Finite Group Databasebeta

← C151×#22062 #50326987

Subgroups — C151×#22062 #50326987

Order 38656.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3002×C151C211yesmaximal, characteristic
2#2930×C151C211yesmaximal, characteristic, complemented
3#2879×C151C211yesmaximal, characteristic, complemented
4#1975×C151C211yesmaximal, characteristic, complemented
5#1974×C151C211yesmaximal, characteristic, complemented
6#1938×C151C211yesmaximal, characteristic, complemented
7#1937×C151C211yesmaximal, characteristic, complemented
8#1929×C151C211yesmaximal, characteristic, complemented
9#1929×C151C211yesmaximal, characteristic, complemented
10#1876×C151C211yesmaximal, characteristic, complemented
11#1876×C151C211yesmaximal, characteristic, complemented
12#1871×C151C211yesmaximal, characteristic, complemented
13#1855×C151C211yesmaximal, characteristic, complemented
14#1789×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C2×#135×C151C2211yescharacteristic
18C2×#135×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic, complemented
20C22×M16×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22#525×C151C2211yescharacteristic
23#452×C151C411yescharacteristic, complemented
24#452×C151C411yescharacteristic, complemented
25#451×C151C411yescharacteristic, complemented
26#450×C151C411yescharacteristic, complemented
27#449×C151C411yescharacteristic, complemented
28#449×C151C411yescharacteristic, complemented
29#448×C151C411yescharacteristic, complemented
30#447×C151C411yescharacteristic, complemented
31#436×C151—21no—
32#436×C151—21no—
33#435×C151—21no—
34#435×C151—21no—
35C2×#108×C151C2211yescharacteristic, complemented
36C2×#108×C151C2211yescharacteristic, complemented
37#424×C151C2211yescharacteristic, complemented
38C2×#104×C151C2211yescharacteristic
39C2×#104×C151C2211yescharacteristic
40C2×#104×C151C2211yescharacteristic
41C2×#104×C151C2211yescharacteristic
42C2×#104×C151C2211yescharacteristic, complemented
43C2×#104×C151C2211yescharacteristic, complemented
44#416×C151C2211yescharacteristic
45#416×C151C2211yescharacteristic
46#408×C151—21no—
47#408×C151—21no—
48#408×C151C2211yescharacteristic
49#408×C151C2211yescharacteristic
50#408×C151C2211yescharacteristic
51#408×C151C2211yescharacteristic
52#408×C151C2211yescharacteristic, complemented
53#407×C151—21no—
54#407×C151—21no—
55#407×C151C2211yescharacteristic
56C2×C22⋊C8×C151C2211yescharacteristic
57#405×C151C2211yescharacteristic, complemented
58C2×#97×C151C2211yescharacteristic, complemented
59C2×C4×C8×C151C2211yescharacteristic, complemented
60C4×C22⋊C4×C151C2211yescharacteristic
61#341×C151C2211yescharacteristic, complemented
62#341×C151C2211yescharacteristic, complemented
63#339×C151C2211yescharacteristic, complemented
64#339×C151C2211yescharacteristic, complemented
65#336×C151C2211yescharacteristic, complemented
66#336×C151C2211yescharacteristic, complemented
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×#41×C151—41no—
70C2×#41×C151—41no—
71C2×#41×C151—41no—
72C2×#41×C151—41no—
73C2×#41×C151C2×C411yescharacteristic
74C2×#41×C151C2×C411yescharacteristic
75C2×#41×C151C2311yescharacteristic
76C2×#41×C151C2311yescharacteristic
77C2×#41×C151C2311yescharacteristic
78C22×Q8×C151C2×C411yescharacteristic
