Finite Group Databasebeta

← #2703×C151 #34066035

Subgroups — #2703×C151 #34066035

Order 19328.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C151C211yesmaximal, characteristic, complemented
2C2×#121×C151C211yesmaximal, characteristic, complemented
3#400×C151C211yesmaximal, characteristic, complemented
4#397×C151C211yesmaximal, characteristic, complemented
5#394×C151C211yesmaximal, characteristic, complemented
6#392×C151C211yesmaximal, characteristic, complemented
7#392×C151C211yesmaximal, characteristic, complemented
8#392×C151C211yesmaximal, characteristic, complemented
9#390×C151C211yesmaximal, characteristic, complemented
10#388×C151C211yesmaximal, characteristic, complemented
11#388×C151C211yesmaximal, characteristic, complemented
12#386×C151C211yesmaximal, characteristic, complemented
13#386×C151C211yesmaximal, characteristic, complemented
14#386×C151C211yesmaximal, characteristic, complemented
15#380×C151C211yesmaximal, characteristic, complemented
16C22×D4×C151C2211yescharacteristic
17C22×D4×C151C2211yescharacteristic
18C22×D4×C151C2211yescharacteristic
19C22×D4×C151C2211yescharacteristic
20C22×D4×C151C2211yescharacteristic
21C22×D4×C151C2211yescharacteristic
22C23×C4×C151C2211yescharacteristic
23C23×C4×C151C2211yescharacteristic
24#123×C151—24no—
25#121×C151—24no—
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30C2×C22⋊C4×C151C2211yescharacteristic
31C2×C22⋊C4×C151C2211yescharacteristic
32C2×C22⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2211yescharacteristic
36C2×C22⋊C4×C151C2211yescharacteristic
37C2×C22⋊C4×C151C2211yescharacteristic
38C2×C22⋊C4×C151C2211yescharacteristic
39C2×C22⋊C4×C151C2211yescharacteristic
40C2×C22⋊C4×C151C2211yescharacteristic
41C2×C22⋊C4×C151C2211yescharacteristic
42C2×C22⋊C4×C151C2211yescharacteristic
43C2×C22⋊C4×C151C2211yescharacteristic
44C2×C42×C151C2211yescharacteristic
45#95×C151C2211yescharacteristic
46#95×C151C2211yescharacteristic
47#95×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C24×C151C2311yescharacteristic
54C24×C151C2311yescharacteristic
55C24×C151C2311yescharacteristic
56C24×C151C2311yescharacteristic
57C2×D4×C151—22no—
58C2×D4×C151—22no—
59C2×D4×C151—22no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—22no—
63C2×D4×C151—22no—
64C2×D4×C151—22no—
65C2×D4×C151—41no—
66C2×D4×C151—41no—
67C2×D4×C151—41no—
68C2×D4×C151—41no—
69C2×D4×C151—41no—
70C2×D4×C151—41no—
71C2×D4×C151—41no—
72C2×D4×C151—41no—
73C2×D4×C151—41no—
74C2×D4×C151—41no—
75C22×C4×C151—22no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151—41no—
79C22×C4×C151—41no—
80C22×C4×C151—41no—
81C22×C4×C151C2311yescharacteristic
82C22×C4×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C4⋊C4×C151—22no—
93C4⋊C4×C151—22no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—41no—
96C22⋊C4×C151—22no—
97C22⋊C4×C151—22no—
98C22⋊C4×C151—22no—
99C22⋊C4×C151—22no—
100C22⋊C4×C151—41no—
101C22⋊C4×C151—41no—
102C22⋊C4×C151—41no—
103C22⋊C4×C151—41no—
104C22⋊C4×C151—41no—
105C22⋊C4×C151—41no—
106C22⋊C4×C151—41no—
107C22⋊C4×C151—41no—
108C22⋊C4×C151—41no—
109C22⋊C4×C151D414yescomplemented
110C42×C151—41no—
111C23×C151—21no—
112C23×C151—21no—
113C23×C151—21no—
114C23×C151—21no—
115C23×C151—21no—
116C23×C151—21no—
117C23×C151—21no—
118C23×C151—21no—
119C23×C151—21no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151—21no—
