Finite Group Databasebeta

← #34055779

Subgroups — #34055779

Order 19072.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750194C211yesmaximal, characteristic, complemented
2#23750015C211yesmaximal, characteristic, complemented
3#23750007C211yesmaximal, characteristic, complemented
4#23749987C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749847C211yesmaximal, characteristic, complemented
7#23749840C211yesmaximal, characteristic, complemented
8#23749825C211yesmaximal, characteristic, complemented
9#23749820C211yesmaximal, characteristic, complemented
10#23749785C211yesmaximal, characteristic, complemented
11#23749775C211yesmaximal, characteristic, complemented
12#23749768C211yesmaximal, characteristic, complemented
13#23749758C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#542×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic, complemented
19C2×#14558724C2211yescharacteristic, complemented
20C2×#14558723C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558723C2211yescharacteristic, complemented
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25C2×#14558721C2211yescharacteristic, complemented
26#18011908C2211yescharacteristic
27#18011908C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011899C2211yescharacteristic
30#18011886—21no—
31#18011886—21no—
32#18011881—21no—
33#18011881—21no—
34C4⋊#11924746C2211yescharacteristic, complemented
35C4⋊#11924746C2211yescharacteristic, complemented
36#18011834C2211yescharacteristic, complemented
37#18011834C2211yescharacteristic, complemented
38#18011831C2211yescharacteristic
39#18011831C2211yescharacteristic
40#18011831C2211yescharacteristic
41#18011831C2211yescharacteristic
42#18011831C2211yescharacteristic, complemented
43#18011831C2211yescharacteristic, complemented
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48C4⋊Q8×C149C2211yescharacteristic, complemented
49#126×C149—21no—
50#124×C149—21no—
51#124×C149C2211yescharacteristic, complemented
52#123×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic, complemented
57C4×D4×C149C2211yescharacteristic, complemented
58#117×C149C2211yescharacteristic
59C23×D149—21no—
60#14558736—41no—
61#14558736—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—41no—
69C2×D596—41no—
70C2×D596C2311yescharacteristic
71C2×D596C2311yescharacteristic
72C2×D596C2311yescharacteristic
73C2×C22⋊D149—21no—
74C2×C4×D149—21no—
75#14558726—41no—
76#14558724—41no—
77#14558723—41no—
78#14558723—41no—
79#14558723—41no—
80#14558721—41no—
81#14558721—41no—
82#14558721—41no—
83C2×#11924746C2311yescharacteristic
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C2×Q8×C149—21no—
92C2×Q8×C149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149C2311yescharacteristic
95C22×C4×C149—21no—
96C22×C4×C149C2311yescharacteristic
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149D411yescharacteristic
101C4⋊C4×C149D411yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149—21no—
109C22⋊C4×C149D411yescharacteristic
110C22⋊C4×C149D411yescharacteristic
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C42×C149C2311yescharacteristic
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—42no—
118C22×D149—81no—
119C22×D149—81no—
120Dic298—21no—
121Dic298—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—42no—
129D596—81no—
130D596—81no—
131D596—81no—
132D596—81no—
133C22⋊D149—42no—
134C2×Dic149—21no—
135C4×D149—42no—
136#11924746—21no—
137#11924746—21no—
138#11924746—21no—
139#11924746—21no—
140C23×C149—21no—
141C23×C149C2×D411yescharacteristic
142Q8×C149—21no—
143Q8×C149—21no—
144Q8×C149—81no—
145D4×C149—21no—
146D4×C149—21no—
147D4×C149—81no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—81no—
154C2×C4×C149C2×D411yescharacteristic
155C2×C4×C149C2×D411yescharacteristic
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2411yescharacteristic
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149C22×D411yescharacteristic
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—84no—
177C4×C149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—41no—
183C4×C149—41no—
184C4×C149—41no—
185C4×C149H(5,𝔽2)11yescharacteristic
186C4×C149H(5,𝔽2)11yescharacteristic
187Dic149—41no—
188C2×C149—41no—
189C2×C149—81no—
190C2×C149#53511yescharacteristic
191C2×C149#57611yescharacteristic
192C2×C149#57711yescharacteristic
193D149—81no—
194D149—81no—
195D149—81no—
196C149#322411yescharacteristic, complemented, Sylow
197#3224—1491nomaximal, Sylow
198#542D14911yescharacteristic, complemented
199#535—1491no—
