Finite Group Databasebeta

← C151×#21879 #50326804

Subgroups — C151×#21879 #50326804

Order 38656.

1044 conjugacy classes of subgroups.

The subgroup lattice has 536 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#1997×C151C212yesmaximal, complemented
5#1966×C151C212yesmaximal, complemented
6#1901×C151C214yesmaximal
7#1801×C151C214yesmaximal, complemented
8C22×M16×C151C2212yes—
9#533×C151—21no—
10#533×C151—21no—
11#533×C151—21no—
12#533×C151—21no—
13#533×C151—21no—
14#533×C151—21no—
15#533×C151—21no—
16#533×C151—21no—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#125×C151C412yes—
20C2×C22⋊Q8×C151C412yes—
21C2×C22⋊Q8×C151C2212yes—
22C2×C4×Q8×C151C412yes—
23C2×C4×Q8×C151C2212yes—
24C2×#117×C151C412yes—
25C22×C42×C151C2211yescharacteristic
26#432×C151—21no—
27#432×C151—21no—
28#431×C151—21no—
29#431×C151—21no—
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×C151—21no—
37C2×#101×C151C2218yes—
38#407×C151C2212yes—
39C4×M16×C151C2212yes—
40#343×C151C2218yes—
41C22×Q8×C151C2×C412yes—
42C22×Q8×C151C2312yes—
43C23×C4×C151C2×C411yescharacteristic
44C23×C4×C151C2×C411yescharacteristic
45C23×C4×C151C2311yescharacteristic
46C2×M16×C151—22no—
47C2×M16×C151—44no—
48C2×M16×C151C2314yes—
49C2×M16×C151C2314yes—
50C22×C8×C151—22no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59#125×C151—22no—
60#125×C151—22no—
61#125×C151—22no—
62#125×C151—22no—
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×C151—22no—
82#117×C151—22no—
83C2×C4⋊C4×C151C2×C412yes—
84C2×C4⋊C4×C151C2×C412yes—
85C2×C4⋊C4×C151C2×C412yes—
86C2×C4⋊C4×C151C2×C414yes—
87C2×C4⋊C4×C151C2×C414yes—
88C2×C4⋊C4×C151C2312yes—
89C2×C22⋊C4×C151C2×C414yes—
90C2×C42×C151C2×C414yes—
91C2×C42×C151C2×C411yescharacteristic
92C2×C42×C151C2×C411yescharacteristic
93C2×C42×C151D411yescharacteristic
94C2×C42×C151D411yescharacteristic
95C2×C42×C151D411yescharacteristic
96C2×C42×C151D411yescharacteristic
97C2×C42×C151D411yescharacteristic
98C2×C42×C151D411yescharacteristic
99C2×C42×C151D411yescharacteristic
100C2×C42×C151D411yescharacteristic
101C2×C42×C151C2311yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C4⋊C8×C151—22no—
104C4⋊C8×C151—22no—
105C4⋊C8×C151—22no—
106C4⋊C8×C151—22no—
107C4⋊C8×C151—22no—
108C4⋊C8×C151—22no—
109#101×C151—48no—
110C22⋊C8×C151—22no—
111C22⋊C8×C151—22no—
112#97×C151—22no—
113C4×C8×C151—22no—
114C24×C151C22×C411yescharacteristic
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—24no—
120C2×Q8×C151—24no—
121C2×Q8×C151—44no—
122C22×C4×C151—24no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—42no—
126C22×C4×C151C22⋊C411yescharacteristic
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×C414yes—
135C22×C4×C151C22×C411yescharacteristic
136C22×C4×C151C22×C411yescharacteristic
137C22×C4×C151C22×C411yescharacteristic
138C22×C4×C151C22×C411yescharacteristic
139C22×C4×C151C22×C414yes—
140C22×C4×C151C22×C411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146M16×C151—24no—
147M16×C151—28no—
148M16×C151—24no—
149M16×C151—44no—
150C2×C8×C151—24no—
151C2×C8×C151—24no—
152C2×C8×C151—44no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—24no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C22⋊C4×C151—24no—
166C22⋊C4×C151—24no—
167C42×C151—24no—
168C42×C151—24no—
169C42×C151C22⋊C411yescharacteristic
170C42×C151C22⋊C411yescharacteristic
171C42×C151C22⋊C411yescharacteristic
172C42×C151C22⋊C411yescharacteristic
173C42×C151C22⋊C411yescharacteristic
174C42×C151C22⋊C411yescharacteristic
175C42×C151C22⋊C411yescharacteristic
