Finite Group Databasebeta

← #34071808

Subgroups — #34071808

Order 19328.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012711C211yesmaximal, characteristic
2C2×C4×C22⋊D151C211yesmaximal, characteristic, complemented
3#23752103C211yesmaximal, characteristic, complemented
4#23752100C211yesmaximal, characteristic, complemented
5#23752096C211yesmaximal, characteristic, complemented
6#23752093C211yesmaximal, characteristic, complemented
7#23752092C211yesmaximal, characteristic, complemented
8#23752091C211yesmaximal, characteristic, complemented
9#23752089C211yesmaximal, characteristic, complemented
10#23752088C211yesmaximal, characteristic, complemented
11#23752085C211yesmaximal, characteristic, complemented
12#23752083C211yesmaximal, characteristic, complemented
13#23752070C211yesmaximal, characteristic, complemented
14C2×C151⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×D4×C151C211yesmaximal, characteristic, complemented
16C22×C22⋊D151C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C23×Dic151C2211yescharacteristic
19C23×Dic151C2211yescharacteristic
20C22×C4×D151C2211yescharacteristic
21#18012711C418yescomplemented
22C4×C22⋊D151—24no—
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×Dic151⋊C4C2211yescharacteristic
27C2×C22⋊Dic151C2211yescharacteristic
28C2×C22⋊Dic151C2211yescharacteristic
29C2×C22⋊Dic151C2211yescharacteristic
30C2×C22⋊Dic151C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×C4×Dic151C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C22×D4×C151C2211yescharacteristic
47C23×C4×C151C2211yescharacteristic
48C23×C4×C151C2211yescharacteristic
49C4×D4×C151—24no—
50C2×C4⋊C4×C151C2211yescharacteristic
51C2×C22⋊C4×C151C2211yescharacteristic
52C2×C22⋊C4×C151C2211yescharacteristic
53C2×C42×C151C2211yescharacteristic
54C23×D151C2311yescharacteristic
55C2×C22⋊D151—22no—
56C2×C22⋊D151—22no—
57C2×C22⋊D151—41no—
58C2×C22⋊D151—41no—
59C2×C22⋊D151C2×C414yescomplemented
60C2×C22⋊D151C2×C414yescomplemented
61C22×Dic151—22no—
62C22×Dic151—41no—
63C22×Dic151—41no—
64C22×Dic151—41no—
65C22×Dic151—41no—
66C22×Dic151C2×C414yescomplemented
67C22×Dic151C2311yescharacteristic
68C22×Dic151C2311yescharacteristic
69C22×Dic151C2311yescharacteristic
70C22×Dic151C2311yescharacteristic
71C22×Dic151C2311yescharacteristic
72C22×Dic151C2311yescharacteristic
73C22×Dic151C2311yescharacteristic
74C2×C4×D151—22no—
75C2×C4×D151—41no—
76C2×C4×D151—41no—
77Dic151⋊C4—22no—
78Dic151⋊C4—41no—
79Dic151⋊C4—41no—
80Dic151⋊C4C2×C414yescomplemented
81C22⋊Dic151—22no—
82C22⋊Dic151—41no—
83C22⋊Dic151—41no—
84C22⋊Dic151C2×C414yescomplemented
85(C2×D151)⋊C4—22no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4—41no—
88(C2×D151)⋊C4C2×C414yescomplemented
89C4×Dic151—22no—
90C24×C151C2311yescharacteristic
91C24×C151C2311yescharacteristic
92C2×D4×C151—22no—
93C2×D4×C151—22no—
94C2×D4×C151C2×C414yescomplemented
95C22×C4×C151—22no—
96C22×C4×C151—41no—
97C22×C4×C151—41no—
98C22×C4×C151—41no—
99C22×C4×C151—41no—
100C22×C4×C151D414yescomplemented
101C22×C4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C22×C4×C151C2311yescharacteristic
106C4⋊C4×C151—22no—
107C22⋊C4×C151—22no—
108C22⋊C4×C151—22no—
109C42×C151—22no—
110C22×D151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151C22×C412yes—
117C22⋊D151—28no—
118C22⋊D151—44no—
