Finite Group Databasebeta

← #34077130

Subgroups — #34077130

Order 19328.

478 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012724C211yesmaximal, characteristic
2C2×#18012717C211yesmaximal, characteristic, complemented
3#23752146C211yesmaximal, characteristic, complemented
4#23752145C211yesmaximal, characteristic, complemented
5#23752141C211yesmaximal, characteristic, complemented
6#23752141C211yesmaximal, characteristic, complemented
7#23752139C211yesmaximal, characteristic, complemented
8#23752134C211yesmaximal, characteristic, complemented
9#23752134C211yesmaximal, characteristic, complemented
10#23752132C211yesmaximal, characteristic, complemented
11#23752130C211yesmaximal, characteristic
12#23752129C211yesmaximal, characteristic
13#23752125C211yesmaximal, characteristic, complemented
14#23752069C211yesmaximal, characteristic, complemented
15#398×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19#18012724—24no—
20#18012717—24no—
21C2×C4⋊Dic151C2211yescharacteristic
22C2×C4⋊Dic151C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×Dic151⋊C4C2211yescharacteristic
27C2×Dic151⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×(C2×D151)⋊C4C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×(C2×D151)⋊C4C2211yescharacteristic
37C2×(C2×D151)⋊C4C2211yescharacteristic
38C2×(C2×D151)⋊C4C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C4⋊C4×C151C2211yescharacteristic
48C2×C4⋊C4×C151C2211yescharacteristic
49C2×C4⋊C4×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C23×D151C2311yescharacteristic
54C23×D151C2311yescharacteristic
55C2×Dic302—22no—
56C2×Dic302—41no—
57C2×Dic302—41no—
58C2×D604—22no—
59C2×D604—41no—
60C2×D604—41no—
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C2×C4×D151—41no—
68C2×C4×D151—41no—
69C2×C4×D151D414yes—
70C4⋊Dic151—41no—
71C4⋊Dic151—41no—
72Dic151⋊C4—22no—
73Dic151⋊C4—22no—
74Dic151⋊C4—22no—
75Dic151⋊C4—41no—
76Dic151⋊C4—41no—
77(C2×D151)⋊C4—22no—
78(C2×D151)⋊C4—22no—
79(C2×D151)⋊C4—22no—
80(C2×D151)⋊C4—22no—
81(C2×D151)⋊C4—22no—
82(C2×D151)⋊C4—41no—
83(C2×D151)⋊C4—41no—
84(C2×D151)⋊C4—41no—
85(C2×D151)⋊C4—41no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4—41no—
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C22×C4×C151C2311yescharacteristic
95C4⋊C4×C151—22no—
96C4⋊C4×C151—22no—
97C4⋊C4×C151—41no—
98C4⋊C4×C151—41no—
99C22×D151—21no—
100C22×D151—21no—
101C22×D151—21no—
102C22×D151—21no—
103C22×D151—21no—
104C22×D151—21no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151—21no—
112C22×D151C2×D412yes—
113Dic302—44no—
114D604—44no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151C2×D412yes—
133C4×D151—44no—
134C23×C151C2411yescharacteristic
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151C2×D412yes—
156C22×C151C22×D411yescharacteristic
157C22×C151H(5,𝔽2)11yescharacteristic
158C22×C151H(5,𝔽2)11yescharacteristic
159C22×C151H(5,𝔽2)11yescharacteristic
160C22×C1512−1+411yescharacteristic
161C22×C1512−1+411yescharacteristic
162C22×C1512−1+411yescharacteristic
163C2×D151—22no—
164C2×D151—22no—
165C2×D151—22no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C4×C151—22no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—41no—
184Dic151—22no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189Dic151—41no—
190C2×C151#53411yescharacteristic
191C2×C151#53611yescharacteristic
192C2×C151#53711yescharacteristic
193C2×C151#56211yescharacteristic
194C2×C151#56211yescharacteristic
195C2×C151#56311yescharacteristic
196C2×C151#56311yescharacteristic
197D151—42no—
198D151—81no—
199C151#281411yescharacteristic, complemented, Sylow
200#2814—1511nomaximal, Sylow
201C2×#123—1511no—
202C2×C22⋊Q8—1511no—
203#398—1511no—
204#398—1511no—
205#398D15111yescharacteristic, complemented
206#397—1511no—
207#397—1511no—
