Finite Group Databasebeta

← C151×#17422 #50322347

Subgroups — C151×#17422 #50322347

Order 38656.

1060 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551×C151C211yesmaximal, characteristic
2#2974×C151C212yesmaximal, complemented
3#1473×C151C212yesmaximal, complemented
4#1472×C151C212yesmaximal, complemented
5#1468×C151C212yesmaximal, complemented
6#1465×C151C211yesmaximal, characteristic, complemented
7#1464×C151C211yesmaximal, characteristic, complemented
8#1462×C151C211yesmaximal, characteristic, complemented
9#1459×C151C211yesmaximal, characteristic, complemented
10#1458×C151C211yesmaximal, characteristic, complemented
11C2×#323×C151C211yesmaximal, characteristic, complemented
12#551×C151—22no—
13#551×C151—22no—
14#551×C151—22no—
15#551×C151—22no—
16C2×#126×C151C411yescharacteristic
17C2×#126×C151C2211yescharacteristic
18C2×#124×C151C411yescharacteristic
19C2×#123×C151C411yescharacteristic
20C2×#123×C151C411yescharacteristic
21C2×#123×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C411yescharacteristic
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×#120×C151C411yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×#117×C151C411yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C22×C22⋊C4×C151C411yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31#436×C151—22no—
32#435×C151—22no—
33#435×C151—22no—
34C8×D4×C151—22no—
35#432×C151C2212yescomplemented
36#431×C151C2212yescomplemented
37#407×C151C2212yes—
38#407×C151C2212yescomplemented
39C2×C22⋊C8×C151C2212yes—
40C2×C22⋊C8×C151C2212yescomplemented
41#324×C151C2212yescomplemented
42#324×C151C2212yescomplemented
43#324×C151C2212yescomplemented
44#324×C151C2212yescomplemented
45#323×C151C2211yescharacteristic
46#323×C151C2211yescharacteristic
47#323×C151C2212yes—
48#323×C151C2211yescharacteristic
49#323×C151C2211yescharacteristic
50#323×C151C2212yes—
51C25×C151C2×C411yescharacteristic
52C22×Q8×C151C2×C411yescharacteristic
53C22×D4×C151C2×C411yescharacteristic
54C22×D4×C151C2×C411yescharacteristic
55C22×D4×C151C2×C411yescharacteristic
56C23×C4×C151C2×C411yescharacteristic
57C23×C4×C151C2×C411yescharacteristic
58C23×C4×C151C2×C411yescharacteristic
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C2×M16×C151—22no—
62C2×M16×C151—22no—
63C22×C8×C151—22no—
64C22×C8×C151—22no—
65#126×C151—22no—
66#126×C151—22no—
67#126×C151—22no—
68#126×C151—22no—
69#124×C151—22no—
70#124×C151—22no—
71#123×C151—22no—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75#123×C151—22no—
76#123×C151—22no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—22no—
80C22⋊Q8×C151—22no—
81#120×C151—22no—
82#120×C151—22no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151D412yes—
86C4×D4×C151D412yes—
87C4×D4×C151D412yes—
88C4×D4×C151D412yes—
89#117×C151—21no—
90#117×C151—21no—
91#117×C151—21no—
92#117×C151—21no—
93#117×C151—22no—
94#117×C151—22no—
95C2×C4⋊C4×C151C2×C411yescharacteristic
96C2×C4⋊C4×C151C2×C411yescharacteristic
97C2×C4⋊C4×C151C2×C411yescharacteristic
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊C4×C151C2×C411yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151—22no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C22⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151C2×C411yescharacteristic
