Finite Group Databasebeta

← C151×#18079 #50323004

Subgroups — C151×#18079 #50323004

Order 38656.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3172×C151C211yesmaximal, characteristic
2#2969×C151C211yesmaximal, characteristic
3#2962×C151C211yesmaximal, characteristic, complemented
4#1593×C151C211yesmaximal, characteristic, complemented
5#1590×C151C211yesmaximal, characteristic, complemented
6#1587×C151C211yesmaximal, characteristic, complemented
7#1585×C151C211yesmaximal, characteristic, complemented
8#1584×C151C211yesmaximal, characteristic, complemented
9#1583×C151C211yesmaximal, characteristic, complemented
10SD16⋊C8×C151C211yesmaximal, characteristic, complemented
11C8×Q16×C151C211yesmaximal, characteristic, complemented
12#1565×C151C211yesmaximal, characteristic, complemented
13#1485×C151C211yesmaximal, characteristic, complemented
14#1483×C151C211yesmaximal, characteristic
15#1455×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#529×C151C2211yescharacteristic
18#501×C151C411yescharacteristic
19#497×C151C411yescharacteristic
20#491×C151C411yescharacteristic
21#489×C151C411yescharacteristic
22#470×C151C411yescharacteristic
23#470×C151C411yescharacteristic
24#468×C151C411yescharacteristic
25#468×C151C411yescharacteristic
26#446×C151—21no—
27#446×C151—21no—
28#446×C151C2211yescharacteristic
29#446×C151C2211yescharacteristic
30#446×C151C2211yescharacteristic
31C8×Q8×C151C2211yescharacteristic
32C8×Q8×C151C2211yescharacteristic
33C8×Q8×C151C2211yescharacteristic
34C4×Q16×C151C2211yescharacteristic
35C4×Q16×C151C2211yescharacteristic
36C4×SD16×C151C2211yescharacteristic
37C4×SD16×C151C2211yescharacteristic
38#436×C151—21no—
39#436×C151C2211yescharacteristic
40#435×C151—21no—
41C8×D4×C151C2211yescharacteristic
42#433×C151—21no—
43#431×C151C2211yescharacteristic
44#424×C151—21no—
45C2×C4⋊C8×C151C2211yescharacteristic
46#405×C151—21no—
47#405×C151—21no—
48C4×M16×C151C2211yescharacteristic
49C4×M16×C151C2211yescharacteristic
50C4×M16×C151C2211yescharacteristic
51#335×C151C2211yescharacteristic
52#335×C151C2211yescharacteristic
53#334×C151C2211yescharacteristic
54#334×C151C2211yescharacteristic
55Q8⋊C8×C151C2211yescharacteristic
56Q8⋊C8×C151C2211yescharacteristic
57Q8⋊C8×C151C2211yescharacteristic
58Q8⋊C8×C151C2211yescharacteristic
59Q8⋊C8×C151C2211yescharacteristic
60Q8⋊C8×C151C2211yescharacteristic
61D4⋊C8×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63#322×C151C2211yescharacteristic
64#322×C151C2211yescharacteristic
65#322×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×Q16×C151C2×C411yescharacteristic
68C2×Q16×C151C2×C411yescharacteristic
69C2×SD16×C151C2×C411yescharacteristic
70C2×SD16×C151C2×C411yescharacteristic
71C2×M16×C151—21no—
72C2×M16×C151—21no—
73C2×M16×C151C2×C411yescharacteristic
74C2×M16×C151C2×C411yescharacteristic
75C2×M16×C151D411yescharacteristic
76C2×M16×C151D411yescharacteristic
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C4⋊Q8×C151C2×C411yescharacteristic
80C4⋊Q8×C151C2×C411yescharacteristic
81#126×C151—21no—
82#125×C151—21no—
83#125×C151C2×C411yescharacteristic
84#124×C151C2×C411yescharacteristic
85#123×C151—21no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151C2×C411yescharacteristic
88C22⋊Q8×C151C2×C411yescharacteristic
89C22⋊Q8×C151C2×C411yescharacteristic
90#121×C151C2×C411yescharacteristic
91C4×Q8×C151—21no—
92C4×Q8×C151C2311yescharacteristic
93C4×Q8×C151C2311yescharacteristic
94C4×Q8×C151C2311yescharacteristic
95C4×D4×C151—21no—
96C4×D4×C151C2311yescharacteristic
97#117×C151—21no—
98#117×C151—21no—
99C2×C42×C151C2311yescharacteristic
100#107×C151C2×C411yescharacteristic
101#107×C151C2×C411yescharacteristic
