Finite Group Databasebeta

← #34055537

Subgroups — #34055537

Order 19072.

422 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
1#23750189C211yesmaximal, characteristic, complemented
2#23749963C211yesmaximal, characteristic, complemented
3#23749946C211yesmaximal, characteristic, complemented
4#23749943C211yesmaximal, characteristic, complemented
5#23749938C211yesmaximal, characteristic, complemented
6#23749876C211yesmaximal, characteristic, complemented
7#23749873C211yesmaximal, characteristic, complemented
8#23749859C211yesmaximal, characteristic, complemented
9#23749856C211yesmaximal, characteristic, complemented
10#23749775C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749758C211yesmaximal, characteristic, complemented
14#23749592C211yesmaximal, characteristic, complemented
15#537×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×#14558720C2211yescharacteristic, complemented
22C22×#11924746C2211yescharacteristic, complemented
23#18011907—21no—
24#18011900—21no—
25#18011885C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011885C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011879—21no—
30#18011879—21no—
31#18011870C2211yescharacteristic
32#18011844C2211yescharacteristic, complemented
33#18011844C2211yescharacteristic, complemented
34#18011842C2211yescharacteristic, complemented
35#18011842C2211yescharacteristic, complemented
36#18011835C2211yescharacteristic, complemented
37#18011835C2211yescharacteristic, complemented
38#18011832C2211yescharacteristic, complemented
39#18011832C2211yescharacteristic, complemented
40#18011831C2211yescharacteristic
41#18011831C2211yescharacteristic
42#18011831C2211yescharacteristic
43#18011831C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic, complemented
47C22⋊#11924746C2211yescharacteristic, complemented
48C2×#41×C149C2211yescharacteristic
49C2×#41×C149C2211yescharacteristic, complemented
50C22⋊Q8×C149—21no—
51C22⋊Q8×C149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic, complemented
53#121×C149—21no—
54#121×C149—21no—
55#121×C149—21no—
56#121×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic, complemented
58C2×C4⋊C4×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×D596—21no—
61C2×D596—41no—
62C2×D596—41no—
63C2×D596C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69#14558723—41no—
70#14558723—41no—
71#14558721—41no—
72#14558721—41no—
73#14558720—41no—
74C2×#11924746—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81C22⋊Dic149—21no—
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86C4×Dic149—21no—
87#41×C149—41no—
88#41×C149—41no—
89#41×C149—41no—
90#41×C149—41no—
91C2×Q8×C149D411yescharacteristic
92C2×Q8×C149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149—21no—
95C2×D4×C149—21no—
96C2×D4×C149D411yescharacteristic
97C2×D4×C149D411yescharacteristic
98C2×D4×C149D411yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149—21no—
101C22×C4×C149—21no—
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—81no—
118C22×D149—81no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—42no—
124C22⋊D149—81no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C22⋊D149—81no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130#11924746—21no—
131#11924746—21no—
132#11924746—21no—
133#11924746—21no—
134C23×C149—21no—
135C23×C149C2×D411yescharacteristic
136C23×C149C2×D411yescharacteristic
137C23×C149C2×D411yescharacteristic
138Q8×C149—21no—
139Q8×C149—21no—
140Q8×C149—41no—
141D4×C149—21no—
142D4×C149—21no—
143D4×C149—41no—
144D4×C149—41no—
145D4×C149—41no—
146D4×C149—42no—
147D4×C149—81no—
148D4×C149—81no—
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—42no—
159C2×C4×C149—81no—
160C2×C4×C149C2×D411yescharacteristic
161C2×C4×C149C2×D411yescharacteristic
162C2×C4×C149C2×D411yescharacteristic
163C2×C4×C149C2411yescharacteristic
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149C22×D411yescharacteristic
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—84no—
184C4×C149—21no—
185C4×C149—21no—
186C4×C149—21no—
187C4×C149—41no—
188C4×C149—41no—
189C4×C149—41no—
190C4×C149H(5,𝔽2)11yescharacteristic
191C4×C149H(5,𝔽2)11yescharacteristic
192Dic149—41no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—41no—
196C2×C149—41no—
197C2×C149—81no—
198C2×C149#53411yescharacteristic
199C2×C149#57611yescharacteristic
200C2×C149#57711yescharacteristic
201D149—81no—
202D149—81no—