113C2×C22⋊C4×C151C2×C411yescharacteristic
114C2×C22⋊C4×C151C2×C411yescharacteristic
115C2×C22⋊C4×C151C2×C411yescharacteristic
116C2×C22⋊C4×C151C2×C411yescharacteristic
117C2×C22⋊C4×C151C2×C411yescharacteristic
118C2×C22⋊C4×C151C2×C411yescharacteristic
119C2×C22⋊C4×C151C2×C411yescharacteristic
120C2×C22⋊C4×C151C2×C411yescharacteristic
121C2×C22⋊C4×C151C2311yescharacteristic
122C2×C22⋊C4×C151C2311yescharacteristic
123C2×C42×C151C2×C411yescharacteristic
124C2×C42×C151C2×C411yescharacteristic
125C2×C42×C151C2311yescharacteristic
126C4⋊C8×C151—22no—
127C4⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—22no—
131C22⋊C8×C151—22no—
132C22⋊C8×C151C2312yes—
133C22⋊C8×C151C2312yes—
134C22⋊C8×C151C2312yes—
135C22⋊C8×C151C2312yes—
136#97×C151—22no—
137C4×C8×C151—22no—
138C24×C151—21no—
139C24×C151—21no—
140C24×C151—22no—
141C24×C151—41no—
142C24×C151—42no—
143C24×C151—81no—
144C24×C151C22×C411yescharacteristic
145C24×C151C22×C411yescharacteristic
146C24×C151C22×C411yescharacteristic
147C24×C151C22×C411yescharacteristic
148C2×Q8×C151—22no—
149C2×Q8×C151—81no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—41no—
154C2×D4×C151—42no—
155C2×D4×C151—81no—
156C2×D4×C151C22⋊C412yes—
157C2×D4×C151C22⋊C412yes—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—22no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—41no—
166C22×C4×C151—42no—
167C22×C4×C151—81no—
168C22×C4×C151—81no—
169C22×C4×C151—81no—
170C22×C4×C151C22×C411yescharacteristic
171C22×C4×C151C22×C411yescharacteristic
172C22×C4×C151C22×C411yescharacteristic
173C22×C4×C151C22×C411yescharacteristic
174C22×C4×C151C22×C411yescharacteristic
175C22×C4×C151C22×C411yescharacteristic
176C22×C4×C151C22×C411yescharacteristic
177C22×C4×C151C22×C411yescharacteristic
178C22×C4×C151C22×C411yescharacteristic
179C22×C4×C151C22×C411yescharacteristic
180C22×C4×C151C2×D412yes—
181C22×C4×C151C2×D412yes—
182C22×C4×C151C2×D412yes—
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2411yescharacteristic
185M16×C151—82no—
186M16×C151—82no—
187C2×C8×C151—22no—
188C2×C8×C151—22no—
189C2×C8×C151—22no—
190C2×C8×C151—22no—
191C2×C8×C151—82no—
192C2×C8×C151—82no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151C22⋊C412yes—
203C4⋊C4×C151C22⋊C412yes—
204C22⋊C4×C151—21no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—21no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151C22⋊C411yescharacteristic
221C22⋊C4×C151C22⋊C411yescharacteristic
222C22⋊C4×C151C22⋊C411yescharacteristic
223C22⋊C4×C151C22⋊C411yescharacteristic
224C22⋊C4×C151C22⋊C412yes—
225C22⋊C4×C151C22⋊C412yes—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151C2×D412yes—
231C42×C151C2×D412yes—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—22no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—42no—
246C23×C151—42no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—42no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—42no—
253C23×C151—81no—
254C23×C151—81no—
255C23×C151—84no—
256C23×C151—84no—
257C23×C151C2×C22⋊C411yescharacteristic
258C23×C151C2×C22⋊C412yes—
259C23×C151C2×C22⋊C411yescharacteristic
260C23×C151#13112yes—
261C23×C151C23×C411yescharacteristic
262Q8×C151—82no—
263D4×C151—24no—
264D4×C151—42no—
265D4×C151—44no—
