no—
244C2×Q8C22⋊D14911yescharacteristic
245C2×Q8C22×D14911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—1491no—
251C2×D4—1491no—
252C2×D4C22×D14911yescharacteristic
253C2×D4C22×D14911yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—2981no—
257C22×C4—2981no—
258Q16—5961no—
259SD16—2982no—
260SD16—2982no—
261SD16—5961no—
262SD16—5961no—
263D8—2982no—
264D8—5961no—
265D8—5961no—
266D8—5961no—
267C2×C8—1491no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8—1491no—
271C4⋊C4—21no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4C22⋊D14911yescharacteristic
275C4⋊C4C22⋊D14911yescharacteristic
276C4⋊C4C22⋊D14911yescharacteristic
277C4⋊C4C22×D14911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C42—21no—
291C42—2981no—
292C42C22×D14911yescharacteristic
293C42C22×D14911yescharacteristic
294C42C22×D14911yescharacteristic
295C23—21no—
296C23—21no—
297C23—2981no—
298C23—2981no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—2981no—
303Q8—2981no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—2981no—
311D4—2981no—
312D4—2981no—
313D4—2981no—
314D4—5962no—
315D4—11921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—11921no—
323C2×C4—11921no—
324C2×C4C2×C22⋊D14911yescharacteristic
325C2×C4C2×C22⋊D14911yescharacteristic
326C2×C4C2×C22⋊D14911yescharacteristic
327C2×C4C2×C22⋊D14911yescharacteristic
328C2×C4C2×C22⋊D14911yescharacteristic
329C2×C4C2×C22⋊D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—2981no—
332C8—2981no—
333C8—2981no—
334C8—1492no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22C22×C22⋊D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—5961no—
357C4—5961no—
358C4#41×D14911yescharacteristic
359C4#1801195711yescharacteristic
360C2—81no—
361C2—81no—
362C2—11921no—
363C2—11921no—
364C2#2375029411yescharacteristic
365C2#2375042311yescharacteristic
366C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#559×C149C2
socleC22×C149C22×D4
hypercenter#559D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #23750360C2semidirect
2. #23750015C2semidirect
3. #23750012C2semidirect
4. #23750007C2semidirect
5. #23749847C2semidirect
6. #23749844C2semidirect
7. #23749840C2semidirect
8. #23749837C2semidirect
9. #23749820C2semidirect
10. #23749817C2semidirect
11. #23749756C2semidirect
12. #23749725C2semidirect
13. #23749723C2semidirect
14. C4×#14558721C2semidirect
15. #559×C149C2semidirect
183. C149#3403semidirect
186. #559D149semidirect

Maximal subgroups

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

subgroupindex
#237503602
#237500152
#237500122
#237500072
#237498472
#237498442
#237498402
#237498372
#237498202
#237498172
#237497562
#237497252
#237497232
C4×#145587212
#559×C1492
#3403149