Finite Group Databasebeta

← C151×#17751 #50322676

Subgroups — C151×#17751 #50322676

Order 38656.

996 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C151C211yesmaximal, characteristic
2#2920×C151C211yesmaximal, characteristic
3C2×#423×C151C211yesmaximal, characteristic
4#1561×C151C214yesmaximal, complemented
5#1552×C151C214yesmaximal, complemented
6#1549×C151C212yesmaximal, complemented
7#1546×C151C212yesmaximal, complemented
8C22×M16×C151—21no—
9#533×C151—21no—
10#533×C151—21no—
11#533×C151—21no—
12#533×C151—21no—
13#533×C151C412yes—
14#533×C151C412yes—
15#533×C151C2212yes—
16#533×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#125×C151C412yes—
20C2×C22⋊Q8×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C4×Q8×C151—21no—
23C2×C4×Q8×C151—21no—
24C2×#117×C151C412yes—
25C22×C42×C151C2211yescharacteristic
26#432×C151—21no—
27#432×C151C2212yes—
28#431×C151—21no—
29#431×C151C2212yes—
30#423×C151—21no—
31#423×C151—21no—
32#423×C151C2212yes—
33#423×C151C2212yes—
34#423×C151C2212yes—
35C2×C4⋊C8×C151—21no—
36C2×C4⋊C8×C151C2212yes—
37#407×C151—21no—
38C4×M16×C151—21no—
39#332×C151C2218yescomplemented
40#332×C151C2218yescomplemented
41C22×Q8×C151—21no—
42C22×Q8×C151—21no—
43C23×C4×C151C2×C411yescharacteristic
44C23×C4×C151D411yescharacteristic
45C23×C4×C151D411yescharacteristic
46C2×M16×C151—22no—
47C2×M16×C151—22no—
48C2×M16×C151—22no—
49C2×M16×C151—44no—
50C22×C8×C151—22no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151C2×C412yes—
56C4⋊Q8×C151C2×C412yes—
57C4⋊Q8×C151C2312yes—
58C4⋊Q8×C151C2312yes—
59#125×C151—22no—
60#125×C151—22no—
61#125×C151C2×C414yes—
62#125×C151C2×C414yes—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—22no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×Q8×C151—22no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×Q8×C151—22no—
76C4×Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151C2×C414yes—
82#117×C151C2×C414yes—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151C2×C412yes—
88C2×C4⋊C4×C151C2×C412yes—
89C2×C22⋊C4×C151—22no—
90C2×C42×C151—22no—
91C2×C42×C151C2×C411yescharacteristic
92C2×C42×C151C2×C411yescharacteristic
93C2×C42×C151C2×C411yescharacteristic
94C2×C42×C151D411yescharacteristic
95C2×C42×C151D411yescharacteristic
96C2×C42×C151D411yescharacteristic
97C2×C42×C151D411yescharacteristic
98C2×C42×C151D411yescharacteristic
99C2×C42×C151D411yescharacteristic
100C2×C42×C151C2311yescharacteristic
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C4⋊C8×C151—22no—
104C4⋊C8×C151—22no—
105C4⋊C8×C151—22no—
106C4⋊C8×C151—22no—
107C4⋊C8×C151C2314yes—
108C4⋊C8×C151C2314yes—
109C22⋊C8×C151—22no—
110C22⋊C8×C151—22no—
111#97×C151—22no—
112C4×C8×C151—22no—
113C24×C151C22⋊C411yescharacteristic
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—44no—
119C2×Q8×C151—42no—
120C2×Q8×C151—42no—
121C22×C4×C151—24no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—42no—
127C22×C4×C151C22⋊C411yescharacteristic
128C22×C4×C151C22⋊C411yescharacteristic
129C22×C4×C151C22⋊C411yescharacteristic
130C22×C4×C151C22⋊C411yescharacteristic
131C22×C4×C151C22⋊C411yescharacteristic
132C22×C4×C151C22⋊C411yescharacteristic
133C22×C4×C151C22⋊C411yescharacteristic
134C22×C4×C151C22⋊C411yescharacteristic
135C22×C4×C151C22⋊C411yescharacteristic
136C22×C4×C151C22×C411yescharacteristic
137C22×C4×C151C22×C411yescharacteristic
138C22×C4×C151C22×C411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145M16×C151—44no—
146M16×C151—44no—
147M16×C151—44no—
148C2×C8×C151—24no—
149C2×C8×C151—24no—
150C2×C8×C151—44no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151C22×C414yes—
162C4⋊C4×C151C22×C414yes—
163C22⋊C4×C151—24no—
164C22⋊C4×C151—24no—
165C42×C151—24no—
166C42×C151—24no—
167C42×C151C22⋊C411yescharacteristic
168C42×C151C22⋊C411yescharacteristic
169C42×C151C22⋊C411yescharacteristic
170C42×C151C22⋊C411yescharacteristic
171C42×C151C22⋊C411yescharacteristic
172C42×C151C22⋊C411yescharacteristic
