Finite Group Databasebeta

← #34077191

Subgroups — #34077191

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752153C211yesmaximal, characteristic, complemented
2#23752141C211yesmaximal, characteristic, complemented
3#23752138C211yesmaximal, characteristic, complemented
4#23752130C211yesmaximal, characteristic, complemented
5#23752130C211yesmaximal, characteristic, complemented
6#23752129C211yesmaximal, characteristic, complemented
7#23752129C211yesmaximal, characteristic, complemented
8#23752125C211yesmaximal, characteristic, complemented
9#23752125C211yesmaximal, characteristic, complemented
10#23752125C211yesmaximal, characteristic, complemented
11#23752122C211yesmaximal, characteristic
12#23752090C211yesmaximal, characteristic, complemented
13#23752090C211yesmaximal, characteristic, complemented
14#23752083C211yesmaximal, characteristic, complemented
15#400×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C22×D604C2211yescharacteristic
19C22×D604C2211yescharacteristic
20C22×C4×D151C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×(C2×D151)⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊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
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C2×C4⋊C4×C151C2211yescharacteristic
45C2×C4⋊C4×C151C2211yescharacteristic
46#95×C151C2211yescharacteristic
47#95×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51C23×D151C2311yescharacteristic
52C23×D151C2311yescharacteristic
53C23×D151C2311yescharacteristic
54C2×Dic302—41no—
55C2×Dic302—41no—
56C2×Dic302—41no—
57C2×D604—22no—
58C2×D604—22no—
59C2×D604—41no—
60C2×D604—41no—
61C2×D604—41no—
62C2×D604—41no—
63C2×D604—41no—
64C2×D604—41no—
65C2×D604—41no—
66C22×Dic151C2311yescharacteristic
67C22×Dic151C2311yescharacteristic
68C22×Dic151C2311yescharacteristic
69C22×Dic151C2311yescharacteristic
70C22×Dic151C2311yescharacteristic
71C2×C4×D151—41no—
72C2×C4×D151—41no—
73C2×C4×D151—41no—
74Dic151⋊C4—41no—
75Dic151⋊C4—41no—
76(C2×D151)⋊C4—22no—
77(C2×D151)⋊C4—41no—
78(C2×D151)⋊C4—41no—
79(C2×D151)⋊C4—41no—
80(C2×D151)⋊C4—41no—
81(C2×D151)⋊C4—41no—
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—
88(C2×D151)⋊C4—41no—
89(C2×D151)⋊C4—41no—
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C22×C4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96C22×C4×C151C2311yescharacteristic
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×D151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—21no—
118C22×D151—21no—
119C22×D151#4112yes—
120Dic302—44no—
121D604—44no—
122D604—44no—
123D604—44no—
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×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C4×D151—44no—
140C23×C151C2411yescharacteristic
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×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—
162C22×C151C2×#4111yescharacteristic
163C22×C151H(5,𝔽2)11yescharacteristic
164C22×C151H(5,𝔽2)11yescharacteristic
165C22×C151H(5,𝔽2)11yescharacteristic
166C22×C151H(5,𝔽2)11yescharacteristic
167C22×C151H(5,𝔽2)11yescharacteristic
168C22×C1512−1+411yescharacteristic
169C2×D151—22no—
170C2×D151—22no—
171C2×D151—22no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—41no—
190C4×C151—41no—
191C4×C151—41no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151—41no—
195C4×C151—41no—
196C4×C151—41no—
197Dic151—41no—
198Dic151—41no—
199Dic151—41no—
200Dic151—41no—
201Dic151—41no—
202C2×C151#53811yescharacteristic
203C2×C151#53811yescharacteristic
204C2×C151#53911yescharacteristic
205C2×C151#56011yescharacteristic
206C2×C151H(3,𝔽4)11yescharacteristic
207C2×C151#56211yescharacteristic
208C2×C151#56211yescharacteristic
209D151—42no—
210D151—81no—
211D151—81no—
212C151#282411yescharacteristic, complemented, Sylow
213#2824—1511nomaximal, Sylow
214#400—1511no—
215#400D15111yescharacteristic, complemented
216#397—1511no—
217#397—1511no—
218#394—1511no—
219#394—1511no—
220#394—1511no—
221#394—1511no—
222#393—1511no—
223#393—1511no—
224#393—1511no—
225#392—1511no—
226#386—1511no—
227#386—1511no—
