Finite Group Databasebeta

← C2×#1661×C151 #50323906

Subgroups — C2×#1661×C151 #50323906

Order 38656.

1022 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#562×C151C211yesmaximal, characteristic
2C2×#501×C151C211yesmaximal, characteristic, complemented
3C2×#497×C151C211yesmaximal, characteristic, complemented
4C2×#489×C151C211yesmaximal, characteristic, complemented
5#1661×C151C218yesmaximal, direct product factor
6C2×#330×C151C211yesmaximal, characteristic, complemented
7C2×#329×C151C211yesmaximal, characteristic, complemented
8C2×#329×C151C211yesmaximal, characteristic, complemented
9C22×Q16×C151—21no—
10C22×SD16×C151—21no—
11#562×C151—22no—
12#562×C151—22no—
13#562×C151—22no—
14#562×C151C2214yes—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151C2211yescharacteristic
17C2×#124×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×#123×C151—21no—
20C2×#123×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C22⋊Q8×C151—21no—
23C2×#121×C151—21no—
24C2×#121×C151—21no—
25#501×C151—22no—
26#501×C151C2214yescomplemented
27#497×C151—22no—
28#497×C151C2214yescomplemented
29#489×C151—22no—
30#489×C151C2214yescomplemented
31C2×#107×C151—21no—
32C2×#106×C151—21no—
33C2×#103×C151—21no—
34C2×#102×C151—21no—
35C2×#97×C151C2211yescharacteristic
36C2×#97×C151C2211yescharacteristic
37C2×#97×C151C2211yescharacteristic
38#330×C151C2214yescomplemented
39#329×C151C2214yescomplemented
40#329×C151C2214yescomplemented
41C22×Q8×C151—21no—
42C22×Q8×C151D411yescharacteristic
43C22×Q8×C151D411yescharacteristic
44C22×D4×C151—21no—
45C22×D4×C151—21no—
46C22×D4×C151D411yescharacteristic
47C22×D4×C151D411yescharacteristic
48C23×C4×C151—21no—
49C23×C4×C151—21no—
50C2×Q16×C151—24no—
51C2×Q16×C151—44no—
52C2×SD16×C151—24no—
53C2×SD16×C151—44no—
54C22×C8×C151—21no—
55C22×C8×C151—21no—
56C22×C8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151C2312yes—
61#125×C151—21no—
62#125×C151—21no—
63#125×C151D412yes—
64#125×C151C2312yes—
65#124×C151—21no—
66#124×C151—21no—
67#124×C151—21no—
68#124×C151—21no—
69#124×C151D412yes—
70#124×C151D412yes—
71#124×C151C2312yes—
72#124×C151C2312yes—
73#123×C151—24no—
74#123×C151—24no—
75#123×C151—24no—
76#123×C151—24no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—24no—
81#121×C151—24no—
82#121×C151—24no—
83#121×C151—24no—
84#121×C151—24no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C42×C151C2311yescharacteristic
100#107×C151—24no—
101#106×C151—24no—
102#103×C151—24no—
103#102×C151—24no—
104#97×C151—21no—
105#97×C151—21no—
106#97×C151—21no—
107#97×C151C2312yes—
108#97×C151C2312yes—
109#97×C151C2312yes—
110C24×C151—21no—
111C24×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—42no—
116C2×Q8×C151—42no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151—41no—
120C2×Q8×C151C2×D412yes—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—24no—
123C2×D4×C151—24no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—42no—
127C2×D4×C151—42no—
128C2×D4×C151—82no—
129C2×D4×C151—82no—
130C2×D4×C151C2×D412yes—
131C2×D4×C151C2×D412yes—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—24no—
137C22×C4×C151—24no—
138C22×C4×C151—41no—
139C22×C4×C151—82no—
140C22×C4×C151—82no—
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144Q16×C151—48no—
145SD16×C151—48no—
146C2×C8×C151—24no—
147C2×C8×C151—24no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—42no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—41no—
163C4⋊C4×C151—41no—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151C2×D412yes—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—22no—
175C22⋊C4×C151—22no—
176C42×C151C2×D411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2411yescharacteristic
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151#12011yescharacteristic
189Q8×C151—42no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151—42no—
193Q8×C151—81no—
194Q8×C151—81no—
195Q8×C151—82no—
196D4×C151—42no—
197D4×C151—42no—
198D4×C151—81no—
199D4×C151—81no—
200D4×C151—84no—
201D4×C151—84no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—84no—
215C2×C4×C151—84no—
216C2×C4×C151—82no—
217C2×C4×C151#12011yescharacteristic
218C2×C4×C151#12011yescharacteristic
219C2×C4×C151#12011yescharacteristic
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C8×C151—24no—
224C8×C151—24no—
225C8×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—84no—
233C22×C151—84no—
234C22×C151#45312yes—
235C22×C151#45512yes—
236C22×C151#45612yes—
237C22×C151C2×#12011yescharacteristic
238C4×C151—21no—
239C4×C151—21no—
240C4×C151—21no—
241C4×C151—21no—
242C4×C151—21no—
243C4×C151—21no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—82no—
249C2×C151—82no—
250C2×C151—82no—
251C2×C151#166114yesdirect product factor
252C2×C151C2×#45311yescharacteristic
253C2×C151C2×#45511yescharacteristic
254C2×C151C2×#45611yescharacteristic
255C2×#1661C15111yesmaximal, characteristic, direct product factor, Sylow
256C151C2×#166111yescharacteristic, direct product factor, Sylow
