Finite Group Databasebeta

← C151×#22889 #50327814

Subgroups — C151×#22889 #50327814

Order 38656.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3002×C151C211yesmaximal, characteristic
2C2×#443×C151C211yesmaximal, characteristic, complemented
3#2933×C151C211yesmaximal, characteristic, complemented
4C2×#421×C151C211yesmaximal, characteristic, complemented
5#2880×C151C211yesmaximal, characteristic, complemented
6#1975×C151C211yesmaximal, characteristic, complemented
7#1937×C151C211yesmaximal, characteristic, complemented
8#1929×C151C211yesmaximal, characteristic, complemented
9#1897×C151C211yesmaximal, characteristic, complemented
10#1876×C151C211yesmaximal, characteristic, complemented
11#1876×C151C211yesmaximal, characteristic, complemented
12#1866×C151C211yesmaximal, characteristic, complemented
13#1855×C151C211yesmaximal, characteristic, complemented
14#1765×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C2×#135×C151C2211yescharacteristic
18C2×#135×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic
20C2×#131×C151C2211yescharacteristic
21C2×#131×C151C2211yescharacteristic, complemented
22C22×M16×C151C2211yescharacteristic
23#525×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25#452×C151C411yescharacteristic, complemented
26#452×C151C411yescharacteristic, complemented
27#451×C151C411yescharacteristic, complemented
28#450×C151C411yescharacteristic, complemented
29#449×C151C411yescharacteristic, complemented
30#449×C151C411yescharacteristic, complemented
31#448×C151C411yescharacteristic, complemented
32#447×C151C411yescharacteristic, complemented
33#443×C151—24no—
34#436×C151—21no—
35#435×C151—21no—
36#435×C151—21no—
37C8×D4×C151—21no—
38C2×#108×C151C2211yescharacteristic, complemented
39C2×#108×C151C2211yescharacteristic, complemented
40#424×C151C2211yescharacteristic, complemented
41#421×C151—24no—
42C2×#104×C151C2211yescharacteristic
43C2×#104×C151C2211yescharacteristic
44C2×#104×C151C2211yescharacteristic
45C2×#104×C151C2211yescharacteristic
46C2×#104×C151C2211yescharacteristic, complemented
47C2×#104×C151C2211yescharacteristic, complemented
48#416×C151C2211yescharacteristic
49#416×C151C2211yescharacteristic
50#408×C151—21no—
51#408×C151—21no—
52#408×C151C2211yescharacteristic
53#408×C151C2211yescharacteristic
54#408×C151C2211yescharacteristic, complemented
55#407×C151—21no—
56#407×C151C2211yescharacteristic
57C2×C22⋊C8×C151—21no—
58C2×C22⋊C8×C151C2211yescharacteristic
59C2×C22⋊C8×C151C2211yescharacteristic
60#405×C151C2211yescharacteristic, complemented
61C2×#97×C151C2211yescharacteristic, complemented
62C2×C4×C8×C151C2211yescharacteristic, complemented
63#341×C151C2211yescharacteristic, complemented
64#341×C151C2211yescharacteristic, complemented
65#339×C151C2211yescharacteristic, complemented
66#339×C151C2211yescharacteristic, complemented
67#336×C151C2211yescharacteristic, complemented
68#336×C151C2211yescharacteristic, complemented
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C2×#41×C151C2×C411yescharacteristic
76C2×#41×C151C2×C411yescharacteristic
77C2×#41×C151C2311yescharacteristic
78C2×#41×C151C2311yescharacteristic
79C2×#41×C151C2311yescharacteristic
80C22×Q8×C151C2×C411yescharacteristic
81C22×D4×C151—21no—
82C22×D4×C151C2×C411yescharacteristic
83C23×C4×C151—21no—
84C23×C4×C151C2311yescharacteristic
85#135×C151—22no—
86#135×C151—22no—