228#385—1511no—
229C22×Q8—1511no—
230C22×D4—1511no—
231C22×D4—1511no—
232C22×D4—1511no—
233C23×C4—1511no—
234C2×C4⋊C4—1511no—
235C2×C4⋊C4—1511no—
236C2×C4⋊C4C2×D15111yescharacteristic
237C2×C4⋊C4C2×D15111yescharacteristic
238C2×C22⋊C4—1511no—
239C2×C22⋊C4—1511no—
240C2×C22⋊C4—1511no—
241C2×C22⋊C4—1511no—
242C2×C22⋊C4—1511no—
243C2×C22⋊C4—1511no—
244C2×C22⋊C4—1511no—
245C2×C22⋊C4—1511no—
246C2×C22⋊C4—1511no—
247C2×C22⋊C4—1511no—
248C2×C22⋊C4—1511no—
249C2×C22⋊C4—1511no—
250C2×C22⋊C4—1511no—
251C2×C22⋊C4—1511no—
252#95—1511no—
253#95—1511no—
254#95—1511no—
255#95—1511no—
256#95—1511no—
257#95—1511no—
258#95—1511no—
259#95C2×D15111yescharacteristic
260#95C2×D15111yescharacteristic
261#95C2×D15111yescharacteristic
262#95C2×D15111yescharacteristic
263#95C2×D15111yescharacteristic
264C24—1511no—
265C24—1511no—
266C24—1511no—
267C2×Q8—6041no—
268C2×Q8—6041no—
269C2×Q8—6041no—
270C2×D4—3022no—
271C2×D4—3022no—
272C2×D4—6041no—
273C2×D4—6041no—
274C2×D4—6041no—
275C2×D4—6041no—
276C2×D4—6041no—
277C2×D4—6041no—
278C2×D4—6041no—
279C22×C4—6041no—
280C22×C4—6041no—
281C22×C4—6041no—
282C22×C4—1511no—
283C22×C4—1511no—
284C22×C4—1511no—
285C22×C4—1511no—
286C22×C4—1511no—
287C22×C4C22×D15111yescharacteristic
288C22×C4C22×D15111yescharacteristic
289C22×C4C22×D15111yescharacteristic
290C22×C4C22×D15111yescharacteristic
291C22×C4C22×D15111yescharacteristic
292C22×C4C22×D15111yescharacteristic
293C22×C4C22×D15111yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—6041no—
297C4⋊C4—6041no—
298C22⋊C4—3022no—
299C22⋊C4—6041no—
300C22⋊C4—6041no—
301C22⋊C4—6041no—
302C22⋊C4—6041no—
303C22⋊C4—6041no—
304C22⋊C4—6041no—
305C22⋊C4—6041no—
306C22⋊C4—6041no—
307C22⋊C4—6041no—
308C22⋊C4—6041no—
309C22⋊C4—6041no—
310C22⋊C4—6041no—
311C22⋊C4—6041no—
312C23—3021no—
313C23—3021no—
314C23—3021no—
315C23—3021no—
316C23—3021no—
317C23—3021no—
318C23—3021no—
319C23—3021no—
320C23—3021no—
321C23—3021no—
322C23—3021no—
323C23—3021no—
324C23—3021no—
325C23—3021no—
326C23—3021no—
327C23—3021no—
328C23—3021no—
329C23—3021no—
330C23—3021no—
331C23—3021no—
332C23—1512no—
333C23C23×D15111yescharacteristic
334Q8—6044no—
335D4—6044no—
336D4—6044no—
337D4—6044no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
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—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—3021no—
370C2×C4—3021no—
371C2×C4—3021no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—6044no—
375C22—3022no—
376C22—3022no—
377C22—3022no—
378C22—6041no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22—6041no—
388C22—6041no—
389C22—6041no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22—6041no—
396C22#41×D15111yescharacteristic
397C22#1801278411yescharacteristic
398C22#1801278511yescharacteristic
399C22#1801278511yescharacteristic
400C22#1801278511yescharacteristic
401C22#1801278511yescharacteristic
402C22#1801278711yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—6041no—
411C4—6041no—
412C4—6041no—
413C4—6041no—
414C4—6041no—
415C2—6042no—
416C2—12081no—
417C2—12081no—
418C2#2375279811yescharacteristic
419C2#2375280111yescharacteristic
420C2#2375281011yescharacteristic
421C2#2375295311yescharacteristic
422C2#2375295411yescharacteristic
423C2#2375295811yescharacteristic
424C2#2375296011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#400×C151C2
prime radical#23752122C2
hypercenter#400D151
hypocenterC151#2824
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23752153C2semidirect
2. #23752141C2semidirect
3. #23752138C2semidirect
4. #23752130C2semidirect
5. #23752130C2semidirect
6. #23752129C2semidirect
7. #23752129C2semidirect
8. #23752125C2semidirect
9. #23752125C2semidirect
10. #23752125C2semidirect
12. #23752090C2semidirect
13. #23752090C2semidirect
14. #23752083C2semidirect
15. #400×C151C2semidirect
212. C151#2824semidirect
215. #400D151semidirect

Maximal subgroups

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

subgroupindex
#237521532
#237521412
#237521382
#237521302
#237521292
#237521252
#237521222
#237520902
#237520832
#400×C1512
#2824151