173C42×C151C22×C411yescharacteristic
174C42×C151C22×C411yescharacteristic
175C42×C151C22×C411yescharacteristic
176C42×C151C2×D411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2411yescharacteristic
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—41no—
186C23×C151C2×C22⋊C411yescharacteristic
187C23×C151C2×C22⋊C411yescharacteristic
188C23×C151C2×C22⋊C411yescharacteristic
189Q8×C151—44no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151—44no—
193Q8×C151—44no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
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—24no—
210C2×C4×C151—24no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—44no—
215C2×C4×C151—44no—
216C2×C4×C151#10114yes—
217C2×C4×C151C2×C22⋊C411yescharacteristic
218C2×C4×C151C2×C22⋊C411yescharacteristic
219C2×C4×C151C2×C22⋊C411yescharacteristic
220C2×C4×C151C2×C22⋊C411yescharacteristic
221C2×C4×C151C2×C22⋊C411yescharacteristic
222C2×C4×C151C2×C22⋊C411yescharacteristic
223C2×C4×C151C2×C22⋊C411yescharacteristic
224C2×C4×C151C2×C22⋊C411yescharacteristic
225C2×C4×C151C2×C22⋊C411yescharacteristic
226C2×C4×C151AGL(1,ℤ/8)12yes—
227C2×C4×C151#13712yes—
228C2×C4×C151C23×C411yescharacteristic
229C2×C4×C151C22×D411yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C8×C151—44no—
232C8×C151—44no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—21no—
237C22×C151—21no—
238C22×C151—21no—
239C22×C151—21no—
240C22×C151—44no—
241C22×C151C2×#10112yes—
242C22×C151#41712yes—
243C22×C151C22×C22⋊C411yescharacteristic
244C4×C151—21no—
245C4×C151—21no—
246C4×C151—21no—
247C4×C151—21no—
248C4×C151—21no—
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—44no—
252C4×C151—44no—
253C4×C151C2×#10112yes—
254C4×C151C2×#10112yes—
255C4×C151#41712yes—
256C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
257C4×C151C2×#13711yescharacteristic
258C4×C151#57512yes—
259C2×C151—22no—
260C2×C151—22no—
261C2×C151—41no—
262C2×C151C22×#10111yescharacteristic
263C2×C151C2×#41711yescharacteristic
264C2×C151#289611yescharacteristic
265#17751C15111yesmaximal, characteristic, direct product factor, Sylow
266C151#1775111yescharacteristic, direct product factor, Sylow
267C2×#533C2×C15111yescharacteristic
268#2920C2×C15111yescharacteristic
269C2×#423C2×C15111yescharacteristic
270#1561C2×C15114yescomplemented
271#1552C2×C15114yescomplemented
272#1549C2×C15112yescomplemented
273#1546C2×C15112yescomplemented
274C22×M16—21no—
275#533—21no—
276#533—21no—
277#533—21no—
278#533—21no—
279#533C4×C15112yes—
280#533C4×C15112yes—
281#533C22×C15112yes—
282#533C22×C15112yes—
283C2×C4⋊Q8C22×C15111yescharacteristic
284C2×C4⋊Q8C22×C15111yescharacteristic
285C2×#125C4×C15112yes—
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8—21no—
288C2×C4×Q8—21no—
289C2×C4×Q8—21no—
290C2×#117C4×C15112yes—
291C22×C42C22×C15111yescharacteristic
292#432—21no—
293#432C22×C15112yes—
294#431—21no—
295#431C22×C15112yes—
296#423—21no—
297#423—21no—
298#423C22×C15112yes—
299#423C22×C15112yes—
300#423C22×C15112yes—
301C2×C4⋊C8—21no—
302C2×C4⋊C8C22×C15112yes—
303#407—21no—
304C4×M16—21no—
305#332C22×C15118yescomplemented
306#332C22×C15118yescomplemented
307C22×Q8—21no—
308C22×Q8—21no—
309C23×C4C2×C4×C15111yescharacteristic
310C23×C4D4×C15111yescharacteristic
311C23×C4D4×C15111yescharacteristic
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—44no—
316C22×C8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8C2×C4×C15112yes—
322C4⋊Q8C2×C4×C15112yes—
323C4⋊Q8C23×C15112yes—
324C4⋊Q8C23×C15112yes—
325#125—22no—
326#125—22no—
327#125C2×C4×C15114yes—
328#125C2×C4×C15114yes—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345#117—22no—
346#117—22no—
347#117C2×C4×C15114yes—
348#117C2×C4×C15114yes—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4C2×C4×C15112yes—
354C2×C4⋊C4C2×C4×C15112yes—
355C2×C22⋊C4—22no—
356C2×C42—22no—
357C2×C42C2×C4×C15111yescharacteristic
358C2×C42C2×C4×C15111yescharacteristic
359C2×C42C2×C4×C15111yescharacteristic