123C23×C151—21no—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151—21no—
136C23×C151—21no—
137C23×C151C2×D412yes—
138C23×C151#4112yes—
139C23×C151C2411yescharacteristic
140D4×C151—44no—
141D4×C151—44no—
142D4×C151—44no—
143D4×C151—44no—
144D4×C151—44no—
145D4×C151—44no—
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—
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—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—44no—
177C2×C4×C151—44no—
178C2×C4×C151C2×D412yes—
179C2×C4×C151C2×D412yes—
180C2×C4×C151#4112yes—
181C22×C151—22no—
182C22×C151—22no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—22no—
186C22×C151—22no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—41no—
193C22×C151—41no—
194C22×C151—41no—
195C22×C151—41no—
196C22×C151—41no—
197C22×C151—41no—
198C22×C151—41no—
199C22×C151—41no—
200C22×C151—41no—
201C22×C151—41no—
202C22×C151—41no—
203C22×C151—41no—
204C22×C151—41no—
205C22×C151—41no—
206C22×C151—41no—
207C22×C151—41no—
208C22×C151—41no—
209C22×C151C22×D411yescharacteristic
210C22×C151C2×#4111yescharacteristic
211C22×C151C2×#4111yescharacteristic
212C22×C151H(5,𝔽2)11yescharacteristic
213C22×C151H(5,𝔽2)11yescharacteristic
214C22×C151H(5,𝔽2)11yescharacteristic
215C22×C151H(5,𝔽2)11yescharacteristic
216C4×C151—22no—
217C4×C151—22no—
218C4×C151—22no—
219C4×C151—41no—
220C4×C151—41no—
221C4×C151—41no—
222C4×C151—41no—
223C4×C151—41no—
224C4×C151—41no—
225C4×C151—41no—
226C4×C151—41no—
227C2×C151—42no—
228C2×C151—42no—
229C2×C151—81no—
230C2×C151—81no—
231C2×C151#53511yescharacteristic
232C2×C151#53811yescharacteristic
233C2×C151#54011yescharacteristic
234C2×C151#54611yescharacteristic
235C2×C151#54611yescharacteristic
236C2×C151#55311yescharacteristic
237C2×C151#56011yescharacteristic
238C151#270311yescharacteristic, direct product factor, Sylow
239#2703C15111yesmaximal, characteristic, direct product factor, Sylow
240C2×#123C2×C15111yescharacteristic, complemented
241C2×#121C2×C15111yescharacteristic, complemented
242#400C2×C15111yescharacteristic, complemented
243#397C2×C15111yescharacteristic, complemented
244#394C2×C15111yescharacteristic, complemented
245#392C2×C15111yescharacteristic, complemented
246#392C2×C15111yescharacteristic, complemented
247#392C2×C15111yescharacteristic, complemented
248#390C2×C15111yescharacteristic, complemented
249#388C2×C15111yescharacteristic, complemented
250#388C2×C15111yescharacteristic, complemented
251#386C2×C15111yescharacteristic, complemented
252#386C2×C15111yescharacteristic, complemented
253#386C2×C15111yescharacteristic, complemented
254#380C2×C15111yescharacteristic, complemented
255C22×D4C22×C15111yescharacteristic
256C22×D4C22×C15111yescharacteristic
257C22×D4C22×C15111yescharacteristic
258C22×D4C22×C15111yescharacteristic
259C22×D4C22×C15111yescharacteristic
260C22×D4C22×C15111yescharacteristic
261C23×C4C22×C15111yescharacteristic
262C23×C4C22×C15111yescharacteristic
263#123—24no—
264#121—24no—
265C2×C4⋊C4C22×C15111yescharacteristic
266C2×C4⋊C4C22×C15111yescharacteristic
267C2×C4⋊C4C22×C15111yescharacteristic
268C2×C4⋊C4C22×C15111yescharacteristic
269C2×C22⋊C4C22×C15111yescharacteristic
270C2×C22⋊C4C22×C15111yescharacteristic
271C2×C22⋊C4C22×C15111yescharacteristic
272C2×C22⋊C4C22×C15111yescharacteristic
273C2×C22⋊C4C22×C15111yescharacteristic
274C2×C22⋊C4C22×C15111yescharacteristic