79C22×D4×C151—21no—
80C22×D4×C151C2×C411yescharacteristic
81C23×C4×C151—21no—
82C23×C4×C151C2311yescharacteristic
83#135×C151—41no—
84#135×C151—41no—
85#135×C151—41no—
86#135×C151—41no—
87C2×Q16×C151C2×C411yescharacteristic
88C2×Q16×C151C2×C411yescharacteristic
89C2×SD16×C151C2×C411yescharacteristic
90C2×SD16×C151C2×C411yescharacteristic
91C2×SD16×C151C2×C411yescharacteristic
92C2×SD16×C151C2×C411yescharacteristic
93C2×D8×C151C2×C411yescharacteristic
94C2×D8×C151C2×C411yescharacteristic
95#131×C151—41no—
96#131×C151—41no—
97C2×M16×C151—21no—
98C2×M16×C151—21no—
99C2×M16×C151—41no—
100C2×M16×C151—41no—
101C2×M16×C151—41no—
102C2×M16×C151—41no—
103C2×M16×C151D411yescharacteristic
104C2×M16×C151D411yescharacteristic
105C2×M16×C151D411yescharacteristic
106C2×M16×C151D411yescharacteristic
107C2×M16×C151C2311yescharacteristic
108C2×M16×C151C2311yescharacteristic
109C2×M16×C151C2311yescharacteristic
110C2×M16×C151C2311yescharacteristic
111C22×C8×C151—21no—
112C22×C8×C151—21no—
113C22×C8×C151C2311yescharacteristic
114C22×C8×C151C2311yescharacteristic
115C22×C8×C151C2311yescharacteristic
116C22×C8×C151C2311yescharacteristic
117#123×C151—21no—
118C22⋊Q8×C151C2×C411yescharacteristic
119C22⋊Q8×C151C2×C411yescharacteristic
120#121×C151C2×C411yescharacteristic
121#121×C151C2×C411yescharacteristic
122#120×C151—21no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125#117×C151C2311yescharacteristic
126C2×C22⋊C4×C151—21no—
127C2×C42×C151C2311yescharacteristic
128C2×C42×C151C2311yescharacteristic
129#108×C151—41no—
130#108×C151—41no—
131C4⋊C8×C151—21no—
132C4⋊C8×C151—21no—
133#104×C151—41no—
134#104×C151—41no—
135#104×C151—41no—
136#104×C151—41no—
137#104×C151—41no—
138#104×C151—41no—
139#103×C151C2×C411yescharacteristic
140#103×C151C2×C411yescharacteristic
141#103×C151C2×C411yescharacteristic
142#103×C151C2×C411yescharacteristic
143#102×C151C2×C411yescharacteristic
144#102×C151C2×C411yescharacteristic
145#102×C151C2×C411yescharacteristic
146#102×C151C2×C411yescharacteristic
147C22⋊C8×C151—21no—
148C22⋊C8×C151—21no—
149C22⋊C8×C151—21no—
150C22⋊C8×C151—21no—
151C22⋊C8×C151—21no—
152C22⋊C8×C151—21no—
153C22⋊C8×C151—21no—
154C22⋊C8×C151—21no—
155C22⋊C8×C151—21no—
156C22⋊C8×C151—21no—
157C22⋊C8×C151—21no—
158C22⋊C8×C151—21no—
159C22⋊C8×C151C2×C411yescharacteristic
160C22⋊C8×C151C2×C411yescharacteristic
161C22⋊C8×C151C2×C411yescharacteristic
162C22⋊C8×C151C2×C411yescharacteristic
163#97×C151—21no—
164#97×C151—41no—
165C4×C8×C151—21no—
166C4×C8×C151—41no—
167#95×C151—21no—
168C24×C151—21no—
169C24×C151#4111yescharacteristic
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—21no—
173#41×C151—21no—
174#41×C151—21no—
175#41×C151—21no—
176#41×C151—21no—
177#41×C151—21no—
178#41×C151—21no—
179#41×C151—21no—
180#41×C151—21no—
181#41×C151—21no—
182#41×C151—41no—
183#41×C151—41no—
184#41×C151—41no—
185#41×C151—41no—
186#41×C151—42no—
187#41×C151—42no—
188#41×C151—42no—
189#41×C151—42no—
190C2×Q8×C151—21no—
191C2×Q8×C151—41no—
192C2×Q8×C151—41no—
193C2×Q8×C151C22×C411yescharacteristic
194C2×Q8×C151C22×C411yescharacteristic
195C2×Q8×C151C22×C411yescharacteristic
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—41no—
205C2×D4×C151—41no—
206C2×D4×C151—42no—
207C2×D4×C151—42no—
