Finite Group Databasebeta

← #34080847

Subgroups — #34080847

Order 19328.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012759C211yesmaximal, characteristic, complemented
2C22×#14558994C211yesmaximal, characteristic, complemented
3#23752871C211yesmaximal, characteristic, complemented
4#23752594C211yesmaximal, characteristic, complemented
5#23752451C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752434C211yesmaximal, characteristic, complemented
8#23752431C211yesmaximal, characteristic, complemented
9#23752374C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752350C211yesmaximal, characteristic, complemented
13C4×#14558994C211yesmaximal, characteristic, complemented
14D4×C151⋊C8C211yesmaximal, characteristic, complemented
15#548×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18#18012759—24no—
19C2×#14558994—24no—
20C2×#14558994C2211yescharacteristic
21C2×#14558994C2211yescharacteristic
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic
26C2×#14558991C2211yescharacteristic
27C2×#14558991C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C22×C151⋊C8C2211yescharacteristic
30C22×C151⋊C8C2211yescharacteristic
31#18012727C2211yescharacteristic
32#18012725—21no—
33#18012718C2211yescharacteristic
34#18012717—21no—
35#18012713C2211yescharacteristic
36#18012711—21no—
37C4×Dic302C2211yescharacteristic
38(C22⋊D151)⋊C4—21no—
39#18012672C2211yescharacteristic
40C4⋊(C151⋊C8)C2211yescharacteristic
41#18012663C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47C22⋊(C151⋊C8)C2211yescharacteristic
48C22⋊(C151⋊C8)C2211yescharacteristic
49C4×C151⋊C8C2211yescharacteristic
50C2×#41×C151C2211yescharacteristic
51C22×Q8×C151C2211yescharacteristic
52#124×C151—21no—
53#124×C151C2211yescharacteristic
54C22⋊Q8×C151—21no—
55C22⋊Q8×C151C2211yescharacteristic
56#121×C151—21no—
57#121×C151C2211yescharacteristic
58C4×Q8×C151C2211yescharacteristic
59C4×D4×C151—21no—
60C4×D4×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—41no—
63C2×Dic302—22no—
64C2×Dic302—21no—
65C2×Dic302—41no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73#14558994—22no—
74#14558994—22no—
75#14558994—22no—
76#14558994D414yescomplemented
77#14558992—22no—
78#14558992—41no—
79#14558991—22no—
80#14558991—41no—
81#14558989—22no—
82C2×C151⋊C8—22no—
83C2×C151⋊C8—22no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96#41×C151—22no—
97#41×C151—41no—
98C2×Q8×C151—21no—
99C2×Q8×C151—22no—
100C2×Q8×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151D411yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151D411yescharacteristic
114C4⋊C4×C151C2311yescharacteristic
115C22⋊C4×C151—21no—
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C22⋊C4×C151D411yescharacteristic
120C22⋊C4×C151D411yescharacteristic
121C42×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124Dic302—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—42no—
128Dic302C2×D412yes—
129D604—21no—
130D604—21no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—42no—
137C4×D151—42no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C151⋊C8C2×D412yes—
142C23×C151—21no—
143C23×C151C2×D411yescharacteristic
144C23×C151C2×D411yescharacteristic
145Q8×C151—21no—
146Q8×C151—21no—
147Q8×C151—21no—
148Q8×C151—42no—
149Q8×C151C2×D412yes—
150D4×C151—22no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—42no—
154D4×C151—42no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2×D411yescharacteristic
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C22×C151—21no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151#13512yescomplemented
178C22×C151C22×D411yescharacteristic
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C4×C151—21no—
183C4×C151—21no—
184C4×C151—22no—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—41no—
188C4×C151—41no—
189C4×C151C22×D411yescharacteristic
190C4×C151H(5,𝔽2)11yescharacteristic
191Dic151—22no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—22no—
195C2×C151—41no—
196C2×C151—81no—
197C2×C151D4211yescharacteristic
198C2×C151C2×#13511yescharacteristic
199C2×C151#57811yescharacteristic
200D151—81no—
201C151#328511yescharacteristic, complemented, Sylow
202#3285—1511nomaximal, Sylow
