Finite Group Databasebeta

← #34054236

Subgroups — #34054236

Order 19072.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011940C211yesmaximal, characteristic, complemented
2C2×#18011932C211yesmaximal, characteristic
3#23750200C211yesmaximal, characteristic, complemented
4#23750104C211yesmaximal, characteristic, complemented
5#23749850C211yesmaximal, characteristic, complemented
6#23749848C211yesmaximal, characteristic, complemented
7#23749842C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749834C211yesmaximal, characteristic, complemented
10#23749832C211yesmaximal, characteristic, complemented
11#23749828C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749625C211yesmaximal, characteristic, complemented
14#103×D149C211yesmaximal, characteristic, complemented
15#461×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19#18011940—24no—
20#18011932—24no—
21C2×Dic596C2211yescharacteristic
22C2×#14558726C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×#14558724C2211yescharacteristic
26C2×#14558721C2211yescharacteristic
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011909C2211yescharacteristic
30#18011900C2211yescharacteristic
31#18011899C2211yescharacteristic
32#18011896—21no—
33#18011896—21no—
34#18011889—21no—
35#18011889—21no—
36C4×Dic298C2211yescharacteristic
37#18011876C2211yescharacteristic
38D4×Dic149C2211yescharacteristic
39C4×C22⋊D149—21no—
40#18011871—21no—
41#18011868C2211yescharacteristic
42#18011867—21no—
43C2×#14558715—21no—
44C4⋊C4×D149C2211yescharacteristic
45C4⋊#11924746C2211yescharacteristic
46#18011840C2211yescharacteristic
47#18011840C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011835C2211yescharacteristic
50#18011835C2211yescharacteristic
51#18011834C2211yescharacteristic
52#18011833C2211yescharacteristic
53#18011831C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×SD16×C149C2211yescharacteristic
56C4⋊Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58C4⋊C8×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#103×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—22no—
63#14558735—22no—
64#14558735D414yes—
65C2×Dic298—21no—
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68Q8×D149—22no—
69Q8×D149—22no—
70C2×D596—21no—
71C2×D596C2311yescharacteristic
72C2×C22⋊D149—21no—
73C22×Dic149—21no—
74C22×Dic149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77C2×C4×D149—21no—
78C2×C4×D149C2311yescharacteristic
79Dic596—22no—
80#14558726—22no—
81#14558726—22no—
82#14558725—22no—
83#14558724—22no—
84#14558721—22no—
85#14558719—22no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C8×D149—22no—
89C4⋊Dic149C2311yescharacteristic
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93#14558715—21no—
94#14558715—21no—
95#14558715D411yescharacteristic
96#14558715D411yescharacteristic
97C22⋊Dic149—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713D411yescharacteristic
103#14558713D411yescharacteristic
104C4×Dic149—21no—
105C4×Dic149—21no—
106C4×Dic149C2311yescharacteristic
107C2×Q8×C149C2311yescharacteristic
108C2×Q8×C149C2311yescharacteristic
109C2×D4×C149C2311yescharacteristic
110C22×C4×C149—21no—
111SD16×C149—22no—
112SD16×C149—22no—
113C2×C8×C149C2311yescharacteristic
114C2×C8×C149C2311yescharacteristic
115C4⋊C4×C149—21no—
116C4⋊C4×C149—21no—
117C4⋊C4×C149C2311yescharacteristic
118C22⋊C4×C149—21no—
119C42×C149C2311yescharacteristic
120C22×D149—21no—
121C22×D149C2×D411yescharacteristic
122Dic298—21no—
123Dic298—21no—
124Dic298—21no—
125Dic298—42no—
126Dic298C2×D412yes—
127D596—21no—
128D596—21no—
129D596—42no—
130C22⋊D149—24no—
131C2×Dic149—21no—
132C2×Dic149—24no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—81no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—42no—
140C4×D149—42no—
141C4×D149—81no—
142C4×D149C2×D412yes—
143C4×D149#4112yes—
144#11924746—21no—
145#11924746—21no—
146C23×C149—21no—
147Q8×C149—21no—
148Q8×C149—21no—
149Q8×C149—21no—
150Q8×C149—21no—
151D4×C149—21no—
152D4×C149C2×D412yes—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—81no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2411yescharacteristic
160C8×C149—21no—
161C8×C149—21no—
162C22×C149—22no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149C22×D411yescharacteristic
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149#12112yes—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—41no—
175C4×C149—41no—
176C4×C149—41no—