87#135×C151—41no—
88#135×C151—41no—
89C2×Q16×C151C2×C411yescharacteristic
90C2×Q16×C151C2×C411yescharacteristic
91C2×SD16×C151C2×C411yescharacteristic
92C2×SD16×C151C2×C411yescharacteristic
93C2×SD16×C151C2×C411yescharacteristic
94C2×SD16×C151C2×C411yescharacteristic
95C2×D8×C151C2×C411yescharacteristic
96C2×D8×C151C2×C411yescharacteristic
97#131×C151—22no—
98#131×C151—22no—
99#131×C151—22no—
100#131×C151—41no—
101#131×C151—41no—
102#131×C151—41no—
103C2×M16×C151—21no—
104C2×M16×C151—21no—
105C2×M16×C151—21no—
106C2×M16×C151—21no—
107C2×M16×C151—22no—
108C2×M16×C151—41no—
109C2×M16×C151C2311yescharacteristic
110C2×M16×C151C2311yescharacteristic
111C2×M16×C151C2311yescharacteristic
112C2×M16×C151C2311yescharacteristic
113C22×C8×C151—21no—
114C22×C8×C151—21no—
115C22×C8×C151—21no—
116C22×C8×C151—21no—
117C22×C8×C151C2311yescharacteristic
118C22×C8×C151C2311yescharacteristic
119C22×C8×C151C2311yescharacteristic
120C22×C8×C151C2311yescharacteristic
121#123×C151—21no—
122C22⋊Q8×C151C2×C411yescharacteristic
123C22⋊Q8×C151C2×C411yescharacteristic
124#121×C151C2×C411yescharacteristic
125#121×C151C2×C411yescharacteristic
126#120×C151—21no—
127C4×D4×C151—21no—
128C4×D4×C151—21no—
129#117×C151—22no—
130#117×C151—41no—
131#117×C151C2311yescharacteristic
132C2×C4⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C42×C151C2311yescharacteristic
135C2×C42×C151C2311yescharacteristic
136#108×C151—22no—
137#108×C151—41no—
138C4⋊C8×C151—21no—
139C4⋊C8×C151—21no—
140#104×C151—22no—
141#104×C151—22no—
142#104×C151—22no—
143#104×C151—22no—
144#104×C151—41no—
145#104×C151D414yescomplemented
146#103×C151C2×C411yescharacteristic
147#103×C151C2×C411yescharacteristic
148#103×C151C2×C411yescharacteristic
149#103×C151C2×C411yescharacteristic
150#102×C151C2×C411yescharacteristic
151#102×C151C2×C411yescharacteristic
152#102×C151C2×C411yescharacteristic
153#102×C151C2×C411yescharacteristic
154C22⋊C8×C151—21no—
155C22⋊C8×C151—21no—
156C22⋊C8×C151—21no—
157C22⋊C8×C151—21no—
158C22⋊C8×C151—21no—
159C22⋊C8×C151—21no—
160C22⋊C8×C151—21no—
161C22⋊C8×C151—21no—
162C22⋊C8×C151C2×C411yescharacteristic
163C22⋊C8×C151C2×C411yescharacteristic
164C22⋊C8×C151C2×C411yescharacteristic
165C22⋊C8×C151C2×C411yescharacteristic
166C22⋊C8×C151D411yescharacteristic
167C22⋊C8×C151D411yescharacteristic
168C22⋊C8×C151D411yescharacteristic
169C22⋊C8×C151D411yescharacteristic
170#97×C151—21no—
171#97×C151—41no—
172C4×C8×C151—21no—
173C4×C8×C151—22no—
174C24×C151—21no—
175C24×C151#4111yescharacteristic
176#41×C151—21no—
177#41×C151—21no—
178#41×C151—22no—
179#41×C151—22no—
180#41×C151—21no—
181#41×C151—21no—
182#41×C151—21no—
183#41×C151—21no—
184#41×C151—21no—
185#41×C151—21no—
186#41×C151—21no—
187#41×C151—21no—
188#41×C151—42no—
189#41×C151—42no—
190#41×C151—41no—
191#41×C151—41no—
192#41×C151—42no—
193#41×C151—42no—
194#41×C151C2×D412yes—
195#41×C151#4112yes—
196C2×Q8×C151—21no—
197C2×Q8×C151—22no—
198C2×Q8×C151—41no—
199C2×Q8×C151C22×C411yescharacteristic
200C2×Q8×C151C22×C411yescharacteristic
201C2×Q8×C151C22×C411yescharacteristic
202C2×D4×C151—21no—
203C2×D4×C151—22no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—41no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151C22×C411yescharacteristic
215C2×D4×C151C22×C411yescharacteristic
216C2×D4×C151C22×C411yescharacteristic
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—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—42no—