203C2×#135—1511no—
204C22×Q16—1511no—
205#548—1511no—
206#548D15111yescharacteristic, complemented
207#495—1511no—
208#467—1511no—
209#466—1511no—
210#464—1511no—
211#464—1511no—
212#452—1511no—
213#452—1511no—
214#448—1511no—
215#448—1511no—
216C4×Q16—1511no—
217C8×D4—1511no—
218C2×#41—1511no—
219C2×#41C2×D15111yescharacteristic
220C22×Q8—1511no—
221C22×Q8C2×D15111yescharacteristic
222#135—3024no—
223C2×Q16—3024no—
224C2×Q16—1511no—
225C2×Q16—1511no—
226C2×Q16—1511no—
227C2×Q16—1511no—
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×D8—1511no—
233C22×C8—1511no—
234C22×C8—1511no—
235#124—21no—
236#124—3021no—
237#124—1511no—
238#124C2×D15111yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—3021no—
241C22⋊Q8—1511no—
242C22⋊Q8C2×D15111yescharacteristic
243#121—21no—
244#121—3021no—
245#121—1511no—
246#121C2×D15111yescharacteristic
247C4×Q8—1511no—
248C4×Q8C2×D15111yescharacteristic
249C4×D4—21no—
250C4×D4—3021no—
251C4×D4C2×D15111yescharacteristic
252#107—1511no—
253C4⋊C8—1511no—
254#103—1511no—
255#103—1511no—
256#103—1511no—
257#103—1511no—
258#102—1511no—
259#102—1511no—
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262C4×C8—1511no—
263#41—22no—
264#41—41no—
265#41—3022no—
266#41—6041no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—3022no—
271C2×Q8—3021no—
272C2×Q8—6041no—
273C2×Q8—1511no—
274C2×Q8—1511no—
275C2×Q8C22×D15111yescharacteristic
276C2×Q8C22×D15111yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—1511no—
282C2×D4C22⋊D15111yescharacteristic
283C2×D4C22×D15111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4C22×D15111yescharacteristic
289C22×C4C22×D15111yescharacteristic
290Q16—3022no—
291Q16—3022no—
292Q16—3022no—
293Q16—1514no—
294SD16—3022no—
295SD16—3022no—
296SD16—6041no—
297SD16—6041no—
298D8—3022no—
299C2×C8—3022no—
300C2×C8—3022no—
301C2×C8—1511no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8—1511no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4C22⋊D15111yescharacteristic
311C4⋊C4C22×D15111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4C22⋊D15111yescharacteristic
321C22⋊C4C22⋊D15111yescharacteristic
322C42—21no—
323C42—3021no—
324C42C22×D15111yescharacteristic
325C23—21no—
326C23—3021no—
327C23C2×C22⋊D15111yescharacteristic
328C23C2×C22⋊D15111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—3021no—
334Q8—3021no—
335Q8—3021no—
336Q8—6042no—
337Q8—1512no—
338Q8D4×D15112yes—
339D4—22no—
340D4—21no—
341D4—21no—
342D4—42no—
343D4—42no—
344D4—3021no—
345D4—3021no—
346D4—6042no—
347D4—6042no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—6042no—
361C2×C4—6042no—
362C2×C4C2×C22⋊D15111yescharacteristic
363C2×C4C2×C22⋊D15111yescharacteristic
364C2×C4C2×C22⋊D15111yescharacteristic
365C2×C4C2×C22⋊D15111yescharacteristic
366C2×C4C23×D15111yescharacteristic
367C8—3021no—
368C8—3021no—
369C8—3021no—
370C8—1512no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22#1801275912yescomplemented
383C22C22×C22⋊D15111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—3022no—
392C4—6041no—
393C4—6041no—
394C4C2×D4×D15111yescharacteristic
395C4#1801278411yescharacteristic
396C2—22no—
397C2—41no—
398C2—81no—
399C2—12081no—
400C2D4×C22⋊D15111yescharacteristic
401C2C2×#1801275911yescharacteristic
402C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#548×C151C2
socleC22×C151C22×D4
hypercenter#548D151
hypocenterC151#3285
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#18012759C2semidirect
2. C22×#14558994C2semidirect
3. #23752871C2semidirect
4. #23752594C2semidirect
5. #23752451C2semidirect
6. #23752446C2semidirect
7. #23752434C2semidirect
8. #23752431C2semidirect
9. #23752374C2semidirect
10. #23752372C2semidirect
11. #23752351C2semidirect
12. #23752350C2semidirect
13. C4×#14558994C2semidirect
14. D4×C151⋊C8C2semidirect
15. #548×C151C2semidirect
76. #14558994D4semidirect
177. C22×C151#135semidirect
201. C151#3285semidirect
206. #548D151semidirect
382. C22#18012759semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
C22×#145589942
#237528712
#237525942
#237524512
#237524462
#237524342
#237524312
#237523742
#237523722
#237523512
#237523502
C4×#145589942
D4×C151⋊C82
#548×C1512
#3285151