266D4×C151—82no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—41no—
280C2×C4×C151—42no—
281C2×C4×C151—42no—
282C2×C4×C151—42no—
283C2×C4×C151—42no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—42no—
288C2×C4×C151—42no—
289C2×C4×C151—42no—
290C2×C4×C151—42no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—81no—
296C2×C4×C151—81no—
297C2×C4×C151C2×C22⋊C412yes—
298C2×C4×C151C2×C22⋊C411yescharacteristic
299C2×C4×C151C2×C22⋊C411yescharacteristic
300C2×C4×C151C2×C22⋊C411yescharacteristic
301C2×C4×C151C2×C22⋊C411yescharacteristic
302C2×C4×C151C2×C22⋊C412yes—
303C2×C4×C151C22×D412yes—
304C8×C151—42no—
305C8×C151—42no—
306C8×C151—42no—
307C8×C151—42no—
308C22×C151—21no—
309C22×C151—21no—
310C22×C151—21no—
311C22×C151—21no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—21no—
315C22×C151—22no—
316C22×C151—21no—
317C22×C151—21no—
318C22×C151—22no—
319C22×C151—42no—
320C22×C151—42no—
321C22×C151—42no—
322C22×C151—42no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—84no—
331C22×C151—81no—
332C22×C151—81no—
333C22×C151—84no—
334C22×C151#41312yes—
335C22×C151C22×C22⋊C411yescharacteristic
336C22×C151C2×#13111yescharacteristic
337C22×C151#56811yescharacteristic
338C4×C151—21no—
339C4×C151—21no—
340C4×C151—22no—
341C4×C151—21no—
342C4×C151—21no—
343C4×C151—22no—
344C4×C151—22no—
345C4×C151—41no—
346C4×C151—41no—
347C4×C151—41no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—41no—
351C2×C151—21no—
352C2×C151—21no—
353C2×C151—22no—
354C2×C151—41no—
355C2×C151—42no—
356C2×C151—42no—
357C2×C151—81no—
358C2×C151#288011yescharacteristic
359C2×C151#288311yescharacteristic
360C2×C151C2×#41311yescharacteristic
361#17422C15111yesmaximal, characteristic, direct product factor, Sylow
362C151#1742211yescharacteristic, direct product factor, Sylow
363C2×#551C2×C15111yescharacteristic
364#2974C2×C15112yescomplemented
365#1473C2×C15112yescomplemented
366#1472C2×C15112yescomplemented
367#1468C2×C15112yescomplemented
368#1465C2×C15111yescharacteristic, complemented
369#1464C2×C15111yescharacteristic, complemented
370#1462C2×C15111yescharacteristic, complemented
371#1459C2×C15111yescharacteristic, complemented
372#1458C2×C15111yescharacteristic, complemented
373C2×#323C2×C15111yescharacteristic, complemented
374#551—22no—
375#551—22no—
376#551—22no—
377#551—22no—
378C2×#126C4×C15111yescharacteristic
379C2×#126C22×C15111yescharacteristic
380C2×#124C4×C15111yescharacteristic
381C2×#123C4×C15111yescharacteristic
382C2×#123C4×C15111yescharacteristic
383C2×#123C22×C15111yescharacteristic
384C2×C22⋊Q8C4×C15111yescharacteristic
385C2×C22⋊Q8C22×C15111yescharacteristic
386C2×#120C4×C15111yescharacteristic
387C2×C4×D4C22×C15111yescharacteristic
388C2×C4×D4C22×C15111yescharacteristic
389C2×#117C4×C15111yescharacteristic
390C2×#117C22×C15111yescharacteristic
391C22×C22⋊C4C4×C15111yescharacteristic
392C22×C22⋊C4C22×C15111yescharacteristic
393#436—22no—
394#435—22no—
395#435—22no—
396C8×D4—22no—
397#432C22×C15112yescomplemented
398#431C22×C15112yescomplemented
399#407C22×C15112yes—
400#407C22×C15112yescomplemented
401C2×C22⋊C8C22×C15112yes—
402C2×C22⋊C8C22×C15112yescomplemented
403#324C22×C15112yescomplemented
404#324C22×C15112yescomplemented
405#324C22×C15112yescomplemented