230C22×C4×C151—42no—
231C22×C4×C151C22×C411yescharacteristic
232C22×C4×C151C22×C411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151#4111yescharacteristic
236C22×C4×C151C2411yescharacteristic
237Q16×C151—22no—
238Q16×C151—41no—
239SD16×C151—22no—
240SD16×C151—22no—
241SD16×C151—41no—
242SD16×C151—41no—
243D8×C151—22no—
244D8×C151—41no—
245M16×C151—21no—
246M16×C151—21no—
247M16×C151—21no—
248M16×C151—21no—
249M16×C151—21no—
250M16×C151—21no—
251M16×C151—21no—
252M16×C151—42no—
253M16×C151—42no—
254M16×C151—42no—
255M16×C151—42no—
256M16×C151C2×D412yes—
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—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—42no—
270C2×C8×C151—42no—
271C2×C8×C151—42no—
272C2×C8×C151—42no—
273C2×C8×C151C22×C411yescharacteristic
274C2×C8×C151C22×C411yescharacteristic
275C2×C8×C151C22×C411yescharacteristic
276C2×C8×C151C22×C411yescharacteristic
277C2×C8×C151C2×D411yescharacteristic
278C2×C8×C151C2×D411yescharacteristic
279C2×C8×C151C2×D411yescharacteristic
280C2×C8×C151C2×D411yescharacteristic
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—42no—
284C4⋊C4×C151C22×C411yescharacteristic
285C4⋊C4×C151C22×C411yescharacteristic
286C22⋊C4×C151—21no—
287C22⋊C4×C151—21no—
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—42no—
292C42×C151—21no—
293C42×C151—21no—
294C42×C151—21no—
295C42×C151—21no—
296C42×C151C2×D412yes—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—42no—
305C23×C151—42no—
306C23×C151—81no—
307C23×C151C4×D411yescharacteristic
308C23×C151C4×D411yescharacteristic
309C23×C151C2×#4111yescharacteristic
310Q8×C151—21no—
311Q8×C151—21no—
312Q8×C151—21no—
313Q8×C151—21no—
314Q8×C151—21no—
315Q8×C151—42no—
316Q8×C151C4×D412yes—
317D4×C151—22no—
318D4×C151—22no—
319D4×C151—21no—
320D4×C151—21no—
321D4×C151—21no—
322D4×C151—21no—
323D4×C151—21no—
324D4×C151—42no—
325D4×C151—42no—
326D4×C151—42no—
327D4×C151—42no—
328D4×C151—41no—
329D4×C151—41no—
330D4×C151—41no—
331D4×C151—41no—
332D4×C151—81no—
333D4×C151C4×D412yes—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—22no—
342C2×C4×C151—21no—
343C2×C4×C151—21no—
344C2×C4×C151—22no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—22no—
352C2×C4×C151—42no—
353C2×C4×C151—42no—
354C2×C4×C151—42no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151C4×D411yescharacteristic
365C2×C4×C151C4×D411yescharacteristic
366C2×C4×C151C23×C411yescharacteristic
367C2×C4×C151C22×D411yescharacteristic
368C2×C4×C151C22×D411yescharacteristic
369C2×C4×C151C2×#4111yescharacteristic
370C2×C4×C151H(5,𝔽2)11yescharacteristic
371C2×C4×C151H(5,𝔽2)11yescharacteristic
372C8×C151—21no—
373C8×C151—21no—
374C8×C151—21no—
375C8×C151—21no—
376C8×C151—21no—
377C8×C151—21no—
378C8×C151—22no—
379C8×C151—21no—
380C8×C151—21no—
381C8×C151—41no—
382C8×C151—41no—
383C8×C151—41no—
384C22×C151—21no—
385C22×C151—21no—
386C22×C151—21no—
387C22×C151—21no—
388C22×C151—22no—
389C22×C151—21no—
390C22×C151—21no—
391C22×C151—21no—
392C22×C151—21no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—84no—
404C22×C151C2×C4×D411yescharacteristic
405C22×C151#54611yescharacteristic
406C22×C151#55111yescharacteristic
407C4×C151—21no—
408C4×C151—21no—
409C4×C151—22no—
410C4×C151—42no—
411C4×C151—41no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—41no—
415C4×C151—81no—
