Finite Group Databasebeta

← #34080009

Subgroups — #34080009

Order 19328.

402 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#23752791C211yesmaximal, characteristic, complemented
2#23752790C211yesmaximal, characteristic, complemented
3#23752548C211yesmaximal, characteristic, complemented
4#23752546C211yesmaximal, characteristic, complemented
5#23752524C211yesmaximal, characteristic, complemented
6#23752523C211yesmaximal, characteristic, complemented
7#23752457C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752452C211yesmaximal, characteristic, complemented
10#23752445C211yesmaximal, characteristic, complemented
11#23752374C211yesmaximal, characteristic, complemented
12#23752371C211yesmaximal, characteristic, complemented
13#23752354C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012719C2211yescharacteristic
23#18012718—21no—
24#18012718C2211yescharacteristic
25#18012716—21no—
26#18012715C2211yescharacteristic
27#18012715C2211yescharacteristic
28#18012713—21no—
29#18012712—21no—
30#18012711—21no—
31#18012711—21no—
32#18012711—21no—
33#18012710—21no—
34#18012710C2211yescharacteristic
35#18012710C2211yescharacteristic
36#18012710C2211yescharacteristic
37C2×C4⋊Dic151C2211yescharacteristic
38C4⋊C4×D151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012672C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61#14559003—41no—
62#14559003—41no—
63C2×Dic302D411yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604D411yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151D411yescharacteristic
71C2×C22⋊D151D411yescharacteristic
72C22×Dic151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76C2×C4×D151C2311yescharacteristic
77#14558994—41no—
78#14558992—41no—
79#14558987—41no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C8×D151—41no—
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107C22×C4×C151C2311yescharacteristic
108SD16×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151C2×D411yescharacteristic
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118Dic302—41no—
119D604—41no—
120C22⋊D151—41no—
121C22⋊D151—41no—
122C22⋊D151—42no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—42no—
131C2×Dic151—81no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—81no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151C2×D411yescharacteristic
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—42no—
151D4×C151—81no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—42no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2411yescharacteristic
159C8×C151—21no—
160C8×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C4×C151—21no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151H(5,𝔽2)11yescharacteristic
181C4×C151H(5,𝔽2)11yescharacteristic
182Dic151—21no—
183Dic151—21no—
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151—81no—
190C2×C151—81no—
191C2×C151#53411yescharacteristic
192C2×C151#57611yescharacteristic
193C2×C151#57811yescharacteristic
194D151—41no—
195D151—41no—
196C151#320311yescharacteristic, complemented, Sylow
197#3203—1511nomaximal, Sylow
198#537—1511no—
199#537—1511no—
200#484—1511no—
201#484—1511no—
202#480—1511no—
203#480—1511no—
204#468—1511no—
205#468—1511no—
206#467—1511no—
207#466—1511no—
208#452—1511no—
209#452—1511no—
210#449—1511no—
211#449D15111yescharacteristic, complemented
212#408—1511no—
213C2×#41—1511no—
214C2×#41—1511no—
215C2×#41C2×D15111yescharacteristic
216C2×Q16—1511no—
217C2×SD16—1511no—
218C2×SD16C2×D15111yescharacteristic
219C2×D8C2×D15111yescharacteristic
220C2×M16—1511no—
221C22×C8—1511no—
222C22⋊Q8—3021no—
223C22⋊Q8—3021no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8—1511no—
228#121—3021no—
229#121—3021no—
230#121—3021no—
231#121—3021no—
232#121—3021no—
233#121—3021no—
234#121—1511no—
235#121—1511no—
236#121—1511no—
237#121C2×D15111yescharacteristic
238C2×C4⋊C4—1511no—
239C2×C4⋊C4—1511no—
240#107—1511no—
241#107—1511no—
242#107—1511no—
243#107—1511no—
244#103—1511no—
245#103—1511no—
246#103—1511no—
247#103C2×D15111yescharacteristic
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102C2×D15111yescharacteristic
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8C2×D15111yescharacteristic
256#41—41no—
257#41—41no—
258#41—6041no—
259#41—6041no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8—1511no—
264C2×Q8C22×D15111yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—1511no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4C22×D15111yescharacteristic
275C2×D4C22×D15111yescharacteristic
276C22×C4—21no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—1511no—
281C22×C4—1511no—
282C22×C4C22×D15111yescharacteristic
283Q16—6041no—
284SD16—41no—
285SD16—6041no—
286D8—41no—
287M16—6041no—
288C2×C8—6041no—
289C2×C8—1511no—
290C2×C8—1511no—
291C2×C8C22×D15111yescharacteristic
292C2×C8C22×D15111yescharacteristic
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—3021no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—1511no—
300C4⋊C4—1511no—
301C4⋊C4—1511no—
302C4⋊C4C22×D15111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C23—21no—
312C23—21no—
313C23—1511no—
314C23—1511no—
315C23D4×D15111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—3021no—
319Q8—3021no—
320Q8—6041no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—6041no—
328D4—6041no—
329D4—6041no—
330D4—6042no—
331D4—12081no—
332D4—12081no—
333D4—12081no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—6042no—
348C2×C4—1511no—
349C2×C4—1511no—
350C2×C4—12081no—
351C2×C4—12081no—
352C2×C4D4×D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3021no—
357C8—3021no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—3021no—
368C22—3021no—
369C22—3021no—
370C22—3021no—
371C22—3021no—
372C22—3021no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—3021no—
378C4—3021no—
379C4—6041no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—6041no—
389C2—6041no—
390C2#2375277211yescharacteristic
391C2#2375301611yescharacteristic
392C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3203
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752791C2semidirect
2. #23752790C2semidirect
3. #23752548C2semidirect
4. #23752546C2semidirect
5. #23752524C2semidirect
6. #23752523C2semidirect
7. #23752457C2semidirect
8. #23752455C2semidirect
9. #23752452C2semidirect
10. #23752445C2semidirect
11. #23752374C2semidirect
12. #23752371C2semidirect
13. #23752354C2semidirect
14. #23752177C2semidirect
15. #449×C151C2semidirect
196. C151#3203semidirect
211. #449D151semidirect

Maximal subgroups

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

subgroupindex
#237527912
#237527902
#237525482
#237525462
#237525242
#237525232
#237524572
#237524552
#237524522
#237524452
#237523742
#237523712
#237523542
#237521772
#449×C1512
#3203151