Finite Group Databasebeta

← #34056354

Subgroups — #34056354

Order 19072.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011944C211yesmaximal, characteristic, complemented
2C2×#18011940C211yesmaximal, characteristic, complemented
3#23750293C211yesmaximal, characteristic
4#23750288C211yesmaximal, characteristic, complemented
5#23749996C211yesmaximal, characteristic, complemented
6#23749872C211yesmaximal, characteristic, complemented
7#23749834C211yesmaximal, characteristic, complemented
8#23749824C211yesmaximal, characteristic, complemented
9#23749788C211yesmaximal, characteristic, complemented
10#23749785C211yesmaximal, characteristic, complemented
11#23749765C211yesmaximal, characteristic, complemented
12#23749763C211yesmaximal, characteristic, complemented
13#23749719C211yesmaximal, characteristic, complemented
14#23749701C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011944—24no—
21#18011940—24no—
22C2×Dic596C2211yescharacteristic
23C2×Dic596C2211yescharacteristic
24C2×#14558726C2211yescharacteristic
25C2×#14558725C2211yescharacteristic
26C2×#14558725C2211yescharacteristic
27C2×#14558724C2211yescharacteristic
28C2×#14558724C2211yescharacteristic
29C2×#14558723C2211yescharacteristic
30C2×#14558719C2211yescharacteristic
31#18011910—21no—
32#18011909C2211yescharacteristic
33#18011907—21no—
34#18011907C2211yescharacteristic
35#18011891C2211yescharacteristic
36#18011889—21no—
37#18011888—21no—
38#18011886C2211yescharacteristic
39#18011884—21no—
40#18011883—21no—
41#18011876C2211yescharacteristic
42#18011876C2211yescharacteristic
43C4×C22⋊D149C2211yescharacteristic
44#18011871—21no—
45#18011871—21no—
46#18011840C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011831C2211yescharacteristic
51C22⋊#11924746C2211yescharacteristic
52#18011823C2211yescharacteristic
53C8×Dic149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×M16×C149C2211yescharacteristic
56C22⋊Q8×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58#107×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#102×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—41no—
63#14558735—22no—
64#14558735—41no—
65C2×Dic298—21no—
66C2×Dic298—22no—
67C2×Dic298—21no—
68C2×Dic298—41no—
69C2×Dic298C2311yescharacteristic
70C2×Dic298C2311yescharacteristic
71C2×Dic298C2311yescharacteristic
72Q8×D149—22no—
73Q8×D149—41no—
74C2×D596—21no—
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80C2×C22⋊D149D411yescharacteristic
81C22×Dic149—21no—
82C22×Dic149—21no—
83C2×C4×D149—21no—
84C2×C4×D149—21no—
85C2×C4×D149C2311yescharacteristic
86Dic596—22no—
87Dic596D414yescomplemented
88#14558726—22no—
89#14558725—22no—
90#14558725—22no—
91#14558724—22no—
92#14558724—41no—
93#14558723—41no—
94#14558719—22no—
95C2×#11924746C2311yescharacteristic
96C2×#11924746C2311yescharacteristic
97C4⋊Dic149—21no—
98#14558715—21no—
99#14558715—21no—
100#14558715—21no—
101#14558715—21no—
102#14558715D411yescharacteristic
103C22⋊Dic149D411yescharacteristic
104#14558713—21no—
105#14558713—21no—
106#14558713D411yescharacteristic
107C4×Dic149—21no—
108C4×Dic149—21no—
109C4×Dic149C2311yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114SD16×C149—22no—
115M16×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149—21no—
119C4⋊C4×C149C2311yescharacteristic
120C4⋊C4×C149C2311yescharacteristic
121C22⋊C4×C149—21no—
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—42no—
130Dic298—42no—
131Dic298C2×D412yes—
132Dic298C2×D412yes—
133D596—21no—
134D596—21no—
135D596—81no—
136C22⋊D149—22no—
137C22⋊D149—42no—
138C22⋊D149—42no—
139C22⋊D149—42no—
140C22⋊D149—81no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—42no—
145C2×Dic149—42no—
146C2×Dic149C2×D411yescharacteristic
147C2×Dic149C2×D411yescharacteristic
148C2×Dic149C2×D411yescharacteristic
149C4×D149—21no—
150C4×D149—21no—
151C4×D149—42no—
152C4×D149—42no—
153#11924746—21no—
154#11924746—21no—
155C23×C149—21no—
156C23×C149C2×D411yescharacteristic
157Q8×C149—21no—
158Q8×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149—81no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2411yescharacteristic
169C8×C149—21no—
170C8×C149C2×D412yes—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149C22×D411yescharacteristic
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C4×C149—21no—
185C4×C149—41no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149C22×D411yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—22no—
192Dic149—22no—
193Dic149—21no—
194Dic149—41no—