406#324C22×C15112yescomplemented
407#323C22×C15111yescharacteristic
408#323C22×C15111yescharacteristic
409#323C22×C15112yes—
410#323C22×C15111yescharacteristic
411#323C22×C15111yescharacteristic
412#323C22×C15112yes—
413C25C2×C4×C15111yescharacteristic
414C22×Q8C2×C4×C15111yescharacteristic
415C22×D4C2×C4×C15111yescharacteristic
416C22×D4C2×C4×C15111yescharacteristic
417C22×D4C2×C4×C15111yescharacteristic
418C23×C4C2×C4×C15111yescharacteristic
419C23×C4C2×C4×C15111yescharacteristic
420C23×C4C2×C4×C15111yescharacteristic
421C23×C4C23×C15111yescharacteristic
422C23×C4C23×C15111yescharacteristic
423C2×M16—22no—
424C2×M16—22no—
425C22×C8—22no—
426C22×C8—22no—
427#126—22no—
428#126—22no—
429#126—22no—
430#126—22no—
431#124—22no—
432#124—22no—
433#123—22no—
434#123—22no—
435#123—22no—
436#123—22no—
437#123—22no—
438#123—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#120—22no—
444#120—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4D4×C15112yes—
448C4×D4D4×C15112yes—
449C4×D4D4×C15112yes—
450C4×D4D4×C15112yes—
451#117—21no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4C2×C4×C15111yescharacteristic
458C2×C4⋊C4C2×C4×C15111yescharacteristic
459C2×C4⋊C4C2×C4×C15111yescharacteristic
460C2×C4⋊C4C2×C4×C15111yescharacteristic
461C2×C4⋊C4C2×C4×C15111yescharacteristic
462C2×C4⋊C4C2×C4×C15111yescharacteristic
463C2×C4⋊C4C23×C15111yescharacteristic
464C2×C4⋊C4C23×C15111yescharacteristic
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4C2×C4×C15111yescharacteristic
472C2×C22⋊C4C2×C4×C15111yescharacteristic
473C2×C22⋊C4C2×C4×C15111yescharacteristic
474C2×C22⋊C4C2×C4×C15111yescharacteristic
475C2×C22⋊C4C2×C4×C15111yescharacteristic
476C2×C22⋊C4C2×C4×C15111yescharacteristic
477C2×C22⋊C4C2×C4×C15111yescharacteristic
478C2×C22⋊C4C2×C4×C15111yescharacteristic
479C2×C22⋊C4C2×C4×C15111yescharacteristic
480C2×C22⋊C4C2×C4×C15111yescharacteristic
481C2×C22⋊C4C2×C4×C15111yescharacteristic
482C2×C22⋊C4C2×C4×C15111yescharacteristic
483C2×C22⋊C4C23×C15111yescharacteristic
484C2×C22⋊C4C23×C15111yescharacteristic
485C2×C42C2×C4×C15111yescharacteristic
486C2×C42C2×C4×C15111yescharacteristic
487C2×C42C23×C15111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8C23×C15112yes—
495C22⋊C8C23×C15112yes—
496C22⋊C8C23×C15112yes—
497C22⋊C8C23×C15112yes—
498#97—22no—
499C4×C8—22no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—41no—
504C24—42no—
505C24—81no—
506C24C22×C4×C15111yescharacteristic
507C24C22×C4×C15111yescharacteristic
508C24C22×C4×C15111yescharacteristic
509C24C22×C4×C15111yescharacteristic
510C2×Q8—22no—
511C2×Q8—81no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—81no—
518C2×D4C22⋊C4×C15112yes—
519C2×D4C22⋊C4×C15112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C22×C4×C15111yescharacteristic
533C22×C4C22×C4×C15111yescharacteristic
534C22×C4C22×C4×C15111yescharacteristic
535C22×C4C22×C4×C15111yescharacteristic
536C22×C4C22×C4×C15111yescharacteristic
537C22×C4C22×C4×C15111yescharacteristic
538C22×C4C22×C4×C15111yescharacteristic
539C22×C4C22×C4×C15111yescharacteristic
540C22×C4C22×C4×C15111yescharacteristic
541C22×C4C22×C4×C15111yescharacteristic
542C22×C4C2×D4×C15112yes—
543C22×C4C2×D4×C15112yes—
544C22×C4C2×D4×C15112yes—
545C22×C4C2×D4×C15112yes—