257C2×#562C2×C15111yescharacteristic
258C2×#501C2×C15111yescharacteristic, complemented
259C2×#497C2×C15111yescharacteristic, complemented
260C2×#489C2×C15111yescharacteristic, complemented
261#1661C2×C15118yesdirect product factor
262C2×#330C2×C15111yescharacteristic, complemented
263C2×#329C2×C15111yescharacteristic, complemented
264C2×#329C2×C15111yescharacteristic, complemented
265C22×Q16—21no—
266C22×SD16—21no—
267#562—22no—
268#562—22no—
269#562—22no—
270#562C22×C15114yes—
271C2×C4⋊Q8C22×C15111yescharacteristic
272C2×#125C22×C15111yescharacteristic
273C2×#124C22×C15111yescharacteristic
274C2×#124C22×C15111yescharacteristic
275C2×#123—21no—
276C2×#123—21no—
277C2×C22⋊Q8—21no—
278C2×C22⋊Q8—21no—
279C2×#121—21no—
280C2×#121—21no—
281#501—22no—
282#501C22×C15114yescomplemented
283#497—22no—
284#497C22×C15114yescomplemented
285#489—22no—
286#489C22×C15114yescomplemented
287C2×#107—21no—
288C2×#106—21no—
289C2×#103—21no—
290C2×#102—21no—
291C2×#97C22×C15111yescharacteristic
292C2×#97C22×C15111yescharacteristic
293C2×#97C22×C15111yescharacteristic
294#330C22×C15114yescomplemented
295#329C22×C15114yescomplemented
296#329C22×C15114yescomplemented
297C22×Q8—21no—
298C22×Q8D4×C15111yescharacteristic
299C22×Q8D4×C15111yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4D4×C15111yescharacteristic
303C22×D4D4×C15111yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C2×Q16—24no—
307C2×Q16—44no—
308C2×SD16—24no—
309C2×SD16—44no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8C23×C15112yes—
317#125—21no—
318#125—21no—
319#125D4×C15112yes—
320#125C23×C15112yes—
321#124—21no—
322#124—21no—
323#124—21no—
324#124—21no—
325#124D4×C15112yes—
326#124D4×C15112yes—
327#124C23×C15112yes—
328#124C23×C15112yes—
329#123—24no—
330#123—24no—
331#123—24no—
332#123—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C15111yescharacteristic
348C2×C4⋊C4D4×C15111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42C23×C15111yescharacteristic
356#107—24no—
357#106—24no—
358#103—24no—
359#102—24no—
360#97—21no—
361#97—21no—
362#97—21no—
363#97C23×C15112yes—
364#97C23×C15112yes—
365#97C23×C15112yes—
366C24—21no—
367C24—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8—42no—
375C2×Q8—41no—
376C2×Q8C2×D4×C15112yes—
377C2×Q8C2×D4×C15112yes—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—82no—
385C2×D4—82no—
386C2×D4C2×D4×C15112yes—
387C2×D4C2×D4×C15112yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—41no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400Q16—48no—
401SD16—48no—
402C2×C8—24no—
403C2×C8—24no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—42no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4C2×D4×C15112yes—
421C4⋊C4C2×D4×C15112yes—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C42C2×D4×C15111yescharacteristic
433C42C2×D4×C15111yescharacteristic
434C42C2×D4×C15111yescharacteristic
435C42C24×C15111yescharacteristic
436C23—22no—
437C23—22no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23#120×C15111yescharacteristic
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—42no—
449Q8—81no—
450Q8—81no—
451Q8—82no—
452D4—42no—
453D4—42no—
454D4—81no—
455D4—81no—
456D4—84no—
457D4—84no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4—84no—
472C2×C4—82no—
473C2×C4#120×C15111yescharacteristic
474C2×C4#120×C15111yescharacteristic
475C2×C4#120×C15111yescharacteristic
476C2×C4C22×D4×C15111yescharacteristic
477C2×C4C22×D4×C15111yescharacteristic
478C2×C4C22×D4×C15111yescharacteristic
479C8—24no—
480C8—24no—
481C8—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22—84no—
490C22#453×C15112yes—
491C22#455×C15112yes—
492C22#456×C15112yes—
493C22C2×#120×C15111yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—82no—
505C2—82no—
506C2—82no—
507C2#1661×C15114yesdirect product factor
508C2C2×#453×C15111yescharacteristic
509C2C2×#455×C15111yescharacteristic
510C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#562×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#501×C151C2semidirect
3. C2×#497×C151C2semidirect
4. C2×#489×C151C2semidirect
5. #1661×C151C2direct (N × H)
6. C2×#330×C151C2semidirect
7. C2×#329×C151C2semidirect
8. C2×#329×C151C2semidirect
26. #501×C151C22semidirect
28. #497×C151C22semidirect
30. #489×C151C22semidirect
38. #330×C151C22semidirect
39. #329×C151C22semidirect
40. #329×C151C22semidirect
251. C2×C151#1661direct (N × H)
255. C2×#1661C151direct (N × H)
256. C151C2×#1661direct (N × H)
258. C2×#501C2×C151semidirect
259. C2×#497C2×C151semidirect
260. C2×#489C2×C151semidirect
261. #1661C2×C151direct (N × H)
262. C2×#330C2×C151semidirect
263. C2×#329C2×C151semidirect
264. C2×#329C2×C151semidirect
282. #501C22×C151semidirect
284. #497C22×C151semidirect
286. #489C22×C151semidirect
294. #330C22×C151semidirect
295. #329C22×C151semidirect
296. #329C22×C151semidirect
507. C2#1661×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#562×C1512
C2×#501×C1512
C2×#497×C1512
C2×#489×C1512
#1661×C1512
C2×#330×C1512
C2×#329×C1512
C2×#1661151