203C149#319811yescharacteristic, complemented, Sylow
204#3198—1491nomaximal, Sylow
205#537D14911yescharacteristic, complemented
206#535—1491no—
207#485—1491no—
208#482—1491no—
209#481—1491no—
210#480—1491no—
211#469—1491no—
212#468—1491no—
213#466—1491no—
214#465—1491no—
215#450—1491no—
216#449—1491no—
217#449—1491no—
218#447—1491no—
219#408—1491no—
220C2×#41C2×D14911yescharacteristic
221C2×#41C2×D14911yescharacteristic, complemented
222C22×D4—1491no—
223C2×SD16—1491no—
224C2×SD16—1491no—
225C2×D8—1491no—
226C2×D8—1491no—
227C2×M16—1491no—
228C22×C8—1491no—
229#127—2981no—
230#124—2981no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D14911yescharacteristic
233C22⋊Q8C2×D14911yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—1491no—
238#121—1491no—
239#121—1491no—
240#121—1491no—
241#121C2×D14911yescharacteristic
242#121C2×D14911yescharacteristic, complemented
243#120—2981no—
244#120—2981no—
245#117—1491no—
246C2×C4⋊C4C2×D14911yescharacteristic, complemented
247#107—1491no—
248#107—1491no—
249#106—1491no—
250#106—1491no—
251#103—1491no—
252#103—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102—1491no—
257#102—1491no—
258#102—1491no—
259C22⋊C8—1491no—
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262C22⋊C8—1491no—
263C24—2981no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D14911yescharacteristic
269C2×Q8C22×D14911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—5961no—
279C2×D4—5961no—
280C2×D4—1491no—
281C2×D4—1491no—
282C2×D4C22⋊D14911yescharacteristic
283C2×D4C22⋊D14911yescharacteristic
284C2×D4C22⋊D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D14911yescharacteristic
289C22×C4C22×D14911yescharacteristic
290C22×C4C22×D14911yescharacteristic
291SD16—5961no—
292SD16—5961no—
293D8—5961no—
294D8—5961no—
295M16—5961no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8—1491no—
300C2×C8—1491no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4C22×D14911yescharacteristic
307C4⋊C4C22×D14911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C42—2981no—
318C23—21no—
319C23—2981no—
320C23—2981no—
321C23—5962no—
322C23—11921no—
323C23—11921no—
324C23C2×C22⋊D14911yescharacteristic
325C23C2×C22⋊D14911yescharacteristic
326C23C2×C22⋊D14911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—2981no—
339D4—2981no—
340D4—2981no—
341D4—2981no—
342D4—5962no—
343D4—11921no—
344D4—11921no—
345D4—11921no—
346D4—11921no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4C2×C22⋊D14911yescharacteristic
361C2×C4C2×C22⋊D14911yescharacteristic
362C2×C4C2×C22⋊D14911yescharacteristic
363C2×C4C23×D14911yescharacteristic
364C8—2981no—
365C8—2981no—
366C8—2981no—
367C8—2981no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—11924no—
387C22C22×C22⋊D14911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—5961no—
395C4—5961no—
396C4#1801195611yescharacteristic
397C4#1801195611yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—11921no—
403C2—11921no—
404C2#2375018411yescharacteristic
405C2#2375042811yescharacteristic
406C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#537×C149C2
socleC22×C149C22×D4
hypercenter#537D149
hypocenterC149#3198
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #23750189C2semidirect
2. #23749963C2semidirect
3. #23749946C2semidirect
4. #23749943C2semidirect
5. #23749938C2semidirect
6. #23749876C2semidirect
7. #23749873C2semidirect
8. #23749859C2semidirect
9. #23749856C2semidirect
10. #23749775C2semidirect
11. #23749770C2semidirect
12. #23749770C2semidirect
13. #23749758C2semidirect
14. #23749592C2semidirect
15. #537×C149C2semidirect
21. C2×#14558720C22semidirect
22. C22×#11924746C22semidirect
32. #18011844C22semidirect
33. #18011844C22semidirect
34. #18011842C22semidirect
35. #18011842C22semidirect
36. #18011835C22semidirect
37. #18011835C22semidirect
38. #18011832C22semidirect
39. #18011832C22semidirect
46. C22⋊#11924746C22semidirect
47. C22⋊#11924746C22semidirect
49. C2×#41×C149C22semidirect
52. C22⋊Q8×C149C22semidirect
57. #121×C149C22semidirect
58. C2×C4⋊C4×C149C22semidirect
203. C149#3198semidirect
205. #537D149semidirect
221. C2×#41C2×D149semidirect
233. C22⋊Q8C2×D149semidirect
242. #121C2×D149semidirect
246. C2×C4⋊C4C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501892
#237499632
#237499462
#237499432
#237499382
#237498762
#237498732
#237498592
#237498562
#237497752
#237497702
#237497582
#237495922
#537×C1492
#3198149