176C42×C151C22⋊C411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2×D411yescharacteristic
183C42×C151C2×D411yescharacteristic
184C42×C151C2×D411yescharacteristic
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—41no—
188C23×C151C2×C22⋊C411yescharacteristic
189C23×C151C2×C22⋊C411yescharacteristic
190C23×C151C23×C411yescharacteristic
191Q8×C151—44no—
192Q8×C151—42no—
193Q8×C151—42no—
194Q8×C151—44no—
195Q8×C151—44no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
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—22no—
210C2×C4×C151—22no—
211C2×C4×C151—24no—
212C2×C4×C151—24no—
213C2×C4×C151—28no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—44no—
218C2×C4×C151#10114yescomplemented
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×C151C2×C22⋊C411yescharacteristic
227C2×C4×C151C2×C22⋊C411yescharacteristic
228C2×C4×C151C2×C22⋊C411yescharacteristic
229C2×C4×C151C22×D411yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151H(5,𝔽2)12yes—
232C2×C4×C1512−1+412yes—
233C8×C151—44no—
234C8×C151—44no—
235C22×C151—21no—
236C22×C151—21no—
237C22×C151—21no—
238C22×C151—21no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—44no—
243C22×C151C2×#10112yes—
244C22×C151C22×C22⋊C411yescharacteristic
245C22×C151#52012yes—
246C4×C151—21no—
247C4×C151—21no—
248C4×C151—21no—
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—44no—
254C4×C151—44no—
255C4×C151C2×#10112yes—
256C4×C151C2×#10112yes—
257C4×C151#41312yes—
258C4×C151#53511yescharacteristic
259C4×C151#53611yescharacteristic
260C4×C151#53712yes—
261C2×C151—22no—
262C2×C151—22no—
263C2×C151—41no—
264C2×C151#231111yescharacteristic
265C2×C151C22×#10111yescharacteristic
266C2×C151C2×#41311yescharacteristic
267#21879C15111yesmaximal, characteristic, direct product factor, Sylow
268C151#2187911yescharacteristic, direct product factor, Sylow
269C2×#533C2×C15111yescharacteristic
270#2920C2×C15111yescharacteristic
271C2×#423C2×C15111yescharacteristic
272#1997C2×C15112yescomplemented
273#1966C2×C15112yescomplemented
274#1901C2×C15114yes—
275#1801C2×C15114yescomplemented
276C22×M16C22×C15112yes—
277#533—21no—
278#533—21no—
279#533—21no—
280#533—21no—
281#533—21no—
282#533—21no—
283#533—21no—
284#533—21no—
285C2×C4⋊Q8C22×C15111yescharacteristic
286C2×C4⋊Q8C22×C15111yescharacteristic
287C2×#125C4×C15112yes—
288C2×C22⋊Q8C4×C15112yes—
289C2×C22⋊Q8C22×C15112yes—
290C2×C4×Q8C4×C15112yes—
291C2×C4×Q8C22×C15112yes—
292C2×#117C4×C15112yes—
293C22×C42C22×C15111yescharacteristic
294#432—21no—
295#432—21no—
296#431—21no—
297#431—21no—
298#423—21no—
299#423—21no—
300#423C22×C15112yes—
301#423C22×C15112yes—
302#423C22×C15112yes—
303C2×C4⋊C8—21no—
304C2×C4⋊C8—21no—
305C2×#101C22×C15118yes—
306#407C22×C15112yes—
307C4×M16C22×C15112yes—
308#343C22×C15118yes—
309C22×Q8C2×C4×C15112yes—
310C22×Q8C23×C15112yes—
311C23×C4C2×C4×C15111yescharacteristic
312C23×C4C2×C4×C15111yescharacteristic
313C23×C4C23×C15111yescharacteristic
314C2×M16—22no—
315C2×M16—44no—
316C2×M16C23×C15114yes—
317C2×M16C23×C15114yes—
318C22×C8—22no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327#125—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351C2×C4⋊C4C2×C4×C15112yes—
352C2×C4⋊C4C2×C4×C15112yes—
353C2×C4⋊C4C2×C4×C15112yes—
354C2×C4⋊C4C2×C4×C15114yes—
355C2×C4⋊C4C2×C4×C15114yes—
356C2×C4⋊C4C23×C15112yes—
357C2×C22⋊C4C2×C4×C15114yes—
358C2×C42C2×C4×C15114yes—
359C2×C42C2×C4×C15111yescharacteristic
360C2×C42C2×C4×C15111yescharacteristic
361C2×C42D4×C15111yescharacteristic