208C2×D4×C151C22×C411yescharacteristic
209C2×D4×C151C22×C411yescharacteristic
210C2×D4×C151C22×C411yescharacteristic
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—42no—
224C22×C4×C151—42no—
225C22×C4×C151C22×C411yescharacteristic
226C22×C4×C151C22×C411yescharacteristic
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151#4111yescharacteristic
230C22×C4×C151C2411yescharacteristic
231Q16×C151—41no—
232Q16×C151—41no—
233SD16×C151—41no—
234SD16×C151—41no—
235SD16×C151—41no—
236SD16×C151—41no—
237D8×C151—41no—
238D8×C151—41no—
239M16×C151—21no—
240M16×C151—21no—
241M16×C151—21no—
242M16×C151—21no—
243M16×C151—21no—
244M16×C151—21no—
245M16×C151—21no—
246M16×C151—21no—
247M16×C151—41no—
248M16×C151—41no—
249M16×C151—41no—
250M16×C151—41no—
251M16×C151—42no—
252M16×C151—42no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—42no—
266C2×C8×C151—42no—
267C2×C8×C151C22×C411yescharacteristic
268C2×C8×C151C22×C411yescharacteristic
269C2×C8×C151C22×C411yescharacteristic
270C2×C8×C151C22×C411yescharacteristic
271C2×C8×C151C2×D411yescharacteristic
272C2×C8×C151C2×D411yescharacteristic
273C2×C8×C151C2×D411yescharacteristic
274C2×C8×C151C2×D411yescharacteristic
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151C22×C411yescharacteristic
278C4⋊C4×C151C22×C411yescharacteristic
279C22⋊C4×C151—21no—
280C22⋊C4×C151—21no—
281C22⋊C4×C151—21no—
282C22⋊C4×C151—21no—
283C22⋊C4×C151—21no—
284C22⋊C4×C151—42no—
285C42×C151—21no—
286C42×C151—21no—
287C42×C151—21no—
288C42×C151—21no—
289C42×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—42no—
298C23×C151—81no—
299C23×C151—81no—
300C23×C151C4×D411yescharacteristic
301C23×C151C4×D411yescharacteristic
302C23×C151C2×#4111yescharacteristic
303Q8×C151—21no—
304Q8×C151—21no—
305Q8×C151—21no—
306Q8×C151—21no—
307Q8×C151—21no—
308Q8×C151—21no—
309Q8×C151—42no—
310D4×C151—21no—
311D4×C151—21no—
312D4×C151—21no—
313D4×C151—21no—
314D4×C151—21no—
315D4×C151—21no—
316D4×C151—42no—
317D4×C151—42no—
318D4×C151—42no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—41no—
324D4×C151—41no—
325D4×C151—81no—
326D4×C151—81no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—22no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—21no—
343C2×C4×C151—42no—
344C2×C4×C151—42no—
345C2×C4×C151—42no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151C4×D411yescharacteristic
358C2×C4×C151C4×D411yescharacteristic
359C2×C4×C151C23×C411yescharacteristic
360C2×C4×C151C22×D411yescharacteristic
361C2×C4×C151H(5,𝔽2)11yescharacteristic
362C2×C4×C151H(5,𝔽2)11yescharacteristic
363C2×C4×C151H(5,𝔽2)11yescharacteristic
364C2×C4×C151H(5,𝔽2)11yescharacteristic
365C8×C151—21no—
366C8×C151—21no—
367C8×C151—21no—
368C8×C151—21no—
369C8×C151—21no—
370C8×C151—21no—
371C8×C151—21no—
372C8×C151—21no—
373C8×C151—41no—
374C8×C151—41no—
375C8×C151—41no—
376C8×C151—41no—
377C22×C151—21no—
378C22×C151—21no—
379C22×C151—21no—
380C22×C151—21no—
381C22×C151—21no—
382C22×C151—21no—
383C22×C151—21no—
384C22×C151—21no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—81no—
395C22×C151—81no—
396C22×C151—84no—
397C22×C151C2×C4×D411yescharacteristic
398C22×C151#53811yescharacteristic
399C22×C151#53811yescharacteristic
400C4×C151—21no—
401C4×C151—21no—