102#106×C151C2×C411yescharacteristic
103#106×C151C2×C411yescharacteristic
104C4⋊C8×C151—21no—
105C4⋊C8×C151—21no—
106C4⋊C8×C151—21no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151—21no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151C2311yescharacteristic
112C4⋊C8×C151C2311yescharacteristic
113C4⋊C8×C151C2311yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115#103×C151C2×C411yescharacteristic
116#103×C151C2×C411yescharacteristic
117#103×C151C2×C411yescharacteristic
118#103×C151C2×C411yescharacteristic
119#103×C151C2×C411yescharacteristic
120#103×C151C2×C411yescharacteristic
121#102×C151C2×C411yescharacteristic
122#102×C151C2×C411yescharacteristic
123C22⋊C8×C151—21no—
124C22⋊C8×C151—21no—
125C22⋊C8×C151—21no—
126#97×C151—21no—
127#97×C151—21no—
128#97×C151—21no—
129#97×C151—21no—
130#97×C151C2×C411yescharacteristic
131#97×C151C2×C411yescharacteristic
132#97×C151D411yescharacteristic
133#97×C151D411yescharacteristic
134C4×C8×C151—21no—
135C4×C8×C151—21no—
136C4×C8×C151—21no—
137C4×C8×C151—21no—
138C4×C8×C151C2311yescharacteristic
139C4×C8×C151C2311yescharacteristic
140C4×C8×C151C2311yescharacteristic
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151C22×C411yescharacteristic
146C2×Q8×C151C22×C411yescharacteristic
147C2×Q8×C151C22×C411yescharacteristic
148C2×D4×C151—21no—
149C2×D4×C151C22×C411yescharacteristic
150C22×C4×C151—21no—
151C22×C4×C151C22×C411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151#4111yescharacteristic
154Q16×C151—22no—
155Q16×C151—41no—
156SD16×C151—22no—
157SD16×C151—41no—
158M16×C151—22no—
159M16×C151—22no—
160M16×C151—41no—
161M16×C151—41no—
162M16×C151—42no—
163M16×C151—42no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—42no—
171C2×C8×C151—42no—
172C2×C8×C151C22×C411yescharacteristic
173C2×C8×C151C22×C411yescharacteristic
174C2×C8×C151C22×C411yescharacteristic
175C2×C8×C151C22×C411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151C22×C411yescharacteristic
192C4⋊C4×C151C22×C411yescharacteristic
193C4⋊C4×C151C22×C411yescharacteristic
194C4⋊C4×C151C22×C411yescharacteristic
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151C22×C411yescharacteristic
206C42×C151C2×D411yescharacteristic
207C42×C151#4111yescharacteristic
208C42×C151C2411yescharacteristic
209C23×C151—21no—
210C23×C151C4×D411yescharacteristic
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—21no—
215Q8×C151—21no—
216Q8×C151—21no—
217Q8×C151—81no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151—81no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151C4×D411yescharacteristic
236C2×C4×C151C4×D411yescharacteristic
237C2×C4×C151C4×D411yescharacteristic
238C2×C4×C151C23×C411yescharacteristic
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C2×#4111yescharacteristic
241C8×C151—22no—
242C8×C151—21no—
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151#13112yes—
254C8×C151#13712yes—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—21no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151C2×C4×D411yescharacteristic
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—21no—
265C4×C151—21no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—41no—
273C4×C151C2×#13111yescharacteristic
274C4×C151#56811yescharacteristic
275C4×C151C2×#13711yescharacteristic
276C4×C151#57511yescharacteristic
277C2×C151—41no—
278C2×C151—81no—
279C2×C151#293511yescharacteristic
280C2×C151C4×#13711yescharacteristic
281C2×C151#295611yescharacteristic
282#18079C15111yesmaximal, characteristic, direct product factor, Sylow
283C151#1807911yescharacteristic, direct product factor, Sylow
284#3172C2×C15111yescharacteristic