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×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—44no—
138C2×Dic151—44no—
139C2×Dic151C22×C412yes—
140C2×Dic151C22×C412yes—
141C2×Dic151C22×C412yes—
142C4×D151—44no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151—21no—
153C23×C151C22×C412yes—
154C23×C151C22×C412yes—
155C23×C151C2×D412yes—
156C23×C151#4112yes—
157C23×C151C2411yescharacteristic
158D4×C151—28no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—44no—
172C2×C4×C151—44no—
173C2×C4×C151C22×C412yes—
174C2×C4×C151C2×D412yes—
175C2×C4×C151C2×D412yes—
176C22×C151—22no—
177C22×C151—22no—
178C22×C151—22no—
179C22×C151—22no—
180C22×C151—22no—
181C22×C151—22no—
182C22×C151—22no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151C4×D414yes—
190C22×C151C23×C411yescharacteristic
191C22×C151C22×D411yescharacteristic
192C22×C151C2×#4111yescharacteristic
193C22×C151H(5,𝔽2)11yescharacteristic
194C22×C151H(5,𝔽2)11yescharacteristic
195C22×C151H(5,𝔽2)11yescharacteristic
196C22×C1512−1+411yescharacteristic
197C2×D151—22no—
198C2×D151—22no—
199C2×D151—22no—
200C2×D151—41no—
201C2×D151—41no—
202C2×D151—41no—
203C2×D151—41no—
204C4×C151—22no—
205C4×C151—22no—
206C4×C151—22no—
207C4×C151—41no—
208C4×C151—41no—
209Dic151—22no—
210Dic151—22no—
211Dic151—22no—
212Dic151—41no—
213Dic151—41no—
214Dic151—41no—
215Dic151—41no—
216C2×C151—24no—
217C2×C151—42no—
218C2×C151C2×C4×D411yescharacteristic
219C2×C151#51811yescharacteristic
220C2×C151#52011yescharacteristic
221C2×C151#53411yescharacteristic
222C2×C151#53711yescharacteristic
223C2×C151#53811yescharacteristic
224C2×C151#53911yescharacteristic
225D151—42no—
226C151#232511yescharacteristic, complemented, Sylow
227#2325—1511nomaximal, Sylow
228C2×#121—1511no—
229C2×C4×D4—1511no—
230C2×C4×D4D15111yescharacteristic, complemented
231#388—1511no—
232#388—1511no—
233#387—1511no—
234#387—1511no—
235#386—1511no—
236#386—1511no—
237#386—1511no—
238#386—1511no—
239#385—1511no—
240#385—1511no—
241#380—1511no—
242C2×#95—1511no—
243C22×D4—1511no—
244C22×D4—1511no—
245C22×D4C2×D15111yescharacteristic
246C23×C4—1511no—
247C23×C4—1511no—
248C23×C4—1511no—
249C23×C4C2×D15111yescharacteristic
250C23×C4C2×D15111yescharacteristic
251#121—1518no—
252C4×D4—24no—
253C4×D4—3024no—
254C2×C4⋊C4—1511no—
255C2×C4⋊C4—1511no—
256C2×C4⋊C4—1511no—
257C2×C4⋊C4—1511no—
258C2×C4⋊C4C2×D15111yescharacteristic
259C2×C22⋊C4—1511no—
260C2×C22⋊C4—1511no—
261C2×C22⋊C4—1511no—
262C2×C22⋊C4—1511no—
263C2×C22⋊C4—1511no—
264C2×C22⋊C4—1511no—
265C2×C22⋊C4—1511no—
266C2×C22⋊C4—1511no—
267C2×C22⋊C4C2×D15111yescharacteristic
268C2×C22⋊C4C2×D15111yescharacteristic
269C2×C42—1511no—
270C2×C42C2×D15111yescharacteristic
271#95—1511no—
272#95—1511no—
273#95—1511no—
274#95—1511no—
275#95—1511no—
276#95—1511no—
277#95—1511no—
278#95—1511no—
279#95—1511no—
280#95—1511no—
281C24—1511no—
282C24C22×D15111yescharacteristic
283C24C22×D15111yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—3022no—
287C2×D4—3022no—
288C2×D4—6041no—
289C2×D4—6041no—
290C2×D4—1514no—
291C2×D4—1514no—
292C2×D4C4×D15114yescomplemented
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—3022no—
299C22×C4—3022no—
300C22×C4—6041no—
301C22×C4—6041no—
302C22×C4—6041no—
303C22×C4—6041no—
304C22×C4—6041no—
305C22×C4—6041no—
306C22×C4—1511no—
307C22×C4—1511no—
308C22×C4—1511no—
309C22×C4—1511no—
310C22×C4—1511no—
311C22×C4—1511no—
312C22×C4—1511no—