402C4×C151—42no—
403C4×C151—41no—
404C4×C151—41no—
405C4×C151—41no—
406C4×C151—41no—
407C4×C151—41no—
408C4×C151—81no—
409C4×C151#51811yescharacteristic
410C4×C151#51811yescharacteristic
411C4×C151#53411yescharacteristic
412C4×C151#53511yescharacteristic
413C2×C151—21no—
414C2×C151—21no—
415C2×C151—41no—
416C2×C151—41no—
417C2×C151—81no—
418C2×C151—81no—
419C2×C151—81no—
420C2×C151#232111yescharacteristic
421C2×C151#295611yescharacteristic
422C2×C151#295711yescharacteristic
423#22062C15111yesmaximal, characteristic, direct product factor, Sylow
424C151#2206211yescharacteristic, direct product factor, Sylow
425#3002C2×C15111yescharacteristic
426#2930C2×C15111yescharacteristic, complemented
427#2879C2×C15111yescharacteristic, complemented
428#1975C2×C15111yescharacteristic, complemented
429#1974C2×C15111yescharacteristic, complemented
430#1938C2×C15111yescharacteristic, complemented
431#1937C2×C15111yescharacteristic, complemented
432#1929C2×C15111yescharacteristic, complemented
433#1929C2×C15111yescharacteristic, complemented
434#1876C2×C15111yescharacteristic, complemented
435#1876C2×C15111yescharacteristic, complemented
436#1871C2×C15111yescharacteristic, complemented
437#1855C2×C15111yescharacteristic, complemented
438#1789C2×C15111yescharacteristic, complemented
439#1753C2×C15111yescharacteristic, complemented
440C22×#41C22×C15111yescharacteristic
441C2×#135C22×C15111yescharacteristic
442C2×#135C22×C15111yescharacteristic
443C2×#131C22×C15111yescharacteristic, complemented
444C22×M16C22×C15111yescharacteristic
445C22×M16C22×C15111yescharacteristic
446#525C22×C15111yescharacteristic
447#452C4×C15111yescharacteristic, complemented
448#452C4×C15111yescharacteristic, complemented
449#451C4×C15111yescharacteristic, complemented
450#450C4×C15111yescharacteristic, complemented
451#449C4×C15111yescharacteristic, complemented
452#449C4×C15111yescharacteristic, complemented
453#448C4×C15111yescharacteristic, complemented
454#447C4×C15111yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C15111yescharacteristic, complemented
460C2×#108C22×C15111yescharacteristic, complemented
461#424C22×C15111yescharacteristic, complemented
462C2×#104C22×C15111yescharacteristic
463C2×#104C22×C15111yescharacteristic
464C2×#104C22×C15111yescharacteristic
465C2×#104C22×C15111yescharacteristic
466C2×#104C22×C15111yescharacteristic, complemented
467C2×#104C22×C15111yescharacteristic, complemented
468#416C22×C15111yescharacteristic
469#416C22×C15111yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C15111yescharacteristic
473#408C22×C15111yescharacteristic
474#408C22×C15111yescharacteristic
475#408C22×C15111yescharacteristic
476#408C22×C15111yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C15111yescharacteristic
480C2×C22⋊C8C22×C15111yescharacteristic
481#405C22×C15111yescharacteristic, complemented
482C2×#97C22×C15111yescharacteristic, complemented
483C2×C4×C8C22×C15111yescharacteristic, complemented
484C4×C22⋊C4C22×C15111yescharacteristic
485#341C22×C15111yescharacteristic, complemented
486#341C22×C15111yescharacteristic, complemented
487#339C22×C15111yescharacteristic, complemented
488#339C22×C15111yescharacteristic, complemented
489#336C22×C15111yescharacteristic, complemented