177C4×C149C22×D411yescharacteristic
178C4×C149C2×#4111yescharacteristic
179Dic149—22no—
180Dic149—21no—
181Dic149—21no—
182Dic149—41no—
183Dic149—41no—
184Dic149#12112yes—
185C2×C149—42no—
186C2×C149C2×#12111yescharacteristic
187C2×C149#57711yescharacteristic
188C2×C149#57811yescharacteristic
189D149—22no—
190D149—81no—
191C149#304611yescharacteristic, complemented, Sylow
192#3046—1491nomaximal, Sylow
193C2×#137—1491no—
194C2×#135—1491no—
195#536—1491no—
196#520—1491no—
197#464—1491no—
198#464—1491no—
199#463—1491no—
200#463—1491no—
201#462—1491no—
202#462—1491no—
203#461—1491no—
204#461D14911yescharacteristic, complemented
205#424—1491no—
206#417—1491no—
207C2×#103—1491no—
208C2×#41—1491no—
209C2×#41—1491no—
210C22×Q8—1491no—
211#137—2984no—
212#135—2984no—
213C2×Q16—1491no—
214C2×Q16—1491no—
215C2×Q16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×SD16C2×D14911yescharacteristic
219C2×SD16C2×D14911yescharacteristic
220C2×D8—1491no—
221C2×M16—1491no—
222C22×C8—1491no—
223C4⋊Q8—1491no—
224C4⋊Q8C2×D14911yescharacteristic
225#124—1491no—
226#124—1491no—
227#123—2981no—
228#123—2981no—
229C22⋊Q8—2981no—
230C22⋊Q8—2981no—
231C4×Q8—1491no—
232C4×Q8—1491no—
233C4×D4—2981no—
234C4×D4—2981no—
235C4×D4—1491no—
236C4×D4C2×D14911yescharacteristic
237#117—2981no—
238#117—1491no—
239C2×C4⋊C4—2981no—
240C2×C4⋊C4—1491no—
241C4⋊C8—1491no—
242C4⋊C8—1491no—
243C4⋊C8—1491no—
244C4⋊C8C2×D14911yescharacteristic
245#103—1491no—
246#103—1491no—
247#103—1491no—
248#103—1491no—
249#103C2×D14911yescharacteristic
250#103C2×D14911yescharacteristic
251#102—1491no—
252#102—1491no—
253#41—2982no—
254#41—2982no—
255#41—2982no—
256#41—1494no—
257C2×Q8—2981no—
258C2×Q8—2982no—
259C2×Q8—2982no—
260C2×Q8—1491no—
261C2×Q8—1491no—
262C2×Q8C22×D14911yescharacteristic
263C2×Q8C22×D14911yescharacteristic
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—1491no—
267C2×D4C22×D14911yescharacteristic
268C22×C4—21no—
269C22×C4—2981no—
270C22×C4—2981no—
271C22×C4—2981no—
272C22×C4—2981no—
273C22×C4—2981no—
274C22×C4—1491no—
275Q16—2982no—
276Q16—2982no—
277Q16—2982no—
278SD16—22no—
279SD16—22no—
280SD16—2982no—
281SD16—2982no—
282D8—2982no—
283M16—2982no—
284C2×C8—2982no—
285C2×C8—1491no—
286C2×C8—1491no—
287C2×C8C22×D14911yescharacteristic
288C2×C8C22×D14911yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2981no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C42—2981no—
309C42—2981no—
310C42—1491no—
311C42C22×D14911yescharacteristic
312C23—21no—
313C23—2981no—
314C23—1491no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—2981no—
320Q8—2981no—
321Q8—2981no—
322Q8—5962no—
323Q8—1492no—
324D4—21no—
325D4—2984no—
326D4—2981no—
327D4—2981no—
328D4—5962no—
329D4D4×D14912yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—2981no—
335C2×C4—2984no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—5962no—
339C2×C4—5962no—
340C2×C4—1491no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1492no—
344C2×C4—1492no—
345C2×C4—11921no—
346C2×C4—11921no—
347C2×C4D4×D14911yescharacteristic
348C2×C4D4×D14911yescharacteristic
349C2×C4C23×D14911yescharacteristic
350C8—21no—
351C8—21no—
352C8—2981no—
353C8—2981no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—2981no—
358C22—2981no—
359C22—5961no—
360C22—5961no—
361C22—5961no—
362C22—1492no—
363C22C2×D4×D14911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2981no—
370C4—2981no—
371C4—2982no—
372C4—5961no—
373C4—5961no—
374C4—1492no—
375C4C2×D4×D14911yescharacteristic
376C4#41×D14911yescharacteristic
377C2—42no—
378C2—2982no—
379C2—11921no—
380C2#121×D14911yescharacteristic
381C2#2375043111yescharacteristic
382C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#461×C149C2
socleC22×C149C22×D4
prime radicalC2×#18011932C2
hypercenter#461D149
hypocenterC149#3046
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
3. #23750200C2semidirect
4. #23750104C2semidirect
5. #23749850C2semidirect
6. #23749848C2semidirect
7. #23749842C2semidirect
8. #23749840C2semidirect
9. #23749834C2semidirect
10. #23749832C2semidirect
11. #23749828C2semidirect
12. #23749650C2semidirect
13. #23749625C2semidirect
14. #103×D149C2semidirect
15. #461×C149C2semidirect
191. C149#3046semidirect
204. #461D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C2×#180119322
#237502002
#237501042
#237498502
#237498482
#237498422
#237498402
#237498342
#237498322
#237498282
#237496502
#237496252
#103×D1492
#461×C1492
#3046149