360C2×C42D4×C15111yescharacteristic
361C2×C42D4×C15111yescharacteristic
362C2×C42D4×C15111yescharacteristic
363C2×C42D4×C15111yescharacteristic
364C2×C42D4×C15111yescharacteristic
365C2×C42D4×C15111yescharacteristic
366C2×C42C23×C15111yescharacteristic
367C2×C42C23×C15111yescharacteristic
368C2×C42C23×C15111yescharacteristic
369C4⋊C8—22no—
370C4⋊C8—22no—
371C4⋊C8—22no—
372C4⋊C8—22no—
373C4⋊C8C23×C15114yes—
374C4⋊C8C23×C15114yes—
375C22⋊C8—22no—
376C22⋊C8—22no—
377#97—22no—
378C4×C8—22no—
379C24C22⋊C4×C15111yescharacteristic
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—44no—
385C2×Q8—42no—
386C2×Q8—42no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4C22⋊C4×C15111yescharacteristic
394C22×C4C22⋊C4×C15111yescharacteristic
395C22×C4C22⋊C4×C15111yescharacteristic
396C22×C4C22⋊C4×C15111yescharacteristic
397C22×C4C22⋊C4×C15111yescharacteristic
398C22×C4C22⋊C4×C15111yescharacteristic
399C22×C4C22⋊C4×C15111yescharacteristic
400C22×C4C22⋊C4×C15111yescharacteristic
401C22×C4C22⋊C4×C15111yescharacteristic
402C22×C4C22×C4×C15111yescharacteristic
403C22×C4C22×C4×C15111yescharacteristic
404C22×C4C22×C4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411M16—44no—
412M16—44no—
413M16—44no—
414C2×C8—24no—
415C2×C8—24no—
416C2×C8—44no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4C22×C4×C15114yes—
428C4⋊C4C22×C4×C15114yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C42—24no—
432C42—24no—
433C42C22⋊C4×C15111yescharacteristic
434C42C22⋊C4×C15111yescharacteristic
435C42C22⋊C4×C15111yescharacteristic
436C42C22⋊C4×C15111yescharacteristic
437C42C22⋊C4×C15111yescharacteristic
438C42C22⋊C4×C15111yescharacteristic
439C42C22×C4×C15111yescharacteristic
440C42C22×C4×C15111yescharacteristic
441C42C22×C4×C15111yescharacteristic
442C42C2×D4×C15111yescharacteristic
443C42C2×D4×C15111yescharacteristic
444C42C2×D4×C15111yescharacteristic
445C42C2×D4×C15111yescharacteristic
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C24×C15111yescharacteristic
449C23—22no—
450C23—22no—
451C23—41no—
452C23C2×C22⋊C4×C15111yescharacteristic
453C23C2×C22⋊C4×C15111yescharacteristic
454C23C2×C22⋊C4×C15111yescharacteristic
455Q8—44no—
456Q8—44no—
457Q8—42no—
458Q8—42no—
459Q8—44no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4#101×C15114yes—
483C2×C4C2×C22⋊C4×C15111yescharacteristic
484C2×C4C2×C22⋊C4×C15111yescharacteristic
485C2×C4C2×C22⋊C4×C15111yescharacteristic
486C2×C4C2×C22⋊C4×C15111yescharacteristic
487C2×C4C2×C22⋊C4×C15111yescharacteristic
488C2×C4C2×C22⋊C4×C15111yescharacteristic
489C2×C4C2×C22⋊C4×C15111yescharacteristic
490C2×C4C2×C22⋊C4×C15111yescharacteristic
491C2×C4C2×C22⋊C4×C15111yescharacteristic
492C2×C4AGL(1,ℤ/8)×C15112yes—
493C2×C4#137×C15112yes—
494C2×C4C23×C4×C15111yescharacteristic
495C2×C4C22×D4×C15111yescharacteristic
496C2×C4C22×D4×C15111yescharacteristic
497C8—44no—
498C8—44no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—44no—
507C22C2×#101×C15112yes—
508C22#417×C15112yes—
509C22C22×C22⋊C4×C15111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—44no—
518C4—44no—
519C4C2×#101×C15112yes—
520C4C2×#101×C15112yes—
521C4#417×C15112yes—
522C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
523C4C2×#137×C15111yescharacteristic
524C4#575×C15112yes—
525C2—22no—
526C2—22no—
527C2—41no—
528C2C22×#101×C15111yescharacteristic
529C2C2×#417×C15111yescharacteristic
530C2#2896×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1561×C151C2semidirect
5. #1552×C151C2semidirect
6. #1549×C151C2semidirect
7. #1546×C151C2semidirect
39. #332×C151C22semidirect
40. #332×C151C22semidirect
265. #17751C151direct (N × H)
266. C151#17751direct (N × H)
270. #1561C2×C151semidirect
271. #1552C2×C151semidirect
272. #1549C2×C151semidirect
273. #1546C2×C151semidirect
305. #332C22×C151semidirect
306. #332C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
#2920×C1512
C2×#423×C1512
#1561×C1512
#1552×C1512
#1549×C1512
#1546×C1512
#17751151