285#2969C2×C15111yescharacteristic
286#2962C2×C15111yescharacteristic, complemented
287#1593C2×C15111yescharacteristic, complemented
288#1590C2×C15111yescharacteristic, complemented
289#1587C2×C15111yescharacteristic, complemented
290#1585C2×C15111yescharacteristic, complemented
291#1584C2×C15111yescharacteristic, complemented
292#1583C2×C15111yescharacteristic, complemented
293SD16⋊C8C2×C15111yescharacteristic, complemented
294C8×Q16C2×C15111yescharacteristic, complemented
295#1565C2×C15111yescharacteristic, complemented
296#1485C2×C15111yescharacteristic, complemented
297#1483C2×C15111yescharacteristic
298#1455C2×C15111yescharacteristic, complemented
299#533C22×C15111yescharacteristic
300#529C22×C15111yescharacteristic
301#501C4×C15111yescharacteristic
302#497C4×C15111yescharacteristic
303#491C4×C15111yescharacteristic
304#489C4×C15111yescharacteristic
305#470C4×C15111yescharacteristic
306#470C4×C15111yescharacteristic
307#468C4×C15111yescharacteristic
308#468C4×C15111yescharacteristic
309#446—21no—
310#446—21no—
311#446C22×C15111yescharacteristic
312#446C22×C15111yescharacteristic
313#446C22×C15111yescharacteristic
314C8×Q8C22×C15111yescharacteristic
315C8×Q8C22×C15111yescharacteristic
316C8×Q8C22×C15111yescharacteristic
317C4×Q16C22×C15111yescharacteristic
318C4×Q16C22×C15111yescharacteristic
319C4×SD16C22×C15111yescharacteristic
320C4×SD16C22×C15111yescharacteristic
321#436—21no—
322#436C22×C15111yescharacteristic
323#435—21no—
324C8×D4C22×C15111yescharacteristic
325#433—21no—
326#431C22×C15111yescharacteristic
327#424—21no—
328C2×C4⋊C8C22×C15111yescharacteristic
329#405—21no—
330#405—21no—
331C4×M16C22×C15111yescharacteristic
332C4×M16C22×C15111yescharacteristic
333C4×M16C22×C15111yescharacteristic
334#335C22×C15111yescharacteristic
335#335C22×C15111yescharacteristic
336#334C22×C15111yescharacteristic
337#334C22×C15111yescharacteristic
338Q8⋊C8C22×C15111yescharacteristic
339Q8⋊C8C22×C15111yescharacteristic
340Q8⋊C8C22×C15111yescharacteristic
341Q8⋊C8C22×C15111yescharacteristic
342Q8⋊C8C22×C15111yescharacteristic
343Q8⋊C8C22×C15111yescharacteristic
344D4⋊C8C22×C15111yescharacteristic
345D4⋊C8C22×C15111yescharacteristic
346#322C22×C15111yescharacteristic
347#322C22×C15111yescharacteristic
348#322C22×C15111yescharacteristic
349C82C22×C15111yescharacteristic
350C2×Q16C2×C4×C15111yescharacteristic
351C2×Q16C2×C4×C15111yescharacteristic
352C2×SD16C2×C4×C15111yescharacteristic
353C2×SD16C2×C4×C15111yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16C2×C4×C15111yescharacteristic
357C2×M16C2×C4×C15111yescharacteristic
358C2×M16D4×C15111yescharacteristic
359C2×M16D4×C15111yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C4⋊Q8C2×C4×C15111yescharacteristic
363C4⋊Q8C2×C4×C15111yescharacteristic
364#126—21no—
365#125—21no—
366#125C2×C4×C15111yescharacteristic
367#124C2×C4×C15111yescharacteristic
368#123—21no—
369C22⋊Q8—21no—
370C22⋊Q8C2×C4×C15111yescharacteristic
371C22⋊Q8C2×C4×C15111yescharacteristic
372C22⋊Q8C2×C4×C15111yescharacteristic
373#121C2×C4×C15111yescharacteristic
374C4×Q8—21no—
375C4×Q8C23×C15111yescharacteristic
376C4×Q8C23×C15111yescharacteristic
377C4×Q8C23×C15111yescharacteristic
378C4×D4—21no—
379C4×D4C23×C15111yescharacteristic
380#117—21no—
381#117—21no—
382C2×C42C23×C15111yescharacteristic
383#107C2×C4×C15111yescharacteristic
384#107C2×C4×C15111yescharacteristic
385#106C2×C4×C15111yescharacteristic
386#106C2×C4×C15111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398#103C2×C4×C15111yescharacteristic
399#103C2×C4×C15111yescharacteristic
400#103C2×C4×C15111yescharacteristic
401#103C2×C4×C15111yescharacteristic
402#103C2×C4×C15111yescharacteristic