275C2×C22⋊C4C22×C15111yescharacteristic
276C2×C22⋊C4C22×C15111yescharacteristic
277C2×C22⋊C4C22×C15111yescharacteristic
278C2×C22⋊C4C22×C15111yescharacteristic
279C2×C22⋊C4C22×C15111yescharacteristic
280C2×C22⋊C4C22×C15111yescharacteristic
281C2×C22⋊C4C22×C15111yescharacteristic
282C2×C22⋊C4C22×C15111yescharacteristic
283C2×C42C22×C15111yescharacteristic
284#95C22×C15111yescharacteristic
285#95C22×C15111yescharacteristic
286#95C22×C15111yescharacteristic
287#95C22×C15111yescharacteristic
288#95C22×C15111yescharacteristic
289#95C22×C15111yescharacteristic
290#95C22×C15111yescharacteristic
291#95C22×C15111yescharacteristic
292C24C23×C15111yescharacteristic
293C24C23×C15111yescharacteristic
294C24C23×C15111yescharacteristic
295C24C23×C15111yescharacteristic
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C23×C15111yescharacteristic
321C22×C4C23×C15111yescharacteristic
322C22×C4C23×C15111yescharacteristic
323C22×C4C23×C15111yescharacteristic
324C22×C4C23×C15111yescharacteristic
325C22×C4C23×C15111yescharacteristic
326C22×C4C23×C15111yescharacteristic
327C22×C4C23×C15111yescharacteristic
328C22×C4C23×C15111yescharacteristic
329C22×C4C23×C15111yescharacteristic
330C22×C4C23×C15111yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4D4×C15114yescomplemented
349C42—41no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23C2×D4×C15112yes—
377C23#41×C15112yes—
378C23C24×C15111yescharacteristic
379D4—44no—
380D4—44no—
381D4—44no—
382D4—44no—
383D4—44no—
384D4—44no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4C2×D4×C15112yes—
418C2×C4C2×D4×C15112yes—
419C2×C4#41×C15112yes—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22C22×D4×C15111yescharacteristic
449C22C2×#41×C15111yescharacteristic
450C22C2×#41×C15111yescharacteristic
451C22H(5,𝔽2)×C15111yescharacteristic
452C22H(5,𝔽2)×C15111yescharacteristic
453C22H(5,𝔽2)×C15111yescharacteristic
454C22H(5,𝔽2)×C15111yescharacteristic
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C2—42no—
467C2—42no—
468C2—81no—
469C2—81no—
470C2#535×C15111yescharacteristic
471C2#538×C15111yescharacteristic
472C2#540×C15111yescharacteristic
473C2#546×C15111yescharacteristic
474C2#546×C15111yescharacteristic
475C2#553×C15111yescharacteristic
476C2#560×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#123×C151C2semidirect
2. C2×#121×C151C2semidirect
3. #400×C151C2semidirect
4. #397×C151C2semidirect
5. #394×C151C2semidirect
6. #392×C151C2semidirect
7. #392×C151C2semidirect
8. #392×C151C2semidirect
9. #390×C151C2semidirect
10. #388×C151C2semidirect
11. #388×C151C2semidirect
12. #386×C151C2semidirect
13. #386×C151C2semidirect
14. #386×C151C2semidirect
15. #380×C151C2semidirect
109. C22⋊C4×C151D4semidirect
238. C151#2703direct (N × H)
239. #2703C151direct (N × H)
240. C2×#123C2×C151semidirect
241. C2×#121C2×C151semidirect
242. #400C2×C151semidirect
243. #397C2×C151semidirect
244. #394C2×C151semidirect
245. #392C2×C151semidirect
246. #392C2×C151semidirect
247. #392C2×C151semidirect
248. #390C2×C151semidirect
249. #388C2×C151semidirect
250. #388C2×C151semidirect
251. #386C2×C151semidirect
252. #386C2×C151semidirect
253. #386C2×C151semidirect
254. #380C2×C151semidirect
348. C22⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1512
C2×#121×C1512
#400×C1512
#397×C1512
#394×C1512
#392×C1512
#390×C1512
#388×C1512
#386×C1512
#380×C1512
#2703151