416C4×C151C2×C4×D411yescharacteristic
417C4×C151#51811yescharacteristic
418C4×C151D4211yescharacteristic
419C4×C151#54611yescharacteristic
420C2×C151—21no—
421C2×C151—21no—
422C2×C151—41no—
423C2×C151—41no—
424C2×C151—42no—
425C2×C151—81no—
426C2×C151—81no—
427C2×C151#235811yescharacteristic
428C2×C151#295511yescharacteristic
429C2×C151#295711yescharacteristic
430#22889C15111yesmaximal, characteristic, direct product factor, Sylow
431C151#2288911yescharacteristic, direct product factor, Sylow
432#3002C2×C15111yescharacteristic
433C2×#443C2×C15111yescharacteristic, complemented
434#2933C2×C15111yescharacteristic, complemented
435C2×#421C2×C15111yescharacteristic, complemented
436#2880C2×C15111yescharacteristic, complemented
437#1975C2×C15111yescharacteristic, complemented
438#1937C2×C15111yescharacteristic, complemented
439#1929C2×C15111yescharacteristic, complemented
440#1897C2×C15111yescharacteristic, complemented
441#1876C2×C15111yescharacteristic, complemented
442#1876C2×C15111yescharacteristic, complemented
443#1866C2×C15111yescharacteristic, complemented
444#1855C2×C15111yescharacteristic, complemented
445#1765C2×C15111yescharacteristic, complemented
446#1750C2×C15111yescharacteristic, complemented
447C22×#41C22×C15111yescharacteristic
448C2×#135C22×C15111yescharacteristic
449C2×#135C22×C15111yescharacteristic
450C2×#131C22×C15111yescharacteristic
451C2×#131C22×C15111yescharacteristic
452C2×#131C22×C15111yescharacteristic, complemented
453C22×M16C22×C15111yescharacteristic
454#525C22×C15111yescharacteristic
455C2×#117C22×C15111yescharacteristic
456#452C4×C15111yescharacteristic, complemented
457#452C4×C15111yescharacteristic, complemented
458#451C4×C15111yescharacteristic, complemented
459#450C4×C15111yescharacteristic, complemented
460#449C4×C15111yescharacteristic, complemented
461#449C4×C15111yescharacteristic, complemented
462#448C4×C15111yescharacteristic, complemented
463#447C4×C15111yescharacteristic, complemented
464#443—24no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108C22×C15111yescharacteristic, complemented
470C2×#108C22×C15111yescharacteristic, complemented
471#424C22×C15111yescharacteristic, complemented
472#421—24no—
473C2×#104C22×C15111yescharacteristic
474C2×#104C22×C15111yescharacteristic
475C2×#104C22×C15111yescharacteristic
476C2×#104C22×C15111yescharacteristic
477C2×#104C22×C15111yescharacteristic, complemented
478C2×#104C22×C15111yescharacteristic, complemented
479#416C22×C15111yescharacteristic
480#416C22×C15111yescharacteristic
481#408—21no—
482#408—21no—
483#408C22×C15111yescharacteristic
484#408C22×C15111yescharacteristic
485#408C22×C15111yescharacteristic, complemented
486#407—21no—
487#407C22×C15111yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8C22×C15111yescharacteristic
490C2×C22⋊C8C22×C15111yescharacteristic
491#405C22×C15111yescharacteristic, complemented
492C2×#97C22×C15111yescharacteristic, complemented
493C2×C4×C8C22×C15111yescharacteristic, complemented
494#341C22×C15111yescharacteristic, complemented
495#341C22×C15111yescharacteristic, complemented
496#339C22×C15111yescharacteristic, complemented
497#339C22×C15111yescharacteristic, complemented
498#336C22×C15111yescharacteristic, complemented
499#336C22×C15111yescharacteristic, complemented
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C15111yescharacteristic
