Finite Group Databasebeta

← #34055668

Subgroups — #34055668

Order 19072.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750174C211yesmaximal, characteristic, complemented
2#23750160C211yesmaximal, characteristic, complemented
3#23750009C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749982C211yesmaximal, characteristic, complemented
6#23749834C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749819C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749788C211yesmaximal, characteristic, complemented
12#23749773C211yesmaximal, characteristic, complemented
13#23749771C211yesmaximal, characteristic, complemented
14#23749676C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558725C2211yescharacteristic
22C2×#14558724C2211yescharacteristic
23C2×#14558723C2211yescharacteristic
24C2×D1192C2211yescharacteristic
25C2×#14558721C2211yescharacteristic
26#18011909C2211yescharacteristic
27#18011907C2211yescharacteristic
28#18011906—21no—
29#18011899C2211yescharacteristic
30#18011899C2211yescharacteristic
31#18011896—21no—
32#18011891C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011884—21no—
35#18011884—21no—
36#18011876C2211yescharacteristic
37#18011873—21no—
38#18011873C2211yescharacteristic
39#18011871—21no—
40#18011871—21no—
41#18011869—21no—
42C42×D149C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558735—41no—
62#14558735—41no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65C2×D596—21no—
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C22×Dic149—21no—
73C2×C4×D149—21no—
74C2×C4×D149—21no—
75C2×C4×D149D411yescharacteristic
76C2×C4×D149D411yescharacteristic
77C2×C4×D149C2311yescharacteristic
78Dic596—41no—
79#14558726—41no—
80#14558725—41no—
81#14558725—41no—
82#14558724—41no—
83#14558723—41no—
84D1192—41no—
85#14558721—41no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C4⋊Dic149—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99C4×Dic149—21no—
100C4×Dic149D411yescharacteristic
101C4×Dic149D411yescharacteristic
102C4×Dic149C2311yescharacteristic
103C2×Q8×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—21no—
116C22×D149C2×D411yescharacteristic
117Dic298—21no—
118Dic298—21no—
119Dic298—21no—
120Dic298—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—42no—
126D596—42no—
127C22⋊D149—42no—
128C22⋊D149—42no—
129C22⋊D149—42no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—42no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—22no—
139C4×D149—41no—
140C4×D149—42no—
141C4×D149—42no—
142#11924746—21no—
143#11924746—21no—
144C23×C149—21no—
145Q8×C149—21no—
146Q8×C149—21no—
147D4×C149—21no—
148D4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149C2×D411yescharacteristic
153C2×C4×C149C2×D411yescharacteristic
154C2×C4×C149C2411yescharacteristic
155C8×C149—21no—
156C8×C149—21no—
157C22×C149—41no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149C22×D411yescharacteristic
161C2×D149—21no—
162C2×D149—21no—
163C2×D149—21no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C4×C149—21no—
171C4×C149—21no—
172C4×C149—41no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149H(5,𝔽2)11yescharacteristic
176C4×C149H(5,𝔽2)11yescharacteristic
177Dic149—21no—
178Dic149—21no—
179Dic149—41no—
180Dic149—41no—
181Dic149#13512yes—
182C2×C149—81no—
183C2×C149#53511yescharacteristic
184C2×C149C2×#13511yescharacteristic
185C2×C149#57511yescharacteristic
186D149—41no—
187D149—81no—
188D149—81no—
189C149#321211yescharacteristic, complemented, Sylow
190#3212—1491nomaximal, Sylow
191#532—1491no—
192#529—1491no—
193#495—1491no—
194#495—1491no—
195#488—1491no—
196#488D14911yescharacteristic, complemented
197#462—1491no—
198#461—1491no—