362C2×C42D4×C15111yescharacteristic
363C2×C42D4×C15111yescharacteristic
364C2×C42D4×C15111yescharacteristic
365C2×C42D4×C15111yescharacteristic
366C2×C42D4×C15111yescharacteristic
367C2×C42D4×C15111yescharacteristic
368C2×C42D4×C15111yescharacteristic
369C2×C42C23×C15111yescharacteristic
370C2×C42C23×C15111yescharacteristic
371C4⋊C8—22no—
372C4⋊C8—22no—
373C4⋊C8—22no—
374C4⋊C8—22no—
375C4⋊C8—22no—
376C4⋊C8—22no—
377#101—48no—
378C22⋊C8—22no—
379C22⋊C8—22no—
380#97—22no—
381C4×C8—22no—
382C24C22×C4×C15111yescharacteristic
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—24no—
388C2×Q8—24no—
389C2×Q8—44no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
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×C15114yes—
403C22×C4C22×C4×C15111yescharacteristic
404C22×C4C22×C4×C15111yescharacteristic
405C22×C4C22×C4×C15111yescharacteristic
406C22×C4C22×C4×C15111yescharacteristic
407C22×C4C22×C4×C15114yes—
408C22×C4C22×C4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C2×D4×C15111yescharacteristic
413C22×C4C24×C15111yescharacteristic
414M16—24no—
415M16—28no—
416M16—24no—
417M16—44no—
418C2×C8—24no—
419C2×C8—24no—
420C2×C8—44no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C42—24no—
436C42—24no—
437C42C22⋊C4×C15111yescharacteristic
438C42C22⋊C4×C15111yescharacteristic
439C42C22⋊C4×C15111yescharacteristic
440C42C22⋊C4×C15111yescharacteristic
441C42C22⋊C4×C15111yescharacteristic
442C42C22⋊C4×C15111yescharacteristic
443C42C22⋊C4×C15111yescharacteristic
444C42C22⋊C4×C15111yescharacteristic
445C42C2×D4×C15111yescharacteristic
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C2×D4×C15111yescharacteristic
449C42C2×D4×C15111yescharacteristic
450C42C2×D4×C15111yescharacteristic
451C42C2×D4×C15111yescharacteristic
452C42C2×D4×C15111yescharacteristic
453C23—22no—
454C23—22no—
455C23—41no—
456C23C2×C22⋊C4×C15111yescharacteristic
457C23C2×C22⋊C4×C15111yescharacteristic
458C23C23×C4×C15111yescharacteristic
459Q8—44no—
460Q8—44no—
461Q8—42no—
462Q8—42no—
463Q8—44no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—28no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—44no—
486C2×C4#101×C15114yescomplemented
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×C4C2×C22⋊C4×C15111yescharacteristic
493C2×C4C2×C22⋊C4×C15111yescharacteristic
494C2×C4C2×C22⋊C4×C15111yescharacteristic
495C2×C4C2×C22⋊C4×C15111yescharacteristic
496C2×C4C2×C22⋊C4×C15111yescharacteristic
497C2×C4C22×D4×C15111yescharacteristic
498C2×C4C22×D4×C15111yescharacteristic
499C2×C4H(5,𝔽2)×C15112yes—
500C2×C42−1+4×C15112yes—
501C8—44no—
502C8—44no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—44no—
511C22C2×#101×C15112yes—
512C22C22×C22⋊C4×C15111yescharacteristic
513C22#520×C15112yes—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—44no—
522C4—44no—
523C4C2×#101×C15112yes—
524C4C2×#101×C15112yes—
525C4#413×C15112yes—
526C4#535×C15111yescharacteristic
527C4#536×C15111yescharacteristic
528C4#537×C15112yes—
529C2—22no—
530C2—22no—
531C2—41no—
532C2#2311×C15111yescharacteristic
533C2C22×#101×C15111yescharacteristic
534C2C2×#413×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1997×C151C2semidirect
5. #1966×C151C2semidirect
7. #1801×C151C2semidirect
218. C2×C4×C151#101semidirect
267. #21879C151direct (N × H)
268. C151#21879direct (N × H)
272. #1997C2×C151semidirect
273. #1966C2×C151semidirect
275. #1801C2×C151semidirect
486. C2×C4#101×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
#1997×C1512
#1966×C1512
#1901×C1512
#1801×C1512
#21879151