507C2×#41C2×C4×C15111yescharacteristic
508C2×#41C23×C15111yescharacteristic
509C2×#41C23×C15111yescharacteristic
510C2×#41C23×C15111yescharacteristic
511C22×Q8C2×C4×C15111yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C15111yescharacteristic
514C23×C4—21no—
515C23×C4C23×C15111yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C15111yescharacteristic
521C2×Q16C2×C4×C15111yescharacteristic
522C2×SD16C2×C4×C15111yescharacteristic
523C2×SD16C2×C4×C15111yescharacteristic
524C2×SD16C2×C4×C15111yescharacteristic
525C2×SD16C2×C4×C15111yescharacteristic
526C2×D8C2×C4×C15111yescharacteristic
527C2×D8C2×C4×C15111yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C15111yescharacteristic
541C2×M16C23×C15111yescharacteristic
542C2×M16C23×C15111yescharacteristic
543C2×M16C23×C15111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C15111yescharacteristic
549C22×C8C23×C15111yescharacteristic
550C22×C8C23×C15111yescharacteristic
551C22×C8C23×C15111yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C15111yescharacteristic
554C22⋊Q8C2×C4×C15111yescharacteristic
555#121C2×C4×C15111yescharacteristic
556#121C2×C4×C15111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C15111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C15111yescharacteristic
566C2×C42C23×C15111yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C15114yescomplemented
577#103C2×C4×C15111yescharacteristic
578#103C2×C4×C15111yescharacteristic
579#103C2×C4×C15111yescharacteristic
580#103C2×C4×C15111yescharacteristic
581#102C2×C4×C15111yescharacteristic
582#102C2×C4×C15111yescharacteristic
583#102C2×C4×C15111yescharacteristic
584#102C2×C4×C15111yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C15111yescharacteristic
594C22⋊C8C2×C4×C15111yescharacteristic
595C22⋊C8C2×C4×C15111yescharacteristic
596C22⋊C8C2×C4×C15111yescharacteristic
597C22⋊C8D4×C15111yescharacteristic
598C22⋊C8D4×C15111yescharacteristic
599C22⋊C8D4×C15111yescharacteristic
600C22⋊C8D4×C15111yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C15111yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C15112yes—
626#41#41×C15112yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C15111yescharacteristic
631C2×Q8C22×C4×C15111yescharacteristic
632C2×Q8C22×C4×C15111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C15111yescharacteristic
646C2×D4C22×C4×C15111yescharacteristic
647C2×D4C22×C4×C15111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C15111yescharacteristic
663C22×C4C22×C4×C15111yescharacteristic
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4#41×C15111yescharacteristic
667C22×C4C24×C15111yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C15112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C15111yescharacteristic
705C2×C8C22×C4×C15111yescharacteristic
706C2×C8C22×C4×C15111yescharacteristic
707C2×C8C22×C4×C15111yescharacteristic
708C2×C8C2×D4×C15111yescharacteristic
709C2×C8C2×D4×C15111yescharacteristic
710C2×C8C2×D4×C15111yescharacteristic
711C2×C8C2×D4×C15111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C15111yescharacteristic
716C4⋊C4C22×C4×C15111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C15112yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C15111yescharacteristic
739C23C4×D4×C15111yescharacteristic