195Dic149#13712yescomplemented
196C2×C149—41no—
197C2×C149—81no—
198C2×C149D4211yescharacteristic
199C2×C149C2×#13711yescharacteristic
200C2×C149#57711yescharacteristic
201D149—41no—
202D149—81no—
203C149#327811yescharacteristic, complemented, Sylow
204#3278—1491nomaximal, Sylow
205C2×#137—1491no—
206C2×#137—1491no—
207#550—1491no—
208D4×Q8—1491no—
209#492—1491no—
210#468—1491no—
211#468D14911yescharacteristic, complemented
212#462—1491no—
213#460—1491no—
214#452—1491no—
215#452—1491no—
216#448—1491no—
217#448—1491no—
218C4×Q16—1491no—
219#436—1491no—
220C2×#41—1491no—
221C2×#41—1491no—
222C22×Q8—1491no—
223C22×Q8—1491no—
224#137—2984no—
225#137—2984no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×Q16—1491no—
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16C2×D14911yescharacteristic
235C2×M16—1491no—
236C2×M16C2×D14911yescharacteristic
237C4⋊Q8—2981no—
238C4⋊Q8—1491no—
239#127—2981no—
240#127—1491no—
241C22⋊Q8—2981no—
242C22⋊Q8—2981no—
243C22⋊Q8—1491no—
244C22⋊Q8C2×D14911yescharacteristic
245#121—2981no—
246#121—2981no—
247#121—1491no—
248#121C2×D14911yescharacteristic
249C4×Q8—1491no—
250C4×Q8—1491no—
251C4×D4—2981no—
252C4×D4—2981no—
253C4×D4—1491no—
254#107C2×D14911yescharacteristic
255C4⋊C8—1491no—
256#103—1491no—
257#103—1491no—
258#103—1491no—
259#103C2×D14911yescharacteristic
260#102—1491no—
261#102C2×D14911yescharacteristic
262C22⋊C8—1491no—
263C22⋊C8—1491no—
264C4×C8—1491no—
265#41—2982no—
266#41—2982no—
267#41—5961no—
268#41—5961no—
269C2×Q8—2981no—
270C2×Q8—2982no—
271C2×Q8—2981no—
272C2×Q8—2982no—
273C2×Q8—5961no—
274C2×Q8—5961no—
275C2×Q8—1491no—
276C2×Q8—1491no—
277C2×Q8—1491no—
278C2×Q8C22×D14911yescharacteristic
279C2×D4—21no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—1491no—
286C2×D4—1491no—
287C2×D4C22×D14911yescharacteristic
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—2981no—
292C22×C4—1491no—
293C22×C4C22×D14911yescharacteristic
294Q16—2982no—
295Q16—2982no—
296Q16—1494no—
297SD16—22no—
298SD16—2982no—
299SD16—2982no—
300SD16—2982no—
301SD16—5961no—
302SD16—5961no—
303M16—22no—
304M16—2982no—
305C2×C8—1491no—
306C2×C8—1491no—
307C2×C8C22×D14911yescharacteristic
308C2×C8C22×D14911yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—2981no—
311C4⋊C4—2981no—
312C4⋊C4—2981no—
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—1491no—
316C4⋊C4C22×D14911yescharacteristic
317C4⋊C4C22×D14911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—1491no—
323C22⋊C4—1491no—
324C42—2981no—
325C42—2981no—
326C42—1491no—
327C23—21no—
328C23—2981no—
329C23—1491no—
330C23D4×D14911yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—2981no—
334Q8—2981no—
335Q8—2981no—
336Q8—2981no—
337Q8—5962no—
338Q8—5962no—
339Q8—1492no—
340Q8—1492no—
341D4—21no—
342D4—21no—
343D4—81no—
344D4—2982no—
345D4—2981no—
346D4—2981no—
347D4—5962no—
348D4—5962no—
349D4—5962no—
350D4—11921no—
351D4—11921no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—5962no—
363C2×C4—5962no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—1491no—
367C2×C4—1491no—
368C2×C4—1491no—
369C2×C4D4×D14911yescharacteristic
370C2×C4C23×D14911yescharacteristic
371C8—21no—
372C8—2981no—
373C8—2981no—
374C8D4×D14912yes—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—2981no—
382C22—2981no—
383C22—2981no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22C2×D4×D14911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—2981no—
393C4—2981no—
394C4—2982no—
395C4—2982no—
396C4—5961no—
397C4—1492no—
398C4C2×D4×D14911yescharacteristic
399C4#1801195711yescharacteristic
400C2—41no—
401C2—81no—
402C2—5961no—
403C2—11921no—
404C2#2375025911yescharacteristic
405C2#137×D14911yescharacteristic
406C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
prime radical#23750293C2
hypercenter#468D149
hypocenterC149#3278
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C2×#18011940C2semidirect
4. #23750288C2semidirect
5. #23749996C2semidirect
6. #23749872C2semidirect
7. #23749834C2semidirect
8. #23749824C2semidirect
9. #23749788C2semidirect
10. #23749785C2semidirect
11. #23749765C2semidirect
12. #23749763C2semidirect
13. #23749719C2semidirect
14. #23749701C2semidirect
15. #468×C149C2semidirect
87. Dic596D4semidirect
195. Dic149#137semidirect
203. C149#3278semidirect
211. #468D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C2×#180119402
#237502932
#237502882
#237499962
#237498722
#237498342
#237498242
#237497882
#237497852
#237497652
#237497632
#237497192
#237497012
#468×C1492
#3278149