199#460—1491no—
200#459—1491no—
201#452—1491no—
202#452—1491no—
203#449—1491no—
204#449—1491no—
205#431—1491no—
206C2×#41—1491no—
207C2×#41—1491no—
208C2×Q16—1491no—
209C2×Q16—1491no—
210C2×SD16—1491no—
211C2×SD16—1491no—
212C2×SD16—1491no—
213C2×SD16—1491no—
214C2×D8—1491no—
215C2×D8—1491no—
216C4⋊Q8—1491no—
217#127—1491no—
218#126—2981no—
219#125C2×D14911yescharacteristic
220#124—1491no—
221#124—1491no—
222#124C2×D14911yescharacteristic
223#123—2981no—
224C22⋊Q8—1491no—
225#121—2981no—
226#121—2981no—
227#121—1491no—
228C4×Q8—1491no—
229C4×D4—2981no—
230C4×D4—2981no—
231C4×D4—2981no—
232C4×D4—1491no—
233#117—2981no—
234C2×C42—1491no—
235C4⋊C8—1491no—
236C4⋊C8—1491no—
237#103—1491no—
238#103—1491no—
239#103C2×D14911yescharacteristic
240#103C2×D14911yescharacteristic
241#102—1491no—
242#102—1491no—
243#102C2×D14911yescharacteristic
244#102C2×D14911yescharacteristic
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C4×C8—1491no—
248C4×C8C2×D14911yescharacteristic
249#41—5961no—
250#41—5961no—
251#41—5961no—
252#41—5961no—
253C2×Q8—1491no—
254C2×Q8—1491no—
255C2×Q8C22×D14911yescharacteristic
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4C22×D14911yescharacteristic
264C22×C4—2981no—
265C22×C4—2981no—
266C22×C4—2981no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4—1491no—
270Q16—5961no—
271Q16—5961no—
272SD16—5961no—
273SD16—5961no—
274SD16—5961no—
275SD16—5961no—
276D8—5961no—
277D8—5961no—
278C2×C8—1491no—
279C2×C8—1491no—
280C2×C8C22×D14911yescharacteristic
281C2×C8C22×D14911yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—2981no—
285C4⋊C4—2981no—
286C4⋊C4—2981no—
287C4⋊C4—2981no—
288C4⋊C4C22×D14911yescharacteristic
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C42—2981no—
300C42—1491no—
301C42—1491no—
302C42—1491no—
303C42C22×D14911yescharacteristic
304C23—21no—
305C23—2981no—
306C23—2981no—
307C23—1491no—
308Q8—21no—
309Q8—21no—
310Q8—2981no—
311Q8—2981no—
312Q8—2981no—
313Q8—2981no—
314D4—21no—
315D4—21no—
316D4—2981no—
317D4—2981no—
318D4—2981no—
319D4—2981no—
320D4—5962no—
321D4—5962no—
322D4—5962no—
323D4—5962no—
324D4—5962no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2982no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—5961no—
334C2×C4—5962no—
335C2×C4—5962no—
336C2×C4—5962no—
337C2×C4—1491no—
338C2×C4—1491no—
339C2×C4—1491no—
340C2×C4D4×D14911yescharacteristic
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—2981no—
351C22—2981no—
352C22—2981no—
353C22—5961no—
354C22—5961no—
355C22—5961no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22C2×D4×D14911yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—2981no—
366C4—2981no—
367C4—5961no—
368C4—5961no—
369C4—1492no—
370C4#1801195711yescharacteristic
371C4#1801195711yescharacteristic
372C2—81no—
373C2—5961no—
374C2—11921no—
375C2—11921no—
376C2#2375019311yescharacteristic
377C2#135×D14911yescharacteristic
378C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
hypercenter#488D149
hypocenterC149#3212
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750174C2semidirect
2. #23750160C2semidirect
3. #23750009C2semidirect
4. #23750007C2semidirect
5. #23749982C2semidirect
6. #23749834C2semidirect
7. #23749829C2semidirect
8. #23749824C2semidirect
9. #23749819C2semidirect
10. #23749790C2semidirect
11. #23749788C2semidirect
12. #23749773C2semidirect
13. #23749771C2semidirect
14. #23749676C2semidirect
15. #488×C149C2semidirect
189. C149#3212semidirect
196. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237501742
#237501602
#237500092
#237500072
#237499822
#237498342
#237498292
#237498242
#237498192
#237497902
#237497882
#237497732
#237497712
#237496762
#488×C1492
#3212149