208#397—1511no—
209#396—1511no—
210#396—1511no—
211#395—1511no—
212#394—1511no—
213#394—1511no—
214#393—1511no—
215#380—1511no—
216C22×Q8—1511no—
217C22×D4—1511no—
218C23×C4—1511no—
219#123—3024no—
220C22⋊Q8—3024no—
221C2×C4⋊C4—1511no—
222C2×C4⋊C4—1511no—
223C2×C4⋊C4—1511no—
224C2×C4⋊C4—1511no—
225C2×C4⋊C4—1511no—
226C2×C4⋊C4—1511no—
227C2×C4⋊C4—1511no—
228C2×C4⋊C4C2×D15111yescharacteristic
229C2×C4⋊C4C2×D15111yescharacteristic
230C2×C4⋊C4C2×D15111yescharacteristic
231C2×C4⋊C4C2×D15111yescharacteristic
232C2×C22⋊C4—1511no—
233C2×C22⋊C4—1511no—
234C2×C22⋊C4—1511no—
235C2×C22⋊C4—1511no—
236C2×C22⋊C4—1511no—
237C2×C22⋊C4—1511no—
238C2×C22⋊C4—1511no—
239C2×C22⋊C4—1511no—
240C2×C22⋊C4—1511no—
241C2×C22⋊C4—1511no—
242C2×C22⋊C4—1511no—
243#95—1511no—
244#95—1511no—
245#95—1511no—
246#95—1511no—
247#95—1511no—
248#95—1511no—
249#95—1511no—
250#95C2×D15111yescharacteristic
251#95C2×D15111yescharacteristic
252#95C2×D15111yescharacteristic
253C24—1511no—
254C24—1511no—
255C2×Q8—3022no—
256C2×Q8—6041no—
257C2×Q8—6041no—
258C2×D4—3022no—
259C2×D4—6041no—
260C2×D4—6041no—
261C22×C4—6041no—
262C22×C4—6041no—
263C22×C4—1511no—
264C22×C4—1511no—
265C22×C4—1511no—
266C22×C4—1511no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4—1514no—
270C22×C4C22×D15111yescharacteristic
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273C22×C4C22×D15111yescharacteristic
274C22×C4C22×D15111yescharacteristic
275C22×C4C22×D15111yescharacteristic
276C22×C4C22×D15111yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—3022no—
282C4⋊C4—3022no—
283C4⋊C4—3022no—
284C4⋊C4—6041no—
285C4⋊C4—6041no—
286C4⋊C4—6041no—
287C4⋊C4—6041no—
288C22⋊C4—3022no—
289C22⋊C4—3022no—
290C22⋊C4—3022no—
291C22⋊C4—3022no—
292C22⋊C4—3022no—
293C22⋊C4—6041no—
294C22⋊C4—6041no—
295C22⋊C4—6041no—
296C22⋊C4—6041no—
297C22⋊C4—6041no—
298C22⋊C4—6041no—
299C23—3021no—
300C23—3021no—
301C23—3021no—
302C23—3021no—
303C23—3021no—
304C23—3021no—
305C23—3021no—
306C23—3021no—
307C23—3021no—
308C23—3021no—
309C23—3021no—
310C23—3021no—
311C23—3021no—
312C23—1512no—
313C23C23×D15111yescharacteristic
314Q8—6044no—
315D4—6044no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
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—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—6044no—
354C2×C4—1512no—
355C2×C4D4×D15112yes—
356C22—3022no—
357C22—3022no—
358C22—3022no—
359C22—6041no—
360C22—6041no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22C2×D4×D15111yescharacteristic
371C22#1801278411yescharacteristic
372C22#1801278511yescharacteristic
373C22#1801278511yescharacteristic
374C22#1801278611yescharacteristic
375C22#1801278711yescharacteristic
376C22#1801278711yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—3022no—
385C4—6041no—
386C4—6041no—
387C4—6041no—
388C4—6041no—
389C4—6041no—
390C2—6042no—
391C2—12081no—
392C2#2375277011yescharacteristic
393C2#2375278511yescharacteristic
394C2#2375279211yescharacteristic
395C2#2375295911yescharacteristic
396C2#2375296011yescharacteristic
397C2#2375296111yescharacteristic
398C2#2375296611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#398×C151C2
prime radicalC22×D604C22
hypercenter#398D151
hypocenterC151#2814
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#18012717C2semidirect
3. #23752146C2semidirect
4. #23752145C2semidirect
5. #23752141C2semidirect
6. #23752141C2semidirect
7. #23752139C2semidirect
8. #23752134C2semidirect
9. #23752134C2semidirect
10. #23752132C2semidirect
13. #23752125C2semidirect
14. #23752069C2semidirect
15. #398×C151C2semidirect
199. C151#2814semidirect
205. #398D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127242
C2×#180127172
#237521462
#237521452
#237521412
#237521392
#237521342
#237521322
#237521302
#237521292
#237521252
#237520692
#398×C1512
#2814151