403#103C2×C4×C15111yescharacteristic
404#102C2×C4×C15111yescharacteristic
405#102C2×C4×C15111yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409#97—21no—
410#97—21no—
411#97—21no—
412#97—21no—
413#97C2×C4×C15111yescharacteristic
414#97C2×C4×C15111yescharacteristic
415#97D4×C15111yescharacteristic
416#97D4×C15111yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C15111yescharacteristic
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C4×C8C23×C15111yescharacteristic
425C4×C8C23×C15111yescharacteristic
426C4×C8C23×C15111yescharacteristic
427C2×Q8—21no—
428C2×Q8C22×C4×C15111yescharacteristic
429C2×Q8C22×C4×C15111yescharacteristic
430C2×Q8C22×C4×C15111yescharacteristic
431C2×D4—21no—
432C2×D4C22×C4×C15111yescharacteristic
433C22×C4—21no—
434C22×C4C22×C4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4#41×C15111yescharacteristic
437Q16—22no—
438Q16—41no—
439SD16—22no—
440SD16—41no—
441M16—22no—
442M16—22no—
443M16—41no—
444M16—41no—
445M16—42no—
446M16—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8C22×C4×C15111yescharacteristic
456C2×C8C22×C4×C15111yescharacteristic
457C2×C8C22×C4×C15111yescharacteristic
458C2×C8C22×C4×C15111yescharacteristic
459C2×C8C2×D4×C15111yescharacteristic
460C2×C8C2×D4×C15111yescharacteristic
461C2×C8C2×D4×C15111yescharacteristic
462C2×C8C2×D4×C15111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×C4×C15111yescharacteristic
475C4⋊C4C22×C4×C15111yescharacteristic
476C4⋊C4C22×C4×C15111yescharacteristic
477C4⋊C4C22×C4×C15111yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42C22×C4×C15111yescharacteristic
489C42C2×D4×C15111yescharacteristic
490C42#41×C15111yescharacteristic
491C42C24×C15111yescharacteristic
492C23—21no—
493C23C4×D4×C15111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—81no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4C4×D4×C15111yescharacteristic
519C2×C4C4×D4×C15111yescharacteristic
520C2×C4C4×D4×C15111yescharacteristic
521C2×C4C23×C4×C15111yescharacteristic
522C2×C4C22×D4×C15111yescharacteristic
523C2×C4C2×#41×C15111yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8#131×C15112yes—
537C8#137×C15112yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×D4×C15111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4C2×#131×C15111yescharacteristic
557C4#568×C15111yescharacteristic
558C4C2×#137×C15111yescharacteristic
559C4#575×C15111yescharacteristic
560C2—41no—
561C2—81no—
562C2#2935×C15111yescharacteristic
563C2C4×#137×C15111yescharacteristic
564C2#2956×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
socleC22×C151C2×C4×D4
prime radical#121×C151C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C4×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2962×C151C2semidirect
4. #1593×C151C2semidirect
5. #1590×C151C2semidirect
6. #1587×C151C2semidirect
7. #1585×C151C2semidirect
8. #1584×C151C2semidirect
9. #1583×C151C2semidirect
10. SD16⋊C8×C151C2semidirect
11. C8×Q16×C151C2semidirect
12. #1565×C151C2semidirect
13. #1485×C151C2semidirect
15. #1455×C151C2semidirect
282. #18079C151direct (N × H)
283. C151#18079direct (N × H)
286. #2962C2×C151semidirect
287. #1593C2×C151semidirect
288. #1590C2×C151semidirect
289. #1587C2×C151semidirect
290. #1585C2×C151semidirect
291. #1584C2×C151semidirect
292. #1583C2×C151semidirect
293. SD16⋊C8C2×C151semidirect
294. C8×Q16C2×C151semidirect
295. #1565C2×C151semidirect
296. #1485C2×C151semidirect
298. #1455C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3172×C1512
#2969×C1512
#2962×C1512
#1593×C1512
#1590×C1512
#1587×C1512
#1585×C1512
#1584×C1512
#1583×C1512
SD16⋊C8×C1512
C8×Q16×C1512
#1565×C1512
#1485×C1512
#1483×C1512
#1455×C1512
#18079151