313C22×C4—1514no—
314C22×C4C22⋊D15114yescomplemented
315C22×C4C22×D15111yescharacteristic
316C22×C4C22×D15111yescharacteristic
317C22×C4C22×D15111yescharacteristic
318C22×C4C22×D15111yescharacteristic
319C22×C4C22×D15111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—3022no—
322C4⋊C4—6041no—
323C4⋊C4—6041no—
324C4⋊C4—1514no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—3022no—
328C22⋊C4—3022no—
329C22⋊C4—6041no—
330C22⋊C4—6041no—
331C22⋊C4—6041no—
332C22⋊C4—6041no—
333C22⋊C4—1514no—
334C22⋊C4—1514no—
335C42—22no—
336C42—3022no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—3021no—
348C23—3021no—
349C23—3021no—
350C23—3021no—
351C23—3021no—
352C23—3021no—
353C23—1512no—
354C23C2×C4×D15112yes—
355C23C2×C4×D15112yes—
356C23C2×C22⋊D15112yes—
357C23#1455900412yes—
358C23C23×D15111yescharacteristic
359D4—28no—
360D4—3028no—
361D4—6044no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—3021no—
380C2×C4—3021no—
381C2×C4—3021no—
382C2×C4—3021no—
383C2×C4—3021no—
384C2×C4—3021no—
385C2×C4—3021no—
386C2×C4—3021no—
387C2×C4—3021no—
388C2×C4—3021no—
389C2×C4—3021no—
390C2×C4—3021no—
391C2×C4—3021no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—6044no—
395C2×C4—6044no—
396C2×C4—6044no—
397C2×C4—1512no—
398C2×C4—1512no—
399C2×C4—1512no—
400C2×C4C2×C4×D15112yes—
401C2×C4C2×C22⋊D15112yes—
402C2×C4C2×C22⋊D15112yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—3022no—
417C22—3022no—
418C22—3022no—
419C22—6041no—
420C22—6041no—
421C22—6041no—
422C22—6041no—
423C22C4×C22⋊D15114yes—
424C22C22×C4×D15111yescharacteristic
425C22C22×C22⋊D15111yescharacteristic
426C22C2×#1455900411yescharacteristic
427C22#1801278411yescharacteristic
428C22#1801278411yescharacteristic
429C22#1801278511yescharacteristic
430C22#1801278611yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—3022no—
437C4—3022no—
438C4—3022no—
439C4—6041no—
440C4—6041no—
441C4—6041no—
442C4—6041no—
443C2—24no—
444C2—42no—
445C2—6042no—
446C2C2×C4×C22⋊D15111yescharacteristic
447C2#2375268411yescharacteristic
448C2#2375269111yescharacteristic
449C2#2375277111yescharacteristic
450C2#2375279011yescharacteristic
451C2#2375279511yescharacteristic
452C2#2375280411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
FittingC2×C4×D4×C151C2
socle, cosocleC23×C151C24
prime radicalC2×#18012711C2
hypercenterC2×C4×D4D151
hypocenterC151#2325
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D151C2semidirect
3. #23752103C2semidirect
4. #23752100C2semidirect
5. #23752096C2semidirect
6. #23752093C2semidirect
7. #23752092C2semidirect
8. #23752091C2semidirect
9. #23752089C2semidirect
10. #23752088C2semidirect
11. #23752085C2semidirect
12. #23752083C2semidirect
13. #23752070C2semidirect
14. C2×C151⋊#95C2semidirect
15. C2×C4×D4×C151C2semidirect
21. #18012711C4semidirect
59. C2×C22⋊D151C2×C4semidirect
60. C2×C22⋊D151C2×C4semidirect
66. C22×Dic151C2×C4semidirect
80. Dic151⋊C4C2×C4semidirect
84. C22⋊Dic151C2×C4semidirect
88. (C2×D151)⋊C4C2×C4semidirect
94. C2×D4×C151C2×C4semidirect
100. C22×C4×C151D4semidirect
226. C151#2325semidirect
230. C2×C4×D4D151semidirect
292. C2×D4C4×D151semidirect
314. C22×C4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127112
C2×C4×C22⋊D1512
#237521032
#237521002
#237520962
#237520932
#237520922
#237520912
#237520892
#237520882
#237520852
#237520832
#237520702
C2×C151⋊#952
C2×C4×D4×C1512
#2325151