740C23C2×#41×C15111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C15112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C15112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C15111yescharacteristic
796C2×C4C4×D4×C15111yescharacteristic
797C2×C4C23×C4×C15111yescharacteristic
798C2×C4C22×D4×C15111yescharacteristic
799C2×C4C22×D4×C15111yescharacteristic
800C2×C4C2×#41×C15111yescharacteristic
801C2×C4H(5,𝔽2)×C15111yescharacteristic
802C2×C4H(5,𝔽2)×C15111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C15111yescharacteristic
836C22#546×C15111yescharacteristic
837C22#551×C15111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C15111yescharacteristic
848C4#518×C15111yescharacteristic
849C4D42×C15111yescharacteristic
850C4#546×C15111yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2358×C15111yescharacteristic
859C2#2955×C15111yescharacteristic
860C2#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 ◁ C2×C22⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C151C2semidirect
3. #2933×C151C2semidirect
4. C2×#421×C151C2semidirect
5. #2880×C151C2semidirect
6. #1975×C151C2semidirect
7. #1937×C151C2semidirect
8. #1929×C151C2semidirect
9. #1897×C151C2semidirect
10. #1876×C151C2semidirect
11. #1876×C151C2semidirect
12. #1866×C151C2semidirect
13. #1855×C151C2semidirect
14. #1765×C151C2semidirect
15. #1750×C151C2semidirect
21. C2×#131×C151C22semidirect
25. #452×C151C4semidirect
26. #452×C151C4semidirect
27. #451×C151C4semidirect
28. #450×C151C4semidirect
29. #449×C151C4semidirect
30. #449×C151C4semidirect
31. #448×C151C4semidirect
32. #447×C151C4semidirect
38. C2×#108×C151C22semidirect
39. C2×#108×C151C22semidirect
40. #424×C151C22semidirect
46. C2×#104×C151C22semidirect
47. C2×#104×C151C22semidirect
54. #408×C151C22semidirect
60. #405×C151C22semidirect
61. C2×#97×C151C22semidirect
62. C2×C4×C8×C151C22semidirect
63. #341×C151C22semidirect
64. #341×C151C22semidirect
65. #339×C151C22semidirect
66. #339×C151C22semidirect
67. #336×C151C22semidirect
68. #336×C151C22semidirect
145. #104×C151D4semidirect
430. #22889C151direct (N × H)
431. C151#22889direct (N × H)
433. C2×#443C2×C151semidirect
434. #2933C2×C151semidirect
435. C2×#421C2×C151semidirect
436. #2880C2×C151semidirect
437. #1975C2×C151semidirect
438. #1937C2×C151semidirect
439. #1929C2×C151semidirect
440. #1897C2×C151semidirect
441. #1876C2×C151semidirect
442. #1876C2×C151semidirect
443. #1866C2×C151semidirect
444. #1855C2×C151semidirect
445. #1765C2×C151semidirect
446. #1750C2×C151semidirect
452. C2×#131C22×C151semidirect
456. #452C4×C151semidirect
457. #452C4×C151semidirect
458. #451C4×C151semidirect
459. #450C4×C151semidirect
460. #449C4×C151semidirect
461. #449C4×C151semidirect
462. #448C4×C151semidirect
463. #447C4×C151semidirect
469. C2×#108C22×C151semidirect
470. C2×#108C22×C151semidirect
471. #424C22×C151semidirect
477. C2×#104C22×C151semidirect
478. C2×#104C22×C151semidirect
485. #408C22×C151semidirect
491. #405C22×C151semidirect
492. C2×#97C22×C151semidirect
493. C2×C4×C8C22×C151semidirect
494. #341C22×C151semidirect
495. #341C22×C151semidirect
496. #339C22×C151semidirect
497. #339C22×C151semidirect
498. #336C22×C151semidirect
499. #336C22×C151semidirect
576. #104D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3002×C1512
C2×#443×C1512
#2933×C1512
C2×#421×C1512
#2880×C1512
#1975×C1512
#1937×C1512
#1929×C1512
#1897×C1512
#1876×C1512
#1866×C1512
#1855×C1512
#1765×C1512
#1750×C1512
#22889151