546C22×C4C24×C15111yescharacteristic
547M16—82no—
548M16—82no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—82no—
554C2×C8—82no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4C22⋊C4×C15112yes—
565C4⋊C4C22⋊C4×C15112yes—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4C22⋊C4×C15111yescharacteristic
583C22⋊C4C22⋊C4×C15111yescharacteristic
584C22⋊C4C22⋊C4×C15111yescharacteristic
585C22⋊C4C22⋊C4×C15111yescharacteristic
586C22⋊C4C22⋊C4×C15112yes—
587C22⋊C4C22⋊C4×C15112yes—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42C2×D4×C15112yes—
593C42C2×D4×C15112yes—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—81no—
616C23—81no—
617C23—84no—
618C23—84no—
619C23C2×C22⋊C4×C15111yescharacteristic
620C23C2×C22⋊C4×C15112yes—
621C23C2×C22⋊C4×C15111yescharacteristic
622C23#131×C15112yes—
623C23C23×C4×C15111yescharacteristic
624Q8—82no—
625D4—24no—
626D4—42no—
627D4—44no—
628D4—82no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4C2×C22⋊C4×C15111yescharacteristic
660C2×C4C2×C22⋊C4×C15111yescharacteristic
661C2×C4C2×C22⋊C4×C15111yescharacteristic
662C2×C4C2×C22⋊C4×C15111yescharacteristic
663C2×C4C2×C22⋊C4×C15112yes—
664C2×C4C2×C22⋊C4×C15112yes—
665C2×C4C22×D4×C15112yes—
666C8—42no—
667C8—42no—
668C8—42no—
669C8—42no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—22no—
675C22—22no—
676C22—21no—
677C22—22no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—81no—
691C22—81no—
692C22—84no—
693C22—81no—
694C22—81no—
695C22—84no—
696C22#413×C15112yes—
697C22C22×C22⋊C4×C15111yescharacteristic
698C22C2×#131×C15111yescharacteristic
699C22#568×C15111yescharacteristic
700C4—21no—
701C4—21no—
702C4—22no—
703C4—21no—
704C4—21no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C2—21no—
714C2—21no—
715C2—22no—
716C2—41no—
717C2—42no—
718C2—42no—
719C2—81no—
720C2#2880×C15111yescharacteristic
721C2#2883×C15111yescharacteristic
722C2C2×#413×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#120×C151C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2974×C151C2semidirect
3. #1473×C151C2semidirect
4. #1472×C151C2semidirect
5. #1468×C151C2semidirect
6. #1465×C151C2semidirect
7. #1464×C151C2semidirect
8. #1462×C151C2semidirect
9. #1459×C151C2semidirect
10. #1458×C151C2semidirect
11. C2×#323×C151C2semidirect
35. #432×C151C22semidirect
36. #431×C151C22semidirect
38. #407×C151C22semidirect
40. C2×C22⋊C8×C151C22semidirect
41. #324×C151C22semidirect
42. #324×C151C22semidirect
43. #324×C151C22semidirect
44. #324×C151C22semidirect
361. #17422C151direct (N × H)
362. C151#17422direct (N × H)
364. #2974C2×C151semidirect
365. #1473C2×C151semidirect
366. #1472C2×C151semidirect
367. #1468C2×C151semidirect
368. #1465C2×C151semidirect
369. #1464C2×C151semidirect
370. #1462C2×C151semidirect
371. #1459C2×C151semidirect
372. #1458C2×C151semidirect
373. C2×#323C2×C151semidirect
397. #432C22×C151semidirect
398. #431C22×C151semidirect
400. #407C22×C151semidirect
402. C2×C22⋊C8C22×C151semidirect
403. #324C22×C151semidirect
404. #324C22×C151semidirect
405. #324C22×C151semidirect
406. #324C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#551×C1512
#2974×C1512
#1473×C1512
#1472×C1512
#1468×C1512
#1465×C1512
#1464×C1512
#1462×C1512
#1459×C1512
#1458×C1512
C2×#323×C1512
#17422151