490#336C22×C15111yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C15111yescharacteristic
498C2×#41C2×C4×C15111yescharacteristic
499C2×#41C23×C15111yescharacteristic
500C2×#41C23×C15111yescharacteristic
501C2×#41C23×C15111yescharacteristic
502C22×Q8C2×C4×C15111yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C15111yescharacteristic
505C23×C4—21no—
506C23×C4C23×C15111yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C15111yescharacteristic
512C2×Q16C2×C4×C15111yescharacteristic
513C2×SD16C2×C4×C15111yescharacteristic
514C2×SD16C2×C4×C15111yescharacteristic
515C2×SD16C2×C4×C15111yescharacteristic
516C2×SD16C2×C4×C15111yescharacteristic
517C2×D8C2×C4×C15111yescharacteristic
518C2×D8C2×C4×C15111yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C15111yescharacteristic
528C2×M16D4×C15111yescharacteristic
529C2×M16D4×C15111yescharacteristic
530C2×M16D4×C15111yescharacteristic
531C2×M16C23×C15111yescharacteristic
532C2×M16C23×C15111yescharacteristic
533C2×M16C23×C15111yescharacteristic
534C2×M16C23×C15111yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C15111yescharacteristic
538C22×C8C23×C15111yescharacteristic
539C22×C8C23×C15111yescharacteristic
540C22×C8C23×C15111yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C15111yescharacteristic
543C22⋊Q8C2×C4×C15111yescharacteristic
544#121C2×C4×C15111yescharacteristic
545#121C2×C4×C15111yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C15111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C15111yescharacteristic
552C2×C42C23×C15111yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C15111yescharacteristic
564#103C2×C4×C15111yescharacteristic
565#103C2×C4×C15111yescharacteristic
566#103C2×C4×C15111yescharacteristic
567#102C2×C4×C15111yescharacteristic
568#102C2×C4×C15111yescharacteristic
569#102C2×C4×C15111yescharacteristic
570#102C2×C4×C15111yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C15111yescharacteristic
584C22⋊C8C2×C4×C15111yescharacteristic
585C22⋊C8C2×C4×C15111yescharacteristic
586C22⋊C8C2×C4×C15111yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C15111yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C15111yescharacteristic
618C2×Q8C22×C4×C15111yescharacteristic
619C2×Q8C22×C4×C15111yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C15111yescharacteristic
633C2×D4C22×C4×C15111yescharacteristic
634C2×D4C22×C4×C15111yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C15111yescharacteristic
650C22×C4C22×C4×C15111yescharacteristic
651C22×C4C2×D4×C15111yescharacteristic
652C22×C4C2×D4×C15111yescharacteristic
653C22×C4#41×C15111yescharacteristic
654C22×C4C24×C15111yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C15111yescharacteristic
692C2×C8C22×C4×C15111yescharacteristic
693C2×C8C22×C4×C15111yescharacteristic
694C2×C8C22×C4×C15111yescharacteristic
695C2×C8C2×D4×C15111yescharacteristic
696C2×C8C2×D4×C15111yescharacteristic
697C2×C8C2×D4×C15111yescharacteristic
698C2×C8C2×D4×C15111yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C15111yescharacteristic
702C4⋊C4C22×C4×C15111yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C15111yescharacteristic
725C23C4×D4×C15111yescharacteristic