200#496—1491no—
201#495—1491no—
202#489—1491no—
203#486—1491no—
204#464—1491no—
205#463—1491no—
206#460—1491no—
207#459—1491no—
208#452—1491no—
209#450—1491no—
210#449—1491no—
211#447—1491no—
212#433—1491no—
213C2×#41—1491no—
214C22×D4—1491no—
215C2×Q16—1491no—
216C2×SD16—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×D8—1491no—
221C2×D8—1491no—
222C2×D8—1491no—
223C4⋊Q8C2×D14911yescharacteristic, complemented
224#127—1491no—
225#127—1491no—
226#126—21no—
227#124—21no—
228#124—1491no—
229#124—1491no—
230#124C2×D14911yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D14911yescharacteristic
234#121—2981no—
235#121—2981no—
236#121C2×D14911yescharacteristic
237#120—2981no—
238#120—2981no—
239C4×Q8C2×D14911yescharacteristic, complemented
240C4×D4C2×D14911yescharacteristic, complemented
241#117C2×D14911yescharacteristic
242C4⋊C8—1491no—
243C4⋊C8—1491no—
244#103—1491no—
245#103—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252C22⋊C8—1491no—
253C22⋊C8—1491no—
254#97—1491no—
255C4×C8—1491no—
256C24—2981no—
257#41—5961no—
258#41—5961no—
259C2×Q8—21no—
260C2×Q8—1491no—
261C2×Q8C22×D14911yescharacteristic
262C2×D4—21no—
263C2×D4—2981no—
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—5961no—
270C2×D4—5961no—
271C2×D4—1491no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4C22×D14911yescharacteristic
275C22×C4—21no—
276C22×C4—2981no—
277C22×C4C22×D14911yescharacteristic
278Q16—5961no—
279SD16—5961no—
280SD16—5961no—
281SD16—5961no—
282SD16—5961no—
283D8—5961no—
284D8—5961no—
285D8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D14911yescharacteristic
294C4⋊C4C22⋊D14911yescharacteristic
295C4⋊C4C22×D14911yescharacteristic
296C4⋊C4C22×D14911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4C22⋊D14911yescharacteristic
307C22⋊C4C22⋊D14911yescharacteristic
308C42—21no—
309C42C22×D14911yescharacteristic
310C42C22×D14911yescharacteristic
311C23—21no—
312C23—2981no—
313C23—2981no—
314C23—2981no—
315C23—5962no—
316C23—11921no—
317C23—11921no—
318C23C2×C22⋊D14911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—2981no—
323Q8—2981no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—2981no—
328D4—2981no—
329D4—2981no—
330D4—2981no—
331D4—2981no—
332D4—2981no—
333D4—5962no—
334D4—5962no—
335D4—11921no—
336D4—11921no—
337D4—11921no—
338D4—11921no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—2981no—
346C2×C4—5962no—
347C2×C4C2×C22⋊D14911yescharacteristic
348C2×C4C2×C22⋊D14911yescharacteristic
349C2×C4C2×C22⋊D14911yescharacteristic
350C2×C4C2×C22⋊D14911yescharacteristic
351C2×C4C2×C22⋊D14911yescharacteristic
352C2×C4C23×D14911yescharacteristic
353C8—2981no—
354C8—2981no—
355C8—2981no—
356C8—2981no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—5961no—
364C22—5961no—
365C22—5961no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—11924no—
373C22C22×C22⋊D14911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—5961no—
383C4#1801195711yescharacteristic
384C4#1801195711yescharacteristic
385C2—41no—
386C2—81no—
387C2—11921no—
388C2—11921no—
389C2—11921no—
390C2#2375018911yescharacteristic
391C2#2375042811yescharacteristic
392C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#542×C149C2
socleC22×C149C22×D4
hypercenter#542D149
hypocenterC149#3224
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23750194C2semidirect
2. #23750015C2semidirect
3. #23750007C2semidirect
4. #23749987C2semidirect
5. #23749973C2semidirect
6. #23749847C2semidirect
7. #23749840C2semidirect
8. #23749825C2semidirect
9. #23749820C2semidirect
10. #23749785C2semidirect
11. #23749775C2semidirect
12. #23749768C2semidirect
13. #23749758C2semidirect
14. #23749686C2semidirect
15. #542×C149C2semidirect
18. C2×#14558726C22semidirect
19. C2×#14558724C22semidirect
22. C2×#14558723C22semidirect
25. C2×#14558721C22semidirect
34. C4⋊#11924746C22semidirect
35. C4⋊#11924746C22semidirect
36. #18011834C22semidirect
37. #18011834C22semidirect
42. #18011831C22semidirect
43. #18011831C22semidirect
46. #18011822C22semidirect
47. C4×#11924746C22semidirect
48. C4⋊Q8×C149C22semidirect
51. #124×C149C22semidirect
56. C4×Q8×C149C22semidirect
57. C4×D4×C149C22semidirect
196. C149#3224semidirect
198. #542D149semidirect
223. C4⋊Q8C2×D149semidirect
230. #124C2×D149semidirect
239. C4×Q8C2×D149semidirect
240. C4×D4C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501942
#237500152
#237500072
#237499872
#237499732
#237498472
#237498402
#237498252
#237498202
#237497852
#237497752
#237497682
#237497582
#237496862
#542×C1492
#3224149