726C23C2×#41×C15111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C15111yescharacteristic
782C2×C4C4×D4×C15111yescharacteristic
783C2×C4C23×C4×C15111yescharacteristic
784C2×C4C22×D4×C15111yescharacteristic
785C2×C4H(5,𝔽2)×C15111yescharacteristic
786C2×C4H(5,𝔽2)×C15111yescharacteristic
787C2×C4H(5,𝔽2)×C15111yescharacteristic
788C2×C4H(5,𝔽2)×C15111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C15111yescharacteristic
822C22#538×C15111yescharacteristic
823C22#538×C15111yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C15111yescharacteristic
834C4#518×C15111yescharacteristic
835C4#534×C15111yescharacteristic
836C4#535×C15111yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#2321×C15111yescharacteristic
845C2#2956×C15111yescharacteristic
846C2#2957×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radical#3002×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2930×C151C2semidirect
3. #2879×C151C2semidirect
4. #1975×C151C2semidirect
5. #1974×C151C2semidirect
6. #1938×C151C2semidirect
7. #1937×C151C2semidirect
8. #1929×C151C2semidirect
9. #1929×C151C2semidirect
10. #1876×C151C2semidirect
11. #1876×C151C2semidirect
12. #1871×C151C2semidirect
13. #1855×C151C2semidirect
14. #1789×C151C2semidirect
15. #1753×C151C2semidirect
19. C2×#131×C151C22semidirect
23. #452×C151C4semidirect
24. #452×C151C4semidirect
25. #451×C151C4semidirect
26. #450×C151C4semidirect
27. #449×C151C4semidirect
28. #449×C151C4semidirect
29. #448×C151C4semidirect
30. #447×C151C4semidirect
35. C2×#108×C151C22semidirect
36. C2×#108×C151C22semidirect
37. #424×C151C22semidirect
42. C2×#104×C151C22semidirect
43. C2×#104×C151C22semidirect
52. #408×C151C22semidirect
57. #405×C151C22semidirect
58. C2×#97×C151C22semidirect
59. C2×C4×C8×C151C22semidirect
61. #341×C151C22semidirect
62. #341×C151C22semidirect
63. #339×C151C22semidirect
64. #339×C151C22semidirect
65. #336×C151C22semidirect
66. #336×C151C22semidirect
423. #22062C151direct (N × H)
424. C151#22062direct (N × H)
426. #2930C2×C151semidirect
427. #2879C2×C151semidirect
428. #1975C2×C151semidirect
429. #1974C2×C151semidirect
430. #1938C2×C151semidirect
431. #1937C2×C151semidirect
432. #1929C2×C151semidirect
433. #1929C2×C151semidirect
434. #1876C2×C151semidirect
435. #1876C2×C151semidirect
436. #1871C2×C151semidirect
437. #1855C2×C151semidirect
438. #1789C2×C151semidirect
439. #1753C2×C151semidirect
443. C2×#131C22×C151semidirect
447. #452C4×C151semidirect
448. #452C4×C151semidirect
449. #451C4×C151semidirect
450. #450C4×C151semidirect
451. #449C4×C151semidirect
452. #449C4×C151semidirect
453. #448C4×C151semidirect
454. #447C4×C151semidirect
459. C2×#108C22×C151semidirect
460. C2×#108C22×C151semidirect
461. #424C22×C151semidirect
466. C2×#104C22×C151semidirect
467. C2×#104C22×C151semidirect
476. #408C22×C151semidirect
481. #405C22×C151semidirect
482. C2×#97C22×C151semidirect
483. C2×C4×C8C22×C151semidirect
485. #341C22×C151semidirect
486. #341C22×C151semidirect
487. #339C22×C151semidirect
488. #339C22×C151semidirect
489. #336C22×C151semidirect
490. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3002×C1512
#2930×C1512
#2879×C1512
#1975×C1512
#1974×C1512
#1938×C1512
#1937×C1512
#1929×C1512
#1876×C1512
#1871×C1512
#1855×C1512
#1789×C1512
#1753×C1512
#22062151